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 Title:
 Impact of selected regulatory policies on the U.S. fruit and vegetable industry
 Creator:
 NaLampang, Sikavas
 Publication Date:
 2004
 Language:
 English
 Physical Description:
 xiii, 120 leaves : ill. ; 29 cm.
Subjects
 Subjects / Keywords:
 Bromides ( jstor )
Commodities ( jstor ) Crops ( jstor ) Cucumbers ( jstor ) Elasticity of demand ( jstor ) Peppers ( jstor ) Standard error ( jstor ) Strawberries ( jstor ) Tomatoes ( jstor ) Vegetables ( jstor ) Dissertations, Academic  Food and Resource Economics  UF Food and Resource Economics thesis, Ph. D City of Gainesville ( local )
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 bibliography ( marcgt )
theses ( marcgt ) nonfiction ( marcgt )
Notes
 Thesis:
 Thesis (Ph. D.)University of Florida, 2004.
 Bibliography:
 Includes bibliographical references.
 General Note:
 Printout.
 General Note:
 Vita.
 Statement of Responsibility:
 by Sikavas NaLampang.
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 University of Florida
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 University of Florida
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 The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. Â§107) for nonprofit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact the RDS coordinator (ufdissertations@uflib.ufl.edu) with any additional information they can provide.
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880637197 ( OCLC ) 880438703 ( OCLC )

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IMPACT OF SELECTED REGULATORY POLICIES ON
THE U.S. FRUIT AND VEGETABLE INDUSTRY
By
SIKAVAS NALAMPANG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004
Copyright 2004 by
Sikavas NaLampang
This work is dedicated to my parents and my wife.
ACKNOWLEDGMENTS
I have been very fortunate to work with my supervisory committee, whose
guidance and encouragement were essential to the completion of my research. I would like to express my deep gratitude and appreciation to the chair of my supervisory committee, Dr. John VanSickle, for his exceptional advice, patience, and for the financial support through my graduate study in the Food and Resource Economics Department. I benefited from many discussions, insightful comments, and ideas from Dr. Edward Evans. His dedication allowed me to live up to my potential. I would also like to acknowledge my other committee members (Dr. Allen Wysocki, Dr. Richard Weldon, and Dr. Chunrong Ai) and Dr. Mark Brown for their concrete ideas and support. Finally, I would like to thank my wife and my parents for their enduring love and support.
iv
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ................................................................................... iv
LIST O F T A B LE S ..................................................... ........ ........................................ vii
LIST O F FIG U R E S ............................................... ...................................................... xi
A B STR A C T ...................................................................................................................... xii
CHAPTER
1 IN TR O D U C T IO N ....................................................................................................... 1
Overview of the Fruit and Vegetable Industry ...................................................... 1
Study O verview ..................................................................................................... 6
2 DEMAND ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY .................... 7
Problem atic Situation............................................................................................ 7
H ypothesis ........................................................................................................... 8
O bjectives .............................................................................................................. 8
Conceptual Fram ew ork.......................................................................................... 9
Inverse Demand Model ............................................................................. 9
Scale and Quantity Comparative Statics ....................................... ....... 18
Econometric Model Development............................................................ 24
Methodology for Demand Analysis.............................................. 28
Seemingly Unrelated Regressions Model.................................. ......... 29
Barten's Method of Estimation............................................. 31
Unconstrained estimation ..................................... .... ............... 33
Estimation under the homogeneity condition............................ ..... 34
Estimation under the symmetry and homogeneity conditions ................. 35
Em pirical R esults ............................................. .................................................... 37
Inverse Demand System Analysis ......................................... ............ 38
Elasticity Analysis ............................................................................... .. 39
Scale effect and scale elasticity ....................................... ........... 39
Quantity effect and own substitution elasticity .................................... 41
C onclusions................................. ......................... . .............................................. 43
v
3 PARTIAL EQUILIBRIUM ANALYSIS ON FRUIT AND VEGETABLE
INDUSTRY .................. ....................................................................................... 67
Background ................................................................................................................ 68
Research Problem ..... .......................................................................................... 72
Hypotheses................................................................................................................. 73
Objectives ................................................................... .......................... 73
Theoretical Framework......................................................................................... 73
Fundam ental Theory of the Partial Equilibrium M odel ..................................... 76
Impact of the Phaseout of M ethyl Brom ide ..................................................... 78
Impact of NAFTA ..............................................................79
M ethodology .............................................................................................................. 82
Empirical Results ............................................................. 97
Tom atoes ................... ................................................................................... 97
Bell peppers ......................... .............................................. 99
Cucumbers ..................................................................................................... 101
Squash.............................................................................................. ........ 102
Eggplant .................................................................................................. ....... 103
W aterm elons .................................................................................................. 103
Strawberries ................................................................................................. ...104
Aggregate impacts ......................................................................................... 105
Conclusions........................................................................................................ 106
4 SUM M ARY AND CONCLUSIONS ................................................................... 114
Summ ary ................................................................................................... 114
Suggestions for Further Research and Limitation of the Study ............................ 116
LIST OF REFERENCES ............................................................................................. 117
BIOGRAPHICAL SKETCH ........................................ 120
vi
LIST OF TABLES
Table page
21. Estimation of the RIDS model for the Atlanta market by using the mean of the
budget share.................................... ........................... ........ 45
22. Estimation of the AIIDS model for the Atlanta market by using the mean of the
budget share........................................................................... ....... 45
23. Estimation of the LaTheil model for the Atlanta market by using the mean of the
budget share..................................................................... ....... 46
24. Estimation of the RAIIDS model for the Atlanta market by using the mean of the
budget share .................... ................................................................................... 46
25. Estimation of the RIDS model for the Los Angeles market by using the mean of
the budget share .............................................................. ............................ 47
26. Estimation of the AIIDS model for the Los Angeles market by using the mean of
the budget share ....................................................................................................... 47
27. Estimation of the LaTheil model for the Los Angeles market by using the mean
of the budget share ........................................... ................................................. 48
28. Estimation of the RAIIDS model for the Los Angeles market by using the mean
of the budget share ........................................... ................................................. 48
29. Estimation of the RIDS model for the Chicago market by using the mean of the
budget share............................................................................................................. 49
210. Estimation of the AIIDS model for the Chicago market by using the mean of the
budget share............................................................................................................. 49
211. Estimation of the LaTheil model for the Chicago market by using the mean of
the budget share ............................................ ..................................................... 50
212. Estimation of the RAIIDS model for the Chicago market by using the mean of
the budget share ............................................ ..................................................... 50
213. Estimation of the RIDS model for the New York market by using the mean of
the budget share ................................................................................................ 51
vii
214. Estimation of the AIIDS model for the New York market by using the mean of
the budget share ............................................ ..................................................... 51
215. Estimation of the LaTheil model for the New York market by using the mean
of the budget share .................................................................. .... ............ 52
216. Estimation of the RAIIDS model for the New York market by using the mean
of the budget share ................................................................ 52
217. Estimation of the RIDS model for the Atlanta market by using the moving
average of the budget share ............................................................................ 53
218. Estimation of the AIIDS model for the Atlanta market by using the moving
average of the budget share ...................................................................... ... 53
219. Estimation of the LaTheil model for the Atlanta market by using the moving
average of the budget share .......................................................................... 54
220. Estimation of the RAIIDS model for the Atlanta market by using the moving
average of the budget share ........................................................................... 54
221. Estimation of the RIDS model for the Los Angeles Market by using the moving
average of the budget share ........................................................................... 55
222. Estimation of the AIIDS model for the Los Angeles market by using the moving
average of the budget share .......................................................................... 55
223. Estimation of the LaTheil model for the Los Angeles market by using the
moving average of the budget share ......................................... ............. 56
224. Estimation of the RAIIDS model for the Los Angeles market by using the
moving average of the budget share ......................................... ............. 56
225. Estimation of the RIDS model for the Chicago market by using the moving
average of the budget share ........................................................................... 57
226. Estimation of the AIIDS model for the Chicago market by using the moving
average of the budget share....................................... ........................ 57
227. Estimation of the LaTheil model for the Chicago market by using the moving
average of the budget share................................................................ 58
228. Estimation of the RAIIDS model for the Chicago market by using the moving
average of the budget share ..................................... ......................... 58
229. Estimation of the RIDS model for the New York market by using the moving
average of the budget share ........................................................................... 59
viii
230. Estimation of the AIIDS model for the New York market by using the moving
average of the budget share ........................................................................... 59
231. Estimation of the LaTheil model for the New York market by using the moving
average of the budget share ........................................................................... 60
232. Estimation of the RAIIDS model for the New York market by using the moving
average of the budget share ...................................... 60
233. Unconstrained estimation of the RIDS model for the Atlanta market.................... 61
234. Unconstrained estimation of the RIDS model for the Los Angeles market ........... 61
235. Unconstrained estimation of the RIDS model for the Chicago market ............... 62
236. Unconstrained estimation of the RIDS model for the New York market......... 62
237. Barten's estimation with the homogeneity condition of the RIDS model for the
Atlanta m arket .................................................................. 63
238. Barten's estimation with the homogeneity condition of the RIDS model for the
Los Angeles m arket .................................................................................... 63
239. Barten's estimation with the homogeneity condition of the RIDS model for the
Chicago m arket............. ..................................................................................... 64
240. Barten's estimation with the homogeneity condition of the RIDS model for the
N ew York m arket ................................................................................. .... 64
241. Elasticities for the Atlanta market ............................................................... 65
242. Elasticities for the Los Angeles market ......................................................... 65
243. Elasticities for the Chicago market ................................................................ 66
244. Elasticities for the New York market ....................................... ............ 66
31. Schedules of the phaseout of methyl bromide ...................................... ...... 70
32. Effect of the methyl bromide in Florida and California ..................................... 84
33. Planted acreage in the baseline model, in the methyl bromide ban model, and in
the NAFTA model, by crop and area ..................................... 108
34. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by area ..................................... 109
35. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by crop and area ........................ 110
ix
36. Baseline revenues and changes in revenues from the methyl bromide ban effect
and the NAFTA effect, by crop and area ............................................................ 111
37. Baseline revenues and changes in revenues from the methyl bromide ban effect
and the NA FTA effect, by area .......................................................................... 112
38. Baseline average prices and percentage changes in prices from the methyl
bromide ban effect and the NAFTA effect, by crop................................. 112
39. Baseline demand and percentage changes in demand from the methyl bromide
ban effect and the NAFTA effect, by crop and market ..................................... 113
x
LIST OF FIGURES
Figure page
31. Aggregate demand and aggregate supply .............................................................. 76
32. Partial equilibrium under effect of the phaseout of methyl bromide ..................... 79
33. Partial equilibrium under the effect of tariff.............................. ............ 82
34. Partial equilibrium of aggregate demand and aggregate supply............................ 96
xi
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
IMPACT OF SELECTED REGULATORY POLICIES ON
THE U.S. FRUIT AND VEGETABLE INDUSTRY By
Sikavas NaLampang
August 2004
Chair: John J. VanSickle
Major Department: Food and Resource Economics
The United States is one of the world's leading producers and consumers of fruit
and vegetables. Fruit and vegetable production occurs throughout the United States, with the largest fresh fruit and vegetable acreage in California, Florida, and Texas. Our study used the spatial equilibrium model to determine the expected economic impacts of the North America Free Trade Agreement (NAFTA) and the phaseout of methyl bromide in the U.S. fruit and vegetable industry.
The first analysis relates to implementation of NAFTA. International trade is an important component of the U.S. fresh fruit and vegetable industry. Under NAFTA, all agricultural tariffs on trade between the United States, Mexico, and Canada will be eliminated. As a result, Mexican growers are expected to increase shipments to the United States as tariffs are eliminated for exports to the United States.
The second analysis relates to a ban on methyl bromide. Methyl bromide has been a critical soil fumigant used in the production of many agricultural commodities for many
xii
years. The U.S. Clean Air Act of 1992, as amended in 1998, requires that methyl bromide be phased out of use by 2005. While significant progress has been made in developing alternatives to methyl bromide, no alternative has been identified that permits a seamless transition (where comparative advantage is minimally impacted by the elimination of methyl bromide, and the affected producers continue to compete with other producers).
To satisfy the utilitymaximization condition, the elasticities used in the spatial equilibrium model are calculated from the popular functional forms of the inverse demand system. Demand analyses can be very sensitive to the chosen functional forms. Our study addresses this concern by proposing a formulation that obviates the need to choose among various functional forms of the inverse demand system.
Results of the spatial equilibrium analysis indicate that total production in the
United States is expected to decrease after the implementation of NAFTA and the ban on methyl bromide. Mexico is expected to become a larger supplier of vegetables in the United States.
xli
CHAPTER 1
INTRODUCTION
Overview of the Fruit and Vegetable Industry
The United States is one of the world's leading producers and consumers of fruits and vegetables. According to the U.S. Department of Agriculture, farmers earned $17.7 billion from the sale of fruits and vegetables in 2002. Annual percapita use of fruits and vegetables rose 7% from 19901992 to 20002002, reaching 442 pounds as fresh consumption increased and processed consumption fell. Consumer expenditures for fruits and vegetables are growing faster than any food group (except meats).
The United States harvested 1.4 million tons of fruits and vegetables in 1999 (a 20% increase from 1990). Even though output has been rising, aggregate fruit and vegetable acreage has been relatively stable, indicating increasing production per acre. The major source of higher yields has been the introduction of more prolific hybrid varieties, many of which exhibit improved disease resistance and improved fruit set. Shifting from lessproductive areas to higheryielding areas has also contributed to higher U.S. yields over time. Fruit and vegetable output will likely continue to rise faster than population growth over the next decade because of increasing consumer demand and concerns about health and nutrition.
Fruit and vegetable production occurs throughout the United States, with the largest fresh fruit and vegetable acreage in California, Florida, Georgia, Arizona, and Texas. California and Florida produce the largest selection and quantity of fresh vegetables. Climate causes most domestic fruit and vegetable production to be seasonal, with the
1
2
largest harvests occurring during the summer and fall. Imports supplement domestic supplies, especially fresh products during the winter, resulting in increased choices for consumers. For example, Florida produces the majority of its domestic warmseason vegetables, such as fresh tomatoes, during the winter and spring, while California produces the bulk of its domestic output in the summer and fall. Freshtomato imports, primarily from Mexico, boost total supply during the first few months of the year, and compete directly with winter and early spring production from Florida. In value terms, Mexico supplies more than half (61%) of all the fruit and vegetable imports to the United States, with the majority being freshmarket vegetables. Canada is the second leading foreign supplier, with about 27% of the U.S. import market. Because of their obvious transportation advantages, Mexico and Canada have historically been the top two import suppliers to the United States. In value terms, fresh fruits and vegetables account for the largest share of fruit and vegetable imports, with about $2 billion in 1999. There is a definite seasonal pattern to U.S. fresh vegetable imports, with twothirds of the import volume arriving between December and April (when U.S. production is low and is limited to the southern portions of the country). Most of these imports are tender warmseason vegetables such as tomatoes, peppers, squash, and cucumbers.
The United States is one of the world's leading producers of tomatoes, ranking second only to China. California and Florida make up almost twothirds of the acreage used to grow fresh tomatoes in the United States. Fresh tomatoes lead in farm value ($920 million in 1999), along with lettuce and potatoes. U.S. freshtomato production steadily increased until 1992, when it peaked. Production then trended downward. Declines reflected sharply rising imports, weather extremes (excessive rains, wind, and
3
frost for several years), and increased competition from rapidly expanding greenhouse tomato growers. Peracre yields for fresh tomatoes were off substantially in 1995 and 1996 from freezes, heavy rain, and low market prices. Severe flooding in Mexico sharply reduced its production and its exports to the United States. A smaller volume of imports and higher prices prompted Florida growers to harvest fields more intensively, resulting in recordhigh yields in Florida.
Although acreage has decreased over the past decade, Florida remains the leading domestic source of fresh tomatoes. Florida produced 42% of U.S. fresh tomatoes from 1997 through 1999. Florida's season (October to June) has the greatest production in April and May and again from November to January. The leading counties are Collier, Manatee, and Dade. Tomatoes, one of the highestvalued crops in Florida, bring in onethird of the state's vegetable cash receipts and 7% of all its agricultural cash receipts. As a result of decreased production in the northern states, Florida was able to increase its percentage of the U.S. domestic output from about 25% in 1960 to 42% in 1999. Because of higher prices during the winter, Florida accounts for 43% of the total value of the U.S. freshtomato crop.
California is the secondlargest tomatoproducing state, accounting for 31% of the fresh crop. Fresh tomatoes are produced across many counties in each season, except winter, with San Diego (spring and fall) and Fresno (summer) accounting for about onethird of the crop. Other important tomatoproducing states in 1999 included Virginia, Georgia, Ohio, South Carolina, Tennessee, North Carolina, and New Jersey.
International trade is an important component of the U.S. freshtomato industry. The United States imported 32% of the fresh tomatoes it consumed in 1999 (up from
4
19% in 1994), and exported 7% of its annual crop. The percentage imported rose steadily after 1993 until low domestic prices discouraged imports in 1999. The United States, as a net importer of fresh tomatoes, had a tomato trade deficit in 1999 of $567 million. Mexico and Canada are important suppliers of freshtomatoes to the United States. Freshtomato imports mostly arrive from Mexico (about 83% in 1999).
Over the past two decades, the demand for bell peppers has been rising, reaching a record high in 2000. The United States is one of the world's biggest producers of bell peppers, ranking sixth behind China, Mexico, Turkey, Spain, and Nigeria. Because of strong demand, U.S. growers harvested 12% more bell pepper acreage in 2000 than in 1999. Bell peppers are produced and marketed yearround, with the domestic market peaking during May and June, and the import market peaking during the winter months. Although bell peppers are grown in 48 states, the U.S. industry is largely concentrated in California, Florida, and Texas. Trade plays an important role in the U.S. fresh bellpepper market, with about 20% of fresh bell peppers coming from Canada and Mexico.
Originating in India, cucumbers were brought to the United States by Columbus, and have been grown here for several centuries. The United States produces 3% of the world's cucumbers, ranking fourth behind China, Turkey, and Iran. U.S. freshcucumber production reached a record high in 1999, but has trended lower since. Florida and Georgia are the leading states in the production of freshmarket cucumbers. Freshcucumber prices are the highest from January through April because of limited domestic supplies and higher production costs, and are the lowest in June when supplies are available from many areas. As a result, imports are strongest in January and February when U.S. production is limited by cool weather, and are the weakest in summer during
5
the height of the domestic season. Imports accounted for 45% of U.S. freshcucumber consumption from 2001 through 2003, with most of the imports coming from Mexico and Canada.
Cultivated for thousands of years, watermelon is thought to have originated in
Africa, and to have made its way to the United States with African slaves and European colonists. The United States ranks fourth in the world's watermelon production. Florida is the leading domestic source of fresh watermelon, followed by Texas, California, Georgia, and Arizona. Although value and production have been rising, the acreage devoted to watermelon has been trending lower over the past few decades. During the most recent decade, declining acreage has been due to a combination of rising peracre yields and successive years of freeze damage in Florida and drought in Texas. Most watermelon is consumed fresh, even though there are several processed products in the market such as roasted seeds, pickled rind, and watermelon juice. Percapita consumption of watermelon is highest in the West and lowest in the South.
In 1995 and 1996, fresh fruit and vegetable imports to the United States surged due to the combined effects of the devaluation of the Mexican peso, the rising demand for improved extended shelflife varieties, and reduced domestic output due to adverse weather conditions. Florida and Mexico historically compete for the U.S. winter and early spring market. For example, Mexico dominates the market in the winter (when southern Florida is the predominant U.S. producer), and Florida dominates the market during the spring (when Mexican production seasonally declines). Another factor has been NAFTA. Under NAFTA, some of the tariffs on freshmarket tomatoes from Mexico were phased out over a 5year period (19941998), while others had a 10year
phaseout (19942003). For those tariffs phased out over the 10year period, a tariffratequota (TRQ), which increased at a 3% compound annual rate, was imposed. For example, cherry tomatoes have no TRQ because they were on the 5year phaseout schedule. If tomato imports exceeded the quota, the overquota volume was assessed tariffs at whichever was lower: the preNAFTA Most Favored Nation (MFN) tariff rate or the current MFN rate in effect. The tariff on freshmarket tomato imports from Canada fell to zero in 1998. However, a tariff snapback to the MFN rate can be triggered by certain price and acreage conditions until 2008.
The phaseout of methyl bromide also disadvantaged U.S. fruit and vegetable
producers. Methyl bromide has been a critical soil fumigant in agricultural production for many years. While significant progress has been made in developing alternatives to methyl bromide, no alternative has been identified that permits a seamless transition (where comparative advantage is minimally impacted by eliminating of methyl bromide and the affected producers can continue to compete).
Study Overview
Our main objective of this study was to use the spatial equilibrium model to assess both the impacts of NAFTA and the phaseout of methyl bromide on the fruit and vegetable industry. To satisfy the utilitymaximization condition, the elasticities used in the spatial equilibrium model were calculated from the inverse demand system. Consequently, the second objective was to examine the method of estimation and the method used to develop the model for the inverse demand system. The specified objectives are satisfied in twoessay format with the first essay concentrated on the estimation of the inverse demand system and the second essay concentrated on the spatial equilibrium analysis.
CHAPTER 2
DEMAND ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY
Demand analyses can be very sensitive to chosen functional forms. Since no one specification best fits all data, researchers have been preoccupied with finding ways to select among various functional forms. Our study addresses this concern by proposing a formulation that obviates the need to choose among the various functional forms of the demand system. This approach was tested using four functional forms of the inverse demand system: the Rotterdam Inverse Demand System, the Laitinen and Theil's Inverse Demand System, the Almost Ideal Inverse Demand System, and the Rotterdam Almost Ideal Inverse Demand System.
Problematic Situation
Several studies in the past have considered the issue of how to choose among popular functional forms when conducting demand analyses. Parks (1969) used the average information inaccuracy concept. A relatively high average inaccuracy is taken to be an indicator of lesssatisfactory behavior. Deaton (1978) applied a nonnested test to compare demand systems with the same dependent variables. However, this procedure is not suitable when comparing models with different dependent variables (as in the case of comparing the Almost Ideal Demand System with the Rotterdam Demand System).
Barten (1993) developed a method that can deal with nonnested models with different dependent variables. Briefly, the method starts with a hypothetical general model as a matrixweighted linear combination of two or more basic models. A solution is found for one of the dependent variables, followed by estimating consistently the
7
transformed matrix weights associated with the other models. Next, statistical tests are carried out on the matrix weights to determine whether they are significantly different from zero. This matrixweighted linear combination can be considered a synthetic demandallocation system (which, under appropriate restrictions, yields different forms of the demand system). The synthetic model can therefore be used to statistically test which model best fits a particular data set. One drawback in applying this procedure is that it is necessary to impose a set of restrictions for the purpose of estimating. For example, the differentials need to be replaced by finite first differences, and the budget share needs to be replaced by its moving average. As a result, each functional form generates a different result.
Hypothesis
Our main hypothesis is that if the theoretical elasticities from the demand system in the theory are the same across all functional forms, then the empirical results of the elasticities from the demand system should also be the same across all functional forms.
Objectives
Our primary objective was to propose a formulation that obviates the need to
choose among the popular functional forms when conducting a demand analysis and to empirically test this formulation using data on selected fruits and vegetables. The goal was to verify that the elasticities are the same across every functional form of the demand system. The secondary objective was to analyze the elasticities calculated from the coefficients of the inverse demand system.
9
Conceptual Framework
Inverse Demand Model
Barten and Bettendorf (1989) investigated the demand for fish by using the
Rotterdam Inverse Demand System, which expresses relative or normalized prices as a function of total real expenditure and quantities of all goods. The Rotterdam Inverse Demand System is the inverse analog of the regular Rotterdam Demand System. From an empirical viewpoint, inverse and direct demand systems are not equivalent. To avoid statistical inconsistencies, the righthand side variables in the systems should not be controlled by the decision maker. Therefore, it is better to use the inverse demand system for fresh fruits and vegetables.
It will be helpful to recall the consumer theory about ordinary direct demand functions derived from budgetconstrained utility maximization. Types of consumer theory leading to systems of demand functions were summarized by Barten (1993), Deaton and Muellbauer (1980), and Theil (1965). Consumers pay piq, for the desired amounts of commodity i, where pi is the price of good i and q, is the quantity of good i. These expenditures satisfy the budget equation, ,, pjq = m, where m is the total budget of the consumer's allocation. The consumer's problem is to satisfy the budget constraint by selecting the quantities that maximize the utility function. This consumer problem can be stated as the utility maximization problem. It can be shown that under the appropriate form of the utility function, there exists a unique set of optimal quantities that maximize the utility function (subject to the budget constraint) for any set of given positive prices and income. These optimal quantities of income and prices are the Marshallian (Walrasian) demand functions,
qi = J(m, p,.. ., pn), (21)
10
with Walras' law: Yjpiqi = m. These demand functions follow the neoclassical restrictions, which include addingup, homogeneity of degree zero in p and m, symmetry of the matrix of Slutsky substitution effects, and negative semidefiniteness of the matrix of Slutsky substitution effects. The implied restrictions are most conveniently expressed in terms of elasticities, which are derivatives of the logarithmic version of the direct demand functions,
d(ln q,) = qi d(ln m)+ Ip, i d(ln p), i,j 1,..., n, (22) where qr is the income (budget, wealth, total expenditure) elasticity of demand for commodity i and is defined as
rli = (aqi / am)(m / q;) = 8(ln qj) / a(ln m), (23) 1u is the uncompensated price elasticity and is defined as
up = (dqi / opj)(pj / q,) = a(ln q,) / 8(ln pj), (24) dx is the derivative of variable x, and In x is the natural logarithm of variable x. The Slutsky, or compensated price, elasticity, vE;, can be represented in terms of the uncompensated price and income elasticities using the Slutsky equation,
ey = Py + 7w, (25) which involves the budget share,
wi = piq, / m. (26) This compensated price elasticity corresponds to the substitution effect of price changes, keeping utility constant. These elasticities inherit certain properties from the four neoclassical restrictions of qj.
First, the addingup conditions are
X, wirl = 1 (Engel aggregation), (27)
11
X; wu = wj (Cournot aggregation), (28) ; wcy = 0 (Slutsky aggregation). (29) Second, the homogeneity of degree zero in p and m is
YEj u = 7/r, (210) j El = 0. (211) Third, the symmetry of the matrix of Slutsky substitution effects is
w, = wtAy. (212) Fourth, the negativity condition is
E, ijx wi Xj<0 x,, xj # constant. (213) From Walras' law, we can show that d(ln m) = d(ln P) + d(ln Q):
m = Yipiq,
dm = i q; dpi + Y1 pi dq,,
dm / m = Yi (q / m) dpi + i (pi / m) dqi,
d(ln m) = ZC (piqi / m)(dp, / pi) + Y, (pq, / m)(dq, / qi),
d(ln m) = Ei wi d(ln pi) + 1, wi d(ln q,),
d(ln m) = d(ln P) + d(ln Q), (214) where
d(ln P) = E, w, d(ln pi) (the Divisia price index), (215) d(ln Q) = Xi wi d(ln qi) (the Divisia volume index). (216)
An inverse demand system expresses the prices paid as a function of the total real expenditure and the quantities available of all goods. The coefficients of the quantities in the various inverse demand relations reflect interactions among the goods in their ability to satisfy wants. From an empirical viewpoint, inverse and regular demand systems are not equivalent. To avoid statistical inconsistencies, variables on the righthand side in such systems of randomdecision rules should be the ones that are not controlled by the
12
decision maker. In most industrialized economies, the consumer is both a price taker and a quantity adjuster for most of the products usually purchased. This is suitable with the regular demand system. On the other hand, for certain goods like fresh vegetables, supply is very inelastic in the short run, and the producers are virtually price takers. Pricetaking producers and pricetaking consumers are linked by traders who select a price they expect to clear in the market. The traders set the prices as a function of the quantities that are suitable in the inverse demand system.
To apply consumerdemand specifications to the model, the basic results of
consumerdemand theory should be reviewed. From the utilitymaximization problem for the consumer, we obtained a system of uncompensated inverse demand equations from the firstorder conditions,
= (au / aq) /; j (au / q)qj, i = 1, 2, ..., n, (217) where n7= p / m is total expenditure or income (m) = Zipiqi, u is utility, and pi and q; are price and quantity for good i, respectively. The budget share (wi) can be found by using Equation 26 and ax = x[a(ln x)],
wi = [6(ln u) / t(ln qi)] / ,j [O(ln u) / a(ln qj)]. (218)
First, we consider the Rotterdam Inverse Demand System (RIDS) by following Brown et al. (1995). A system of compensated inverse demand relationships can be found by working with the distance function, which is dual to the utilitymaximization problem. The distance function indicates the minimum expenditure necessary to attain a specific utility level, u, at a given quality, q, which can be written as g(u, q). By differentiating the distance function with respect to quantity, we get the compensated
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inverse demands (which express price as a function of the quantities and specific utility level),
p; = Og(u, q) / aq; = p(u, q). (219) Consequently, we can also represent the compensated inverse demands for normalized prices, z = pi / m, where Li piq; = m, by
& = p,(u, q) / 7 [p;(u, q).q] = g(u, q). (220) Next, we find the RIDS by totally differentiating this system of compensated inverse demand relationships. As zn is a function of u and q,, the total differentiate of ;z is
d7m = (8~n / au) du + Ej (Oa / aqj) dqj. (221) Consider a proportionate increase in q (i.e., dq = kq*) where k is a positive scalar. We can then transform the term (Orau) du to
(a / au) du = ;r[8(ln r,) / (ln u)] d(ln u),
(a, / Bu) du = zj[a(ln z) / a(ln k)] {d(In u) / [a(ln u) / a(ln k)]},
(an / au) du = [t[(In nj) / (ln k)] { [Y (a(ln u) / 8(ln qj)) d(ln q)] / [Lj (d(ln u) / 8(ln q))] },
(a / au) du = ri[a(ln z) / O(ln k)] Ej wj d(ln qj). (222) From dn = ,z d(ln ni), we get the logarithmic version of the RIDS model,
Y d(ln z;) = 4i[a(ln ;) / a(ln k)] Y w, d(ln qj) + ,[J((ln 4) / a(ln qj)) d(ln qj)],
d(ln z) = [a(ln ir) / a(ln k)] Yi w. d(In qj) + Y, [a(ln ;) / 8(ln q,)] d(ln qj),
d(ln ;) =; ( d(ln Q) + Ej d(ln q), (223) where
= a(ln ~) / a(ln k) (the scale elasticity), (224) = a(ln n) / a(ln qj) (the compensated quantity elasticity). (225) In order to satisfy the symmetry condition, we premultiply both sides by w,. The RIDS model now can be written as
wi d(ln r) = w,; d(ln Q) + Ej wj; d(ln qj),
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w, d(ln 7r) = hi d(ln Q) + Yj h d(ln qj), (226) where
hi = w,; (227) hy= w iy. (228) As dq = kq *, the scale elasticity, ;j, is h, / w,. The compensated quantity elasticity (flexibility), U, is hy / wi with the following properties. First, the addingup conditions are
Zi h; = 1, (229) Y, hu = 0. (230) Second, the homogeneity condition is
Yj ho. = 0. (231) Third, the symmetry condition is
hy = hj (Antonelli symmetry). (232) Fourth, the negativity condition is
Ei ,Y xi wi ho x < 0 xi, x # constant. (233)
The second functional form of the inverse demand system is the Laitinen and
Theil's Inverse Demand System (LaTheil). Following Laitinen and Theil (1979), we describe the consumer's preferences as g(u, q), where g(u, q) is the distance function which is linearly homogeneous in q. The Antonelli matrix is
A = [ar], ai = og / a(pjq;)o(pjqj). (234) From this Antonelli matrix, we can find the inverse demand system,
d[ln (p/P)] = 4 d(ln Q) + LY d(ln qj) + Ej w. d(ln q.),
d[ln (p,/P)] = (4 +1) d(ln Q) + j, ; d(In q.).
15
We also can get the logarithmic version of the LaTheil model from the logarithmic version of the RIDS model (Equation 223) by adding d(In Q) to both sides,
d(ln Itr) + d(ln Q) = (4 +1) d(ln Q) + Ej 4 d(ln qj),
d(ln p,) d(ln P) d(ln Q) + d(ln Q) = (4, +1) d(ln Q) + Ej, 4 d(In qj),
d[ln (p/P)] = (4 +1) d(ln Q) + Zj 4 d(ln qj). (235) In order to satisfy the symmetry condition, we premultiply both sides of Equation 235 by wi, so the LaTheil model is
w, d[ln (p/lP)] = wi(, +1) d(ln Q) + ij wij d(ln qj), wi d[ln (pI/P)] = (w; + w;) d(ln Q) + ,j hy d(In qj),
wi d[ln (pj/P)] = (hi + wi) d(ln Q) + Ej hy d(ln q1),
w, d[in (p;/P)] = b, d(ln Q) + Yj h, d(ln qj), (236) where
bi = hi + Wi. (237) The coefficients of the LaTheil model also satisfy the neoclassical restrictions with parameter hy, which can be defined by Equation 227. Having the same properties as parameter hy in the RIDS model (Equation 226), the addingup condition requires
Ei b; = 0. (238) The third functional form of the inverse demand system is the Almost Ideal Inverse Demand System (AIIDS), which can be obtained from the distance function,
In g(u, q) = (1 u) In a(q) u In b(q), (239) where
In a(q) = to + Xk ak In qk + (1/2)Zk y 7kj* In qk In q, (240) In b(q) = In a(q) + /3oIk qkP. (241) The AIIDS cost function is written as
In g(u, q) = (1 u) In a(q) + u[ln a(q) + folIk qk],
In g(u, q) = In a(q) + ufolk qk,
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In g(u, q) = ao + k In qk + (I/2)yk I vk* In qk In qj + U3oIk qk, (242) where a y*, /I are the parameters. By using the derivative property of the cost function, pi = ag / aqi and m = g(u*, q), the budget share of good i can be written as
wi = piq, / m
wi = (ag / pi)pi / g
wi = a(ln g) / a(ln p). (243) Hence, from Equation 242, the logarithmic differentiation gives the budget shares as a function of prices and utility,
wi = a( + y7, In q, + bulolk qk, (244) where vy = (1/2)(7 j* + yi*).
As an approximation, we can replace ufolTIk qk with E, w; In q;. The differential form of the AIIDS model is
dw; = b, wi d(In q,) + Yij d(In qj),
dw; = bi d(ln Q) + Yj .y d(In q.). (245) There are four properties for the coefficients of the AIIDS model that satisfy the neoclassical restrictions. First, the addingup conditions are
E; 7Y = 0, (246) b; = 0. (247) Second, the homogeneous of degree zero is
Yj gY = 0. (248) Third, the Slutsky symmetry is
7Y' = y7j. (249) Fourth, the negativity condition is
;j Ej x,i 7 xj < 0 xi, xj # constant. (250)
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In addition, from the logarithmic version of the LaTheil model (Equation 235), we can get the logarithmic version of the AIIDS model by adding d(In q,) d(ln Q) to both sides,
d(ln p,) d(ln P) + d(ln q,) d(ln Q) = (4; +1) d(ln Q) + Yj y d(ln qj) + d(ln q,) d(In Q),
d(ln zj) + d(ln q) = (,; +1) d(ln Q) + Xj (4. + wj) d(ln qj),
d(ln wi) = (,; +1) d(ln Q) + 4j ( y + g w) d(ln qj).
We also can derive the logarithmic version of the AIIDS model by adding d(ln qj) on both sides of the logarithmic version of the RIDS model (Equation 223),
d(ln txr) + d(ln q;) = 4; d(ln Q) + @Yj d(ln qj) + d(ln q,),
d(ln r,) + d(ln q) = 4; d(ln Q) + d(ln Q) + 4 d(In q.) + d(In q,) d(ln Q),
d(ln w;) = (c; +1) d(ln Q) + Yj (4y + S w,) d(ln q). (251) In order to satisfy the symmetry condition, we premultiply both sides of Equation 251 by w,, so the AIIDS model is
w, d(ln w,) = (wi(, + w;) d(In Q) + Xj (wj4 + wiS w;wj) d(ln qj),
dw, = b, d(ln Q) + 4j y. d(ln qj),
which is the same as Equation 245 and
4 = w,@ + wi; wiw. (252)
The last functional form of the inverse demand system is the Rotterdam Almost Ideal Inverse Demand System (RAIIDS). We can get the logarithmic version of the RAIIDS model by subtracting d(ln Q) from both sides of the logarithmic version of the AIIDS model (Equation 251),
d(In w l) d(In Q) = (;+1) d(ln Q) + (4 + y w) d(n qj) d(ln Q),
d(ln w) d(ln Q) = d(In Q) + ( + 5 wj) d(ln q,).
We also can get the logarithmic version of the RAIIDS model by adding d(ln q,) d(ln Q) to both sides of the logarithmic version of the RIDS model (Equation 223),
d(In ;r,) + d(ln q,) d(ln Q) = 4; d(ln Q) + Yj 4 d(In q.) + d(n q,) d(ln Q),
d(ln ;,) + d(ln q) d(ln Q) = 4; d(ln Q) + E, (4; + y wj) d(ln qj),
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d(ln w) d(In Q) = d(In Q) + Yi (4 + ,y wi) d(In qi). (253) In order to satisfy the symmetry condition, we premultiply both sides of Equation 253 by wi, so the RAIIDS model is
wi[d(n wi) d(ln Q)] = wi; d(ln Q) + Yj (w;i + wSy wiwj) d(ln qj),
dwi w, d(ln Q) = hi d(ln Q) + 1j y d(ln qi). (254) By using our new formulation, the properties of parameter hi, which can be defined by Equation 227, are equivalent to the ones in the RIDS model (Equation 226), and the properties of parameter 7yj, which can be defined by Equation 237, are equivalent to the ones in the AIIDS model (Equation 245). As a result, the RAIIDS model has the RIDS scale effects and the AIIDS quantity effects. On the other hand, the LaTheil model has the AIIDS scale effects and the RIDS quantity effects. Scale and Quantity Comparative Statics
We can examine relations for inverse demands by following Anderson (1980) to express price as a function of quantities and total expenditure,
pi =(q, m), (255) and normalized prices, 4 =pi / m, as a function of quantities,
4 =j(q, 1) =f'(q). (256) As it is true about quantity elasticities of prices being equivalent to those about quantity elasticities of normalized prices, we confine our discussion to normalized prices in what follows. Quantity elasticities are the natural analogs for inverse demands of price elasticities, puy, in direct demands. They tell how much price i must change to induce the consumer to absorb marginally more of goodj. The quantity elasticity of good i with respect to goodj is defined as
v4; = [af'(q) / q][q /fiJ(q)]. (257)
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When dealing with inverse demands, an interesting question is: how much will price i change in response to a proportionate increase in all commodities, or how do prices change as you increase the scale of the commodity vector along a ray radiating from the origin through a commodity vector? We formalize this notion for marginal increases in the scale of consumption by defining the scale elasticity to derive restrictions relating to quantity and scale elasticities. These restrictions show that the scale elasticity is analogous to total expenditure elasticity, tr;, in direct demands. Let q* be a reference vector in commodity space so that we can represent the consumption vector of interest as q = kq*, where k is a scalar. We can express the inverse demands as
n =f'(kq*) = g '(k, q*). (258) The scale elasticity of good i is defined as
= [,g '(k, q*) / 8k][k / g '(k, q*)]. (259) Quantity and scale elasticities obey restrictions that are directly analogous to restrictions for direct demands. For the homogeneity of degree zero restriction, we can write
4 = Xj [af'(q) / aqj~qj*[k If '(q)],
,= Ij [f '(q) / eq][ [k / f'(q)],
= LY ryj, (260) which is analogous to j Fp = r7i in the direct demand system. For the addingup conditions, we start by writing the budget equation, w; = nrq;, as
wi =f'(q) q,. (261) From Zi wi= 1, we get
~1f'(q) q, = 1. (262) Differentiating with respect to qj, we have
;i, [8f'(q) / aq]qi + f'(q) = 0,
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Yi [af'(q) / aq]q, = f '(q).
By multiplying both sides by qj, we obtain
Yi [f'(q) / Oqj][qj / f(q)] f '(q) q, = f'(q) qj.
As Vjj = [f'(q) / aqj][q /f(q)] and w, =f'(q) qi, we have
;Zi lwi = w, (263) which is analogous to the Cournot aggregation, Z; w jy = wj. Next, the analogous to the Engel aggregation, X, wir;i =1, is obtained by
F i W, Yj ri = Yj wj.
As ( = Zj V, and 1 w, = 1, we get
X, w;i = 1. (264)
Scale and quantity elasticities are the natural concepts of uncompensated elasticities for inverse demands. We derive the constantutilityquantity elasticities, or compensatedquantity elasticities, from the transportation function, T(q, u), which is dual to the cost function and satisfies
U[q*/ T(q*, u*)] = u' (265) for all feasible q* and u*. The transformation informs how much a particular consumption vector must be divided to place the consumer on some particular indifference curve. By differentiating with respect to goods, we get the constant utility or compensated inverse demands,
r =f*(q, u) = oT(q, u) / aq,. (266) These price functions give the levels of normalized prices that induce consumers to choose a consumption bundle that is along the ray passing through q and that gives utility u. The constant utility quantity effects, or the Antonelli substitution effects, state the
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amounts normalized prices change with respect to a marginal change of reference consumption qj, keeping the consumer on the same indifference level. We can express the Antonelli substitution effects in elasticity form, which is analogous to the compensatedprice elasticity, co. The constantutilityquantity elasticity of good i with respect to goodj is defined as
y = [2T(q, u ) q, qj] {qj / [8T(q, u) / q]},
4y = (8iz4 / a9q)(qj / g,). (267) T(q, u) is homogeneous of degree one in q, and f* (q, u) is homogeneous of degree zero in q. From the direct application of Euler's theorem, we get
Yj = 0, (268) which is analogous to the restriction, Yj cE = 0. From the properties of the transformation function, which include the decrease in u, and the increase, linearhomogeneous, and concave in q, the matrix of Antonelli effects is negative semidefinite. This implies 3y < 0 which can be called the Law of Inverse Demand. Next, we describe the implicit compensation scheme to derive the inverse demand equation, which is analogous of the Slutsky equation. The total change in prices associated with an increase in one quantity can be decomposed, as total effect equals the summation of the substitution effect and the scale effect.
Now, consider a marginal change in the price in response to a marginal change in relative quantity and in scale. By totally differentiating n = g i(k, q*), we get
dnr = [ag '(k, q*) / dqj*] dqj* + [ag '(k, q*) / 8k] dk. (269) The change in scale must compensate for the change in qj* so as to leave the utility unchanged, du = 0. With in = (au / q,) / Xj (u/laqj)qj, we get
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du = 1i (au / aq,*)q* dk + (au / aqj*)k dqj* = 0, (270) dk = [(au / aqj*) / Y1 (au / aqi*)qi*]k dq.* = rj k dq. (271) From Equations 269, 270, and 271, we get
diz = [ag '(k,(k) d4 + [ag'(I, q ) / 8k]( 7 k dq*),
da/ dqj* = [g '(k, q ) / aqj*] [ag '(k, q*) / ak]4j k. By multiplying both sides by (q / r), we get
(d dqji)(qj* / z) = (a / aqj*)(qj / ) (ari/ k) k(qj* / ,r),
(di / dqj,)(qj* / ,) = (O / aq,')(qj / r) (az / ak)(k / n)(r q.). (272) As wj = 7. qj, gy = (dan / dqj)(qj / g), ; = (ai / 8k)(k / zr) and Wy = (8nz / aqj)(qj / n), it is convenient to express this in elasticity terms,
4 = 4 ;wj. (273) This states the Antonelli substitution effects in terms of scale and uncompensatedquantity changes. It is fully analogous to the Slutsky equation (Equation 25) of standard theory,
(ahi / pj)(pj / h,) = (aqi / apj)(pj / q,) + (aqi / am)(m / q,)(pjqj / m)
e. = py + 77wj,
where h;(p, u) is the Hicksian compensated demand function, which allows the demand analyst working with inverse demands to compute compensated elasticities from the uncompensated elasticities directly (without being obliged to explicitly consider the transformation function or compensated inverse demands). Finally, from E, y~w = wj and 1E w ; = 1, we can derive the analog to Slutsky aggregation
Y, wi4j = Yi wy y 1 w,1wj,
X; w j = wj (1)wj,
Ei wij = 0. (274)
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The symmetry of dan / dq,* implies that compensatedquantity cross derivatives between any two goods, i andj, must satisfy dzri / dqj* = dyj / dq,. The symmetry property reflects the fact that the cross derivatives of a function are equal. We also get the symmetry of the matrix of Antonelli substitution effects from this symmetry property,
di / dqj* = dq / dq*.
By multiplying by q,*qj* on both sides, we get
(d; / dqj )(qi*qj) = (dnj / dq,')(q,'qj*),
(dn / dqj)(qj*qj)(rj; / z~) = (dj / dqj*)(qj*qj*)(4zj / nj), (rq,')(d)z / da *)(qj / nr) = (jqj')(dj / dq,*)(qi* / j).
As w, = 7z q,, j = (d7 / dqi)(qj / 4i), we get Antonelli symmetry,
w,4 = wji,, (275) which is analogous to Slutsky symmetry, wiy = wj~ji (Equation 212).
From the AIIDS model, we can prove for the addingup condition, Equation 246, by using the summation of Equation 252 over i (1E ~ = E; wj + Z, w,jy wiX i w;). As ; wi1 = O0, wi = i wigy, and Zi w, = 1, we get Equation 246 (, y = 0). The proof for Equation 247 can be obtained by working with Equation 237 (Y, b, = E; w,4 + Z, w,). As Fj w, = 1 and EZ w; = 1, we get Equation 247 (E; bi = 0). Next, we prove the homogeneity of degree zero, Equation 248, by using the summation of Equation 252 overj (Ej yy = wi j + + )wi wiy wi i wj). Asj 0, w = 0, w i= j wyand jwi ;= 1, we get Equation 248 (;j My = 0). We also prove the Antonelli symmetry, Equation 249, by working with Equation 252 (yu = w;&y + wi8, wiw,). As w,j = wji, and wio, = w~ij;, we get y, = w + wi4i wiw, which means y = j, (Equation 249).
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Econometric Model Development
For the purpose of estimating, operator d is the logchange operator; that is, if x is any variable and xi, is its value in year t, then
d(ln xi) = A(ln xit) = In xit In xi t = In (xt / xi 1). (276) For the budget share, Barten (1993) replaced wi by the moving average, w,, where
w = (wi, + wit) / 2. (277) As a result, each functional form generates different elasticities. The big disadvantage is on the coefficients of the demand systems. To solve this problem, we proposed a new formulation by using the mean of the budget share, i,, where
w, = Etwit / T, (278) where t = 1, ..., T. By using this formulation, each coefficient of the demand systems is a function of instead of w ,, and the calculated elasticities are expected to be unchanged across the functional forms.
First, by replacing d(ln j) with A(ln g,), d(ln Q) with A(In Qt), and d(ln qj) with A(ln qj,) in Equation 226, the econometric model development for the RIDS model can be written as
w, A(ln nt) = w, A(ln Q,) + ij W, 4 A(In qt) + vil,
A(In rit) = hi A(ln Qt) + j h,1 A(ln qjt) + v, (279) where
hi= j 4 (280) hi, t J. (281)
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Second, we get the econometric model development for the LaTheil model (which has the RIDS scale coefficients and the AIIDS quantity coefficients) by adding w, A(ln Qt) on both sides of the RIDS model (Equation 279),
A(ln n,) + W, A(ln Qt) = ( w, + W, ) A(ln Q) + Ij A(ln qjt) + Vit,
[A(In 7,t) + A(In Qe)] = b, A(ln Q) + hy A(ln qj,) + vit,
W, A[ln (pit / P,)] = bi A(ln Qt) + Ij hy A(ln qjt) + vit, (282) where
A[ln (Pi, / P,)] = [A(In pit) A(ln P,)] = W, [ A(ln a,) + A(ln Qt)]. (283)
Next, we consider the Almost Ideal Inverse Demand System. We introduce parameter A(ln Qt*) for the AIIDS model, where
A(ln Qt,) = j w, A(ln qj). (284) By using this parameter, the coefficients of the AIIDS will be the function ofWj, not the function of w,. We get the econometric model development for the AIIDS model from Equation 245 by replacing dwi with dwit, d(ln Q) with A(ln Q,), and d(ln qj) with A(ln qj,),
dw,, = (, ; + ) A(ln Q,) + ,j (< Wi + w, W, w*, ) A(ln qit) + vit,
dwj + j w,*, A(ln qjt) ~ w, A(ln qjt)
= (, + ) A(ln Qt)+ ( + w, w,) A(ln qjt) + v,,, dwi, + iw [A(In Q,) A(In Qt*)] = b, A(ln Q,) + y A(ln qj,) + vit,
w, [A(ln 4,) + A(ln qit) + A(ln Q,) A(In Q,*)]
= b; d(ln Q,) + Yj 7, A(ln qit) + vi, (285) where
dwt = iv, A(ln wit) = W, [A(ln 7it) + A(ln qit)], (286) bi = ;, + w,, (287) Y= W, 4 + w, i w w,. (288)
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For the last functional form, we get the econometric model development for the RAIIDS model that has the AIIDS scale coefficients and the RIDS quantity coefficients by subtracting w, A(ln Qt) on both sides of the AIIDS model (Equation 285),
dw, + W [A(ln Qt) A(ln Q'*)] W A(ln Qt)
= W A(ln Qt) + ,j (W, j + W j w, w ) A(ln qt)+ Vit,
dwit W, A(n Qt* ) = hi A(n Qt) + Ij v A(In qit) + vit,
W [A(ln tri) + A(ln qit) A(ln Qt*)] = hi A(ln Q) + Yj TU A(ln q,) + vu. (289) From the coefficients of each functional form of inverse demand system, we can calculate the scale elasticity and the compensated quantity elasticity by using the following equations:
= hi / = (bi / ,) 1, (290) j= hy / ii = (yy / ,) + Wj Sy. (291) The uncompensated quantity elasticity can be calculated by using the Antonelli equation,
Wyg = 4 + 4i (292)
Because functional forms of the demand systems can be related to each other
theoretically, we can show that standard errors are unchanged across the functional forms of the inverse demand system. The standard error can be calculated from the disturbance,
Vit = Yi ,it = Afxit Xit, (293) where is the estimation of the dependent or explained variable, yit, f, is the estimation of the coefficient, ,and xit is the independent or explanatory variable. The disturbance for the RIDS model (Equation 226) is
Vit = [hi A(ln Qt) + Z, ho A(ln qjt)] [ A(ln Qt) + j A(ln qit)],
vii = (hi ) A(ln Qt) + j (h, ,j )A(In qgt). (294)
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The disturbance for the LaTheil model (Equation 236) is
vi = [b, A(n Q,) + Lj h A(ln qit)] [b, A(ln Qt) + Zj h, A(ln qj,)],
v, = (bi )A(ln Q,) + Lj (h h, )A(In qj). (295) The disturbance for the model AIIDS (Equation 245) is
vit = [b; A(In Q,) + Yj yj A(ln qjt)] [ A(ln Q,) + ij Y, A(ln q1)],
v,t = (bi )A(ln Q,) + Ij (,j, ,,)A(ln qit). (296) The disturbance for the RAIIDS model (Equation 254) is
vi, = [h, A(ln Q,) + Ij y, A(ln qj,)] [ h, A (n Q) + Ij Y,; A(ln qjt)],
vit = (hi h,) A(ln Q,) + Xj (r Y. )A(ln qj,). (297) From the coefficients of these four functional forms of inverse demand system, we can show that
h, h = w, 4, = ,(4, Q), (298) h, hy= w ,7 w, Zj= W (ij ), (299)
b, =( + ,)(c, + ;)= ,( ), (2100) Y =(, iv4+ ivjwI wij )(, e+ W,5 w, w)= W( y ), (2101) where h, is the estimation of hi, h, is the estimation of h., b, is the estimation of b, is the estimation of j, and and r, are the estimations of ;j and 4y, respectively. Consequently, for all functional forms of the inverse demand system, we get the same disturbance,
v= ;, [(4i )A(In Q,) + j ( e )A(ln qj,)]. (2102)
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Because we get the same disturbance for every functional form of the inverse demand system, we also get the same standard error and loglikelihood value across all functional forms.
Methodology for Demand Analysis
In following Barten (1969) to estimate the inverse demand system, we used the maximumlikelihood method of estimation with constraints imposed. We imposed the homogeneity and symmetry constraints by working with the concentrated loglikelihood function. We estimated every demand equation in the system at the same time by applying the Seemingly Unrelated Regression Estimation. GAUSS (a mathematical and statistical software package), was used to perform the estimation.
There are four scenarios in our study. The first scenario is to estimate each
functional form of the inverse demand system by using the mean of the budget share to multiply the logarithmic version of the inverse demand system. The second scenario is to estimate each functional form of the inverse demand system by using the moving average of the budget share to multiply the logarithmic version of the inverse demand system. In addition, the first and second scenarios estimate the inverse demand system by using Barten's estimation method with the homogeneity and symmetry constraints imposed. The third scenario is to estimate the RIDS model by using Barten's unconstrained estimation method. The fourth scenario is to estimate the RIDS model by using Barten's estimation method with the homogeneity constraint imposed.
Results are based on time series data from 1994 to 1998 for four commodities of
selected vegetables and fruits, n = 4. Weekly wholesale prices and quantity unloads were collected from the Market News Branch of the Fruit and Vegetable Division, Agricultural Marketing Service, United States Department of Agriculture. There are 208 observations
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of quantities and prices for each commodity in each market, T = 208. The commodities are tomatoes, bell peppers, cucumbers, and strawberries. The markets include Atlanta, New York, Los Angeles, and Chicago. Seemingly Unrelated Regressions Model
Following Greene (2000), the inverse demand systems can be written as
yl = XB + e1, Y2 = XB + 4,
y,, = XB + En, (2103) where
e'= [el, ..., ], (2104)
E[e] =0. (2105)
The disturbance formulation is
aI a 2I ... o.,I
E [E.] = V= [21 22 2n. (2106) LO'.l .2l ... o.aIJ
There are n equations and T observations in the data sample. For the demand
system, we can apply Seemingly Unrelated Regressions (SUR) with identical regressors or the Generalized Least Square (GLS) with identical regressors,
y, X 0 ... O B,
o 2 0 X ... 0 B2 2 (2107)
y to 0 ... X B, ,
For the th observation, the n x n covariance matrix of the disturbances is
30
S, (12 ... In
d,= 21 "22 2n (2108)
n C. 2 ... C,nn
so, from Equation 2106, we get
V= DO 1I (2109) and
V1 = (2' 0 I. (2110) We find that the GLS estimator is
= [X'X' X'V'y
B= [X(TD' 0 )X]' X(n' X 1)y
o,,(XX)' cr,2(XX)' ... ,,(XX)' (XX) si"b,
r21 (XX)' U22(XX) ... n(XX) (XX)E i'2/ b (2111)
a,,(XX)' r,,(XX)' ... a.(XX)' (XX) ,"'b, where l= 1, ..., n.
After multiplication, the moment matrices cancel, and we are left with
B, = ij cri a b,,
B, = bI(, oi o') + b2(Xj Olj a) + ... + b,(Yj o,j in), (2112) wherej, and l= 1, ..., n, and
bi = (XX)'Xv. (2113) The terms in parentheses in the second line of Equation 2112 are the elements of the first row of XZZ' = I, so the end result is B, = b,. Using a similar method, the same results are true for the remaining subvectors, B, = b,. That is, in the Seemingly Unrelated Regressions model, when all equations have the same regressors, the efficient estimator is
31
singleequation ordinary least squares (OLS is the same as GLS). Also, the asymptotic covariance matrix of B is given by the large matrix in brackets above, which would be estimated by
Est. Asy. Var[B] = $10 (XXY)"', (2114) where
!b= Sj = (1/T) e,'e, (2115) or
Est. Asy. Cov[B, ] = rt,, (XX)', (2116) where i,j = 1, ..., n.
Barten's Method of Estimation
Following Barten (1969), the Maximum Likelihood (ML) method has been used to estimate the coefficients of the demand systems. Maximumlikelihood estimators are consistent, asymptotically efficient, and asymptotically normally distributed. The disadvantages in using the ML procedure are the possible smallsample bias of the estimator for the variances and covariances, the need to specify a distribution for the random variables in the model, and the procedure's computational difficulties. The likelihood function is to be maximized with respect to the coefficient of the system and the elements of the covariance matrix ,. Derivation of the ML estimators will be done in terms of maximizing the concentrated version of the logarithmiclikelihood function,
In L = 1/2 (Tln n T(n 1) (1+ In 2r) Tlno41), (2117) where
A = (1 / T) Yt vvt' (2118) and
32
vt = y, Dxt. (2119) An alternative way of writing vt is
V= YXD', (2120) where
V'= [VI,V2, .., VT], (2121) X'= [x, X2, 2,, T], (2122) Y' = [yi, y2, A *, yT]. (2123) Then
A = (1 / T) V'V+ ii'
A = (1/T) [Y'Y DX'Y Y'XD' + DX'XD] + ii', (2124) where
i =(1 / \n)t (2125) and i is the summation vector.
The resulting estimators of the coefficients of the system are used to obtain an estimator of variance, and hence a numerical estimate for the covariance of the disturbances, (2. The set of equations will be estimated jointly by using a maximum likelihood procedure (Barten, 1969). First, we estimate without the use of any restriction, next we impose a constraint for homogeneity condition, and then we impose constraints for both homogeneity and symmetry conditions. The assumption is made that prices and total expenditure are stochastic and independent of the disturbance term. We also assumed that vt are vectors of independent random drawings from a multivariatenormal distribution with mean zero and covariance matrix, 12.
33
Unconstrained estimation
Starting from an unconstrained estimation, the estimator of hi and h. will be
derived, which corresponds with the maximum of the concentrated likelihood function without the use of any restriction. For the firstorder conditions for a maximum of the concentrated likelihood function with respect to the elements of D,
(1ln L) / dOD = c [1/2 (Tln n T(n 1) (1+ In 2n) T ln41)] / BcD,
8(In L) / D = (1/2)8 (Tin 1A) / BD, a(In L) / 8D = (1/2)A'[(TA) / aD], from (ln J(x)) / ax =f'(x) [ J(x) / ax],
a(In L) / aD = (1/2)A' {a[T(1/T) (Y'Y DX'Y Y'XD' + DX'XD) ] / aD), from a(ax) / ox = a, If xa = (xa) then a(xa) / ax = a(xa)'/ ax = a(a 'x) / x = a' and 8(x'ax) / ox = ax + (x'a)'= ax + a x (a(x'ax) / ax = 2ax, if a = a), then
a(In L) / aD = (1/2)A [2Y'X 2DiX'X],
(ln L) / D = A' [Y'XDX'X]. (2126) From a In L / D= 0 and A' 0, we can solve for D1,
Y'X DIX'X= 0, D1 (XX)' = Y'X, D1 = Y'X(X'X)',
D = (X'X) 'X'Y, (2127) where D1 is the unconstrained ML estimator. The covariance matrix of this estimator is
E[(d' d)(d' d)] = 2Q (X'X)"', (2128) where d' is an n(n + 2) component vector by arranging the n columns of Di'. It is obvious that this is simply the ordinary least squares (OLS) estimator applied to each equation separately.
34
Estimation under the homogeneity condition
The homogeneity condition states that ij hy = 0. This can also be formulated in terms of D as
Dr= 0, (2129) where r is defined by
'= [0, 1, 1, .., 1] (n+ I). (2130) The Lagrangean expression with the homogeneity condition is
.' = In L + K'Dr, (2131) where c is an nelement vector of Lagrangean multipliers. By differentiating this Lagrangean expression with respect to the element of D,
a(ln L+ K' Dr) / aD = 8(ln L) / aD + (Dr) / D,
from 8(a cb) / ox = ab'and a(ln L) / 8D = A' [Y'X DX'X], then
a(In L+ l' Dr) / BD = A' [Y'X D2X'X] + tcz'.
By premultiplying this expression by A, postmultiplying it by (XX)"', and then using D1 = YX(X'X), we obtain
a(ln L+ K' Dr) / OD = AA' [Y'X D2X'X] (X'X) + A K'(X'X)'
a(ln L+ Dr) / D = YX(XX)' D2 + AKr' (X'X)'
a(ln L+ K'Dr) / aD = Di D2 + A (X'X)'. (2132) Since D2 is the ML estimator under the homogeneity condition, it has to satisfy D2r = 0. Postmultiplying Equation 2132 by r, we get
D1 r D2r+AK (X)"1 r= 0
AK= D r/ [f (X'X)' r]
AK= ODr, (2133) where Ois a scalar equaling 1 / r' (XX1 r. Then we get
35
Di D2 ODI rr' (XX)' = 0 D2'= [I 0(X'X)' rr'] D1'
D2'= [I 0(XX)"' rT] [(X'X)IX'Y
D2' = [(XX)"' O(X'X)' ri (X'Xy)'] X'Y
D2'= GX'Y, (2134) where
G = [(XXY)' O(X'X)' r' (X'X)'] (2135) and
r'G = 0. (2136) The complete covariance matrix of the ML estimator under the homogeneity condition is
E[(d2 d)(d2 d)'] = d2 G, (2137) where d2 is a n(n+2) component vector by arranging the n columns of D2'. Estimation under the symmetry and homogeneity conditions
The symmetry condition, hy = hji, can also be formulated in terms of d by
r'd= hy hii = 0, (2138) where d, the n(n + 2) component vector, is formally defined by
(I D)e = d, (2139) with e being an n2 component vector of the following structure,
e'= [el', e2, ., e,'], (2140) and r is a row vector with one in the [(i 1)(n + 1) +j + 1]th position minus one in the [(f 1)(n + 1) + i + 1]th position, and otherwise consisting of zeros. There are 0.5n(n 1) different symmetry conditions. These will be represented by
Rd= 0, (2141) where R is a matrix of 0.5n(n 1) rows and n(n + 2) columns. The homogeneity condition can also be formulated in terms of d by
36
[I Dle = [1 r'] [I D']e = [I r]d= 0. (2142) The Lagrangean expression to be maximized under the homogeneity and symmetry condition is
'O = In L + r'[I rjd + p'Rd, (2143) where K is a vector of n Lagrange multipliers for the homogeneity condition, and p is a vector of 0.5n(n 1) Lagrange multipliers for the symmetry condition. The vector of firstorder derivatives of In L with respect to d can be written as
(ln L) / ad = I (a In L / aD),
a(ln L) / ad = [I (X'Y X'XD3) A' ]e,
a(ln L) / d = [A' (X'YX'XD3 )]e, (2144) and from a ax / Ox = a'then
aK'[I r]d / ad= a[ r]d / ad,
ar[I r]d / ad= [i' r',
a'[I Jd/ ad / = [K r], (2145) and
a p'Rd / ad = ('R)' = R'p. (2146) The firstorder condition with respect to d of the Lagrangean expression with the homogeneity and symmetry conditions, Equation 2143, is
[A' (X'YX'XD3')]e + [K r] + R'/ = 0. (2147) Since it is required that FrD3' = 0 in view of the homogeneity condition, and we know that D2' = GX'Y and r'G = 0, by premultiplying Equation 2143 by [A G], we get
[A 0 G] [A' (X'YX'XD3')]e + [A G] [tK r] + [A 0 G]R'tp= 0
[I (GX'Y GX'XD3')]e + [AK Gr] + [A 0 G]R'p = 0
[I (D2' [I 0(XX)"' r']D3')]e + [A G]R'p = 0
[I (D2' D3')]e + [A G]R'p= 0
d d + [A 0 G]R' = 0. (2148)
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Since Rd3= 0 meets the symmetry condition. By premultiplying Equation 2148 by R, we get
Rd2 Rd + R[A 0 G]Rp = 0
u = [R(A 0 G)R'] 'R(d2 d)
u= [R(A 0 G)R']Rd2. (2149) From Equation 2148 and Equation 2149, we get
d = 2 (A 0 G)R'[R(A 0 G)R'"'Rd = Hd2, (2150) where
H= I (A 0 G)R'[R(A 0 G)R']'R. (2151) The covariance matrix of d3 can be approximated by
E[(d d)(d d)'] = H(.2 0 G)H'. (2152) Empirical Results
The results of the estimation with the homogeneity and symmetry conditions (using the mean of the budget share to multiply the logarithmic version of the inverse demand system by following Barten's estimation method for each functional form in each market) are presented in Tables 21 through 216. Next, the results of the estimation of the homogeneity and symmetry conditions (using the moving average of the budget share to multiply the logarithmic version of inverse demand system by following Barten's estimation for each functional form in each market) are presented in Tables 217 through 232. The results from the unconstraint estimation for each market are presented in Tables 233 through 236. The results from the estimation of the RIDS model with the homogeneity condition (by following Barten's estimation method in each market) are presented in Tables 237 through 240. The elasticities calculated from the coefficients of the inverse demand system for each market are presented in Tables 241 through 244.
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Inverse Demand System Analysis
The results from the estimation of the inverse demand system in every market
(Tables 21 through 216) show that by using the mean of the budget share to multiply the logarithmic version of the inverse demand system, the RIDS has the same scale coefficients as the RAIIDS model, and the AIIDS model has the same scale coefficients as the LaTheil model. The quantity coefficients are the same between the RIDS model and the LaTheil model, and are the same between the AIIDS model and the RAIIDS model. The scale elasticity, quantity elasticity, and standard errors are unchanged across all four functional forms of the inverse demand system.
The results from the estimation using the moving average of the budget share
(Tables 217 through 232) show that the coefficients are different from the estimation using the mean of the budget share. We also can see that by using the moving average, a different functional form generates a different result.
The results from the unconstrained estimation (Tables 233 through 236) show that the relative size of the estimated asymptotic standard errors is so large that not too much value can be attached to these results. Therefore, the unconstrained estimation results in imprecise point estimates. Moreover, the results of the estimation with the homogeneity constraint imposed (Tables 237 through 240) show that the homogeneity condition on it own cannot contribute much to the precision of the estimator. Though we could have expected smaller values for the standard errors, because of the use of a more restrictive model, this hope is almost not realized. In this respect much more can be expected from using the symmetry condition.
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Elasticity Analysis
We calculated the elasticities for each market from the estimation of the RIDS model by using Barten's method of estimation with homogeneity and symmetry constraints imposed (Tables 21, 25, 29, and 213). The results from Tables 241 through 244 show that all elasticities in every market have the correct sign according to theory. Tomato has the highest absolute value of the own substitution elasticity when compared with other commodities for every market. In contrast, strawberry has the lowest absolute value of the own substitution elasticity when compared with other commodities for every market. The elasticities for the inverse demand system are closer between the Atlanta and Los Angeles markets and between the Chicago and New York markets.
Scale effect and scale elasticity
Scale effects show how much the normalized price of good i will change in
response to a proportional increase in the total quantity in all commodities. This reflects the change in total expenditure. It denotes the change in utility, and addresses the question of how prices change as you increase the scale of the commodity vector along a ray radiating from the origin through a commodity vector. It measures the change in the Divisia quantity index, showing the movement from one indifference curve to another. Scale effects are converted into scale elasticities by dividing the scale effects by the budget share. The scale elasticities are considered analogous to the total expenditure (income) elasticities in the direct demand system. All the estimates for the scale effects are statistically significant at the 5% probability level and have the expected sign.
Tomatoes. The obtained estimates for the scale effects of tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are 0.5427, 0.5224, 0.4488, and 0.4577,
40
respectively. This showed that for a 1% increase in aggregate quantity in each market, the wholesale price of tomatoes will fall between 0.4488% and 0.5427%. The scale elasticities are 0.9617, 0.9075, 1.0259, and 1.0453 in the Atlanta, Los Angeles, Chicago, and New York markets, respectively (almost unit elastic in the Atlanta market, with the highest fluctuations in the New York market).
Bell peppers. The estimates of the scale effects of bell peppers had the expected negative sign (which showed that as aggregate quantity increases, the normalized price goes down). Since it is expected that the change in normalized price is proportional for both wholesale and retail prices, the magnitude of the above change would be reflected at both the wholesale and retail levels. As such, the obtained estimates of the scale effects can be used to infer that if there is a 1% increase in the quantity of the product group as a whole, the price of bell pepper will fall by 0.1777%, 0.1885%, 0.2226%, and 0.1968% in the Atlanta, Los Angeles, Chicago, and New York markets, respectively. The scale elasticities range from 1.0040 to 1.0905, which are elastic in the Atlanta, Los Angeles and Chicago markets with the scale elasticities equal to 1.0460, 1.0302, and 1.0905, respectively (almost unit elastic in the New York market, with the scale elasticity equal to
1.0040).
Cucumbers. The estimates show that for a 1% increase in the aggregate quantity in each market, the normalized wholesale prices will decrease by 0.1911%, 0.1517%,
0.2319%, and 0.2388% in the Atlanta, Los Angeles, Chicago, and New York markets, respectively. The scale elasticities of cucumbers are 1.0485, 1.0365, 0.892, and 0.9438 in the Atlanta, Los Angeles, Chicago, and New York markets, respectively (inelastic in the Chicago and New York markets and elastic in the Atlanta and Los Angeles markets).
41
Strawberries. The obtained estimates for the scale effects of strawberries in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0963, 0.1157, 0.0805, and 0.1120, respectively. This showed that for a 1% increase in aggregate quantity, the price for strawberries will decrease by 0.0963%, 0.1157%, 0.0805%, and 0.1120% for the Atlanta, Los Angeles, Chicago, and New York markets, respectively. The scale elasticities of strawberries are 1.1526, 1.2194, 0.8188, and 0.9910 in the Atlanta, Los Angeles, Chicago, and New York markets, respectively (elastic in the Atlanta and Los Angeles markets, elastic in the Chicago market, and almost unit elastic in the New York market).
Quantity effect and own substitution quantity elasticity
Quantity effects represent the compensated or substitution effects of quantity change. These effects show movement along a given indifference surface. These are converted into quantity elasticities by dividing the quantity effects by the budget share. The quantity elasticities are analogous to the price elasticities in the direct demand. They reflect how much the price of good i must change to induce the consumer to absorb more of goodj. The uncompensated quantity elasticities can be calculated by using the Antonelli equation (Equation292). In an inverse demand system, a negative quantity effect denotes substitution and a positive quantity denotes complimentarily (the reverse of the direct demand system). The obtained estimates of the own substitution effects have the expected sign, and are statistically significant at the 5% probability level for all commodities in the Atlanta, Los Angeles and New York markets. In the Chicago market, it is statistically significant only for the own substitution effect of strawberries.
In terns of the quantity effects, in the Atlanta market, the estimate combinations of tomato and cucumber and of tomato and bell pepper are statistically significant at the 5%
42
probability level. In the Los Angeles market, the estimate combination of tomato and cucumber, the estimate combinations of tomato and bell pepper, and of tomato and strawberry are statistically significant at the 5% probability level. In the New York market, the estimate combinations of tomato and cucumber, of tomato and strawberry, and of cucumber and bell pepper are statistically significant at the 5% probability level. In the Chicago market, the estimate combination of cucumber and strawberry is statistically significant at the 5% probability level.
Tomatoes. The obtained estimates for the own substitution quantity effects of tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0763,
0.1124, 0.0220, and 0.0245, respectively. The compensated own substitution quantity elasticities of tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are
0.1352, 0.1953, 0.0502, 0.0560, respectively. The uncompensated own substitution quantity elasticities of tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are 0.6778, 0.7178, 0.4990, 0.5138, respectively.
Bell peppers. The obtained estimates for the own substitution quantity effects of bell peppers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0412,
0.0382, 0.0192, and 0.0284, respectively. The compensated own substitution quantity elasticities of bell peppers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.2426, 0.2086, 0.0938, 0.1447, respectively. The uncompensated own substitution quantity elasticities of bell peppers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.4204, 0.3971, 0.3165, 0.3416, respectively.
Cucumbers. The obtained estimates for the own substitution quantity effects of cucumbers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0320,
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0.0366, 0.0189, and 0.0432, respectively. The compensated own substitution quantity elasticities of cucumbers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.1754, 0.2500, 0.0726, 0.1709, respectively. The uncompensated own substitution quantity elasticities of cucumbers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.3665, 0.4018, 0.3045, 0.4097, respectively.
Strawberries. The obtained estimates for the own substitution quantity effects of strawberries in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0111,
0.0182, 0.0186, and 0.0164, respectively. The compensated own substitution quantity elasticities of strawberries in the Atlanta, Los Angeles, Chicago, and New York markets are 0.1328, 0.1915, 0.1896, 0.1451, respectively. The uncompensated own substitution quantity elasticities of strawberries in the Atlanta, Los Angeles, Chicago, and New York markets are 0.2291, 0.3073, 0.2701, 0.2571, respectively.
Conclusions
To get the demand system that satisfies the neoclassical restrictions, we multiply the budget share by the logarithmic of the demand system. On the empirical estimation, it is better to use the mean of the budget share, w,, instead of the moving average of the budget share, w ,,, to multiply the logarithmic of the demand system. The results show the significant effect by using the mean of the budget share on every functional form of both direct and inverse demand systems. Moreover, by using the mean of the budget share, we can obviate the need to choose among various functional forms. The results also show that the estimation of the elasticity and the disturbance of the demand system are the same across all functional forms of the inverse demand system. Overall, it is better to use the RIDS model for fruits and vegetables to avoid statistical inconsistencies
44
(as the righthand side variables in the systems should not be controlled by the decision maker) and to avoid the problem with the statistical significant test of the coefficients.
The elasticities were calculated from the estimation of the RIDS model by using
Barten's method of estimation with homogeneity and symmetry constraints imposed. All the estimations of scale effects are statistically significant at the 5% probability level and have the expected sign. In terms of own substitution quantity effects, these estimations have the expected sign, and are statistically significant at the 5% probability level for all commodities in the Atlanta, Los Angeles, and New York markets. In the Chicago market, the estimation is statistically significant only for strawberry. In every market, tomato has the highest absolute value of own uncompensated quantity elasticity while strawberry has the lowest. In addition, own substitution quantity elasticities for tomato and bell pepper in the Atlanta and Los Angeles markets are higher than in the Chicago and New York markets.
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Table 21. Estimation of the RIDS model for the Atlanta market by using the mean of the
budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5427 0.1777 0.1911 0.0963 (0.0287) (0.0180) (0.0171) (0.0106) hTomato 0.0763 (0.0181)
hBell Pepper 0.0475 0.0412 (0.0107) (0.0104)
hCucumber 0.0254 0.0037 0.0320 (0.0107) (0.0075) (0.0100) hStrawberry 0.0033 0.0025 0.0103 0.0111 (0.0064) (0.0049) (0.0049) (0.0047) Standard Error (a) 0.0600 0.0379 0.0358 0.0221
R2 0.7022 0.3433 0.3840 0.3225 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 22. Estimation of the AIIDS model for the Atlanta market by using the mean of
the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0216 0.0078 0.0088 0.0127 (0.0287) (0.0180) (0.0171) (0.0106) Yromato 0.1696 (0.0181)
Bell Pepper 0.0484 0.0998 (0.0107) (0.0104)
YCucumber 0.0774 0.0347 0.1171 (0.0107) (0.0075) (0.0100) Strawberry 0.0438 0.0167 0.0050 0.0655 (0.0064) (0.0049) (0.0049) (0.0047) Standard Error (a) 0.0600 0.0379 0.0358 0.0221
R2 0.3080 0.3304 0.3877 0.4842 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
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Table 23. Estimation of the LaTheil model for the Atlanta market by using the mean of
the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0216 0.0078 0.0088 0.0127 (0.0287) (0.0180) (0.0171) (0.0106) hTomato 0.0763 (0.0181)
hBell Pepper 0.0475 0.0412 (0.0107) (0.0104)
hCucumber 0.0254 0.0037 0.0320 (0.0107) (0.0075) (0.0100) hStrawberry 0.0033 0.0025 0.0103 0.0111 (0.0064) (0.0049) (0.0049) (0.0047) Standard Error (a) 0.0600 0.0379 0.0358 0.0221
R2 0.0616 0.1278 0.0253 0.0488 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 24. Estimation of the RAIIDS model for the Atlanta market by using the mean of
the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5427 0.1777 0.1911 0.0963 (0.0287) (0.0180) (0.0171) (0.0106) tomatoo 0.1696 (0.0181)
13ell Pepper 0.0484 0.0998 (0.0107) (0.0104)
YCucumber 0.0774 0.0347 0.1171 (0.0107) (0.0075) (0.0100) YStrawberry 0.0438 0.0167 0.0050 0.0655 (0.0064) (0.0049) (0.0049) (0.0047) Standard Error (a) 0.0600 0.0379 0.0358 0.0221
R2 0.6284 0.5406 0.6141 0.6190 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
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Table 25. Estimation of the RIDS model for the Los Angeles market by using the mean
of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5224 0.1885 0.1517 0.1157 (0.0306) (0.0211) (0.0189) (0.0128) hTomato 0.1124 (0.0209)
hBell Pepper 0.0348 0.0382 (0.0133) (0.0144)
hCucumber 0.0500 0.0003 0.0366 (0.0118) (0.0100) (0.0120) hStrawberry 0.0276 0.0037 0.0131 0.0182 (0.0083) (0.0073) (0.0065) (0.0071) Standard Error (a) 0.0682 0.0479 0.0425 0.0289 R2 0.7011 0.2894 0.2223 0.2804 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 26. Estimation of the AIIDS model for the Los Angeles market by using the mean
of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0533 0.0055 0.0053 0.0208 (0.0306) (0.0211) (0.0189) (0.0128) Yromato 0.1318 (0.0209)
}3ell Pepper 0.0706 0.1113 (0.0133) (0.0144)
7Cucumber 0.0342 0.0271 0.0884 (0.0118) (0.0100) (0.0120) tStrawberry 0.0270 0.0137 0.0270 0.0677 (0.0083) (0.0073) (0.0065) (0.0071) Standard Error (a) 0.0682 0.0479 0.0425 0.0289 R2 0.2349 0.2186 0.1830 0.3226 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
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Table 27. Estimation of the LaTheil model for the Los Angeles market by using the
mean of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0533 0.0055 0.0053 0.0208 (0.0306) (0.0211) (0.0189) (0.0128) hTomato 0.1124 (0.0209)
hBell Pepper 0.0348 0.0382 (0.0133) (0.0144)
hCucumber 0.0500 0.0003 0.0366 (0.0118) (0.0100) (0.0120) hstrawberry 0.0276 0.0037 0.0131 0.0182 (0.0083) (0.0073) (0.0065) (0.0071) Standard Error (a) 0.0682 0.0479 0.0425 0.0289
R2 0.1338 0.0441 0.0657 0.0552 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 28. Estimation of the RAIIDS model for the Los Angeles market by using the
mean of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5224 0.1885 0.1517 0.1157 (0.0306) (0.0211) (0.0189) (0.0128) YTomato 0.1318
(0.0209)
YBeII Pepper 0.0706 0.1113 (0.0133) (0.0144)
YCucumber 0.0342 0.0271 0.0884 (0.0118) (0.0100) (0.0120) YStrawberry 0.0270 0.0137 0.0270 0.0677 (0.0083) (0.0073) (0.0065) (0.0071) Standard Error (a) 0.0682 0.0479 0.0425 0.0289
R2 0.5879 0.4712 0.4171 0.5113 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
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Table 29. Estimation of the RIDS model for the Chicago market by using the mean of
the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4488 0.2226 0.2319 0.0805 (0.0246) (0.0189) (0.0189) (0.0118) hTomato 0.0220 (0.0142)
hBell Pepper 0.0125 0.0192 (0.0095) (0.0105)
hcuumber 0.0006 0.0088 0.0189 (0.0098) (0.0081) (0.0110) hStrawberry 0.0101 0.0021 0.0107 0.0186 (0.0061) (0.0052) (0.0053) (0.0052) Standard Error (a) 0.0668 0.0515 0.0515 0.0317
R2 0.6287 0.4029 0.4386 0.1982 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 210. Estimation of the AIIDS model for the Chicago market by using the mean of
the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0113 0.0185 0.0281 0.0178 (0.0246) (0.0189) (0.0189) (0.0118) romato 0.2241 (0.0142)
7"ell Pepper 0.0769 0.1433 (0.0095) (0.0105)
YCucumber 0.1143 0.0443 0.1735 (0.0098) (0.0081) (0.0110) Strawberry 0.0329 0.0222 0.0149 0.0700 (0.0061) (0.0052) (0.0053) (0.0052) Standard Error (a) 0.0668 0.0515 0.0515 0.0317 R2 0.5212 0.4744 0.5653 0.4762 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
50
Table 211. Estimation of the LaTheil model for the Chicago market by using the mean
of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0113 0.0185 0.0281 0.0178 (0.0246) (0.0189) (0.0189) (0.0118) hTomato 0.0220 (0.0142)
hBell Pepper 0.0125 0.0192 (0.0095) (0.0105)
hCucumber 0.0006 0.0088 0.0189 (0.0098) (0.0081) (0.0110) hStrawberry 0.0101 0.0021 0.0107 0.0186 (0.0061) (0.0052) (0.0053) (0.0052) Standard Error (a) 0.0668 0.0515 0.0515 0.0317
R2 0.0229 0.0137 0.0163 0.0787 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 212. Estimation of the RAIIDS model for the Chicago market by using the mean
of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4488 0.2226 0.2319 0.0805 (0.0246) (0.0189) (0.0189) (0.0118) Yromato 0.2241 (0.0142)
bell Pepper 0.0769 0.1433 (0.0095) (0.0105)
rCucumber 0.1143 0.0443 0.1735 (0.0098) (0.0081) (0.0110) Strawberry 0.0329 0.0222 0.0149 0.0700 (0.0061) (0.0052) (0.0053) (0.0052) Standard Error (a) 0.0668 0.0515 0.0515 0.0317
R2 0.7224 0.6100 0.6603 0.5739 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
51
Table 213. Estimation of the RIDS model for the New York market by using the mean
of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4577 0.1968 0.2388 0.1120 (0.0190) (0.0130) (0.0159) (0.0089) hTomato 0.0245 (0.0122)
hBell Pepper 0.0015 0.0284 (0.0070) (0.0079)
hCucumber 0.0151 0.0232 0.0432 (0.0092) (0.0067) (0.0103) strawberry 0.0079 0.0036 0.0049 0.0164 (0.0053) (0.0045) (0.0048) (0.0048) Standard Error (a) 0.0785 0.0511 0.0674 0.0364
R2 0.7956 0.5853 0.5880 0.5370 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 214. Estimation of the AIIDS model for the New York market by using the mean
of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0199 0.0008 0.0142 0.0010 (0.0190) (0.0130) (0.0159) (0.0089) Yromato 0.2216 (0.0122)
71ell Pepper 0.0843 0.1292 (0.0070) (0.0079)
YCucumber 0.0957 0.0264 0.1458 (0.0092) (0.0067) (0.0103) trawbrry 0.0416 0.0185 0.0237 0.0839 (0.0053) (0.0045) (0.0048) (0.0048) Standard Error (c) 0.0785 0.0511 0.0674 0.0364 R2 0.6571 0.6573 0.4973 0.6015 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
52
Table 215. Estimation of the LaTheil model for the New York market by using the
mean of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0199 0.0008 0.0142 0.0010 (0.0190) (0.0130) (0.0159) (0.0089) hTomato 0.0245 (0.0122)
hBell Pepper 0.0015 0.0284 (0.0070) (0.0079)
hCucumber 0.0151 0.0232 0.0432 (0.0092) (0.0067) (0.0103) strawberry 0.0079 0.0036 0.0049 0.0164 (0.0053) (0.0045) (0.0048) (0.0048) Standard Error (a) 0.0785 0.0511 0.0674 0.0364
R2 0.0334 0.0563 0.0946 0.0589 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 216. Estimation of the RAIIDS model for the New York market by using the
mean of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4577 0.1968 0.2388 0.1120 (0.0190) (0.0130) (0.0159) (0.0089) oromato 0.2216 (0.0122)
13ell Pepper 0.0843 0.1292 (0.0070) (0.0079)
YCucumber 0.0957 0.0264 0.1458 (0.0092) (0.0067) (0.0103) ?Strawberry 0.0416 0.0185 0.0237 0.0839 (0.0053) (0.0045) (0.0048) (0.0048) Standard Error (a) 0.0785 0.0511 0.0674 0.0364 R2 0.7536 0.8456 0.7560 0.6830 Note: Asymptotic standard error of each estimated parameter is shown in parentheses
53
Table 217. Estimation of the RIDS model for the Atlanta market by using the moving
average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5421 0.1706 0.1871 0.1014 (0.0276) (0.0199) (0.0165) (0.0116) hTomato 0.0856 (0.0179)
hBell Pepper 0.0490 0.0428 (0.0112) (0.0112)
hCucumber 0.0291 0.0009 0.0372 (0.0102) (0.0077) (0.0099) strawberry 0.0075 0.0053 0.0091 0.0112 (0.0069) (0.0054) (0.0051) (0.0052) Standard Error (a) 0.0574 0.0422 0.0346 0.0244
R2 0.7264 0.2814 0.3916 0.2906 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 218. Estimation of the AIIDS model for the Atlanta market by using the moving
average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0157 0.0048 0.0004 0.0118 (0.0277) (0.0200) (0.0167) (0.0124) 7romato 0.1601 (0.0180)
3Bell Pepper 0.0432 0.0912 (0.0112) (0.0113)
YCucumber 0.0807 0.0314 0.1137 (0.0103) (0.0077) (0.0100) Strawberry 0.0362 0.0166 0.0016 0.0545 (0.0073) (0.0057) (0.0054) (0.0056) Standard Error (a) 0.0577 0.0424 0.0349 0.0260
R2 0.2907 0.2653 0.3773 0.3170 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
54
Table 219. Estimation of the LaTheil model for the Atlanta market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0231 0.0044 0.0090 0.0108 (0.0276) (0.0200) (0.0163) (0.0114) hTomato 0.0765 (0.0179)
hBell Pepper 0.0472 0.0397 (0.0112) (0.0112)
hCucumber 0.0244 0.0017 0.0322 (0.0102) (0.0076) (0.0097) hstrawberr 0.0050 0.0058 0.0095 0.0087 (0.0068) (0.0054) (0.0051) (0.0051) Standard Error (a) 0.0574 0.0424 0.0342 0.0240
R2 0.0758 0.1008 0.0287 0.0301 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 220. Estimation of the RAIIDS model for the Atlanta market by using the moving
average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5493 0.1709 0.1786 0.1024 (0.0278) (0.0200) (0.0171) (0.0128) Yromato 0.1507 (0.0181)
3ell Pepper 0.0415 0.0885 (0.0112) (0.0113)
YCucumber 0.0756 0.0308 0.1087 (0.0106) (0.0079) (0.0104) Strawberry 0.0336 0.0161 0.0022 0.0519 (0.0075) (0.0058) (0.0056) (0.0058) Standard Error (a) 0.0578 0.0423 0.0359 0.0270
R2 0.6493 0.4549 0.5789 0.4635 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
55
Table 221. Estimation of the RIDS model for the Los Angeles Market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5534 0.1794 0.1674 0.1031 (0.0309) (0.0208) (0.0203) (0.0138) hTomato 0.1184 (0.0213)
hBell Pepper 0.0425 0.0432 (0.0133) (0.0147)
hCucumber 0.0520 0.0008 0.0370 (0.0127) (0.0106) (0.0134) hStrawberry 0.0239 0.0015 0.0141 0.0113 (0.0088) (0.0078) (0.0072) (0.0078) Standard Error (a) 0.0687 0.0471 0.0456 0.0309
R2 0.7200 0.2743 0.2378 0.2170 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 222. Estimation of the AIIDS model for the Los Angeles market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0300 0.0006 0.0137 0.0190 (0.0300) (0.0208) (0.0196) (0.0141) Yromato 0.1279 (0.0207)
Y13el Pepper 0.0639 0.1010 (0.0133) (0.0150)
YCucumber 0.0353 0.0255 0.0872 (0.0123) (0.0105) (0.0129) Strawberry 0.0286 0.0116 0.0263 0.0665 (0.0090) (0.0080) (0.0073) (0.0081) Standard Error (c) 0.0668 0.0473 0.0439 0.0317 R2 0.2123 0.1954 0.1721 0.2682 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
56
Table 223. Estimation of the LaTheil model for the Los Angeles market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0429 0.0083 0.0163 0.0216 (0.0297) (0.0205) (0.0194) (0.0133) hTomato 0.1076 (0.0204)
hBell Pepper 0.0355 0.0364 (0.0131) (0.0146)
hCucumber 0.0480 0.0011 0.0314 (0.0122) (0.0103) (0.0128) hstrawberry 0.0241 0.0019 0.0155 0.0104 (0.0085) (0.0076) (0.0070) (0.0076) Standard Error (a) 0.0660 0.0465 0.0435 0.0298
R2 0.1277 0.0435 0.0545 0.0491 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 224. Estimation of the RAIIDS model for the Los Angeles market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5663 0.1717 0.1649 0.1004 (0.0315) (0.0213) (0.0208) (0.0148) YTomato 0.1171
(0.0217)
YBell Pepper 0.0570 0.0942 (0.0136) (0.0151)
YCucumber 0.0312 0.0254 0.0815 (0.0130) (0.0109) (0.0137) YStrawberry 0.0289 0.0118 0.0249 0.0656 (0.0094) (0.0083) (0.0077) (0.0085) Standard Error (a) 0.0701 0.0482 0.0467 0.0332
R2 0.6159 0.4073 0.3806 0.3984 Note: Asymptotic standard error of each estimated parameter is shown in parentheseses.
57
Table 225. Estimation of the RIDS model for the Chicago market by using the moving
average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4441 0.2316 0.2487 0.0758 (0.0248) (0.0203) (0.0209) (0.0130) hTomato 0.0246 (0.0148)
hBell Pepper 0.0164 0.0220 (0.0100) (0.0113)
hCucumber 0.0019 0.0109 0.0196 (0.0105) (0.0088) (0.0120) hstrawberry 0.0101 0.0054 0.0107 0.0154 (0.0066) (0.0057) (0.0059) (0.0057) Standard Error (a) 0.0674 0.0553 0.0568 0.0348 R2 0.6201 0.3872 0.4250 0.1583 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 226. Estimation of the AIIDS model for the Chicago market by using the moving
average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0221 0.0224 0.0223 0.0219 (0.0233) (0.0196) (0.0203) (0.0140) 7romato 0.2188 (0.0141)
}ell Pepper 0.0762 0.1421 (0.0096) (0.0110)
Ytucumber 0.1089 0.0418 0.1685 (0.0100) (0.0086) (0.0117) strawberry 0.0337 0.0241 0.0178 0.0756 (0.0068) (0.0059) (0.0061) (0.0062) Standard Error (a) 0.0632 0.0533 0.0552 0.0377 R2 0.5404 0.4506 0.5111 0.4199 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
58
Table 227. Estimation of the LaTheil model for the Chicago market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0210 0.0217 0.0231 0.0193 (0.0231) (0.0198) (0.0201) (0.0129) hTomato 0.0234 (0.0138)
hBell Pepper 0.0143 0.0215 (0.0096) (0.0111)
hcucumber 0.0014 0.0111 0.0190 (0.0099) (0.0086) (0.0116) hstrawbefy 0.0104 0.0040 0.0092 0.0157 (0.0064) (0.0057) (0.0058) (0.0057) Standard Error (o) 0.0627 0.0539 0.0546 0.0345
R2 0.0267 0.0191 0.0141 0.0630 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 228. Estimation of the RAIIDS model for the Chicago market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4453 0.2322 0.2496 0.0732 (0.0250) (0.0201) (0.0210) (0.0143) Yromato 0.2177 (0.0151)
1Bell Pepper 0.0741 0.1415 (0.0100) (0.0111)
YCucumbcr 0.1094 0.0420 0.1678 (0.0105) (0.0087) (0.0120) Strawberry 0.0341 0.0254 0.0164 0.0759 (0.0071) (0.0060) (0.0062) (0.0063) Standard Error (a) 0.0679 0.0545 0.0569 0.0383
R2 0.7096 0.5853 0.6146 0.4957 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
59
Table 229. Estimation of the RIDS model for the New York market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4646 0.2118 0.2208 0.1066 (0.0182) (0.0135) (0.0169) (0.0100) hTomato 0.0294 (0.0119)
hBell Pepper 0.0003 0.0255 (0.0072) (0.0084)
hCucumber 0.0177 0.0212 0.0406 (0.0095) (0.0072) (0.0113) hstrwberry 0.0120 0.0046 0.0017 0.0184 (0.0058) (0.0050) (0.0054) (0.0054) Standard Error (a) 0.0745 0.0527 0.0720 0.0413
R2 0.8176 0.6108 0.5146 0.4475 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 230. Estimation of the AIIDS model for the New York market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.0041 0.0152 0.0230 0.0076 (0.0186) (0.0138) (0.0165) (0.0103) Yromato 0.2047 (0.0124)
Ytell Pepper 0.0772 0.1256 (0.0074) (0.0086)
YCucumber 0.0879 0.0234 0.1353 (0.0094) (0.0073) (0.0110) Strawberry 0.0396 0.0251 0.0241 0.0887 (0.0060) (0.0050) (0.0054) (0.0055) Standard Error (a) 0.0761 0.0545 0.0700 0.0427
R2 0.6377 0.6319 0.4528 0.5514 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
60
Table 231. Estimation of the LaTheil model for the New York market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
b 0.4646 0.2118 0.2208 0.1066 (0.0182) (0.0135) (0.0169) (0.0100) hTomato 0.0294 (0.0119)
hBell Pepper 0.0003 0.0255 (0.0072) (0.0084)
hcucumber 0.0177 0.0212 0.0406 (0.0095) (0.0072) (0.0113) hstrawbenrry 0.0120 0.0046 0.0017 0.0184 (0.0058) (0.0050) (0.0054) (0.0054) Standard Error (6) 0.0728 0.0506 0.0671 0.0386 R2 0.0414 0.0542 0.0660 0.0584 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 232. Estimation of the RAIIDS model for the New York market by using the
moving average of the budget share
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4568 0.2273 0.2080 0.1117 (0.0188) (0.0149) (0.0178) (0.0108) Yromato 0.2030 (0.0124)
}Bell Pepper 0.0818 0.1268 (0.0078) (0.0093)
YCucumber 0.0814 0.0224 0.1296 (0.0098) (0.0080) (0.0121) strawberry 0.0398 0.0226 0.0258 0.0882 (0.0062) (0.0054) (0.0058) (0.0058) Standard Error (o) 0.0768 0.0591 0.0758 0.0444
R2 0.7525 0.8237 0.6596 0.6025 Note: Asymptotic standard error of each estimated parameter is shown in parentheses
61
Table 233. Unconstrained estimation of the RIDS model for the Atlanta market Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5868 0.0225 0.2231 0.0993 (0.1905) (0.1209) (0.1151) (0.0715) hTomato 0.0548 0.0576 0.0395 0.0004 (0.1120) (0.0710) (0.0676) (0.0420) hBell Pepper 0.0154 0.0715 0.0183 0.0006 (0.0366) (0.0232) (0.0221) (0.0137) hCucumber 0.0603 0.0640 0.0247 0.0181 (0.0418) (0.0265) (0.0252) (0.0157) hStrawberry 0.0299 0.0251 0.0032 0.0123 (0.0194) (0.0123) (0.0117) (0.0073) Standard Error (a) 0.0588 0.0373 0.0355 0.0221
R2 0.7137 0.3648 0.3947 0.3276 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 234. Unconstrained estimation of the RIDS model for the Los Angeles market Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.3980 0.2997 0.0717 0.0846 (0.1786) (0.1262) (0.1110) (0.0749) hTomato 0.1874 0.1039 0.0908 0.0928 (0.1079) (0.0763) (0.0671) (0.0452) hBell Pepper 0.0073 0.0171 0.0370 0.0330 (0.0394) (0.0279) (0.0245) (0.0165) hCucumber 0.0632 0.0102 0.0765 0.0511 (0.0370) (0.0261) (0.0230) (0.0155) strawberry 0.0048 0.0172 0.0245 0.0342 (0.0249) (0.0176) (0.0154) (0.0104) Standard Error (a) 0.0676 0.0478 0.0420 0.0283
R2 0.7059 0.2931 0.2409 0.3061 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
62
Table 235. Unconstrained estimation of the RIDS model for the Chicago market Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.3565 0.1354 0.2338 0.0799 (0.1251) (0.0963) (0.0964) (0.0118) hTomato 0.0649 0.0301 0.0018 0.0049 (0.0541) (0.0416) (0.0416) (0.0071) hBell Pepper 0.0033 0.0372 0.0111 0.0047 (0.0312) (0.0240) (0.0240) (0.0066) hCucumber 0.0291 0.0137 0.0176 0.0165 (0.0344) (0.0265) (0.0265) (0.0068) strawberry 0.0074 0.0036 0.0035 0.0167 (0.0167) (0.0129) (0.0129) (0.0053) Standard Error (a) 0.0667 0.0513 0.0514 0.0316 R2 0.6306 0.4074 0.4404 0.2036 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 236. Unconstrained estimation of the RIDS model for the New York market Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5173 0.2015 0.1055 0.0943 (0.0746) (0.0486) (0.0632) (0.0347) hTomato 0.0008 0.0073 0.0306 0.0016 (0.0327) (0.0213) (0.0277) (0.0152) hBell Pepper 0.0060 0.0288 0.0026 0.0044 (0.0223) (0.0146) (0.0189) (0.0104) hCucumber 0.0233 0.0146 0.0803 0.0006 (0.0218) (0.0142) (0.0185) (0.0101) hstrawberry 0.0235 0.0062 0.0246 0.0192 (0.0138) (0.0090) (0.0117) (0.0064) Standard Error (a) 0.0782 0.0510 0.0662 0.0363
R2 0.7972 0.5880 0.6020 0.5386 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
63
Table 237. Barten's estimation with the homogeneity condition of the RIDS model for
the Atlanta market
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5378 0.1879 0.1881 0.0927 (0.0283) (0.0181) (0.0171) (0.0106) hTomato 0.0835 0.0658 0.0190 0.0035 (0.0185) (0.0118) (0.0112) (0.0069) hBell Pepper 0.0069 0.0350 0.0122 0.0005 (0.0164) (0.0105) (0.0099) (0.0061) cucumber 0.0505 0.0217 0.0318 0.0168 (0.0177) (0.0113) (0.0107) (0.0067) hstrawberry 0.0261 0.0091 0.0005 0.0128 (0.0131) (0.0084) (0.0079) (0.0049) Standard Error (a) 0.0588 0.0376 0.0355 0.0221
RE 0.7136 0.3553 0.3944 0.3275 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 238. Barten's estimation with the homogeneity condition of the RIDS model for
the Los Angeles market
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.5184 0.1912 0.1456 0.1159 (0.0305) (0.0216) (0.0191) (0.0130) hTomato 0.1150 0.0386 0.0399 0.0278 (0.0209) (0.0148) (0.0131) (0.0089) hBell Pepper 0.0146 0.0369 0.0027 0.0035 (0.0229) (0.0162) (0.0143) (0.0098) cucumber 0.0840 0.0085 0.0390 0.0165 (0.0210) (0.0149) (0.0132) (0.0090) hStrawberry 0.0164 0.0068 0.0036 0.0149 (0.0182) (0.0129) (0.0114) (0.0078) Standard Error (a) 0.0677 0.0479 0.0424 0.0289
R2 0.7052 0.2905 0.2264 0.2813 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
64
Table 239. Barten's estimation with the homogeneity condition of the RIDS model for
the Chicago market
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4457 0.2194 0.2349 0.0799 (0.0249) (0.0192) (0.0191) (0.0118) hTomato 0.0271 0.0054 0.0023 0.0049 (0.0151) (0.0116) (0.0116) (0.0071) hBell Pepper 0.0170 0.0181 0.0114 0.0047 (0.0140) (0.0107) (0.0107) (0.0066) hCucumber 0.0064 0.0077 0.0173 0.0165 (0.0144) (0.0111) (0.0111) (0.0068) hstrawberry 0.0165 0.0049 0.0036 0.0167 (0.0111) (0.0086) (0.0086) (0.0053) Standard Error (a) 0.0668 0.0514 0.0514 0.0321
R2 0.6296 0.4051 0.4404 0.1752 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 240. Barten's estimation with the homogeneity condition of the RIDS model for
the New York market
Parameter Tomato Bell Pepper Cucumber Strawberry
h 0.4678 0.2022 0.2320 0.1147 (0.0204) (0.0133) (0.0175) (0.0095) hTomato 0.0216 0.0075 0.0224 0.0102 (0.0127) (0.0083) (0.0109) (0.0059) hBell Pepper 0.0067 0.0286 0.0350 0.0008 (0.0128) (0.0083) (0.0109) (0.0059) hCucumber 0.0109 0.0148 0.0487 0.0057 (0.0125) (0.0081) (0.0107) (0.0058) hStrawberry 0.0173 0.0063 0.0087 0.0166 (0.0104) (0.0068) (0.0089) (0.0049) Standard Error (o) 0.0783 0.0510 0.0669 0.0364
R2 0.7967 0.5880 0.5936 0.5377 Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
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Table 241. Elasticities for the Atlanta market
Parameter Tomato Bell Pepper Cucumber Strawberry
4' 0.9617 1.0460 1.0485 1.1526
Tomato 0.1352 0.2795 0.1396 0.0401
Bell Pepper 0.0842 0.2426 0.0205 0.0302
Cucumber 0.0451 0.0220 0.1754 0.1229 Strawberry 0.0059 0.0148 0.0563 0.1328 ITomato 0.6778 0.3108 0.4520 0.6103
VIBell Pepper 0.0793 0.4204 0.1987 0.2260 V/Cucumber 0.1302 0.2126 0.3665 0.0872 /Strawberry 0.0744 0.1022 0.0313 0.2291 Note: (is scale elasticity, 4 is compensated elasticity, and y is uncompensated elasticity.
Table 242. Elasticities for the Los Angeles market
Parameter Tomato Bell Pepper Cucumber Strawberry
0.9075 1.0302 1.0365 1.2194 Tomato 0.1953 0.1901 0.3418 0.2910
Bell Pepper 0.0604 0.2086 0.0021 0.0389
Cucumber 0.0869 0.0017 0.2500 0.1384 Strawberry 0.0480 0.0202 0.0897 0.1915 V Tomato 0.7178 0.4030 0.2549 0.4110
V Bell Pepper 0.1056 0.3971 0.1917 0.1842 V Cucumber 0.0459 0.1525 0.4018 0.3169 V Strawberry 0.0382 0.0776 0.1881 0.3073
Note: (is scale elasticity, J is compensated elasticity, and V/is uncompensated elasticity.
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Table 243. Elasticities for the Chicago market
Parameter Tomato Bell Pepper Cucumber Strawberry
1.0259 1.0905 0.8920 0.8188 Tomato 0.0502 0.0610 0.0022 0.1026
4ellPepper 0.0285 0.0938 0.0338 0.0212
Cucumber 0.0013 0.0431 0.0726 0.1083
Strawberry 0.0231 0.0102 0.0410 0.1896
yrTomato 0.4990 0.4161 0.3925 0.2556
YlBell Pepper 0.1810 0.3165 0.1483 0.1884 YCucumber 0.2681 0.2404 0.3045 0.1046 YIStrawberry 0.0778 0.1175 0.0468 0.2701
Note: (is scale elasticity, ( is compensated elasticity, and Vg is uncompensated elasticity.
Table 244. Elasticities for the New York market
Parameter Tomato Bell Pepper Cucumber Strawberry
1.0453 1.0040 0.9438 0.9910 4Tomato 0.0560 0.0079 0.0598 0.0696
Bell Pepper 0.0035 0.1447 0.0917 0.0320 4Cucumber 0.0345 0.1184 0.1709 0.0435 Strawberry 0.0180 0.0185 0.0194 0.1451 /rTomato 0.5138 0.4317 0.3535 0.3644
VIBellPepper 0.2014 0.3416 0.0933 0.1622 PVCucumber 0.2300 0.1357 0.4097 0.2072 VStrawberry 0.1002 0.0950 0.0872 0.2571
Note: (is scale elasticity, ( is compensated elasticity, and V/is uncompensated elasticity.
CHAPTER 3
PARTIAL EQUILIBRIUM ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY This chapter concentrates on the potential impact of two major developments on the U.S. fruit and vegetable industry. The first development is the proposed phasing out of using methyl bromide. Methyl bromide is a critical soil fumigant that has been used in the production of several fresh fruits and vegetables grown in the United States. The U.S. Clean Air Act of 1992 requires that methyl bromide be phased out of use by 2005. The problem is that while significant progress has been made towards developing alternatives to methyl bromide, a suitable alternative has not been identified. The second development is the elimination of all tariff and trade restrictions on exports of fruits and vegetables from Mexico as a result of the implementation of the North American Free Trade Agreement (NAFTA). Under NAFTA, all agricultural tariffs on goods traded between the United States and Mexico will be eliminated by 2008. Some of the tariffs were eliminated in 1994, while others were to be phased out over 5, 10, or 15 years. In addition, negotiations of trade agreements within the World Trade Organization (WTO) or as part of the Free Trade Area of the Americas (FTAA) could significantly affect these tariffs. The elimination of tariffs means that U.S. domestic production of fresh fruits and vegetables is likely to face increased competition from imports.
To assess the impacts of these developments on the U.S. fruit and vegetable
industry, it was essential to develop a partial spatial equilibrium model. Following on a model developed by VanSickle et al., I modified and improved that model by simplifying
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regional effects and changing the objective function so that the model can simulate all fruits and vegetables at the same time.
Background
Methyl bromide has been a critical soil fumigant in the agricultural production for many years. Methyl bromide is a broad spectrum pesticide that can be used to control pest insects, nematodes, weeds, pathogens, and rodents. Under normal conditions, methyl bromide is a colorless and odorless gas. About 21,000 tons of methyl bromide are used annually in agriculture in the United States and about 72,000 tons are used globally each year. When used as a soil fumigant, methyl bromide gas is injected into the soil at a depth of 12 to 24 inches before a crop is planted. This procedure effectively sterilizes the soil, and kills a majority of soil organisms. In addition, commodities may be treated with methyl bromide as part of a quarantine requirement of an importing country. Some commodities are treated several times during both storage and shipment.
Methyl bromide was assigned a 0.4 ozonedepletion potential (methyl bromide has contributed about 4% to the current ozone depletion and may contribute 5% to 15% to future ozone depletion if it is not phased out). Methyl bromide is 40 times more efficient at destroying the ozone than chlorine (which should be phased out as well). The degradation of the ozone layer leads to higher levels of ultraviolet radiation reaching the Earth's surface, which could reduce crop yields and could cause health problems (e.g., skin cancer, eye damage, and impaired immune systems).
The impact of methyl bromide on ozone depletion led to the development of the Montreal Protocol in 1987. According to the U.S. Environmental Protection Agency (EPA), the Montreal Protocol was designed to help revise methyl bromide phaseout schedules on the basis of periodic scientific and technological assessments. The U.S.
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Clean Air Act of 1992, as amended in 1998, requires that methyl bromide be phased out of use on the basis of separate schedules prepared for developed and developing countries who are party to the Montreal Protocol (Table 31). The phaseout of methyl bromide use is being implemented by restricting the volume of methyl bromide that can be produced and sold. So far, efforts to phase out methyl bromide have resulted in a 50% reduction in use (the first two 25% reductions have already occurred in the United States). Table 31 shows the schedule for phasing out methyl bromide. Developing countries can still use methyl bromide until 2015 (10 years after the phaseout in the developed countries). There is concern that developed countries could be placed at a disadvantage (compared to developing countries) if suitable alternatives cannot be found. This is highlighted by the fact that in 2005, when the developed countries should have completed the phaseout of methyl bromide, the developing countries would still be permitted to use methyl bromide on 80% of the base level. Unfortunately, there are very few viable alternatives that are technically and are economically feasible and also acceptable from a public health standpoint. Therefore the Montreal Protocol allowed for exemptions to the phaseout (e.g., the critical use exemption). In March of 2004, a meeting of the Parties to the Montreal Protocol was held in Montreal, Canada, during March 2426, 2004 to address problems related to the methyl bromide phaseout such as nominations and granting conditions for Critical Use Exemptions (CUES). For examples, the United States made a CUE request after a thorough and comprehensive review process. The U.S. EPA will work with the USDA to fully support the U.S. nomination.
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Table 31. Schedules of the phaseout of methyl bromide Developed Countries Developing Countries
1991: Base level 199598 average: Base level 1995: Freeze 2002: Freeze 1999: 75% of base 2003: Review of reductions 2001: 50% of base 2005: 80% of base 2003: 30% of base 2015: Phaseout 2005: Phaseout
Source: U.S. Environmental Protection Agency
Four factors need to be considered when selecting and evaluating suitable
alternatives to methyl bromide. The first factor is technical. Methyl bromide is quite versatile, fairly easy to apply, and can be effective against a wide range of pests (unlike most other pesticide, fumigant, or pest control methods). U.S. producers may consider using Integrated Pest Management (IPM) as an alternative to using methyl bromide. IPM is based on pest identification, and monitoring and establishing pest injury levels. However, a successful IPM program requires more information, analysis, planning, and knowhow than does using methyl bromide.
The second factor is economic (the impact of alternatives on the profitability of the enterprise). While some alternatives may involve a high initial investment cost, especially considering the operating costs of new equipment, they might actually be more costeffective in the long run. This is true because the cost for using methyl bromide is expected to rise in the future. A less effective alternative could be as profitable as using methyl bromide if the costs for using the alternative are sufficiently lower. For the economic factor, profitability needs to be examined.
The third factor is health and safety, and the fourth factor is environmental
concerns. Given the heightened awareness of safety and environmental concerns (from both marketing and environmental perspectives), it is advisable to select alternatives that
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are considered environmental friendly and pose no or minimal risks to users. For example, an alternative should not cause ozone depletion and global warming.
Turning our attention to the potential trade impact, it should be noted that
international trade is an important component of the U.S. fruit and vegetable industry. In 1999, imports accounted for 11.6% of total U.S. fruit and vegetable consumption. The United States imposed ad valorem tariffs on imports of fresh vegetables. The U.S. ad valorem tariffs were 3.1% to 4.6% on fresh tomatoes, 3.0% on fresh bell peppers, and
2.1% to 10.6% on fresh cucumbers. Negotiations of trade agreements within the World Trade Organization (WTO) or as part of the Free Trade Area of the Americas (FTAA) could significantly lower these tariffs. As stated earlier, NAFTA has had a considerable impact on the levels of these tariffs. NAFTA, which went into force on January 1, 1994, is an agreement by the United States, Canada, and Mexico to phase out almost all restrictions on international trade and investment among the three countries. The United States and Canada were already well on the way to eliminating the barriers to trade and investment between them when NAFTA went into effect. The main new feature of NAFTA was the removal of most of the barriers between Mexico and the United States.
Fresh vegetable imports have been under scrutiny since before the implementation of NAFTA in 1994. During the first year of NAFTA, the import share of consumption for fresh fruits and vegetables remained at the preNAFTA level of about 10%. However, following the devaluation of the Mexican peso in December of 1994, U.S. imports of Mexican vegetables rose sharply. Mexican growers increased shipments to the United States because of poor domestic demand and more attractive prices in the United States. As a result of measured exports of fresh vegetables from Mexico, the
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import share of U.S. domestic consumption of vegetables grew steadily from 10% in 1994 to 15% in 1998. In 1999 and into early 2000, low U.S. domestic prices slowed import volume and pushed the import market share down to 14%.
Several empirical studies in the literature on the analysis of internationaltrade issues have focused on partial equilibrium analysis. For example, spatial price equilibrium analysis attempts to predict changes in future trade flows, prices, consumption, and production for a commodity under governmental policies. The results allow the estimation of welfare benefits and costs by using the concept of economic surplus to individual countries from specific trade policies.
Under the partial equilibrium analysis, the assumption is that producers maximize their profits, consumers maximize their utilities, and marketing activities are competitive. Distortions come about only through governmental policies. There is no world price in this model because the price differs among regions by transportation costs, tariffs, and market imperfections. The amounts of consumption, production, exports, imports, and equilibrium prices in each region are determined simultaneously.
Research Problem
With an increase in the number of U.S. sponsored trade agreements and general trends toward opening the market, U.S. producers of fruits and vegetables may face increased competition from foreign sources. Changes in competitiveness could affect trade flows, which could change the structure and geographic distribution of the agricultural industries. Internationaltrade agreements and competition among fruit and vegetable industries have increased. Also, the phaseout of methyl bromide places the United States at a disadvantage in trade with Mexico. Our study analyzes the impacts of internationaltrade agreements and the ban on methyl bromide by estimating the change
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in location of agricultural production and by determining which countries will benefit and which countries will lose.
Hypotheses
Our main hypotheses were as follows:
If a ban on methyl bromide is imposed without viable economic alternatives, then
the production of these crops will decrease. Therefore the decrease in production
causes the prices of fruits and vegetables in the United States to increase.
The impact of NAFTA will decrease fruit and vegetable prices in the United States.
Afterwards, the decrease in prices will cause an increase in the quantity demanded
and a decrease in the domesticquantity supplied.
Objectives
The first objective of our study is to estimate the impact of the phaseout of methyl bromide on consumers, producers, prices, productions, and revenues. The second objective of our study is to investigate the impact of NAFTA on the fruit and vegetable industry. By investigating the impacts of the internationaltrade issues, the model is expected to replicate the evolution of the fruit and vegetable industry.
Theoretical Framework
Following MasColell (2000), in a competitive economy, consumers and producers act as price takers by regarding market prices as unaffected by their own actions. Building on a spatial equilibrium model developed by VanSickle et al., we conducted an investigation of the fruit and vegetable industry. This spatial equilibrium model satisfies a profitmaximizing condition, a utilitymaximizing condition, and a marketclearing condition. These three conditions must be met for a competitive economy to be considered in equilibrium. The profitmaximizing condition states that each firm will choose a production plan that maximizes its profits, given the equilibrium prices of its outputs and inputs. The utilitymaximizing condition requires that each consumer choose
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a consumption bundle that maximizes utility, given the budget constraint imposed by the equilibrium prices and wealth. The marketclearing condition requires that at the equilibrium prices, the aggregate supply of each commodity equals the aggregate demand for that commodity. If excess supply or demand exists for a good at the going prices, the economy would not be at a point of equilibrium. At the equilibrium price that equates demand and supply, consumers do not wish to raise prices, and firms do not wish to lower them.
The partial equilibrium analysis assumes that the market for one good (or several goods), represents a small part of the overall economy. It is also assumed that the wealth effects in a small market will also be small, as the expenditure on the good is a small portion of a consumer's total expenditure. Moreover, given the small size of the market, any changes in this market are expected to have no or negative impact on prices in other markets. In terms of the partial equilibrium interpretation, we consider good g as the good whose market is being investigated, and denote the composite of all other goods as the numeraire. We normalize the price of the numeraire to equal one, and letp denote the price of good g. Each firmj = 1,..., J is able to produce good g from good k. The amount of the numeraire required by firmj to produce qj units of good g is given by the cost function cj(qj). Given equilibrium price p for good g, the profitmaximizing condition implies that firmj's equilibrium output level q must satisfy the profitmaximizing problem,
Max pqj c(qj). (31)
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Likewise the utilitymaximizing condition implies that given the equilibrium price p for good g, consumer i's equilibrium consumption level x, must satisfy the utilitymaximizing problem, subject to the budget constraint,
Max u,(x,), (32) subject to
Ii pxi = m, (33) where m is the budget share.
Because of the market clearing condition assumed, the equilibrium price of good g will be price p at which the aggregate demand equals the aggregate supply,
x = q, (34) where x is an aggregate demand (x = 1Z xi) and q is an aggregate supply (q = Zj qj).
Because consumers and producers are price takers, the inverses of the aggregate
demand and supply functions are of interest. The inverse demand function, P(x) = X'(x), gives the price that results in the aggregate demand of x. That is, when each consumer optimally chooses a consumer demand for good g at this price, total demand exactly equals x. At these individual demand levels, each consumer's marginal benefit from an additional unit of good g is exactly equal to P(x). Moreover, given that the aggregate quantity x is efficiently distributed among the consumers, the value of the inverse demand function, P(x), can also be viewed as the marginal social benefit of good g.
Likewise, inverse supply function, p = Q7'(q), gives the price that results in the aggregate supply of q. That is, when each firm chooses its optimal output level facing this price, the aggregate supply is exactly q. The inverse of the industry supply function can be viewed as the industry marginal cost function, which can be denoted by
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C'(q) = Q'(q). (35) We get the inverse supply function (or the industry marginal cost function) from the profitmaximizing condition and the inverse demand function from the utilitymaximizing condition. Then we can find the equilibrium price at which p(x) = p(q), X'(x) = Q'(q), or P(x) = C'(x) as x = q (Equation 34). Figure 31 represents the partial equilibrium analysis using the Marshallian graphical technique with the equilibrium price at the point of intersection of the aggregate demand and aggregate supply curves.
p 1 C'(*), q(*)
A
p(x) p(q).
P(*), x(*)
x(p) = q(p) x, q
Figure 31. Aggregate demand and aggregate supply Fundamental Theory of the Partial Equilibrium Model
In the partial equilibrium model, it is relatively easy to measure the change in the equilibrium outcome of a competitive market or the change in the level of social welfare, resulting from a change in underlying market conditions such as an improvement in technology, a new government internationaltrade policy, or the elimination of some existing market imperfection. The partial equilibrium model turns out the optimal consumption and production levels for good g that maximize the Marshallian aggregate surplus. Moreover, if price p and allocation (xl, ..., xi, ql, ..., qi) constitute a competitive
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equilibrium, then this allocation is Pareto optimal (which is the first fundamental theorem of welfare economics). A differential change (dxl,..., dx,, dqi,..., dqj) in the quantities of good g (consumed and produced) satisfies dx = Z; dx, = Zj dqj (since x = q, Equation 34). The change in aggregate Marshallian surplus is then
dS = P(x) E; dx C'(q) j dqj,
dS= [P(x) C'(x)] dx. (36)
It is sometimes of interest to distinguish between the two components of aggregate Marshallian surplus that accrue directly to consumers and producers. That is, if the set of active consumers of good g is distinct from the set of producers, then this distinction demonstrates something about the distributional effects of the change in the level of social welfare. There is a change in aggregate consumer surplus when consumers face effective price and aggregate consumption x( ), which is
dCS( ) = [P(x) ] dx. (37) There is also a change in aggregate producer surplus when firms face effective price, J, and aggregate production q(i ), which is
dJ( h) = [ h C'(q)] dq = [ h C'(x)] dx. (38) We can see that the change in aggregate Marshallian surplus is the summation of the change in aggregate consumer surplus and the change in aggregate producer surplus, which can be written as
dS = dCS( ) + dI( ). (39)
We can also integrate Equation 39 to express the total value of the aggregate
Marshallian surplus, the aggregate consumer surplus, and the aggregate producer surplus. By doing this, we get
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So+ [P(s)C s)] ds = f [P(s) ]ds} + {o + [ C'(s)] ds},
O 0 0
So+ [P(s) C'(s)] ds = x(s) ds + o + [ C'(s)] ds, (310)
0 0
where So is a constant of integration equal to the value of the aggregate surplus. When there is no consumption or production of good g, Ho is a constant of integration equal to the value of the profits when qj = 0 for allj and So = H0 (which is equal to 0 if c(0) = 0 for allj). In Figure 31, the aggregate consumer surplus is depicted by area A and the aggregate producer surplus is depicted by Area B. The maximized aggregate Marshallian surplus is depicted by area A plus area B, which is exactly equal to the area lying vertically between the aggregate demand and supply curves for good g, up to equilibrium quantity x.
Impact of the Phaseout of Methyl Bromide
Since currently available alternatives of methyl bromide are more expensive, it can be postulated that in the absence of methyl bromide, cost of production is likely to increase. This can be represented in the model by an upwards shift in the aggregate supply curve, C'm(Z). Figure 32 shows that the new supply curve is Zm,(P) = C'(Z) + C'(Z), where C',,(Z) is the addition marginal cost resulting from the phaseout of the methyl bromide. Figure 32 shows that the upward shift of the supply curve results in an increase in the equilibrium price (from P* to P**) and a decrease in the aggregate shipment quantity (from X* to X**).
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P Zm(P)
Z(P)
P*
x" x" x
Figure 32. Partial equilibrium under effect of the phaseout of methyl bromide Impact of NAFTA
The most important effect of trading with another nation is the economic gains that accrue to both parties as a result of trade. Without trade, each country has to make everything it needs, including those products it is not efficient at producing. On the other hand, when trade is permitted, each country can concentrate its efforts on producing exports in exchange for imports. Gains from trade arise from being able to purchase desired commodities or services from abroad cheaper than it would cost to produce them at home.
As pointed out by SchiavoCampo (1978), countries trade among themselves because of differences in factor endowments. An analysis of the impact of different national endowments of production factors have upon international trade is summarized in the HeckscherOhlin Theorem. This theorem states that a country has a comparative advantage in producing commodities with a relatively abundant factor and importing commodities with a relatively scarce factor. However, there are many barriers to
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international trade, including natural obstacles like the geographic distance between countries and the resulting costs of transport.
The bestknown, and most frequently used, instrument of commercial policy (which is a manmade obstacle to international trade) is the tariff. Tariffs may be expressed in absolute dollarsandcents terms (a specific tariff) or in relative terms as a percentage tax (ad valorem tariff). A tariff is an instrument that is used to economically separate the national market from the world economy by increasing the import price of a commodity over its world price (i.e., a tariff causes an increase in the domestic price, which is the main consequence of tariffs on production, consumption, income distribution, and trade).
The several effects of a tariff can be shown by means of supplyanddemand diagrams that are expanded to include import supply in addition to domestic supply. Figure 33 shows the market situation for a homogeneous product in the importing country. In the complete absence of foreign trade, the market would find its equilibrium at Ed, which is the intersection of domestic demand line Dd and domestic supply line Sd. The product would sell for price Pd. Consumers' surplus under the absence of trade (which is the differences between the market price and the maximum they would be willing to pay) is area PdEdL. Producers' surplus under the absence of trade (which is the difference between the market price and the minimum the producers would be willing to accept) is area MEdPw.
When trade is allowed, the imports increase product supply (Sd + S) and decrease the product price to consumers. Consequently, the market would find its new equilibrium at I (which is the intersection of domestic demand line Dd and domestic supply plus
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foreign supply line Sd + Sf). The product would sell for price P,. The imports are AB (which is the difference between total desired consumption and domestic production). Domestic production is OA, and total quantity demanded is OB. The decrease in price causes an increase in the consumption and a decrease in domestic production. Consumers' welfare gain is area PwlEdPd, and domestic producers' welfare loss is area PwFEdPd. The net gain from trade is area FIEd.
When the domestic country imposes a tariff, the foreign supply is decreased, but
the price of the product is increased. As a result, the market finds its new equilibrium at J (which is the intersection of domestic demand line Dd and domestic supply plus foreign supply with tariff line Sd + Sf + T). The product would sell for price Pw+r. The increase in price causes a decrease in the consumption and an increase in the domestic production. Consumption falls to OD, and domestic production rises to OC. Imports are cut on both accounts to CD. Consumers' welfare loss is area PwlJPw+T, domestic producers' welfare gain is area PWFKPw+T, and tariff revenue effect is area GHJK.
The tariff consumption effect (BD) is related to the price elasticity of demand. A highly elastic demand indicates that a change in price has a considerable effect on the amount that people wish to buy. On the other hand, a relatively inelastic demand means that a price change will lead to only a small change in the quantity demanded. If price elasticity is zero, the quantity will not change at all, regardless of the magnitude of the variation in the price of the product.
The effect from NAFTA (which is an agreement between the United States,
Canada, and Mexico to phaseout almost all restrictions on international trade, including tariffs) will move the equilibrium point back to I and the supply line to the right (where
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the supply of the product is domestic supply plus foreign supply line Sd + Sf). The product would sell for price Pw.
Price
Sd Sd+ Sf+ T Sd+ S
Ed
P d ................................................. ..................
Dd
O A C D B Quantity
Figure 33. Partial equilibrium under the effect of tariff Methodology
A partial equilibrium model can be used to evaluate the effects of a change in the industry on the production and marketing of various crops in various regions. In the VanSickle et al. model, these crops were modeled in a monthly model, considering production from each of the major producing regions in Florida and from other regions in the United States and Mexico. The model was developed to characterize crop production from these regions for the winter months in which Florida ships these commodities.
The VanSickle et al. model allocates crop production across regions based on delivered cost to regional markets, productivity, and regional demand structure in the United States. Inverse demand equations were used in the model based on work by Scott (1991) for squash, eggplant, and watermelons and from Chapter 2 for tomatoes, bell
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peppers, cucumbers, and strawberries. Preharvest and postharvest cost production costs were estimated for each production system and area by Smith and Taylor (2002). The cost budgets were constructed using a computerized budget generator program, AGSYS. Technical coefficients used in constructing the budgets were obtained by consultation with individual growers, county agents, and UF/IFAS researchers. Florida uses several doublecropping systems in which a primary crop is followed by a different (secondary) crop on the same unit of land. Transportation costs were included for delivering these products to each of the regional markets based on mileages determined by the Automap software and an estimation for a fullyloaded refrigerated truck carrying 40,000 pounds at $1.3072 per mile (VanSickle, et al., 1994).
The constrained optimization model was solved using GAMS software. After solving the VanSickle et al. model for a base solution for the 2000/2001 season, the budgets and yields were changed to reflect the costs of growing the crops using an alternative to methyl bromide. The results were compared to determine the impact that the phaseout of methyl bromide may have on the production and marketing of these crops.
In our study, we investigated the effect of the phaseout of methyl bromide on
tomatoes, bell peppers, and eggplant in Florida and on strawberries grown in both Florida and California. Estimates of the impacts on production costs and yields from using alternatives to methyl bromide were determined from discussions with scientists attending USDA meetings (Carpenter and Lynch, 1998). For strawberries, California growers were assumed to have switched to Chloropicrin (with additional hand weeding) as a replacement to methyl bromide. Strawberry producers in West Central Florida were
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assumed to have switched to a Telone Cl 7/Devrinol herbicide combination. For tomatoes, Florida growers were assumed to have switched to a Telone C 17/Chloropicirin/ Tillam herbicide combination. For eggplant and bell peppers, Florida growers were assumed to have switched to a Telone Cl 7/Devrinol herbicide combination. Using Telone requires additional protective equipment that must be worn by applicators and field workers. Table 32 shows the impact of these alternatives to methyl bromide on preharvest cost and yield in each region in Florida and California. Other regions included in the model were assumed to be producing crops without using methyl bromide, and therefore would have no effect on costs and yields from the phaseout.
Table 32. Effect of the methyl bromide in Florida and California
State Region Preharvest Cost Percentage of Yield Impact Reduction
($/acre) (%)
Florida
Dade County (291) 10 Palm Beach County (115) 5 Southwest Florida (74) 10 West Central (139) 5 California
Northern California 653 20 Southern California 653 20 Source: USDA
Next we investigated international trade by changing the production costs for
Mexico to reflect the effect of NAFTA. Our baseline assumed a fixed tariff of $0.1 per unit of imported commodity, which was added to the postharvest cost of production. We found that the impact of NAFTA would be the elimination of all such tariffs.
The VanSickle et al. model was solved using GAMS programming software. The analysis of the impacts from NAFTA and the ban on methyl bromide were conducted in
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two parts. Our study updated the VanSickle et al. model to the 2000/2001 production season by using updated data and quantity elasticities estimated from the inverse demand analysis. This solution provided the baseline for comparison to other solutions where the parameters of the model were adjusted to reflect the impacts of NAFTA and the ban on methyl bromide.
For the first part of the analysis, the model was solved with parameters that assumed continued use of the tariff and methyl bromide. For the second part of the analysis, three scenarios beyond the baseline were solved with the model. The first scenario assumed the next best alternative, given projections on expected cost and yield impacts. The second scenario gave projections on the postharvest production cost that was reduced for Mexico from the elimination of tariffs. The third scenario combined the impacts of NAFTA and the ban on methyl bromide. The adjustments that were made in the parameters reflect changes in production costs and yield by switching to alternatives to methyl bromide and changes in postproduction costs for Mexico by switching to nontariff trade.
The VanSickle et al. model was developed by modifying the North American
winter vegetable market model developed by Spreen et al. (1995). For the demand side of the model, the commodities were assumed to be shipped to one of four demand regions of the United States, including the northeast, southeast, midwest, and west. These demand regions were represented by the New York City, Atlanta, Chicago, and Los Angeles wholesale markets, respectively. The commodities in the model were tomatoes, bell peppers, cucumbers, squash, eggplant, watermelon, and strawberries. There is an inverse demand equation for each commodity in each demand region with an assumption
86
that the slope of the demand function is constant over quantities. The model calculates total production costs by summing preharvest and postharvest costs. The preharvest cost is the product of the number of acres planted and the peracre preharvest costs. The postharvest cost is the product of the number of acres planted, yield, and perunit harvest and postharvest costs. Alternatives are expected to have impacts on both yield and perunit cost. Moreover, the model can calculate the transportation cost that is the product of the quantity of commodity shipped and the perunit transportation cost.
The VanSickle et al. model can be characterized as a spatial equilibrium problem. By using the following indices the model can be mathematically stated as region: i = 1,...,I: index the 12 production points, crops: k = 1,...,K: index the seven crops being considered, market:j = 1,...,J: index the four market centers, production systems: ks = 1,...,KS: index the 16 production systems, time: m =1,...,M: index the 12 months when the crop may be sold.
The demand for these crops is divided into four different markets. The inverse demand curve is represented for the markets as
Pj = aik bjk. Qj, (311) where Pjk, is the wholesale price per ton for crop k in marketj in month m, Qjk, is the quantity of tons of crop k that is sold in marketj in month m, a,,, is the demand curve's intercept,
bjk,, is the slope of the demand function. This formulation assumes that the slopes of the demand functions are constant over all quantities. The model assumes that each region's production is a perfect substitute for
87
that of any other region. Moreover, the model assumes that the price of each commodity is a function of its own quantity alone and that the price is not affected by other crop prices and quantities that may be sold in that market in that month.
To compute the inverse demand function, demand flexibilities were based on wholesale price and arrival data for the various crops. The flexibilities are the uncompensated own quantity elasticities calculated from the Rotterdam Inverse Demand System (RIDS). The RIDS model satisfies the utilitymaximizing condition. Using this information, the parameters for the slope and intercept of the demand equation can be calculated.
Let x,,, = the demand flexibilities for crop k in marketj in month m, where
V/km = (aPjkm / 3Qjkm)(Qjkm / Pjkm). (312) The slope of the inverse demand equation is
bk,,, = (aPjkm / aQjkm),
bj,, = Okm (Pikm / Qj). (313) After bjk, had been calculated, ajkm can be estimated from
aikn = Pik. + byk jk. (314)
For the supply side, the production points are Florida, California, Mexico, Texas,
South Carolina, Virginia, Maryland, Alabama, and Tennessee. Florida was separated into four producing areas: Dade County, Palm Beach County, Southwest Florida, and West Central Florida. Mexico was separated into two producing areas: the states of Sinaloa and Baja California. California was separated into two producing areas: Southern California and Northern California. Also, there are 16 cropping systems, which include both single and double cropping systems. The single cropping systems include tomatoes, fall tomatoes, spring tomatoes, bell peppers, fall peppers, spring peppers, cucumbers,

Full Text 
57
Table 225. Estimation of the RIDS model for the Chicago market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4441
0.2316
0.2487
0.0758
(0.0248)
(0.0203)
(0.0209)
(0.0130)
^Tomato
0.0246
(0.0148)
^Bell Pepper
0.0164
0.0220
(0.0100)
(0.0113)
^Cucumber
0.0019
0.0109
0.0196
(0.0105)
(0.0088)
(0.0120)
^Strawberry
0.0101
0.0054
0.0107
0.0154
(0.0066)
(0.0057)
(0.0059)
(0.0057)
Standard Error (a)
0.0674
0.0553
0.0568
0.0348
R2
0.6201
0.3872
0.4250
0.1583
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 226. Estimation of the AIIDS model for the Chicago market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0221
0.0224
0.0223
0.0219
(0.0233)
(0.0196)
(0.0203)
(0.0140)
Y\ ornato
0.2188
(0.0141)
TheII Pepper
0.0762
0.1421
(0.0096)
(0.0110)
Tfcucutnber
0.1089
0.0418
0.1685
(0.0100)
(0.0086)
(0.0117)
/Strawberry
0.0337
0.0241
0.0178
0.0756
(0.0068)
(0.0059)
(0.0061)
(0.0062)
Standard Error (a)
0.0632
0.0533
0.0552
0.0377
R2
0.5404
0.4506
0.5111
0.4199
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
65
Table 241. Elasticities for the Atlanta market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
0.9617
1.0460
1.0485
1.1526
%Tornato
0.1352
0.2795
0.1396
0.0401
<3Bell Pepper
0.0842
0.2426
0.0205
0.0302
Â£Cucumber
0.0451
0.0220
0.1754
0.1229
Strawberry
0.0059
0.0148
0.0563
0.1328
ornato
0.6778
0.3108
0.4520
0.6103
y^Bell Pepper
0.0793
0.4204
0.1987
0.2260
y/Cucumbex
0.1302
0.2126
0.3665
0.0872
^Strawberry
0.0744
0.1022
0.0313
0.2291
Note: <^is scale elasticity, Â£ is compensated elasticity, and y/ is uncompensated
elasticity.
Table 242. Elasticities for the Los Angeles market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
c
0.9075
1.0302
1.0365
1.2194
Â£Tomato
0.1953
0.1901
0.3418
0.2910
Bell Pepper
0.0604
0.2086
0.0021
0.0389
^Cucumber
0.0869
0.0017
0.2500
0.1384
4Strawberry
0.0480
0.0202
0.0897
0.1915
I//T,ornato
0.7178
0.4030
0.2549
0.4110
y^Bell Pepper
0.1056
0.3971
0.1917
0.1842
y^Cucumbex
0.0459
0.1525
0.4018
0.3169
tyStraw berry
0.0382
0.0776
0.1881
0.3073
Note: Â£is scale elasticity, ^is compensated elasticity, and y/'\s uncompensated
elasticity.
82
the supply of the product is domestic supply plus foreign supply line + Sj). The
product would sell for price Pw.
Methodology
A partial equilibrium model can be used to evaluate the effects of a change in the
industry on the production and marketing of various crops in various regions. In the
VanSickle et al. model, these crops were modeled in a monthly model, considering
production from each of the major producing regions in Florida and from other regions in
the United States and Mexico. The model was developed to characterize crop production
from these regions for the winter months in which Florida ships these commodities.
The VanSickle et al. model allocates crop production across regions based on
delivered cost to regional markets, productivity, and regional demand structure in the
United States. Inverse demand equations were used in the model based on work by Scott
(1991) for squash, eggplant, and watermelons and from Chapter 2 for tomatoes, bell
66
Table 243. Elasticities for the Chicago market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
z
1.0259
1.0905
0.8920
0.8188
Â£Tomato
0.0502
0.0610
0.0022
0.1026
Â£>Bell Pepper
0.0285
0.0938
0.0338
0.0212
Â£Cucumber
0.0013
0.0431
0.0726
0.1083
4Strawberry
0.0231
0.0102
0.0410
0.1896
^Tomato
0.4990
0.4161
0.3925
0.2556
y^Bell Pepper
0.1810
0.3165
0.1483
0.1884
tyCucumber
0.2681
0.2404
0.3045
0.1046
Strawberry
0.0778
0.1175
0.0468
0.2701
Note: C, is scale elasticity, is compensated elasticity, and (// is uncompensated
elasticity.
Table 244. Elasticities for the New York market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
1.0453
1.0040
0.9438
0.9910
%Tomato
0.0560
0.0079
0.0598
0.0696
^Bell Pepper
0.0035
0.1447
0.0917
0.0320
Â£Cucumber
0.0345
0.1184
0.1709
0.0435
Â£Strawberry
0.0180
0.0185
0.0194
0.1451
y^Tornato
0.5138
0.4317
0.3535
0.3644
y^Bell Pepper
0.2014
0.3416
0.0933
0.1622
y^Cucumbex
0.2300
0.1357
0.4097
0.2072
tyStrawberrv
0.1002
0.0950
0.0872
0.2571
Note: C, is scale elasticity, Â£ is compensated elasticity, and iff is uncompensated
elasticity.
31
singleequation ordinary least squares (OLS is the same as GLS). Also, the asymptotic
covariance matrix of B is given by the large matrix in brackets above, which would be
estimated by
Est. Asy. Var[5]= (2114)
where
h=ai={\IT)e'ieJ, (2115)
or
Est. Asy. Cov[ B, BJ ] = (JfX)'1, (2116)
where i,j = 1,... n.
Bartens Method of Estimation
Following Barten (1969), the Maximum Likelihood (ML) method has been used to
estimate the coefficients of the demand systems. Maximumlikelihood estimators are
consistent, asymptotically efficient, and asymptotically normally distributed. The
disadvantages in using the ML procedure are the possible smallsample bias of the
estimator for the variances and covariances, the need to specify a distribution for the
random variables in the model, and the procedures computational difficulties. The
likelihood function is to be maximized with respect to the coefficient of the system and
the elements of the covariance matrix In. Derivation of the ML estimators will be done
in terms of maximizing the concentrated version of the logarithmiclikelihood function,
In L = M2(TlnnT(ji\)(\+ln2n)Tln\A\), (2117)
where
A = (1 / T) E, v,v/ (2118)
and
53
Table 217. Estimation of the RIDS model for the Atlanta market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5421
0.1706
0.1871
0.1014
(0.0276)
(0.0199)
(0.0165)
(0.0116)
^Tomato
0.0856
(0.0179)
^Bell Pepper
0.0490
0.0428
(0.0112)
(0.0112)
^Cucumber
0.0291
0.0009
0.0372
(0.0102)
(0.0077)
(0.0099)
^Strawberry
0.0075
0.0053
0.0091
0.0112
(0.0069)
(0.0054)
(0.0051)
(0.0052)
Standard Error (a)
0.0574
0.0422
0.0346
0.0244
R2
0.7264
0.2814
0.3916
0.2906
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 218. Estimation of the AIIDS model for the Atlanta market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0157
0.0048
0.0004
0.0118
(0.0277)
(0.0200)
(0.0167)
(0.0124)
ornato
0.1601
(0.0180)
Thell Pepper
0.0432
0.0912
(0.0112)
(0.0113)
^Cucumber
0.0807
0.0314
0.1137
(0.0103)
(0.0077)
(0.0100)
^Strawberry
0.0362
0.0166
0.0016
0.0545
(0.0073)
(0.0057)
(0.0054)
(0.0056)
Standard Error (a)
0.0577
0.0424
0.0349
0.0260
R2
0.2907
0.2653
0.3773
0.3170
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
74
a consumption bundle that maximizes utility, given the budget constraint imposed by the
equilibrium prices and wealth. The marketclearing condition requires that at the
equilibrium prices, the aggregate supply of each commodity equals the aggregate demand
for that commodity. If excess supply or demand exists for a good at the going prices, the
economy would not be at a point of equilibrium. At the equilibrium price that equates
demand and supply, consumers do not wish to raise prices, and firms do not wish to
lower them.
The partial equilibrium analysis assumes that the market for one good (or several
goods), represents a small part of the overall economy. It is also assumed that the wealth
effects in a small market will also be small, as the expenditure on the good is a small
portion of a consumers total expenditure. Moreover, given the small size of the market,
any changes in this market are expected to have no or negative impact on prices in other
markets. In terms of the partial equilibrium interpretation, we consider good g as the
good whose market is being investigated, and denote the composite of all other goods as
the numeraire. We normalize the price of the numeraire to equal one, and let p denote the
price of good g. Each firm j = 1,..Jis able to produce good g from good k. The
amount of the numeraire required by firm j to produce qj units of good g is given by the
cost function c/jqj). Given equilibrium price p for good g, the profitmaximizing
condition implies that firm f s equilibrium output level qj must satisfy the profit
maximizing problem,
Max pqj c(qj).
(31)
96
Marshallian surplus is maximized. From Figure 34, demand curve X(P) can be defined
by using the inverse demand function,
X(P) = P( i Qjkm) (337)
7 = 1
The supply curve Z(P) for each production region can be defined by using the
marginal cost function,
Z{P) = C\ { Zikm). (338)
i = \
From the point of intersection of the aggregate demand and aggregate supply
curves, we can find the equilibrium price, P*, and the level of the aggregate shipment
I J
quantity, X, where X= Â£ Â£ Xijkm.
i = 1 7 = 1
7 = 1 i = 1
Figure 34. Partial equilibrium of aggregate demand and aggregate supply
37
Since Rd3 = 0 meets the symmetry condition. By premultiplying Equation 2148 by R,
we get
Rc?R
H = lR(A GW'Ricf cP)
M = [R(A 0 ORf'RtP. (2149)
From Equation 2148 and Equation 2149, we get
cf = S (/I G^T1^ = ^ (2150)
where
H = I(AG)R\R(AG)Rr\AR. (2151)
The covariance matrix of
E[(c? d){ct d)']=H(a G)H\ (2152)
Empirical Results
The results of the estimation with the homogeneity and symmetry conditions (using
the mean of the budget share to multiply the logarithmic version of the inverse demand
system by following Bartens estimation method for each functional form in each market)
are presented in Tables 21 through 216. Next, the results of the estimation of the
homogeneity and symmetry conditions (using the moving average of the budget share to
multiply the logarithmic version of inverse demand system by following Bartens
estimation for each functional form in each market) are presented in Tables 217 through
232. The results from the unconstraint estimation for each market are presented in
Tables 233 through 236. The results from the estimation of the RIDS model with the
homogeneity condition (by following Bartens estimation method in each market) are
presented in Tables 237 through 240. The elasticities calculated from the coefficients
of the inverse demand system for each market are presented in Tables 241 through 244.
113
Table 39. Baseline demand and percentage changes in demand from the methyl bromide
ban effect and the NAFTA effect, by crop and market
Crop
Market
Baseline
MB Ban
NAFTA
MB Ban
and NAFTA
(Units)
(
%
)
Tomatoes
Atlanta
41,080
(1.05)
1.26
0.39
Los Angeles
33,871
(0.82)
0.86
0.18
Chicago
38,744
(1.44)
0.96
(0.24)
New York
66,763
(1.33)
0.51
(0.75)
Bell Peppers
Atlanta
9,955
(3.37)
0.06
(2.60)
Los Angeles
5,529
(1.15)
1.56
0.84
Chicago
11,399
(2.19)
0.79
(1.32)
New York
9,305
(5.91)
0.21
(5.26)
Cucumbers
Atlanta
2,077
1.07
2.81
(0.01)
Los Angeles
1,988
1.60
2.00
2.00
Chicago
2,943
0.72
1.97
(0.07)
New York
2,580
0.66
1.84
(0.11)
Squash
Atlanta
1,808
0.58
1.10
0.81
Los Angeles
1,690
0.42
2.19
1.98
Chicago
1,686
0.61
1.15
0.84
New York
728
1.92
3.58
2.60
Eggplant
Atlanta
1,673
(11.55)
0.17
(11.15)
Los Angeles
2,991
(0.13)
2.34
1.90
Chicago
3,983
(2.68)
0.16
(2.12)
New York
2,162
(7.89)
0.41
(7.74)
Watermelon
Atlanta
468
(59.90)
16.55
(62.93)
Los Angeles
1,348
(6.28)
1.73
(6.60)
Chicago
1,484
(11.64)
3.22
(12.23)
New York
3,174
(4.55)
1.26
(4.78)
Strawberries
Atlanta
11,088
(66.57)
0.00
(66.57)
Los Angeles
16,215
(43.99)
0.00
(43.99)
Chicago
17,554
(49.56)
0.00
(49.56)
New York
20,649
(47.09)
0.00
(47.09)
Note: MB is abbreviated for Methyl Bromide.
80
international trade, including natural obstacles like the geographic distance between
countries and the resulting costs of transport.
The bestknown, and most frequently used, instrument of commercial policy
(which is a manmade obstacle to international trade) is the tariff. Tariffs may be
expressed in absolute dollarsandcents terms (a specific tariff) or in relative terms as a
percentage tax (ad valorem tariff). A tariff is an instrument that is used to economically
separate the national market from the world economy by increasing the import price of a
commodity over its world price (i.e., a tariff causes an increase in the domestic price,
which is the main consequence of tariffs on production, consumption, income
distribution, and trade).
The several effects of a tariff can be shown by means of supplyanddemand
diagrams that are expanded to include import supply in addition to domestic supply.
Figure 33 shows the market situation for a homogeneous product in the importing
country. In the complete absence of foreign trade, the market would find its equilibrium
at Ed, which is the intersection of domestic demand line Dj and domestic supply line S.
The product would sell for price Pd. Consumers surplus under the absence of trade
(which is the differences between the market price and the maximum they would be
willing to pay) is area PdEdL. Producers surplus under the absence of trade (which is the
difference between the market price and the minimum the producers would be willing to
accept) is area MEdPw.
When trade is allowed, the imports increase product supply (S + S/) and decrease
the product price to consumers. Consequently, the market would find its new equilibrium
at I (which is the intersection of domestic demand line Dd and domestic supply plus
18
d(ln w,) d(ln Q) = Â£ d(ln Q) + I, (4 + Sy wj) d(ln qj. (253)
In order to satisfy the symmetry condition, we premultiply both sides of Equation 253 by
wÂ¡, so the RAIIDS model is
wÂ¡[d(ln Wi) d(ln 0] = w,Q d{ln Q) + S, (w,4 + w,Sy W/Wy) %),
dw, wÂ¡ d(ln Q) = h, d(ln Q) + I, /y d(ln qj). (254)
By using our new formulation, the properties of parameter h which can be defined by
Equation 227, are equivalent to the ones in the RIDS model (Equation 226), and the
properties of parameter /y, which can be defined by Equation 237, are equivalent to the
ones in the AIIDS model (Equation 245). As a result, the RAIIDS model has the RIDS
scale effects and the AIIDS quantity effects. On the other hand, the LaTheil model has
the AIIDS scale effects and the RIDS quantity effects.
Scale and Quantity Comparative Statics
We can examine relations for inverse demands by following Anderson (1980) to
express price as a function of quantities and total expenditure,
Pi =A
and normalized prices, nÂ¡ = p, / m, as a function of quantities,
*Â¡=/fo !)=/(?) (256)
As it is true about quantity elasticities of prices being equivalent to those about quantity
elasticities of normalized prices, we confine our discussion to normalized prices in what
follows. Quantity elasticities are the natural analogs for inverse demands of price
elasticities, py, in direct demands. They tell how much price i must change to induce the
consumer to absorb marginally more of good j. The quantity elasticity of good / with
respect to good j is defined as
Vij=WXq)ldqj\[qjlfXq)l
(257)
93
KS KS
d L / 5 Wiks Sjian Â£ diiiskm J] Cl iks 0?
ks = 1 ks = 1
^>0; (dL/dWiks)Wiks = 0.
Let > 0 to get a trial solution, so that d LI d Wlks = 0. Therefore,
KS KS
Sikm~ X Cl Â¡ks/ X djkskn,.
ks = 1 ks = 1
(324)
(325)
The Lagrange multiplier for the acreage equation, sikm, is the marginal cost of preharvest
production.
From the firstorder condition with Z,km, the KuhnTucker condition is
d L / d Zikm = gikm C2* ikm ~ sikm < 0; Zikm >0;(dL/ d Zikm)Zikm = 0, (326)
KS
where C2*ikm = d( Â£ C2iksk Zikm) / d Zikm, for m = 1 12.
ks = 1
Let Zikm > 0, so that d L / d Z,km = 0. From Equation 325, we get
gikm ~ C2 Â¡km + SÂ¡km
KS KS
gikm ~ C2 Â¡km + ( Â£ C\,ks / Â£ dikskm) (327)
As = 1 As = 1
The Lagrange multiplier for the supply equation, g(*OT, is the total marginal cost of
production.
From the firstorder condition with gikm, the KuhnTucker condition is
J
d L / d gikm Zjkm ~ X Xjjkm 0; gikm > 0\ {d L / d gikm)gikm = 0, (328)
7 = 1
Let gikm > 0, so that d L / d gikm = 0. Therefore,
Zikm jr Zijkm
7 = 1
(329)
30
72 =
a\2
 oi
<72\
22
^2n
?n\
2
^"nn
so, from Equation 2106, we get
V=Q1
and
T1 = QA 0 7.
We find that the GLS estimator is
B = [XVlX]A XVly
B=[X\QA I)X\A X\QA I)y
'au(XX)A
au(XX)A
.. ain(XX)A'
'(XX)
A
5 =
a2](XX)A
ct22(XX)a
.. a2n(x'xy'
(XXfo^'b,
*mX{xxy*
crn2(XX)A
nn(x'xr'_
(XX) Â£>'6,
(2108)
(2109)
(2110)
(2111)
where /= 1,... n.
After multiplication, the moment matrices cancel, and we are left with
A = T.j cr,j E/
A = 6.(2,
where j, and / = 1, ... ,n, and
bi = {XX)AXyi. (2113)
The terms in parentheses in the second line of Equation 2112 are the elements of the first
row of EE'1 = 7, so the end result is 5, = b\. Using a similar method, the same results are
true for the remaining subvectors, B, = b,. That is, in the Seemingly Unrelated
Regressions model, when all equations have the same regressors, the efficient estimator is
99
on methyl bromide and that Mexico will gain market share and shipping point revenues.
The average wholesale price of tomatoes is expected to increase by 1.46% under the first
scenario, to decrease by 0.52% under the second scenario, and to increase by 0.82%
under the third scenario (Table 38).
On the demand side, Table 39 shows that consumer demand of tomatoes in every
market is expected to decrease under the first scenario with the highest decrease in the
Chicago market (1.44%) and the lowest decrease in the Los Angeles market (0.82%).
The increase in the percentage change in the consumer demand of tomatoes under the
second scenario is highest in the Atlanta market (1.26%) and is lowest in the New York
market (0.51%). In the third scenario, the consumer demand of tomatoes is expected to
increase in the Atlanta and Los Angeles markets and to decrease in Chicago and New
York markets because the impact of the methyl bromide ban is higher than the impact of
NAFTA in the Chicago and New York markets.
Bell peppers
Banning methyl bromide will have a negative impact on Florida. For example, the
planted acreage of bell peppers is expected to decrease from 7,175 acres to 6,986 acres in
Palm Beach County and to decrease from 10,997 acres to 9,499 acres in West Central
Florida (Table 33). On the other hand, methyl bromide ban is expected to have a
positive impact on Texas and Mexico, offsetting some of the loss experienced in Florida.
The planted acreage of bell peppers is expected to increase from 12,680 acres to 14,458
acres in Texas and to increase from 13,600 acres to 13,901 acres in Mexico.
Under the first scenario, total production of bell peppers is expected to decrease by
1.04% (Table 35). Total shipping point revenues for bell peppers are expected to
decrease by $6.6 million, with Florida suffering a $17.1 million loss in shipping point
44
(as the righthand side variables in the systems should not be controlled by the decision
maker) and to avoid the problem with the statistical significant test of the coefficients.
The elasticities were calculated from the estimation of the RIDS model by using
Bartens method of estimation with homogeneity and symmetry constraints imposed. All
the estimations of scale effects are statistically significant at the 5% probability level and
have the expected sign. In terms of own substitution quantity effects, these estimations
have the expected sign, and are statistically significant at the 5% probability level for all
commodities in the Atlanta, Los Angeles, and New York markets. In the Chicago
market, the estimation is statistically significant only for strawberry. In every market,
tomato has the highest absolute value of own uncompensated quantity elasticity while
strawberry has the lowest. In addition, own substitution quantity elasticities for tomato
and bell pepper in the Atlanta and Los Angeles markets are higher than in the Chicago
and New York markets.
76
C\q) = a\q). (35)
We get the inverse supply function (or the industry marginal cost function) from
the profitmaximizing condition and the inverse demand function from the utility
maximizing condition. Then we can find the equilibrium price at whichp(x) =p(q),
Xx{x) = Q'\q), or P{x) = C'(x) as x = q (Equation 34). Figure 31 represents the partial
equilibrium analysis using the Marshallian graphical technique with the equilibrium price
at the point of intersection of the aggregate demand and aggregate supply curves.
Figure 31. Aggregate demand and aggregate supply
Fundamental Theory of the Partial Equilibrium Model
In the partial equilibrium model, it is relatively easy to measure the change in the
equilibrium outcome of a competitive market or the change in the level of social welfare,
resulting from a change in underlying market conditions such as an improvement in
technology, a new government internationaltrade policy, or the elimination of some
existing market imperfection. The partial equilibrium model turns out the optimal
consumption and production levels for good g that maximize the Marshallian aggregate
surplus. Moreover, if price p and allocation (*i, ..., x q\, ...,qj) constitute a competitive
27
The disturbance for the LaTheil model (Equation 236) is
v [b, A (In Q,) + Zy hy A(ln qJt)\ [b, A (In Q,) + Zy htJ A (In qjt)],
vit = (b, b, )A(In Q,) + Zy (hy hv )A(In qJt). (295)
The disturbance for the model AIIDS (Equation 245) is
v = [b, A (In Q,) +Z\y y,j A (In qJt)\ [ b, A (In Q,) +Z\Â¡ yt] A (In qJt)\,
vu = (b, b, )A(ln Q,) + Zy (y0 ytJ )A(In qJt). (296)
The disturbance for the RAIIDS model (Equation 254) is
vu = [h, A (In Q,) + Zy yv A (In qJt)] [ h, A (In Q,) + Zy ytJ A (In qJt)\,
vit = (h, h,) A (In Q,) + Zy (y0 ytJ )A (In qJt). (297)
From the coefficients of these four functional forms of inverse demand system, we
can show that
h, A, = w, Â£ w, 4' = wÂ¡ (Q 4), (298)
hy hy = w, 4 w, 4 = vv, (4 4), (299)
6, bl = (w,Ci+ w,)(vv, 4 + w,)= w,(4 4), (2100)
ft Yij= (W.$J + 4 w, ) (w, 4 + w, % w, wj) = w, (4 4), (2101)
where h, is the estimation of hÂ¡, hIJ is the estimation of hy, bt is the estimation of b yt
is the estimation of ytJ, and 4, and 4 are the estimations of 4 and 4 respectively.
Consequently, for all functional forms of the inverse demand system, we get the same
disturbance,
Vtf = W, [(4/ 4 )A(In Q,) + Z, (4 4 )A(In qJt)].
(2102)
29
of quantities and prices for each commodity in each market, T 208. The commodities
are tomatoes, bell peppers, cucumbers, and strawberries. The markets include Atlanta,
New York, Los Angeles, and Chicago.
Seemingly Unrelated Regressions Model
Following Greene (2000), the inverse demand systems can be written as
yi = XB+ Â£y,
yi = XB + Si,
yn XB + sn,
(2103)
where
e'= [s\, si,
5 Â£n ]
(2104)
E[s] = 0.
(2105)
The disturbance formulation is
anI
Gnl .
E[es\ = V=
oj
a22I .
(2106)
Vnl1
aJ_
There are n equations and T observations in the data sample. For the demand
system, we can apply Seemingly Unrelated Regressions (SUR) with identical regressors
or the Generalized Least Square (GLS) with identical regressors,
1
_
^ PS
1
_y_
X 0
0 X
0 0
o'
'By'
Â£,
0
b2
+
^2
X
A.
A.
(2107)
th
For the t observation, then xn covariance matrix of the disturbances is
106
hand, total production in Mexico is expected to increase by 11.01%, 50.74%, and 54.78%
under the first, second, and third scenarios, respectively.
Under the first scenario, shipping point revenues are expected to decrease by $70.9
million in Florida, by $272.7 million in California, by $20.5 million in Alabama and
Tennessee, and by $700,600 in Virginia and Maryland (Table 37). In contrast, shipping
point revenues are expected to increase by $8.3 million in Texas, by $19.2 million in
South Carolina, and by $71.5 million in Mexico. However, these gains do not offset the
loss expected under the first scenario. As a result, total revenues are expected to decrease
by $265.9 million. Under the second scenario, Mexicos shipping point revenues are
expected to increase by $336.9 million, while U.S. total shipping point revenues are
expected to decrease by $354.1 million. Under the third scenario, U.S. total shipping
point revenues are expected to decrease by $623.4 million, with California shippers
losing $549.3 million. Mexicos shipping point revenues are expected to increase by
$363.4 million.
Table 39 shows that consumer demand for tomatoes, bell peppers, eggplant,
watermelon, and strawberries is expected to decrease under the first scenario. The
consumer demand of every commodity, except strawberries, is expected to increase under
the second scenario. The highest impacts on the consumer demand for eggplant,
watermelon and strawberries will be in the Atlanta market.
Conclusions
An economic model of the fruit and vegetable industry was used to determine the
projected impacts of NAFTA and the methyl bromide ban. Methyl bromide has been a
critical soil fumigant in the production of many agricultural commodities. Tomatoes, bell
peppers, eggplant, squash, cucumbers, strawberries, and watermelons are the crops with
This work is dedicated to my parents and my wife.
26
For the last functional form, we get the econometric model development for the
RAIIDS model that has the AIIDS scale coefficients and the RIDS quantity coefficients
by subtracting vv, A (In QÂ¡) on both sides of the AIIDS model (Equation 285),
dwu + w, [A (In Q,) A (In Q*)] w, A(ln Q,)
= w, Q A (In Q,) + Ey (w, 4 + w, Sy vv, wJ) A (In qj,) + v,
dw w, A(/ 0,*) = hi A(ln Q,) + E, A(/ qjÂ¡) + v,
w, [A(/ %) + A(/ <7f) A{ln Q*)] = hÂ¡ A (In Q,) + Ey A{ln qJt) + v. (289)
From the coefficients of each functional form of inverse demand system, we can calculate
the scale elasticity and the compensated quantity elasticity by using the following
equations:
Â£i = hi/ w, =(bi/ w,)l, (290)
4 = hV 1 = (jij / w, )+Wj Sy. (291)
The uncompensated quantity elasticity can be calculated by using the Antonelli equation,
y/y = 4 +Â£iWj. (292)
Because functional forms of the demand systems can be related to each other
theoretically, we can show that standard errors are unchanged across the functional forms
of the inverse demand system. The standard error can be calculated from the disturbance,
vu=y y = Pi xit p, xit, (293)
where yu is the estimation of the dependent or explained variable, yÂ¡h /?, is the estimation
of the coefficient, /?, ,and xit is the independent or explanatory variable. The disturbance
for the RIDS model (Equation 226) is
vu = [hi A (In Qt) + Ey hy A (In qj,)] [ h, A (In QÂ¡) + Ey htJ A {In qJt)\,
vit = (hi h,) A (In Q,) + Ey (hy htJ )A (In qJt).
(294)
3
frost for several years), and increased competition from rapidly expanding greenhouse
tomato growers. Peracre yields for fresh tomatoes were off substantially in 1995 and
1996 from freezes, heavy rain, and low market prices. Severe flooding in Mexico sharply
reduced its production and its exports to the United States. A smaller volume of imports
and higher prices prompted Florida growers to harvest fields more intensively, resulting
in recordhigh yields in Florida.
Although acreage has decreased over the past decade, Florida remains the leading
domestic source of fresh tomatoes. Florida produced 42% of U.S. fresh tomatoes from
1997 through 1999. Floridas season (October to June) has the greatest production in
April and May and again from November to January. The leading counties are Collier,
Manatee, and Dade. Tomatoes, one of the highestvalued crops in Florida, bring in one
third of the states vegetable cash receipts and 7% of all its agricultural cash receipts. As
a result of decreased production in the northern states, Florida was able to increase its
percentage of the U.S. domestic output from about 25% in 1960 to 42% in 1999.
Because of higher prices during the winter, Florida accounts for 43% of the total value of
the U.S. freshtomato crop.
California is the secondlargest tomatoproducing state, accounting for 31 % of the
fresh crop. Fresh tomatoes are produced across many counties in each season, except
winter, with San Diego (spring and fall) and Fresno (summer) accounting for about
onethird of the crop. Other important tomatoproducing states in 1999 included
Virginia, Georgia, Ohio, South Carolina, Tennessee, North Carolina, and New Jersey.
International trade is an important component of the U.S. freshtomato industry.
The United States imported 32% of the fresh tomatoes it consumed in 1999 (up from
92
I KS I KS K 12
Total cost of production = Â£ Â£ Cl/fo W,ks + X X X X C2,&* 2,to. (319)
/ = 1 fcs = 1 / = 1 As = 1 Â£ = 1 /w = 1
I J K 12
Cost of transportation = X X X X CljjkmXykm (320)
i = iy = U = lw = l
We can derive the VanSickle et al. model from the Lagrangean equation
J K 12 ^ I KS
L= X X X Qjkm{m)bjkm Â£?jkm] ~ X X Cl/to IC/fo
y = 1 & = 1 w = 1 = 1 As = 1
/ KS K 12 I J K 12
 X X XX ClikskZikm X X X X C'iijkmXijkm
i = \ks = \k = \m = \ i = 1 j = \k = \m = 1
I K \2 KS
+ X X X ( X 4h 1C/*s 2",to)
/ = 1 Â£ = 1 w = 1 As = 1
I K \2 j
+ X X X gi/tm (2,to X Kyto)
i = 1 k =1 m = 1 y = l
J 12 /
+ X X X Ujkm ( XijkmQjkm), (3*21)
j = \k = \m = \ i = 1
where gikm and Ujkm are the Lagrange multipliers.
Both constraints satisfy the regularity condition of the KuhnTucker Theorem as they are
linear. From the firstorder condition with Qjkm, the KuhnTucker condition is
d L I d Qjkm Qjkm ~ bjkm Qjkm ~ 0; Qjkm ^ 0(d L / d Qjkm)Qjkm ~ 0. (322)
Let Qjkm > 0, so that d LI d Qjkm = 0. Therefore,
Qjkm Qjkm ~ bjkm Qjkm (323)
The Lagrange multiplier for the demand constraint is the market price, ujkm = Pjkm
Consequently, we can see that this model satisfies the utilitymaximizing condition.
From the firstorder condition with Wiks, the KuhnTucker condition is
40
respectively. This showed that for a 1% increase in aggregate quantity in each market, the
wholesale price of tomatoes will fall between 0.4488% and 0.5427%. The scale elasticities
are 0.9617, 0.9075, 1.0259, and 1.0453 in the Atlanta, Los Angeles, Chicago, and New
York markets, respectively (almost unit elastic in the Atlanta market, with the highest
fluctuations in the New York market).
Bell peppers. The estimates of the scale effects of bell peppers had the expected
negative sign (which showed that as aggregate quantity increases, the normalized price
goes down). Since it is expected that the change in normalized price is proportional for
both wholesale and retail prices, the magnitude of the above change would be reflected at
both the wholesale and retail levels. As such, the obtained estimates of the scale effects
can be used to infer that if there is a 1 % increase in the quantity of the product group as a
whole, the price of bell pepper will fall by 0.1777%, 0.1885%, 0.2226%, and 0.1968% in
the Atlanta, Los Angeles, Chicago, and New York markets, respectively. The scale
elasticities range from 1.0040 to 1.0905, which are elastic in the Atlanta, Los Angeles
and Chicago markets with the scale elasticities equal to 1.0460, 1.0302, and 1.0905,
respectively (almost unit elastic in the New York market, with the scale elasticity equal to
1.0040).
Cucumbers. The estimates show that for a 1% increase in the aggregate quantity in
each market, the normalized wholesale prices will decrease by 0.1911%, 0.1517%,
0.2319%, and 0.2388% in the Atlanta, Los Angeles, Chicago, and New York markets,
respectively. The scale elasticities of cucumbers are 1.0485, 1.0365, 0.892, and 0.9438
in the Atlanta, Los Angeles, Chicago, and New York markets, respectively (inelastic in the
Chicago and New York markets and elastic in the Atlanta and Los Angeles markets).
97
Empirical Results
The solution to the VanSickle et al. model included shipments, by month and crop,
from each producing area to each market; the planted acreage, production, and revenues
to each cropping system in each production area; and the equilibrium prices and quantity
consumed, by month and crop, in each of the four market areas. The baseline solution
performed reasonably well in replicating the observed pattern of shipments and acres
planted for the 2000/2001 production season.
The baseline acreage planted to each crop in each of the major producing areas is
shown in Table 33, which includes estimates of the expected inputs from the ban on
methyl bromide alone (first scenario), NAFTA alone (second scenario), and the
combination of the ban on methyl bromide and NAFTA together (third scenario).
Percentage changes in production and revenues, compared with the baseline for each crop
in each area, are shown in Table 35. Changes in production, compared with the
baseline, by area, are shown in Table 34. Changes in revenues, compared with the
baseline, by crop, in each area, are shown in Table 36. Changes in production and
revenues, compared with the baseline, by area, are shown in Table 37. Changes in
average prices, compared with the baseline, by crop, are shown in Table 38. Results
show that significant effects may be expected across producing areas for all crops.
Percentage changes in consumer demand for each commodity in each market, compared
with the baseline, are shown in Table 39.
Tomatoes
Tomato production in Dade and Palm Beach Counties in Florida and in the
Alabama/Tennessee region is expected to cease in every scenario. California is expected
104
acres under the second scenario, and to 923 acres under the third scenario. This occurs
because of the decrease in the production of double cropped of watermelons and bell
peppers. The 17,338 baseline acres of watermelon in Southwest Florida are expected to
increase to 18,340 acres under the first scenario, to 18,002 acres under the second
scenario, and to 17,899 acres under the third scenario as a result of the increase in the
production of double cropped of watermelons and tomatoes.
Total production of watermelons is expected to decrease by 0.76% under the first
scenario and by 1.44% under the third scenario (Table 35). Consequently, the average
wholesale price of watermelons is expected to increase by 5.13% under the first scenario
and by 5.39% under the third scenario (Table 38). In contrast, under the second
scenario, total production of watermelons is expected to increase by 2.91%, and the
average wholesale price of watermelons is expected to decrease by 1.42%.
Total shipping point revenues for watermelons are expected to decrease by $7.9
million under the first scenario, by $976,981 under the second scenario, and by $5.7
million under the third scenario (Table 36). Consumer demand of watermelons is
expected to increase in the first and third scenarios in every market (Table 39). On the
other hand, the consumer demand of watermelons is expected to increase in every market
under the second scenario, with the highest impact in the Atlanta market.
Strawberries
The model only estimates the impact of the methyl bromide ban for strawberries
since tariffs are not currently collected on imports. The impact on California is
significant because of the high cost and high productivity of the current production
systems in California. Strawberry production in Northern California is expected to cease
under the first scenario, and the planted acreage of strawberries in Southern California is
This dissertation was submitted to the Graduate Faculty of the College of
Agricultural and Life Sciences and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.,
August 2004
a.
Dean, College of Agricultural ancKLi
Sciences \ )
ife
Dean, Graduate School
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iv
LIST OF TABLES vii
LIST OF FIGURES xi
ABSTRACT xii
CHAPTER
1 INTRODUCTION 1
Overview of the Fruit and Vegetable Industry 1
Study Overview 6
2 DEMAND ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY 7
Problematic Situation 7
Hypothesis 8
Objectives 8
Conceptual Framework 9
Inverse Demand Model 9
Scale and Quantity Comparative Statics 18
Econometric Model Development 24
Methodology for Demand Analysis 28
Seemingly Unrelated Regressions Model 29
Bartens Method of Estimation 31
Unconstrained estimation 33
Estimation under the homogeneity condition 34
Estimation under the symmetry and homogeneity conditions 35
Empirical Results 37
Inverse Demand System Analysis 38
Elasticity Analysis 39
Scale effect and scale elasticity 39
Quantity effect and own substitution elasticity 41
Conclusions 43
v
56
Table 223. Estimation of the LaTheil model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0429
0.0083
0.0163
0.0216
(0.0297)
(0.0205)
(0.0194)
(0.0133)
^Tomato
0.1076
(0.0204)
^Bell Pepper
0.0355
0.0364
(0.0131)
(0.0146)
^Cucumber
0.0480
0.0011
0.0314
(0.0122)
(0.0103)
(0.0128)
^Strawberry
0.0241
0.0019
0.0155
0.0104
(0.0085)
(0.0076)
(0.0070)
(0.0076)
Standard Error (a)
0.0660
0.0465
0.0435
0.0298
R2
0.1277
0.0435
0.0545
0.0491
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 224. Estimation of the RAIIDS model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5663
0.1717
0.1649
0.1004
(0.0315)
(0.0213)
(0.0208)
(0.0148)
YTomato
0.1171
(0.0217)
YBell Pepper
0.0570
0.0942
(0.0136)
(0.0151)
YCucumber
0.0312
0.0254
0.0815
(0.0130)
(0.0109)
(0.0137)
YStrawberry
0.0289
0.0118
0.0249
0.0656
(0.0094)
(0.0083)
(0.0077)
(0.0085)
Standard Error (a)
0.0701
0.0482
0.0467
0.0332
R2
0.6159
0.4073
0.3806
0.3984
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
102
market, except the Los Angeles market, is expected to decrease, as the Los Angeles
market receives more benefits from NAFTA than do the other markets.
Squash
The 3,637 planted baseline acres of squash in Southwest Florida are expected to
increase to 4,423 acres under the first scenario, to 4,286 acres under the second scenario,
and to 4,568 acres under the third scenario (Table 33). On the other hand, the planted
acreage of squash in Dade County is expected to decrease in every scenario from 8,081
acres to 7,880 acres under the first scenario, to 7,647 acres under the second scenario, and
to 7,749 acres under the third scenario.
Squash production in Mexico is expected to decrease by 0.76% under the first
scenario, but is expected to increase by 1.46% under the second scenario and by 1.85%
under the third scenario (Table 35). Squash production in Florida is expected to increase
by 4.99%, 1.83%, and 5.11% under these three scenarios, respectively. Floridas total
shipping point revenues for squash are expected to increase by $327,680 under the first
scenario, by $322,760 under the second scenario, and by $185,970 under the third
scenario, while Mexicos shipping point revenues are expected to decrease by $145,080
under the first scenario, to increase by $125,260 under the second scenario, and to
increase by $198,630 under the third scenario (Table 36).
Table 38 shows that the average wholesale price of squash is expected to decrease
by 0.18% under the first scenario, by 0.50% under the second scenario, and by 0.41%
under the third scenario. Table 39 shows that the consumer demand of squash is
expected to increase under these three scenarios in every market. The highest percentage
change in the consumer demand of squash is in the New York market.
Copyright 2004
by
Sikavas NaLampang
8
transformed matrix weights associated with the other models. Next, statistical tests are
carried out on the matrix weights to determine whether they are significantly different
from zero. This matrixweighted linear combination can be considered a synthetic
demandallocation system (which, under appropriate restrictions, yields different forms
of the demand system). The synthetic model can therefore be used to statistically test
which model best fits a particular data set. One drawback in applying this procedure is
that it is necessary to impose a set of restrictions for the purpose of estimating. For
example, the differentials need to be replaced by finite first differences, and the budget
share needs to be replaced by its moving average. As a result, each functional form
generates a different result.
Hypothesis
Our main hypothesis is that if the theoretical elasticities from the demand system in
the theory are the same across all functional forms, then the empirical results of the
elasticities from the demand system should also be the same across all functional forms.
Objectives
Our primary objective was to propose a formulation that obviates the need to
choose among the popular functional forms when conducting a demand analysis and to
empirically test this formulation using data on selected fruits and vegetables. The goal
was to verify that the elasticities are the same across every functional form of the demand
system. The secondary objective was to analyze the elasticities calculated from the
coefficients of the inverse demand system.
48
Table 27. Estimation of the LaTheil model for the Los Angeles market by using the
mean of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0533
0.0055
0.0053
0.0208
(0.0306)
(0.0211)
(0.0189)
(0.0128)
^Tomato
0.1124
(0.0209)
^Bell Pepper
0.0348
0.0382
(0.0133)
(0.0144)
^Cucumber
0.0500
0.0003
0.0366
(0.0118)
(0.0100)
(0.0120)
^Strawberry
0.0276
0.0037
0.0131
0.0182
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.1338
0.0441
0.0657
0.0552
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 28. Estimation of the RAIIDS model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5224
0.1885
0.1517
0.1157
(0.0306)
(0.0211)
(0.0189)
(0.0128)
YTomato
0.1318
(0.0209)
YBell Pepper
0.0706
0.1113
(0.0133)
(0.0144)
YCucumber
0.0342
0.0271
0.0884
(0.0118)
(0.0100)
(0.0120)
YStrawberry
0.0270
0.0137
0.0270
0.0677
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.5879
0.4712
0.4171
0.5113
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
32
v,=y, DxÂ¡. (2119)
An alternative way of writing v, is
V= YXD', (2120)
where
V'= [vi,v2,..vr], (2121)
X'=[xux2,...,xt\, (2122)
Y'=\y\,yi,.. .,yr\. (2123)
Then
A = (1 / T) VV+ iV
A = (1/7) [Y'Y DX'Y YXD' + DXXD'] + ii\ (2124)
where
/ = (1 / Vw)i (2125)
and i is the summation vector.
The resulting estimators of the coefficients of the system are used to obtain an
estimator of variance, and hence a numerical estimate for the covariance of the
disturbances, Q. The set of equations will be estimated jointly by using a maximum
likelihood procedure (Barten, 1969). First, we estimate without the use of any restriction,
next we impose a constraint for homogeneity condition, and then we impose constraints
for both homogeneity and symmetry conditions. The assumption is made that prices and
total expenditure are stochastic and independent of the disturbance term. We also
assumed that vt are vectors of independent random drawings from a multivariatenormal
distribution with mean zero and covariance matrix, Q.
2
largest harvests occurring during the summer and fall. Imports supplement domestic
supplies, especially fresh products during the winter, resulting in increased choices for
consumers. For example, Florida produces the majority of its domestic warmseason
vegetables, such as fresh tomatoes, during the winter and spring, while California
produces the bulk of its domestic output in the summer and fall. Freshtomato imports,
primarily from Mexico, boost total supply during the first few months of the year, and
compete directly with winter and early spring production from Florida. In value terms,
Mexico supplies more than half (61%) of all the fruit and vegetable imports to the United
States, with the majority being freshmarket vegetables. Canada is the second leading
foreign supplier, with about 27% of the U.S. import market. Because of their obvious
transportation advantages, Mexico and Canada have historically been the top two import
suppliers to the United States. In value terms, fresh fruits and vegetables account for the
largest share of fruit and vegetable imports, with about $2 billion in 1999. There is a
definite seasonal pattern to U.S. fresh vegetable imports, with twothirds of the import
volume arriving between December and April (when U.S. production is low and is
limited to the southern portions of the country). Most of these imports are tender warm
season vegetables such as tomatoes, peppers, squash, and cucumbers.
The United States is one of the worlds leading producers of tomatoes, ranking
second only to China. California and Florida make up almost twothirds of the acreage
used to grow fresh tomatoes in the United States. Fresh tomatoes lead in farm value
($920 million in 1999), along with lettuce and potatoes. U.S. freshtomato production
steadily increased until 1992, when it peaked. Production then trended downward.
Declines reflected sharply rising imports, weather extremes (excessive rains, wind, and
17
In addition, from the logarithmic version of the LaTheil model (Equation 235), we can
get the logarithmic version of the AIIDS model by adding d(ln qÂ¡) d{ln Q) to both sides,
diln pi) d{ln P) + d(ln qÂ¡) d{ln Q) = (4 +1) d(ln Q) + Z7 4 d(ln qj) + d{ln qÂ¡) 
diln Q),
d(ln nÂ¡) + d(ln qj) = (4 +1) d(ln Q) + Z7 (4 + 4 wj) d{ln qÂ¡),
d(ln w,) = (Ci+1) d(ln Q) + S7 (4 + 4 ~ Wy) <7(/n qj).
We also can derive the logarithmic version of the AIIDS model by adding d(ln qÂ¡) on
both sides of the logarithmic version of the RIDS model (Equation 223),
d(ln nÂ¡) + d(ln qÂ¡) = Q d(ln Q) + Â£, 4 d(ln qj) + d(ln qÂ¡),
d{ln nj) + d(ln qÂ¡) = d(ln Q) + d(ln Q) + Z7 4 <7(/
d{ln w,) = (4 +1) d(ln Q) + S7 (4 + Sywj) d{ln qj). (251)
In order to satisfy the symmetry condition, we premultiply both sides of Equation 251 by
Wj, so the AIIDS model is
Wj d(ln wÂ¡) = {wÂ¡Q + wi) d(ln Q) + I7 (w,4 + w,S,j wÂ¡wj) d(ln qj),
dwÂ¡ = bÂ¡ d(ln Q) + Z7 yy d{ln qj),
which is the same as Equation 245 and
Yij = w<4 + w,8,j WjWj. (252)
The last functional form of the inverse demand system is the Rotterdam Almost
Ideal Inverse Demand System (RAIIDS). We can get the logarithmic version of the
RAIIDS model by subtracting d(ln Q) from both sides of the logarithmic version of the
AIIDS model (Equation 251),
diln wt) d(ln 0 = (4+1) diln Q) + Z7 (4 + 4 wj) diln qj) diln Q),
diln wÂ¡) diln Q) = Q diln Q) + Z7 (4 + 4 wj) diln qj).
We also can get the logarithmic version of the RAIIDS model by adding diln qi) d(ln Q)
to both sides of the logarithmic version of the RIDS model (Equation 223),
diln ni) + diln qi) dQn Q) = 4 d{ln Q) + Z7 4 d(ln qj) + d(ln qi) diln Q),
diln ni) + diln qi) diln Q) = 4 d(ln Q) + Z7 (4 + 4 wj) diln qj),
88
squash, eggplant, and strawberries. The double cropping systems include tomatoes and
cucumbers, tomatoes and squash, tomatoes and watermelons, bell peppers and
cucumbers, bell peppers and squash, and bell peppers and watermelons. The model
assumes that all producers in a particular region use the same production technology
(with the same yields and costs), and that crops are produced with fixedproportion
production functions.
The production costs in this model include preharvest cost, harvest cost, post
harvest cost, and transportation cost. The model calculates total production costs by
summing preharvest and postharvest costs. The preharvest cost is the product of the
number of acres planted and the peracre preharvest cost (in which we can apply the
alternative effect). The postharvest cost is the product of the number of acres planted,
yield, and perunit harvest and postharvest costs. The preharvest cost includes both
operating costs and fixed costs. The operating costs include fertilizer, fumigant,
fungicide, herbicide, insecticide, labor, surfactant, transplants, machinery, machinery
labor, scouting, stakes, plastic string, plastic mulch, farm vehicles, and interest on
working capital. The fixed costs include land rent, machinery fixed cost, supervision
cost, and overhead cost. Harvest and postharvest costs include harvesting, cooling,
packing, transportation to shipment point, and marketing costs. These costs for Mexico
also include transportation to the U.S. border and all tariffs and fees to cross the border
into the United States. An average permile transportation cost of $ 1.31 was calculated
using information from the USDA Agricultural Marketing Service. These costs include
truck brokers fees for shipments in truckload volume to a single destination, based on
costs of shipping from the point of origin to the point of destination, and do not include
11
X, WiHij = Wj (Cournot aggregation), (28)
X, WiSij = 0 (Slutsky aggregation). (29)
Second, the homogeneity of degree zero in p and m is
Zy Py = rÂ¡h (210)
Zy % = 0. (211)
Third, the symmetry of the matrix of Slutsky substitution effects is
W,Â£,j = WjÂ£j,. (212)
Fourth, the negativity condition is
X, Xy x, wÂ¡ Sij Xj < 0 Xj, Xj constant. (213)
From Walras law, we can show that d(ln m) = d(ln P) + d(ln 0:
m = X, p,q
dm = X, qÂ¡ dpt + X, pÂ¡ dqÂ¡,
dm / m = 'Zl (q, / m) dpÂ¡ + X, (p, / m) dqÂ¡,
d(ln m) = X, {pfti / m)(dpÂ¡ / p,) + X, (p^, / w)(^, / ^,),
c/(/ m) = X/ w, J(/ pÂ¡) + E, w, Â£/(/ Â£/,),
d{ln m) = d(ln P) + d(ln Q),
(214)
where
d(ln P) = X, Wj d(ln pÂ¡)
(the Divisia price index),
(215)
d(ln Q) = X, w, d(ln q,)
(the Divisia volume index).
(216)
An inverse demand system expresses the prices paid as a function of the total real
expenditure and the quantities available of all goods. The coefficients of the quantities in
the various inverse demand relations reflect interactions among the goods in their ability
to satisfy wants. From an empirical viewpoint, inverse and regular demand systems are
not equivalent. To avoid statistical inconsistencies, variables on the righthand side in
such systems of randomdecision rules should be the ones that are not controlled by the
CHAPTER 2
DEMAND ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY
Demand analyses can be very sensitive to chosen functional forms. Since no one
specification best fits all data, researchers have been preoccupied with finding ways to
select among various functional forms. Our study addresses this concern by proposing a
formulation that obviates the need to choose among the various functional forms of the
demand system. This approach was tested using four functional forms of the inverse
demand system: the Rotterdam Inverse Demand System, the Laitinen and Theils Inverse
Demand System, the Almost Ideal Inverse Demand System, and the Rotterdam Almost
Ideal Inverse Demand System.
Problematic Situation
Several studies in the past have considered the issue of how to choose among
popular functional forms when conducting demand analyses. Parks (1969) used the
average information inaccuracy concept. A relatively high average inaccuracy is taken to
be an indicator of lesssatisfactory behavior. Deaton (1978) applied a nonnested test to
compare demand systems with the same dependent variables. However, this procedure is
not suitable when comparing models with different dependent variables (as in the case of
comparing the Almost Ideal Demand System with the Rotterdam Demand System).
Barten (1993) developed a method that can deal with nonnested models with
different dependent variables. Briefly, the method starts with a hypothetical general
model as a matrixweighted linear combination of two or more basic models. A solution
is found for one of the dependent variables, followed by estimating consistently the
7
4
19% in 1994), and exported 7% of its annual crop. The percentage imported rose steadily
after 1993 until low domestic prices discouraged imports in 1999. The United States, as
a net importer of fresh tomatoes, had a tomato trade deficit in 1999 of $567 million.
Mexico and Canada are important suppliers of freshtomatoes to the United States.
Freshtomato imports mostly arrive from Mexico (about 83% in 1999).
Over the past two decades, the demand for bell peppers has been rising, reaching a
record high in 2000. The United States is one of the worlds biggest producers of bell
peppers, ranking sixth behind China, Mexico, Turkey, Spain, and Nigeria. Because of
strong demand, U.S. growers harvested 12% more bell pepper acreage in 2000 than in
1999. Bell peppers are produced and marketed yearround, with the domestic market
peaking during May and June, and the import market peaking during the winter months.
Although bell peppers are grown in 48 states, the U.S. industry is largely concentrated in
California, Florida, and Texas. Trade plays an important role in the U.S. fresh bellpepper
market, with about 20% of fresh bell peppers coming from Canada and Mexico.
Originating in India, cucumbers were brought to the United States by Columbus,
and have been grown here for several centuries. The United States produces 3% of the
worlds cucumbers, ranking fourth behind China, Turkey, and Iran. U.S. freshcucumber
production reached a record high in 1999, but has trended lower since. Florida and
Georgia are the leading states in the production of freshmarket cucumbers. Fresh
cucumber prices are the highest from January through April because of limited domestic
supplies and higher production costs, and are the lowest in June when supplies are
available from many areas. As a result, imports are strongest in January and February
when U.S. production is limited by cool weather, and are the weakest in summer during
23
The symmetry of dn, / dq* implies that compensatedquantity cross derivatives
between any two goods, i and j, must satisfy dn, / dq* = dnj / dq, The symmetry
property reflects the fact that the cross derivatives of a function are equal. We also get
the symmetry of the matrix of Antonelli substitution effects from this symmetry property,
dn, / dq/ = dnÂ¡ / dq/
By multiplying by q*q/ on both sides, we get
(dm / dq/)(q,*q/) = (dn, / dq*){q*q*\
{dn, / dq/)(q,*q/)(n, / n,) = {dnj / dq*)(q,*q/){^ / nj),
{n,q*){dni / dq/){q/ / n,) = (njq/)(dnj / dq*){q* / nj).
As wÂ¡ = n, q
(275)
which is analogous to Slutsky symmetry, (Equation 212).
From the AIIDS model, we can prove for the addingup condition, Equation 246,
by using the summation of Equation 252 over /' (E, ytJ = E, w,^ + E, E, w(). As
2/ Wjgij = 0, w, = E, w/4, and E, w, = 1, we get Equation 246 (E, ytj = 0). The proof for
Equation 247 can be obtained by working with Equation 237 (E/ bÂ¡ = E, wÂ¡Q + E, wÂ¡).
As E, W& = 1 and E, w, = 1, we get Equation 247 (E, 6, = 0). Next, we prove the
homogeneity of degree zero, Equation 248, by using the summation of Equation 252
over j (Ey y,j w, Ey ^ + Ey w,S,j w, Ey Wy). As Ey Â¡,j = 0, wÂ¡ Ey WjSy and Ey Wy 1, we
get Equation 248 (Ey yÂ¡j = 0). We also prove the Antonelli symmetry, Equation 249, by
working with Equation 252 (y,j = w^y + w,Sy w,wj). As w,
get y,j = WjZjj + wjSji WjWj, which means y,} = y, (Equation 249).
109
Table 33. Continued
Crop/
Acreage
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
(
Acres
)
Eggplant
Florida/Palm Beach
5,327
5,132
5,247
5,075
Mexico/Sinaloa
2,734
2,862
2,897
3,000
Total
8,060
7,994
8,143
8,075
Watermelons
Florida
West Central
1,812
593
1,694
923
Southwest
17,338
18,340
18,002
17,899
Total
19,149
18,933
19,697
18,822
Strawberries
Florida/West Central
4,545
4,692
4,545
4,692
California
Southern
10,518
7,659
10,518
7,659
Northern
9,217
0
9,217
0
Total
24,280
12,351
24,280
12,351
Note: MB is abbreviated for Methyl Bromide.
Table 34. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by area
Area
Production
Baseline
MB Ban
NAFTA MB Ban and NAFTA
(Units)
(
%.
)
Florida
103,851
(6.91)
(7.61)
(7.60)
California
92,674
(31.12)
(42.43)
(72.15)
Texas
7,735
14.02
0.37
10.12
V irginia/Maryland
4,272
(1.64)
(0.52)
(1.38)
South Carolina
6,854
27.44
24.14
25.34
Alabama/Tennessee
2,138
(100.00)
(100.00)
(100.00)
United States
217,524
(16.21)
(21.93)
(34.22)
Mexico
94,509
11.01
50.74
54.78
Total
312,033
(7.97)
0.08
(7.26)
Note: MB is abbreviated for Methyl Bromide.
51
Table 213. Estimation of the RIDS model for the New York market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4577
0.1968
0.2388
0.1120
(0.0190)
(0.0130)
(0.0159)
(0.0089)
^Tomato
0.0245
(0.0122)
^Bell Pepper
0.0015
0.0284
(0.0070)
(0.0079)
^Cucumber
0.0151
0.0232
0.0432
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0079
0.0036
0.0049
0.0164
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (ct)
0.0785
0.0511
0.0674
0.0364
R2
0.7956
0.5853
0.5880
0.5370
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 214. Estimation of the AIIDS model for the New York market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0199
0.0008
0.0142
0.0010
(0.0190)
(0.0130)
(0.0159)
(0.0089)
Yl ornato
0.2216
(0.0122)
Tbell Pepper
0.0843
0.1292
(0.0070)
(0.0079)
^Cucumber
0.0957
0.0264
0.1458
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0416
0.0185
0.0237
0.0839
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (a)
0.0785
0.0511
0.0674
0.0364
R2
0.6571
0.6573
0.4973
0.6015
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
28
Because we get the same disturbance for every functional form of the inverse demand
system, we also get the same standard error and loglikelihood value across all functional
forms.
Methodology for Demand Analysis
In following Barten (1969) to estimate the inverse demand system, we used the
maximumlikelihood method of estimation with constraints imposed. We imposed the
homogeneity and symmetry constraints by working with the concentrated loglikelihood
function. We estimated every demand equation in the system at the same time by
applying the Seemingly Unrelated Regression Estimation. GAUSS (a mathematical and
statistical software package), was used to perform the estimation.
There are four scenarios in our study. The first scenario is to estimate each
functional form of the inverse demand system by using the mean of the budget share to
multiply the logarithmic version of the inverse demand system. The second scenario is to
estimate each functional form of the inverse demand system by using the moving average
of the budget share to multiply the logarithmic version of the inverse demand system. In
addition, the first and second scenarios estimate the inverse demand system by using
Bartens estimation method with the homogeneity and symmetry constraints imposed.
The third scenario is to estimate the RIDS model by using Bartens unconstrained
estimation method. The fourth scenario is to estimate the RIDS model by using Bartens
estimation method with the homogeneity constraint imposed.
Results are based on time series data from 1994 to 1998 for four commodities of
selected vegetables and fruits, n = 4. Weekly wholesale prices and quantity unloads were
collected from the Market News Branch of the Fruit and Vegetable Division, Agricultural
Marketing Service, United States Department of Agriculture. There are 208 observations
75
Likewise the utilitymaximizing condition implies that given the equilibrium price
p for good g, consumer f s equilibrium consumption level x, must satisfy the utility
maximizing problem, subject to the budget constraint,
Max u,{Xj), (32)
subject to
I i pxi = m, (33)
where m is the budget share.
Because of the market clearing condition assumed, the equilibrium price of good g
will be price p at which the aggregate demand equals the aggregate supply,
x = q, (34)
where x is an aggregate demand (x = Â£, xÂ¡) and q is an aggregate supply (q = Â£, qj).
Because consumers and producers are price takers, the inverses of the aggregate
demand and supply functions are of interest. The inverse demand function, P{x) = X'(x),
gives the price that results in the aggregate demand of x. That is, when each consumer
optimally chooses a consumer demand for good g at this price, total demand exactly
equals x. At these individual demand levels, each consumers marginal benefit from an
additional unit of good g is exactly equal to P(x). Moreover, given that the aggregate
quantity x is efficiently distributed among the consumers, the value of the inverse demand
function, P(x), can also be viewed as the marginal social benefit of good g.
Likewise, inverse supply function,/? = Q'\q), gives the price that results in the
aggregate supply of q. That is, when each firm chooses its optimal output level facing
this price, the aggregate supply is exactly q. The inverse of the industry supply function
can be viewed as the industry marginal cost function, which can be denoted by
72
import share of U.S. domestic consumption of vegetables grew steadily from 10% in
1994 to 15% in 1998. In 1999 and into early 2000, low U.S. domestic prices slowed
import volume and pushed the import market share down to 14%.
Several empirical studies in the literature on the analysis of internationaltrade
issues have focused on partial equilibrium analysis. For example, spatial price
equilibrium analysis attempts to predict changes in future trade flows, prices,
consumption, and production for a commodity under governmental policies. The results
allow the estimation of welfare benefits and costs by using the concept of economic
surplus to individual countries from specific trade policies.
Under the partial equilibrium analysis, the assumption is that producers maximize
their profits, consumers maximize their utilities, and marketing activities are competitive.
Distortions come about only through governmental policies. There is no world price in
this model because the price differs among regions by transportation costs, tariffs, and
market imperfections. The amounts of consumption, production, exports, imports, and
equilibrium prices in each region are determined simultaneously.
Research Problem
With an increase in the number of U.S. sponsored trade agreements and general
trends toward opening the market, U.S. producers of fruits and vegetables may face
increased competition from foreign sources. Changes in competitiveness could affect
trade flows, which could change the structure and geographic distribution of the
agricultural industries. Internationaltrade agreements and competition among fruit and
vegetable industries have increased. Also, the phaseout of methyl bromide places the
United States at a disadvantage in trade with Mexico. Our study analyzes the impacts of
internationaltrade agreements and the ban on methyl bromide by estimating the change
95
d LI d sikm = I dikskm Wta Zikm = 0. (333)
ks = 1
From Equation 329, we get
I
KS J
I dikskmWiks= x Xijkm (334)
fcv = 1 y = l
From the firstorder condition with Xykm, the KuhnTucker condition is
dLl d Xijkm = UjJkm g ijh C3ijkm < 0; Xijkm > 0 ;(dL/d Xljkm)X,jkm = 0, (335)
where u jkm = ujkm for /'= 1and g* ljkm = gikm for j = 1,..., J.
To get a trial solution, we let Xijkm > 0, so that dLl d X,jkm = 0. By using Equations 323,
327, and 331, where ujkm is the same for all of we get
I
Qjkm ~ bjlcm ( X Xijkm) ~ C2 ,km + ( C1 Â¡ksk / ^ dikskm) C3ykm (336)
/ = 1 ks 1 ks = 1
Equation 336 ensures the profitmaximizing condition where price equals the marginal
cost.
From Equation 334, the firstorder condition of this model satisfies the profit
maximizing condition of the competitive equilibrium. This model solves the competitive
equilibrium problem by simulating Xykm and fV/ks, which satisfies Equation 332, 334,
and 336. By using the optimal solution of X'ykm, we can find the total demand, Qjkm, by
using Equation 331. We can find the total supply, Zikm, by using Equation 329, and
price, Pjkm, by using Equation 323.
This model can be represented by using the Marshallian graphical technique with
the equilibrium price as the point of intersection of the aggregate demand and aggregate
supply curves. In addition, this model is Pareto optimal because the aggregate
108
Table 33. Planted acreage in the baseline model, in the methyl bromide ban model, and
in the NAFTA model, by crop and area
Crop/
Acreage
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
(
Acres
)
Tomatoes
Florida
Dade
4,408
0
0
0
Palm Beach
2,798
0
0
0
West Central
11,077
12,020
12,761
11,804
Southwest
20,975
22,763
22,288
22,467
California
36,408
35,206
0
0
Alabama/Tennessee
3,448
0
0
0
South Carolina
6,923
8,823
8,595
8,677
V irginia/Maryland
6,282
6,179
6,249
6,195
Mexico
Sinaloa
34,951
39,235
38,583
40,468
Baja
5,369
6,497
27,583
27,472
Total
132,641
130,723
116,060
117,082
Bell Penners
Florida
Palm Beach
7,175
6,986
7,131
6,829
West Central
10,997
9,499
10,900
9,821
Texas
12,680
14,458
12,727
13,963
Mexico/Sinaloa
13,600
13,901
13,963
14,551
Total
44,452
44,845
44,721
45,165
Cucumbers
Florida/Palm Beach
6,693
6,986
6,769
6,829
Mexico/Sinaloa
10,076
10,304
10,361
10,361
Total
16,769
17,290
17,130
17,190
Squash
Florida
Dade
8,081
7,880
7,647
7,749
Southwest
3,637
4,423
4,286
4,568
Mexico/Sinaloa
7,265
7,210
7,371
7,399
Total
18,984
19,513
19,304
19,716
Note: MB is abbreviated for Methyl Bromide.
61
Table 233. Unconstrained estimation of the RIDS model for the Atlanta market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5868
0.0225
0.2231
0.0993
(0.1905)
(0.1209)
(0.1151)
(0.0715)
^Tomato
0.0548
0.0576
0.0395
0.0004
(0.1120)
(0.0710)
(0.0676)
(0.0420)
^Bell Pepper
0.0154
0.0715
0.0183
0.0006
(0.0366)
(0.0232)
(0.0221)
(0.0137)
^Cucumber
0.0603
0.0640
0.0247
0.0181
(0.0418)
(0.0265)
(0.0252)
(0.0157)
^Strawberry
0.0299
0.0251
0.0032
0.0123
(0.0194)
(0.0123)
(0.0117)
(0.0073)
Standard Error (cr)
0.0588
0.0373
0.0355
0.0221
R2
0.7137
0.3648
0.3947
0.3276
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 234. Unconstrained estimation of the RIDS model for the Los Angeles market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.3980
0.2997
0.0717
0.0846
(0.1786)
(0.1262)
(0.1110)
(0.0749)
^Tomato
0.1874
0.1039
0.0908
0.0928
(0.1079)
(0.0763)
(0.0671)
(0.0452)
^Bell Pepper
0.0073
0.0171
0.0370
0.0330
(0.0394)
(0.0279)
(0.0245)
(0.0165)
^Cucumber
0.0632
0.0102
0.0765
0.0511
(0.0370)
(0.0261)
(0.0230)
(0.0155)
^Strawberry
0.0048
0.0172
0.0245
0.0342
(0.0249)
(0.0176)
(0.0154)
(0.0104)
Standard Error (a)
0.0676
0.0478
0.0420
0.0283
R2
0.7059
0.2931
0.2409
0.3061
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
71
are considered environmental friendly and pose no or minimal risks to users. For
example, an alternative should not cause ozone depletion and global warming.
Turning our attention to the potential trade impact, it should be noted that
international trade is an important component of the U.S. fruit and vegetable industry. In
1999, imports accounted for 11.6% of total U.S. fruit and vegetable consumption. The
United States imposed ad valorem tariffs on imports of fresh vegetables. The U.S. ad
valorem tariffs were 3.1% to 4.6% on fresh tomatoes, 3.0% on fresh bell peppers, and
2.1% to 10.6% on fresh cucumbers. Negotiations of trade agreements within the World
Trade Organization (WTO) or as part of the Free Trade Area of the Americas (FTAA)
could significantly lower these tariffs. As stated earlier, NAFTA has had a considerable
impact on the levels of these tariffs. NAFTA, which went into force on January 1,1994,
is an agreement by the United States, Canada, and Mexico to phase out almost all
restrictions on international trade and investment among the three countries. The United
States and Canada were already well on the way to eliminating the barriers to trade and
investment between them when NAFTA went into effect. The main new feature of
NAFTA was the removal of most of the barriers between Mexico and the United States.
Fresh vegetable imports have been under scrutiny since before the implementation
of NAFTA in 1994. During the first year of NAFTA, the import share of consumption
for fresh fruits and vegetables remained at the preNAFTA level of about 10%.
However, following the devaluation of the Mexican peso in December of 1994, U.S.
imports of Mexican vegetables rose sharply. Mexican growers increased shipments to
the United States because of poor domestic demand and more attractive prices in the
United States. As a result of measured exports of fresh vegetables from Mexico, the
34
Estimation under the homogeneity condition
The homogeneity condition states that hÂ¡j = 0. This can also be formulated in
terms of D as
Dt= 0, (2129)
where r is defined by
1*= [0,1,1, ...,l]ix(+i). (2130)
The Lagrangean expression with the homogeneity condition is
^ = lnL+ kDt, (2131)
where k is an element vector of Lagrangean multipliers. By differentiating this
Lagrangean expression with respect to the element of D,
d(ln L+ k' Dt) / dD = d(ln L)/dD+ k'(Dt) / dD,
from d(a 'xb) / dx = ab 'and d(ln L) / dD = A'1 [Y'X DX'X], then
d(ln L+ k1 Dt) / dD = A'1 [YX D2X'X\ + kY.
By premultiplying this expression by A, postmultiplying it by {X'X)A, and then using
D\ = YX(X'Xf\ we obtain
d(ln L+K'DT)/dD = AAA [YX D2X'X\ (X'X)A + A/xf(X'X)A
d{ln L+ kDt)/ dD= YX(XX)A D2 + Aicf (X'X)'1
d(ln L+ k1 Dr) / dD Di D2 + AkY (X'X)'1. (2132)
Since D2 is the ML estimator under the homogeneity condition, it has to satisfy D2t= 0.
Postmultiplying Equation 2132 by r, we get
D\t D2t+ AKi (X'X)A t= 0
Ak=DxtI[Y(X'X)at\
Ak 0D\ r, (2133)
where #is a scalar equaling 1 / f (X'X)A r. Then we get
73
in location of agricultural production and by determining which countries will benefit and
which countries will lose.
Hypotheses
Our main hypotheses were as follows:
If a ban on methyl bromide is imposed without viable economic alternatives, then
the production of these crops will decrease. Therefore the decrease in production
causes the prices of fruits and vegetables in the United States to increase.
The impact of NAFTA will decrease fruit and vegetable prices in the United States.
Afterwards, the decrease in prices will cause an increase in the quantity demanded
and a decrease in the domesticquantity supplied.
Objectives
The first objective of our study is to estimate the impact of the phaseout of methyl
bromide on consumers, producers, prices, productions, and revenues. The second
objective of our study is to investigate the impact of NAFTA on the fruit and vegetable
industry. By investigating the impacts of the internationaltrade issues, the model is
expected to replicate the evolution of the fruit and vegetable industry.
Theoretical Framework
Following MasColell (2000), in a competitive economy, consumers and producers
act as price takers by regarding market prices as unaffected by their own actions.
Building on a spatial equilibrium model developed by VanSickle et al., we conducted an
investigation of the fruit and vegetable industry. This spatial equilibrium model satisfies
a profitmaximizing condition, a utilitymaximizing condition, and a marketclearing
condition. These three conditions must be met for a competitive economy to be
considered in equilibrium. The profitmaximizing condition states that each firm will
choose a production plan that maximizes its profits, given the equilibrium prices of its
outputs and inputs. The utilitymaximizing condition requires that each consumer choose
54
Table 219. Estimation of the LaTheil model for the Atlanta market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0231
0.0044
0.0090
0.0108
(0.0276)
(0.0200)
(0.0163)
(0.0114)
^Tomato
0.0765
(0.0179)
^Bell Pepper
0.0472
0.0397
(0.0112)
(0.0112)
^Cucumber
0.0244
0.0017
0.0322
(0.0102)
(0.0076)
(0.0097)
^Strawberry
0.0050
0.0058
0.0095
0.0087
(0.0068)
(0.0054)
(0.0051)
(0.0051)
Standard Error (a)
0.0574
0.0424
0.0342
0.0240
R2
0.0758
0.1008
0.0287
0.0301
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 220. Estimation of the RAIIDS model for the Atlanta market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5493
0.1709
0.1786
0.1024
(0.0278)
(0.0200)
(0.0171)
(0.0128)
TTomato
0.1507
(0.0181)
The 11 Pepper
0.0415
0.0885
(0.0112)
(0.0113)
Ttucumber
0.0756
0.0308
0.1087
(0.0106)
(0.0079)
(0.0104)
^Strawberry
0.0336
0.0161
0.0022
0.0519
(0.0075)
(0.0058)
(0.0056)
(0.0058)
Standard Error (a)
0.0578
0.0423
0.0359
0.0270
R2
0.6493
0.4549
0.5789
0.4635
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
IMPACT OF SELECTED REGULATORY POLICIES ON
THE U.S. FRUIT AND VEGETABLE INDUSTRY
By
Sikavas NaLampang
August 2004
Chair: John J. VanSickle
Major Department: Food and Resource Economics
The United States is one of the worlds leading producers and consumers of fruit
and vegetables. Fruit and vegetable production occurs throughout the United States, with
the largest fresh fruit and vegetable acreage in California, Florida, and Texas. Our study
used the spatial equilibrium model to determine the expected economic impacts of the
North America Free Trade Agreement (NAFTA) and the phaseout of methyl bromide in
the U.S. fruit and vegetable industry.
The first analysis relates to implementation of NAFTA. International trade is an
important component of the U.S. fresh fruit and vegetable industry. Under NAFTA, all
agricultural tariffs on trade between the United States, Mexico, and Canada will be
eliminated. As a result, Mexican growers are expected to increase shipments to the
United States as tariffs are eliminated for exports to the United States.
The second analysis relates to a ban on methyl bromide. Methyl bromide has been
a critical soil fumigant used in the production of many agricultural commodities for many
xii
101
0.84% (Table 39), due to the greater impact of NAFTA as opposed to the lower impact
of the methyl bromide in the Los Angeles market.
Cucumbers
Floridas 6,693 baseline acreage of cucumber production in Palm Beach County is
expected to increase to 6,986 acres under the first scenario, to 6,769 acres under the
second scenario, and to 6,829 acres under the third scenario (Table 33). Double
cropping of cucumbers and bell peppers can increase total production of cucumbers in
Florida. Cucumber production in Florida is expected to increase by 4.38% under the first
scenario, by 1.14% under the second scenario, and by 2.04% under the third scenario
(Table 35). Cucumber production in Mexico is expected to increase by 2.26% under
scenario one and to increase by 2.83% under scenarios two and three.
Total shipping point revenues for cucumbers are expected to increase under all
three scenarios; that is, by S917,980 under the first scenario, by $1.4 million under the
second scenario, and by $941,490 under the third scenario (Table 36). Floridas
shipping point revenues for cucumbers are expected to decrease by $79,510 under the
first scenario, to increase by $104,430 under the second scenario, and to decrease by
$302,210 under the third scenario. Table 38 shows that the average wholesale price of
cucumbers is expected to decrease by 0.40%, 0.65%, and 0.36% under these three
scenarios, respectively.
Table 39 shows that the consumer demand of cucumbers is expected to increase in
every market under the first scenario because of the decrease in the price of cucumbers.
Under the second scenario, the consumer demand of cucumbers is expected to increase in
every market. Under the third scenario, the consumer demand of cucumbers in every
107
the greatest potential of being impacted under the first scenario. Florida is a major
supplier of these products, and the methyl bromide ban would adversely affect the
competitive position of Florida in these markets. Much of the lost production would
move to Mexico. In addition, Texas could benefit from increased production of bell
peppers, and South Carolina could benefit from increased production of tomatoes.
The production of strawberries in California would be expected to decrease under
the first scenario, and the production of tomatoes in California would be eliminated under
the second scenario. Even though Texas does not use methyl bromide in the production
of bell peppers, its production of bell peppers would not increase much.
The main new feature of NAFTA was the removal of most of the trade barriers
between Mexico and the United States. As a result, total production in Mexico could
increase by more than 50%. For example, production of tomatoes in California could be
eliminated, while production of tomatoes in Baja could increase by more than 400%.
These losses could devastate U.S. agriculture because much of the lost production would
move to Mexico, especially the production of tomatoes. The consumer demand in every
commodity in every market would increase from the benefit of increased imports from
Mexico under the second scenario.
Mexico would become the major supplier of fresh vegetables because of NAFTA
and the Montreal Protocol agreements, which allow Mexico an additional 10 years to use
methyl bromide. Overall, with the advantage from NAFTA, Mexico will be the primary
beneficiary of the ban on methyl bromide because they will likely use methyl bromide to
increase production. This could cause a large shift in production away from the United
States to Mexico.
118
Laitinen, K., and H. Theil. The Antonelli Matrix and the Reciprocal Slutsky Matrix.
Economics Letters 3(1979): 153157.
MasColell, A., M.D. Whinston, and J.R. Green. Microeconomic Theory. New York:
Oxford University Press, 1995.
Neves, P.D. A Class of Differential Demand Systems. Economics Letters 44(1994):
8386.
Parks, R.W. Systems of Demand Equations: An Empirical Comparison of Alternative
Functional Forms. Econometrica 37(1969):629650.
Samuelson, Paul A. Spatial Price Equilibrium and Linear Programming. The American
Economics Review 42, 3(1952): 283303.
SchiavoCampo, S. International Economics: An Introduction to Theory and Policy.
Cambridge, Massachusetts: Winthrop Publishers, Inc. 1978.
Scott, S.W. International Competition and Demand in the U.S. Fresh Winter Vegetable
Industry. Unpublished M.S. Thesis, University of Florida, Gainesville, 1991.
Smith, S.A., and T.G. Taylor. Production Costs for Selected Florida Vegetables, 2001
2002. Florida Cooperative Extension Service, IFAS, University of Florida, 2002.
Spreen, T.H., J. J. VanSickle, A. E. Moseley, M. S. Deepak, and L. Mathers. Use of
Methyl Bromide and the Economic Impact of its Proposed Ban on the Florida Fresh
Fruit and Vegetable Industry. Technical Bulletin 898, University of Florida,
Gainesville, 1995.
Takayama, T., and G.G. Judge. Spatial and Temporal Price and Allocation Models.
Amsterdam: North Holland Publishing Co., 1971.
Texas Cooperative Extension Service. Cost of Producing Peppers. Texas A&M
University, College Station, 1993.
Theil, H. The Information Approach to Demand Analysis. Econometrica 33(1965):
6787.
Theil, H. Principles of Econometrics. New York: John Wiley & Sons, Inc., 1971.
VanSickle, J.J. Probable Economic Effects of the Reduction or Elimination of U.S.
Tariffs on Selected U.S. Fresh Vegetables. International Agricultural Trade and
Policy Center PBTC 022, University of Florida, Gainesville, May 2002.
VanSickle, J.J., C. Brewster and T.H. Spreen. Impact of a Methyl Bromide Ban on the
U.S. Vegetable Industry. Expansion Statistical Bulletin 333, University of Florida,
Gainesville, February 2000.
14
w, d(ln n,) = hi d(ln Q) + Z\Â¡ h,j d(ln q^, (226)
where
h, = WtQ, (227)
hj = w&j. (228)
As dq = kq*, the scale elasticity, Q, is hÂ¡l wÂ¡. The compensated quantity elasticity
(flexibility), 4, is hy / wÂ¡ with the following properties.
First, the addingup conditions are
X,hi = \, (229)
Z, hy = 0. (230)
Second, the homogeneity condition is
Xjhy = 0. (231)
Third, the symmetry condition is
hy = hji (Antonelli symmetry). (232)
Fourth, the negativity condition is
Z, Zy Xj Wj hy Xj < 0 Xj, Xj constant. (233)
The second functional form of the inverse demand system is the Laitinen and
Theils Inverse Demand System (LaTheil). Following Laitinen and Theil (1979), we
describe the consumers preferences as g(u, q), where g(u, q) is the distance function
which is linearly homogeneous in q. The Antonelli matrix is
A = [ay], CLy = &g! d(p,qÂ¡)d{pjqj). (234)
From this Antonelli matrix, we can find the inverse demand system,
d[ln {pJP)] = Q d(ln Q) + Z7 4 d(ln qÂ¡) + ZWjd(ln qj),
d[ln (Pi/P)] = (4 +1) d(ln Q) + Z7 4 d(ln qj).
89
any costs of returning the truck to the point of origin. Perunit transportation cost can be
calculated from the product of the distance between supply region i to demand region j
and the transportation cost of perunit, permile.
The VanSickle et al. model can determine which regions and which production
systems will achieve the most profit from producing each crop in each month (up to the
point where growers have used all the available land). The model attempts to maximize
producers return and consumers benefits while taking into account the constraint on the
amount of land available in each region (i.e., a demand constraint) and that the amount
sold to consumers cannot be greater than the amount supplied (i.e., a supply constraint).
Therefore, the model finds the equilibrium consumption of each commodity in each
demand region. On the supply side, the model calculates the optimal production in
acreage and the quantity of each commodity produced. This model also finds the optimal
level of shipments. By using these optimal solutions, price, production, and revenue can
be calculated. Altogether, the impacts on consumers, producers, price, production, and
revenue can be investigated using this model.
By assuming that all producers in a particular region use the same production
technology, it also can be assumed that they will have the same yields and costs. The
model uses data on each regions crops, yields, constraints, and marketing windows to
determine which regions and which production systems are best for achieving the most
profit from producing each crop in each month (up to the point where the growers have
used all the available land). The model allows growers to choose which of the four
demand market areas to use, given the different market prices and transportation costs for
each market. The model seeks to maximize producers returns and consumers benefits
47
Table 25. Estimation of the RIDS model for the Los Angeles market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5224
0.1885
0.1517
0.1157
(0.0306)
(0.0211)
(0.0189)
(0.0128)
^Tomato
0.1124
(0.0209)
^Bell Pepper
0.0348
0.0382
(0.0133)
(0.0144)
^Cucumber
0.0500
0.0003
0.0366
(0.0118)
(0.0100)
(0.0120)
^Strawberry
0.0276
0.0037
0.0131
0.0182
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.7011
0.2894
0.2223
0.2804
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 26. Estimation of the AIIDS model for the Los Angeles market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0533
0.0055
0.0053
0.0208
(0.0306)
(0.0211)
(0.0189)
(0.0128)
Yl ornato
0.1318
(0.0209)
Thell Pepper
0.0706
0.1113
(0.0133)
(0.0144)
^Cucumber
0.0342
0.0271
0.0884
(0.0118)
(0.0100)
(0.0120)
^Strawberry
0.0270
0.0137
0.0270
0.0677
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.2349
0.2186
0.1830
0.3226
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
13
inverse demands (which express price as a function of the quantities and specific utility
level),
Pi = dg{u, q) / dqÂ¡ = pÂ¡{u, q).
(219)
Consequently, we can also represent the compensated inverse demands for normalized
prices, Ujpi / m, where E, p,q, = m, by
7ti = p{u, q) / E, \p,(u, q).q] = nÂ¡{u, q). (220)
Next, we find the RIDS by totally differentiating this system of compensated inverse
demand relationships. As nÂ¡ is a function of u and q the total differentiate of n, is
dn, = {dn, / du) du + E7 {dn, / dqj) dqj. (221)
Consider a proportionate increase in q (i.e., dq = kq*) where & is a positive scalar. We can
then transform the term {dnjdu) du to
{dnÂ¡ / du) du = nÂ¡[d{ln n,) / d(ln w)] d(ln u),
(dn, / du) du = n,[d(ln nÂ¡) / d{ln k)){d{ln u) / [d(ln u) / d{ln A:)]},
{dn, / du) du = n,[d{ln n,) / d{ln k)\ {[E, {d{ln u) / d{ln qj) d{ln qj] /
[Ey (3(/ u) / 3(/ ^))]},
(3;r; / 3u) /m = n,[d{ln nÂ¡) / d{ln k)] E7 w7 d(ln qj. (222)
From d;r, = n, d{ln n,), we get the logarithmic version of the RIDS model,
n, d{ln n,) = n,[d{ln nÂ¡) / d{ln A)] E7 vv7 c/(/n <7y) + ^i[Ey<3(/ ^) / 3(/ <Â£,)) J(/
f(/ flÂ¡) = [3(/u ;r,) / 3(/u A:)] E7 w7 t/(/ g7) + E7 [3(/u ;r,) / 3(/ qry)] /(/ qj,
d{ln n,) = tj, d{ln Q) + E, 4 d(ln qj), (223)
where
41 d{ln n,) / 3(/ A:) (the scale elasticity), (224)
4 = d{ln n,) / 3(/ qj) (the compensated quantity elasticity). (225)
In order to satisfy thq symmetry condition, we premultiply both sides by wÂ¡. The RIDS
model now can be written as
w, d(ln n,) = w,4 d{ln Q) + E7 w&j d{ln qj,
xml version 1.0 encoding UTF8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID EO2290A03_UZAZV4 INGEST_TIME 20150401T19:05:06Z PACKAGE AA00029864_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
58
Table 227. Estimation of the LaTheil model for the Chicago market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0210
0.0217
0.0231
0.0193
(0.0231)
(0.0198)
(0.0201)
(0.0129)
^Tomato
0.0234
(0.0138)
^Bell Pepper
0.0143
0.0215
(0.0096)
(0.0111)
^Cucumber
0.0014
0.0111
0.0190
(0.0099)
(0.0086)
(0.0116)
^Strawberry
0.0104
0.0040
0.0092
0.0157
(0.0064)
(0.0057)
(0.0058)
(0.0057)
Standard Error (a)
0.0627
0.0539
0.0546
0.0345
R2
0.0267
0.0191
0.0141
0.0630
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 228. Estimation of the RAIIDS model for the Chicago market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4453
0.2322
0.2496
0.0732
(0.0250)
(0.0201)
(0.0210)
(0.0143)
fl ornato
0.2177
(0.0151)
Thell Pepper
0.0741
0.1415
(0.0100)
(0.0111)
^Cucumber
0.1094
0.0420
0.1678
(0.0105)
(0.0087)
(0.0120)
^Strawberry
0.0341
0.0254
0.0164
0.0759
(0.0071)
(0.0060)
(0.0062)
(0.0063)
Standard Error (a)
0.0679
0.0545
0.0569
0.0383
R2
0.7096
0.5853
0.6146
0.4957
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
64
Table 239. Bartens estimation with the homogeneity condition of the RIDS model for
the Chicago market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4457
0.2194
0.2349
0.0799
(0.0249)
(0.0192)
(0.0191)
(0.0118)
^Tomato
0.0271
0.0054
0.0023
0.0049
(0.0151)
(0.0116)
(0.0116)
(0.0071)
^Bell Pepper
0.0170
0.0181
0.0114
0.0047
(0.0140)
(0.0107)
(0.0107)
(0.0066)
^Cucumber
0.0064
0.0077
0.0173
0.0165
(0.0144)
(0.0111)
(0.0111)
(0.0068)
^Strawberry
0.0165
0.0049
0.0036
0.0167
(0.0111)
(0.0086)
(0.0086)
(0.0053)
Standard Error (a)
0.0668
0.0514
0.0514
0.0321
R2
0.6296
0.4051
0.4404
0.1752
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 240. Bartens estimation with the homogeneity condition of the RIDS model for
the New York market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4678
0.2022
0.2320
0.1147
(0.0204)
(0.0133)
(0.0175)
(0.0095)
^Tomato
0.0216
0.0075
0.0224
0.0102
(0.0127)
(0.0083)
(0.0109)
(0.0059)
^Bell Pepper
0.0067
0.0286
0.0350
0.0008
(0.0128)
(0.0083)
(0.0109)
(0.0059)
^Cucumber
0.0109
0.0148
0.0487
0.0057
(0.0125)
(0.0081)
(0.0107)
(0.0058)
^Strawberry
0.0173
0.0063
0.0087
0.0166
(0.0104)
(0.0068)
(0.0089)
(0.0049)
Standard Error (a)
0.0783
0.0510
0.0669
0.0364
R2
0.7967
0.5880
0.5936
0.5377
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
LIST OF FIGURES
Figure page
31. Aggregate demand and aggregate supply 76
32. Partial equilibrium under effect of the phaseout of methyl bromide 79
33. Partial equilibrium under the effect of tariff 82
34. Partial equilibrium of aggregate demand and aggregate supply 96
xi
ACKNOWLEDGMENTS
I have been very fortunate to work with my supervisory committee, whose
guidance and encouragement were essential to the completion of my research. I would
like to express my deep gratitude and appreciation to the chair of my supervisory
committee, Dr. John VanSickle, for his exceptional advice, patience, and for the financial
support through my graduate study in the Food and Resource Economics Department. I
benefited from many discussions, insightful comments, and ideas from Dr. Edward
Evans. His dedication allowed me to live up to my potential. I would also like to
acknowledge my other committee members (Dr. Allen Wysocki, Dr. Richard Weldon,
and Dr. Chunrong Ai) and Dr. Mark Brown for their concrete ideas and support. Finally,
I would like to thank my wife and my parents for their enduring love and support.
IV
230. Estimation of the AIIDS model for the New York market by using the moving
average of the budget share 59
231. Estimation of the LaTheil model for the New York market by using the moving
average of the budget share 60
232. Estimation of the RAIIDS model for the New York market by using the moving
average of the budget share 60
233. Unconstrained estimation of the RIDS model for the Atlanta market 61
234. Unconstrained estimation of the RIDS model for the Los Angeles market 61
235. Unconstrained estimation of the RIDS model for the Chicago market 62
236. Unconstrained estimation of the RIDS model for the New York market 62
237. Bartens estimation with the homogeneity condition of the RIDS model for the
Atlanta market 63
238. Bartens estimation with the homogeneity condition of the RIDS model for the
Los Angeles market 63
239. Bartens estimation with the homogeneity condition of the RIDS model for the
Chicago market 64
240. Bartens estimation with the homogeneity condition of the RIDS model for the
New York market 64
241. Elasticities for the Atlanta market 65
242. Elasticities for the Los Angeles market 65
243. Elasticities for the Chicago market 66
244. Elasticities for the New York market 66
31. Schedules of the phaseout of methyl bromide 70
32. Effect of the methyl bromide in Florida and California 84
33. Planted acreage in the baseline model, in the methyl bromide ban model, and in
the NAFTA model, by crop and area 108
34. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by area 109
35. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by crop and area 110
IX
CHAPTER 4
SUMMARY AND CONCLUSIONS
Summary
The purpose of an economic impact analysis is to help planners, analysts, and
interested individuals estimate the total economic effect of a change in a particular sector
or industry on a regions output, income earnings, and employment. Our study used a
spatial equilibrium model to investigate the economic impact of NAFTA and the ban on
methyl bromide for fruits and vegetables produced in the United States. Our spatial
equilibrium model satisfies the utilitymaximization condition by using the elasticities
from the inverse demand system (we investigated the method to estimate the inverse
demand system in Chapter 2). The results from Chapter 2 showed that by using the mean
of the budget share to develop the inverse demand model, the estimation of the
elasticities is the same across all functional forms of the inverse demand system. We
estimated the inverse demand system by using Bartens method of estimation with
homogeneity and symmetry constraints imposed. Overall, Chapter 2 provided the
method to estimate the elasticities for selected fruits and vegetables in the U.S. market by
using a model that can obviate the need to choose among the popular functional forms.
Based on the results of the estimated coefficients, the scale effects of all
commodities in every market are statistically significant at the 5% probability level and
they have the expected sign. In terms of own substitution, they all have the expected
sign, according to theory, and they are statistically significant at the 5% probability level
for all commodities in the Atlanta, Los Angeles, and New York markets. Strawberry is
114
24
Econometric Model Development
For the purpose of estimating, operator d is the logchange operator; that is, if x is
any variable and xit is its value in year t, then
d(ln x,) = A (In x) = In xit In x, t.\ = In (x,Â¡ / xit.\). (276)
For the budget share, Barten (1993) replaced w, by the moving average, w*, where
w* = (w/,m + wit) / 2. (277)
As a result, each functional form generates different elasticities. The big disadvantage is
on the coefficients of the demand systems. To solve this problem, we proposed a new
formulation by using the mean of the budget share, w], where
w^'LtWu/T, (278)
where t = 1,T. By using this formulation, each coefficient of the demand systems is a
function of vv( instead of w and the calculated elasticities are expected to be unchanged
across the functional forms.
First, by replacing d(ln nÂ¡) with A(//? nlt), d{ln Q) with A (In Qt), and d(ln qj) with
A (In qj,) in Equation 226, the econometric model development for the RIDS model can
be written as
w, A(/n n,t) = w, Q A {In Q,) + Sy w, fo A (In qjt) + v,
w, A (In nu) hi A {In Q,) + I\Â¡ h0 A (In qj,) + vit, (279)
where
a
ll
(280)
hu = w, 4
(281)
79
Figure 32. Partial equilibrium under effect of the phaseout of methyl bromide
Impact of NAFTA
The most important effect of trading with another nation is the economic gains that
accrue to both parties as a result of trade. Without trade, each country has to make
everything it needs, including those products it is not efficient at producing. On the other
hand, when trade is permitted, each country can concentrate its efforts on producing
exports in exchange for imports. Gains from trade arise from being able to purchase
desired commodities or services from abroad cheaper than it would cost to produce them
at home.
As pointed out by SchiavoCampo (1978), countries trade among themselves
because of differences in factor endowments. An analysis of the impact of different
national endowments of production factors have upon international trade is summarized
in the HeckscherOhlin Theorem. This theorem states that a country has a comparative
advantage in producing commodities with a relatively abundant factor and importing
commodities with a relatively scarce factor. However, there are many barriers to
86
that the slope of the demand function is constant over quantities. The model calculates
total production costs by summing preharvest and postharvest costs. The preharvest
cost is the product of the number of acres planted and the peracre preharvest costs. The
postharvest cost is the product of the number of acres planted, yield, and perunit harvest
and postharvest costs. Alternatives are expected to have impacts on both yield and per
unit cost. Moreover, the model can calculate the transportation cost that is the product of
the quantity of commodity shipped and the perunit transportation cost.
The VanSickle et al. model can be characterized as a spatial equilibrium problem.
By using the following indices the model can be mathematically stated as
region: i = 1index the 12 production points,
crops: k = 1 index the seven crops being considered,
market: j = 1index the four market centers,
production systems: ks = index the 16 production systems,
time: m =1 ,...,M index the 12 months when the crop may be sold.
The demand for these crops is divided into four different markets. The inverse
demand curve is represented for the markets as
Pjkm ~ Qjkm ~ bjkm Qjkmi (31 1)
where Pjkm is the wholesale price per ton for crop k in market j in month m,
Qjkm is the quantity of tons of crop k that is sold in market j in month m,
jkm is the demand curves intercept,
bjkm is the slope of the demand function.
This formulation assumes that the slopes of the demand functions are constant over all
quantities. The model assumes that each regions production is a perfect substitute for
90
while taking into account that there are constraints on the amount of land available in
each region and that the amount sold to consumers cannot be greater than the amount
supplied.
The optimal solution to this model provides the equilibrium consumption of each
commodity in every month for each demand region; the optimal level of shipments
between each supply area and each demand region; the optimal production of each
cropping system, by production area; and the quantity of each commodity produced in
each supply region, by month.
The VanSickle et al. model is simulated by using the profitmaximizing problem to
find the optimal production that satisfies the competitive equilibrium market, given the
inverse demand equation, supply constraint, and demand constraint. From the firstorder
condition, the profitmaximizing condition is satisfied, as the inverse demand equation
equals the total marginal cost (which includes both the marginal cost of production and
the marginal cost of transportation). This model applies elasticities calculated from an
inverse demand system that solves the utilitymaximizing problem (so that the utility
maximizing condition is satisfied). Moreover, the market clearing condition is satisfied
as both supply and demand constraints are binding.
To simplify the model, the VanSickle et al. model is simulated by using the profit
maximizing problem to find the optimal production that satisfies the competitive
equilibrium, Equation 31. The quadratic programming model can be written as
J K 12 I KS
Max Y Y Y \ajkmQjkm(\/2)bjkmQ*jkm\ Â£ Â£ C\iks Wih
j = lk = \m = l i = lks = l
I KS K 12 I J K 12
~ Y Y Y Y C2iksk Zikm Y Y Y Y C3ijianXjjkm
i = \ks = \k = \m = \ z = 1 j = \k \m \
(315)
BIOGRAPHICAL SKETCH
Sikavas NaLampang is a native of Thailand. He earned his Bachelor of
Engineering degree in mechanical engineering, from Chulalongkom University,
Thailand. He later held a design engineer position at the environmental engineering
consulting firm where he designed heating, ventilation, and air conditioning systems for
many commercial and government buildings. In 1996, he enrolled in the Engineering
Management program at the University of Florida. He was awarded his Master of
Engineering degree in industrial and systems engineering, with a specialization in
engineering management, in 1998. In 2000, he began pursuing a Ph.D. in food and
resource economics at the University of Florida. His areas of interest are international
trade and econometrics. While studying in the Food and Resource Economics
Department, he served as a Graduate Research/Teaching Assistant.
120
10
with Walras law: E, p,q, = m. These demand functions follow the neoclassical
restrictions, which include addingup, homogeneity of degree zero in p and m, symmetry
of the matrix of Slutsky substitution effects, and negative semidefiniteness of the matrix
of Slutsky substitution effects. The implied restrictions are most conveniently expressed
in terms of elasticities, which are derivatives of the logarithmic version of the direct
demand functions,
d(ln q,) = 7, d(ln m) + Ey ptJ d(ln pj), i,j = 1,..., n, (22)
where 7, is the income (budget, wealth, total expenditure) elasticity of demand for
commodity i and is defined as
7/ = (dqÂ¡ / dm){m / qÂ¡) = d(ln qÂ¡) / d{ln m), (23)
Py is the uncompensated price elasticity and is defined as
Mij = (dqÂ¡ / dpj)(pj / q,) = d(ln q) / d(ln Pj), (24)
dx is the derivative of variable x, and In x is the natural logarithm of variable x.
The Slutsky, or compensated price, elasticity, %, can be represented in terms of the
uncompensated price and income elasticities using the Slutsky equation,
% = My + Wp (25)
which involves the budget share,
w =PÂ¡ / m. (26)
This compensated price elasticity corresponds to the substitution effect of price changes,
keeping utility constant. These elasticities inherit certain properties from the four
neoclassical restrictions of 7,.
First, the addingup conditions are
E, WjTji = 1 (Engel aggregation),
(27)
59
Table 229. Estimation of the RIDS model for the New York market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4646
0.2118
0.2208
0.1066
(0.0182)
(0.0135)
(0.0169)
(0.0100)
^Tomato
0.0294
(0.0119)
^Bell Pepper
0.0003
0.0255
(0.0072)
(0.0084)
^Cucumber
0.0177
0.0212
0.0406
(0.0095)
(0.0072)
(0.0113)
^Strawberry
0.0120
0.0046
0.0017
0.0184
(0.0058)
(0.0050)
(0.0054)
(0.0054)
Standard Error (a)
0.0745
0.0527
0.0720
0.0413
R2
0.8176
0.6108
0.5146
0.4475
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 230. Estimation of the AIIDS model for the New York market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0041
0.0152
0.0230
0.0076
(0.0186)
(0.0138)
(0.0165)
(0.0103)
/Tomato
0.2047
(0.0124)
/bell Pepper
0.0772
0.1256
(0.0074)
(0.0086)
/Cucumber
0.0879
0.0234
0.1353
(0.0094)
(0.0073)
(0.0110)
/Strawberry
0.0396
0.0251
0.0241
0.0887
(0.0060)
(0.0050)
(0.0054)
(0.0055)
Standard Error (a)
0.0761
0.0545
0.0700
0.0427
R2
0.6377
0.6319
0.4528
0.5514
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
87
that of any other region. Moreover, the model assumes that the price of each commodity
is a function of its own quantity alone and that the price is not affected by other crop
prices and quantities that may be sold in that market in that month.
To compute the inverse demand function, demand flexibilities were based on
wholesale price and arrival data for the various crops. The flexibilities are the
uncompensated own quantity elasticities calculated from the Rotterdam Inverse Demand
System (RIDS). The RIDS model satisfies the utilitymaximizing condition. Using this
information, the parameters for the slope and intercept of the demand equation can be
calculated.
Let = the demand flexibilities for crop k in market j in month m, where
Wjkm = (dPjkm / dQjkm)(Qjkm / Pjkm) (312)
The slope of the inverse demand equation is
 bjkm = (dPjkm / dQjkm),
 bjkm Vjkm (Pjkm / Qjkm) (313)
After bjkm had been calculated, aÂ¡km can be estimated from
Qjkm = Pjkm + bjkm Qjkm (314)
For the supply side, the production points are Florida, California, Mexico, Texas,
South Carolina, Virginia, Maryland, Alabama, and Tennessee. Florida was separated into
four producing areas: Dade County, Palm Beach County, Southwest Florida, and West
Central Florida. Mexico was separated into two producing areas: the states of Sinaloa
and Baja California. California was separated into two producing areas: Southern
California and Northern California. Also, there are 16 cropping systems, which include
both single and double cropping systems. The single cropping systems include tomatoes,
fall tomatoes, spring tomatoes, bell peppers, fall peppers, spring peppers, cucumbers,
110
Table 35. Baseline production and percentage changes in production crops in the methyl
Crop/
Production
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
(Units) (
%
)
Tomatoes
Florida
56,506
(10.86)
(10.35)
(12.16)
California
39,321
(3.30)
(100.00)
(100.00)
Alabama/T ennessee
2,138
(100.00)
(100.00)
(100.00)
South Carolina
6,854
27.44
24.14
25.34
V irginia/Maryland
4,272
(1.64)
(0.52)
(138)
United States
109,091
(7.11)
(41.87)
(42.77)
Mexico
73,786
13.42
64.10
68.50
Total
182,876
1.17
0.89
2.13
Bell PeDDers
Florida
18,172
(9.28)
(0.78)
(8.37)
Texas
7,735
14.02
0.37
10.12
United States
25,907
(2.33)
(0.44)
(2.85)
Mexico
10,282
2.22
2.67
6.99
Total
36,189
(1.04)
0.45
(0.06)
Cucumbers
Florida
4,016
4.38
1.14
2.04
Mexico
5,572
2.26
2.83
2.83
Total
9,588
3.15
2.12
2.50
Squash
Florida
4,395
4.99
1.83
5.11
Mexico
1,518
(0.76)
1.46
1.85
Total
5,913
3.51
1.73
4.27
Eeenlant
Florida
7,457
(3.65)
(1.50)
(4.73)
Mexico
3,352
4.69
5.96
9.75
Total
10,809
(1.07)
0.81
(0.24)
Watermelon
Florida
6,475
(0.76)
2.91
(1.44)
Strawberries
Florida
12,725
3.24
0.00
3.24
California
53,354
(51.62)
0.00
(51.62)
Total
66,079
(41.06)
0.00
(41.06)
Note: MB is abbreviated for Methyl Bromide.
91
subject to
Z/km X djkskm ^iks>
(316)
ks = 1
(317)
/
X Xylan Qjkmi
1 = 1
(318)
Qjkm, wik, Zikm, Xijkm > 0 for all of i,j, k, m, and ks,
where d^km = peracre yield of commodity k in month m from cropping system ks in
supply region i,
Wiks = number of acres planted of cropping system ks in supply region i,
Ukskm = the production of commodity k in supply region i and month m for cropping
system ks,
Cl iksk= per acre preharvest production cost of commodity k using cropping system ks in
supply region i,
Zikm ~ the total supply of commodity k from supply region / in month m,
Qjkm = the total demand of commodity k at demand region j in month m,
C2jksk = perunit harvest and postharvest costs associated with commodity k using
cropping system ks in supply region i,
Xijkm = quantity of commodity k shipped from supply region / to demand region j in
month m,
C3 jkm = perunit transportation cost of commodity k shipped from supply region i to
demand region j in month m.
The inverse demand equation, Equation 311, Price = aÂ¡km bÂ¡km Qjkm
43
0.0366, 0.0189, and 0.0432, respectively. The compensated own substitution quantity
elasticities of cucumbers in the Atlanta, Los Angeles, Chicago, and New York markets
are 0.1754, 0.2500, 0.0726, 0.1709, respectively. The uncompensated own
substitution quantity elasticities of cucumbers in the Atlanta, Los Angeles, Chicago, and
New York markets are 0.3665, 0.4018, 0.3045, 0.4097, respectively.
Strawberries. The obtained estimates for the own substitution quantity effects of
strawberries in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0111,
0.0182, 0.0186, and 0.0164, respectively. The compensated own substitution quantity
elasticities of strawberries in the Atlanta, Los Angeles, Chicago, and New York markets
are 0.1328, 0.1915, 0.1896, 0.1451, respectively. The uncompensated own
substitution quantity elasticities of strawberries in the Atlanta, Los Angeles, Chicago, and
New York markets are 0.2291, 0.3073, 0.2701, 0.2571, respectively.
Conclusions
To get the demand system that satisfies the neoclassical restrictions, we multiply
the budget share by the logarithmic of the demand system. On the empirical estimation,
it is better to use the mean of the budget share, vv,, instead of the moving average of the
budget share, w',, to multiply the logarithmic of the demand system. The results show
the significant effect by using the mean of the budget share on every functional form of
both direct and inverse demand systems. Moreover, by using the mean of the budget
share, we can obviate the need to choose among various functional forms. The results
also show that the estimation of the elasticity and the disturbance of the demand system
are the same across all functional forms of the inverse demand system. Overall, it is
better to use the RIDS model for fruits and vegetables to avoid statistical inconsistencies
63
Table 237. Bartens estimation with the homogeneity condition of the RIDS model for
the Atlanta market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5378
0.1879
0.1881
0.0927
(0.0283)
(0.0181)
(0.0171)
(0.0106)
^Tomato
0.0835
0.0658
0.0190
0.0035
(0.0185)
(0.0118)
(0.0112)
(0.0069)
^Bell Pepper
0.0069
0.0350
0.0122
0.0005
(0.0164)
(0.0105)
(0.0099)
(0.0061)
^Cucumber
0.0505
0.0217
0.0318
0.0168
(0.0177)
(0.0113)
(0.0107)
(0.0067)
^Strawberry
0.0261
0.0091
0.0005
0.0128
(0.0131)
(0.0084)
(0.0079)
(0.0049)
Standard Error (a)
0.0588
0.0376
0.0355
0.0221
R2
0.7136
0.3553
0.3944
0.3275
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 238. Bartens estimation with the homogeneity condition of the RIDS model for
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5184
0.1912
0.1456
0.1159
(0.0305)
(0.0216)
(0.0191)
(0.0130)
^Tomato
0.1150
0.0386
0.0399
0.0278
(0.0209)
(0.0148)
(0.0131)
(0.0089)
^Bell Pepper
0.0146
0.0369
0.0027
0.0035
(0.0229)
(0.0162)
(0.0143)
(0.0098)
^Cucumber
0.0840
0.0085
0.0390
0.0165
(0.0210)
(0.0149)
(0.0132)
(0.0090)
^Strawberry
0.0164
0.0068
0.0036
0.0149
(0.0182)
(0.0129)
(0.0114)
(0.0078)
Standard Error (a)
0.0677
0.0479
0.0424
0.0289
R2
0.7052
0.2905
0.2264
0.2813
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
70
Table 31. Schedules of the phaseout of methyl bromide
Developed Countries
Developing Countries
1991: Base level
199598 average: Base level
1995: Freeze
2002: Freeze
1999: 75% of base
2003: Review of reductions
2001: 50% of base
2005: 80% of base
2003: 30% of base
2005: Phaseout
2015: Phaseout
Source: U.S. Environmental Protection Agency
Four factors need to be considered when selecting and evaluating suitable
alternatives to methyl bromide. The first factor is technical. Methyl bromide is quite
versatile, fairly easy to apply, and can be effective against a wide range of pests (unlike
most other pesticide, fumigant, or pest control methods). U.S. producers may consider
using Integrated Pest Management (IPM) as an alternative to using methyl bromide. IPM
is based on pest identification, and monitoring and establishing pest injury levels.
However, a successful IPM program requires more information, analysis, planning, and
knowhow than does using methyl bromide.
The second factor is economic (the impact of alternatives on the profitability of the
enterprise). While some alternatives may involve a high initial investment cost,
especially considering the operating costs of new equipment, they might actually be more
costeffective in the long run. This is true because the cost for using methyl bromide is
expected to rise in the future. A less effective alternative could be as profitable as using
methyl bromide if the costs for using the alternative are sufficiently lower. For the
economic factor, profitability needs to be examined.
The third factor is health and safety, and the fourth factor is environmental
concerns. Given the heightened awareness of safety and environmental concerns (from
both marketing and environmental perspectives), it is advisable to select alternatives that
84
assumed to have switched to a Telone C17/Devrinol herbicide combination. For
tomatoes, Florida growers were assumed to have switched to a Telone C17/Chloropicirin/
Tillam herbicide combination. For eggplant and bell peppers, Florida growers were
assumed to have switched to a Telone C17/Devrinol herbicide combination. Using
Telone requires additional protective equipment that must be worn by applicators and
field workers. Table 32 shows the impact of these alternatives to methyl bromide on
preharvest cost and yield in each region in Florida and California. Other regions
included in the model were assumed to be producing crops without using methyl
bromide, and therefore would have no effect on costs and yields from the phaseout.
Table 32. Effect of the methyl bromide in Florida and California
State
Region
Preharvest Cost
Impact
($/acre)
Percentage of Yield
Reduction
(%)
Florida
Dade County
(291)
10
Palm Beach County
(115)
5
Southwest Florida
(74)
10
West Central
(139)
5
California
Northern California
653
20
Southern California
653
20
Source: USDA
Next we investigated international trade by changing the production costs for
Mexico to reflect the effect of NAFTA. Our baseline assumed a fixed tariff of S0.1 per
unit of imported commodity, which was added to the postharvest cost of production. We
found that the impact of NAFTA would be the elimination of all such tariffs.
The VanSickle et al. model was solved using GAMS programming software. The
analysis of the impacts from NAFTA and the ban on methyl bromide were conducted in
98
to cease tomato production under the second scenario. Mexico is expected to increase its
tomato producing acreage significantly, especially as a result of NAFTA. For example,
the planted acreage of tomatoes in Baja is expected to increase from 5,369 acres to
27,583 acres (Table 33). The results for Mexico in the third scenario (under both
NAFTA and the ban on methyl bromide) are not significantly different from the second
scenario, since Mexico already enjoys significant gains from NAFTA. South Carolina,
West Central Florida, and Southwest Florida are the only U.S. domestic producers that
are expected to gain under the third scenario.
Results from Table 35 show that total production of tomatoes across all areas in
the United States is expected to decrease by 7.11%, 41.88%, and 42.77% in the first,
second, and third scenarios, respectively. On the other hand, tomato production in
Mexico is expected to increase by 13.42%, 64.10%, and 68.50% in the first, second, and
third scenarios, respectively.
The total revenues that growers receive for tomatoes are expected to decrease by
$1.1 million under the first scenario, to decrease by $3.6 million under the second
scenario, and to increase by $1.6 million under the third scenario (Table 36). Florida
will suffer the greatest loss in tomato shipping point revenues under the first scenario,
with a loss of $56.9 million. California will suffer the greatest loss in tomato shipping
point revenues under the second scenario, with a loss of $286 million. On the other hand,
Mexico will increase their shipping point revenues by $67.2 million under the first
scenario, by $332.7 million under the second scenario, and by $353.7 million under the
third scenario. Two significant conclusions to draw from these results for tomatoes are
that the impact from NAFTA in Mexico is more significant than the impact from the ban
6
phaseout (19942003). For those tariffs phased out over the 10year period, a tariffrate
quota (TRQ), which increased at a 3% compound annual rate, was imposed. For
example, cherry tomatoes have no TRQ because they were on the 5year phaseout
schedule. If tomato imports exceeded the quota, the overquota volume was assessed
tariffs at whichever was lower: the preNAFTA Most Favored Nation (MFN) tariff rate
or the current MFN rate in effect. The tariff on freshmarket tomato imports from
Canada fell to zero in 1998. However, a tariff snapback to the MFN rate can be triggered
by certain price and acreage conditions until 2008.
The phaseout of methyl bromide also disadvantaged U.S. fruit and vegetable
producers. Methyl bromide has been a critical soil fumigant in agricultural production
for many years. While significant progress has been made in developing alternatives to
methyl bromide, no alternative has been identified that permits a seamless transition
(where comparative advantage is minimally impacted by eliminating of methyl bromide
and the affected producers can continue to compete).
Study Overview
Our main objective of this study was to use the spatial equilibrium model to assess
both the impacts of NAFTA and the phaseout of methyl bromide on the fruit and
vegetable industry. To satisfy the utilitymaximization condition, the elasticities used in
the spatial equilibrium model were calculated from the inverse demand system.
Consequently, the second objective was to examine the method of estimation and the
method used to develop the model for the inverse demand system. The specified
objectives are satisfied in twoessay format with the first essay concentrated on the
estimation of the inverse demand system and the second essay concentrated on the spatial
equilibrium analysis.
LIST OF REFERENCES
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Carpenter, J., and L. Lynch. Alternatives to Methyl Bromide in California. Briefing
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Bromide Alternatives Workshop, Sacramento, California, June 1998.
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117
LIST OF TABLES
Table
gage
21. Estimation of the RIDS model for the Atlanta market by using the mean of the
budget share 45
22. Estimation of the AIIDS model for the Atlanta market by using the mean of the
budget share 45
23. Estimation of the LaTheil model for the Atlanta market by using the mean of the
budget share 46
24. Estimation of the RAIIDS model for the Atlanta market by using the mean of the
budget share 46
25. Estimation of the RIDS model for the Los Angeles market by using the mean of
the budget share 47
26. Estimation of the AIIDS model for the Los Angeles market by using the mean of
the budget share 47
27. Estimation of the LaTheil model for the Los Angeles market by using the mean
of the budget share 48
28. Estimation of the RAIIDS model for the Los Angeles market by using the mean
of the budget share 48
29. Estimation of the RIDS model for the Chicago market by using the mean of the
budget share 49
210. Estimation of the AIIDS model for the Chicago market by using the mean of the
budget share 49
211. Estimation of the LaTheil model for the Chicago market by using the mean of
the budget share 50
212. Estimation of the RAIIDS model for the Chicago market by using the mean of
the budget share 50
213. Estimation of the RIDS model for the New York market by using the mean of
the budget share 51
vn
19
When dealing with inverse demands, an interesting question is: how much will
price / change in response to a proportionate increase in all commodities, or how do
prices change as you increase the scale of the commodity vector along a ray radiating
from the origin through a commodity vector? We formalize this notion for marginal
increases in the scale of consumption by defining the scale elasticity to derive restrictions
relating to quantity and scale elasticities. These restrictions show that the scale elasticity
is analogous to total expenditure elasticity, r/Â¡, in direct demands. Let q be a reference
vector in commodity space so that we can represent the consumption vector of interest as
q = kq, where k is a scalar. We can express the inverse demands as
nÂ¡ =f\kq*) = g \k, q'). (258)
The scale elasticity of good / is defined as
Ci = [dg % q ) / dk][k / g % q)l (259)
Quantity and scale elasticities obey restrictions that are directly analogous to restrictions
for direct demands. For the homogeneity of degree zero restriction, we can write
Q^jWXq) /%]<&*[* //'(*)],
Ci = 'Zj[dfi(q)/dqJ][qj/fim
Ci = 2/ Vib (260)
which is analogous to Â£, Â¡Xy = rÂ¡, in the direct demand system.
For the addingup conditions, we start by writing the budget equation, w, = n,q as
Wi=f\q)qÂ¡ (261)
From Â£, w, = 1, we get
*ifXq)q, =1
Differentiating with respect to qj, we have
2/ w\q) / dqj\qt +fXq) = 0,
(262)
42
probability level. In the Los Angeles market, the estimate combination of tomato and
cucumber, the estimate combinations of tomato and bell pepper, and of tomato and
strawberry are statistically significant at the 5% probability level. In the New York
market, the estimate combinations of tomato and cucumber, of tomato and strawberry,
and of cucumber and bell pepper are statistically significant at the 5% probability level.
In the Chicago market, the estimate combination of cucumber and strawberry is
statistically significant at the 5% probability level.
Tomatoes. The obtained estimates for the own substitution quantity effects of
tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0763,
0.1124, 0.0220, and 0.0245, respectively. The compensated own substitution quantity
elasticities of tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are
0.1352, 0.1953, 0.0502, 0.0560, respectively. The uncompensated own substitution
quantity elasticities of tomatoes in the Atlanta, Los Angeles, Chicago, and New York
markets are 0.6778, 0.7178, 0.4990, 0.5138, respectively.
Bell peppers. The obtained estimates for the own substitution quantity effects of
bell peppers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0412,
0.0382, 0.0192, and 0.0284, respectively. The compensated own substitution quantity
elasticities of bell peppers in the Atlanta, Los Angeles, Chicago, and New York markets
are 0.2426, 0.2086, 0.0938, 0.1447, respectively. The uncompensated own
substitution quantity elasticities of bell peppers in the Atlanta, Los Angeles, Chicago, and
New York markets are 0.4204, 0.3971, 0.3165, 0.3416, respectively.
Cucumbers. The obtained estimates for the own substitution quantity effects of
cucumbers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0320,
25
Second, we get the econometric model development for the LaTheil model (which
has the RIDS scale coefficients and the AIIDS quantity coefficients) by adding vv, A {In Q,)
on both sides of the RIDS model (Equation 279),
vv, A (In 7r,i) + vv, A (In Q,) = (vv, <Â£ + iv,) A {In Q,) + X, vv, 4 A {In qjt) + vih
vv [A (In n) + A (In Q,)] = b, A (In Q,) + X, hv A (In qjt) + v,
vv, A [In ipit / Pi)] = b, A(ln Qt) + X7 htJ A(ln qJt) + v, (282)
where
vv, A[/ / P,)] = w, [A(/ /?) A(/ P,)] = vv, [ A(/ n,Â¡i) + A (In Q,)]. (283)
Next, we consider the Almost Ideal Inverse Demand System. We introduce
parameter A (In Q*) for the AIIDS model, where
A (In Q,*) = 7Lj w; A {In qJt).
(284)
By using this parameter, the coefficients of the AIIDS will be the function of vv,, not the
function of vv*,. We get the econometric model development for the AIIDS model from
Equation 245 by replacing dw, with dwlh d(ln Q) with A {In QÂ¡), and d(ln qj) with A (In q^),
dwu = (w,Â£i+ vv,) A (In Q,) + X, (vv, 4 + vv, Sy vv, w*, ) A (In qj,) + v,
dwu + X, vv, vv*, A (In qj,) X7 vv, vv, A (In qji)
= (vv, Q + vv,) A (In Qt) + X7 (vv, 4 + iv, S0 vv, vv,) A (In q) + v,
dw,,+w, [A (In Q,) A (In Q*)] = b, A (In Q,) + X, /0 A (In qj,) + v,
vv, [A (In uu) + A (In q) + A {In Q,) A {In Q*)]
= b, d(ln Q,) + X7 Yij &{ln qJt) + v, (285)
where
dwit = vv, A {In w) = vv, [A(/ n) + A {In q)],
(286)
bi = wl;i+ w,,
(287)
/y= w,4 + w, S,j w, w .
(288)
12
decision maker. In most industrialized economies, the consumer is both a price taker and
a quantity adjuster for most of the products usually purchased. This is suitable with the
regular demand system. On the other hand, for certain goods like fresh vegetables,
supply is very inelastic in the short run, and the producers are virtually price takers.
Pricetaking producers and pricetaking consumers are linked by traders who select a
price they expect to clear in the market. The traders set the prices as a function of the
quantities that are suitable in the inverse demand system.
To apply consumerdemand specifications to the model, the basic results of
consumerdemand theory should be reviewed. From the utilitymaximization problem
for the consumer, we obtained a system of uncompensated inverse demand equations
from the firstorder conditions,
n, = (du / dqÂ¡) / Ey (du / dqj)qj, i = 1, 2,..., n, (217)
where nÂ¡ =pÂ¡/ m is total expenditure or income (m) = E, p,qÂ¡, u is utility, and p, and q, are
price and quantity for good respectively. The budget share (w,j can be found by using
Equation 26 and dx = x[d(ln *)],
w, = [d(ln u) / d(ln qÂ¡)] / Â£, [d(ln u) / d(ln qj)\. (218)
First, we consider the Rotterdam Inverse Demand System (RIDS) by following
Brown et al. (1995). A system of compensated inverse demand relationships can be
found by working with the distance function, which is dual to the utilitymaximization
problem. The distance function indicates the minimum expenditure necessary to attain a
specific utility level, u, at a given quality, q, which can be written as g(u, q). By
differentiating the distance function with respect to quantity, we get the compensated
49
Table 29. Estimation of the RIDS model for the Chicago market by using the mean
the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4488
0.2226
0.2319
0.0805
(0.0246)
(0.0189)
(0.0189)
(0.0118)
^Tomato
0.0220
(0.0142)
^Bell Pepper
0.0125
0.0192
(0.0095)
(0.0105)
^Cucumber
0.0006
0.0088
0.0189
(0.0098)
(0.0081)
(0.0110)
^Strawberry
0.0101
0.0021
0.0107
0.0186
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.6287
0.4029
0.4386
0.1982
of
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 210. Estimation of the AIIDS model for the Chicago market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0113
0.0185
0.0281
0.0178
(0.0246)
(0.0189)
(0.0189)
(0.0118)
Yx ornato
0.2241
(0.0142)
Tbell Pepper
0.0769
0.1433
(0.0095)
(0.0105)
^Cucumber
0.1143
0.0443
0.1735
(0.0098)
(0.0081)
(0.0110)
^Strawberry
0.0329
0.0222
0.0149
0.0700
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.5212
0.4744
0.5653
0.4762
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
55
Table 221. Estimation of the RIDS model for the Los Angeles Market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5534
0.1794
0.1674
0.1031
(0.0309)
(0.0208)
(0.0203)
(0.0138)
^Tomato
0.1184
(0.0213)
^Bell Pepper
0.0425
0.0432
(0.0133)
(0.0147)
^Cucumber
0.0520
0.0008
0.0370
(0.0127)
(0.0106)
(0.0134)
^Strawberry
0.0239
0.0015
0.0141
0.0113
(0.0088)
(0.0078)
(0.0072)
(0.0078)
Standard Error (cr)
0.0687
0.0471
0.0456
0.0309
R2
0.7200
0.2743
0.2378
0.2170
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 222. Estimation of the AIIDS model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0300
0.0006
0.0137
0.0190
(0.0300)
(0.0208)
(0.0196)
(0.0141)
/T ornato
0.1279
(0.0207)
/bell Pepper
0.0639
0.1010
(0.0133)
(0.0150)
/Cucumber
0.0353
0.0255
0.0872
(0.0123)
(0.0105)
(0.0129)
/Strawberry
0.0286
0.0116
0.0263
0.0665
(0.0090)
(0.0080)
(0.0073)
(0.0081)
Standard Error (ct)
0.0668
0.0473
0.0439
0.0317
R2
0.2123
0.1954
0.1721
0.2682
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
116
methyl bromide. In the interim, policy makers should consider programs that can help
growers survive over the short run from these impacts.
Suggestions for Further Research and Limitation of the Study
This study provides useful information for discussion about competition in the
market for tomatoes, bell peppers, cucumbers, squash, eggplant, watermelons, and
strawberries. Other commodities could also benefit from a similar study. Other areas of
research would likely enhance the investigation of competition between Florida and
Mexico and of production results from both areas on the vegetable market.
The primary limitation of the study is the assumption regarding finding alternatives
to using methyl bromide as a preplant fumigant. The development of economically
viable alternative fumigants or alternative nonfumigant production systems would alter
the empirical results of this study. Another limitation of the study is that alternative crops
were not extensively analyzed. The assumption was made that current market conditions
limit the potential for expanding the production of these crops. The process of
identifying and developing successful production systems and markets could be difficult.
In addition, the methodology used to estimate the economic impact of the methyl
bromide ban is deterministic based on average yield and cost of production data. In
reality, there is significant yeartoyear variation in harvested production per acre in fresh
fruit and vegetable production. Variation in crop yields is a result of both weather and
economic factors. The uncertainty faced by fresh fruit and vegetable producers is ignored
in this study.
21
amounts normalized prices change with respect to a marginal change of reference
consumption qj, keeping the consumer on the same indifference level. We can express
the Antonelli substitution effects in elasticity form, which is analogous to the
compensatedprice elasticity, Sy. The constantutilityquantity elasticity of good /' with
respect to good j is defined as
4 = u ) / tyi %]{/ / W{q, u) / dq,]},
4 = (dirt / dq,)(qj / 7Ti). (267)
T(q, u) is homogeneous of degree one in q, and f* (q, ) is homogeneous of degree zero
in q. From the direct application of Eulers theorem, we get
2,4 = 0, (268)
which is analogous to the restriction, X7 Â£y = 0. From the properties of the transformation
function, which include the decrease in u, and the increase, linearhomogeneous, and
concave in q, the matrix of Antonelli effects is negative semidefinite. This implies Sy < 0
, which can be called the Law of Inverse Demand. Next, we describe the implicit
compensation scheme to derive the inverse demand equation, which is analogous of the
Slutsky equation. The total change in prices associated with an increase in one quantity
can be decomposed, as total effect equals the summation of the substitution effect and the
scale effect.
Now, consider a marginal change in the price in response to a marginal change in
relative quantity and in scale. By totally differentiating n, = g '(k, q\ we get
dnt = [dg \k, q") / dq/] dq/ + [dg (k, q*) / dk] dk. (269)
The change in scale must compensate for the change in qj* so as to leave the utility
unchanged, du = 0. With n, = (du / dq,) / X) (du/dqj)qj, we get
35
D\D2 0D\ tY {X'X)A = 0
D2'= [I 0(X'X)A rf\ D\
d2' = [i e{Xxf rf] [(xxy'xY]
D2' = [(X'X)' 0{XXf t (X'X)a] X'Y
D2' = GX'Y, (2134)
where
G = [{X'X)'x 0{X'X)A tt? (X'X)'x] (2135)
and
YG = 0. (2136)
The complete covariance matrix of the ML estimator under the homogeneity condition is
E[(dld)(dld)'] = aG, (2137)
where d1 is a (+2) component vector by arranging the n columns of D2.
Estimation under the symmetry and homogeneity conditions
The symmetry condition, hÂ¡j= hjÂ¡, can also be formulated in terms of d by
rW=Atf^( = 0, (2138)
where d, the n(n + 2) component vector, is formally defined by
ClD')e = d, (2139)
with e being an n component vector of the following structure,
e'=[e\\ e2e], (2140)
and r is a row vector with one in the [(/ 1)( + 1) +j + 1]'* position minus one in the
[(/ 1)( + 1) + / + \]lh position, and otherwise consisting of zeros. There are 0.5( 1)
different symmetry conditions. These will be represented by
Rd= 0, (2141)
where R is a matrix of 0.5n(n 1) rows and n(n + 2) columns. The homogeneity
condition can also be formulated in terms of d by
41
Strawberries. The obtained estimates for the scale effects of strawberries in the
Atlanta, Los Angeles, Chicago, and New York markets are 0.0963, 0.1157, 0.0805,
and 0.1120, respectively. This showed that for a 1% increase in aggregate quantity, the
price for strawberries will decrease by 0.0963%, 0.1157%, 0.0805%, and 0.1120% for the
Atlanta, Los Angeles, Chicago, and New York markets, respectively. The scale
elasticities of strawberries are 1.1526, 1.2194, 0.8188, and 0.9910 in the Atlanta, Los
Angeles, Chicago, and New York markets, respectively (elastic in the Atlanta and Los
Angeles markets, elastic in the Chicago market, and almost unit elastic in the New York
market).
Quantity effect and own substitution quantity elasticity
Quantity effects represent the compensated or substitution effects of quantity
change. These effects show movement along a given indifference surface. These are
converted into quantity elasticities by dividing the quantity effects by the budget share.
The quantity elasticities are analogous to the price elasticities in the direct demand. They
reflect how much the price of good i must change to induce the consumer to absorb more
of good j. The uncompensated quantity elasticities can be calculated by using the
Antonelli equation (Equation292). In an inverse demand system, a negative quantity
effect denotes substitution and a positive quantity denotes complimentarily (the reverse
of the direct demand system). The obtained estimates of the own substitution effects
have the expected sign, and are statistically significant at the 5% probability level for all
commodities in the Atlanta, Los Angeles and New York markets. In the Chicago market,
it is statistically significant only for the own substitution effect of strawberries.
In terns of the quantity effects, in the Atlanta market, the estimate combinations of
tomato and cucumber and of tomato and bell pepper are statistically significant at the 5%
CHAPTER 3
PARTIAL EQUILIBRIUM ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY
This chapter concentrates on the potential impact of two major developments on
the U.S. fruit and vegetable industry. The first development is the proposed phasing out
of using methyl bromide. Methyl bromide is a critical soil fumigant that has been used in
the production of several fresh fruits and vegetables grown in the United States. The U.S.
Clean Air Act of 1992 requires that methyl bromide be phased out of use by 2005. The
problem is that while significant progress has been made towards developing alternatives
to methyl bromide, a suitable alternative has not been identified. The second
development is the elimination of all tariff and trade restrictions on exports of fruits and
vegetables from Mexico as a result of the implementation of the North American Free
Trade Agreement (NAFTA). Under NAFTA, all agricultural tariffs on goods traded
between the United States and Mexico will be eliminated by 2008. Some of the tariffs
were eliminated in 1994, while others were to be phased out over 5, 10, or 15 years. In
addition, negotiations of trade agreements within the World Trade Organization (WTO)
or as part of the Free Trade Area of the Americas (FTAA) could significantly affect these
tariffs. The elimination of tariffs means that U.S. domestic production of fresh fruits and
vegetables is likely to face increased competition from imports.
To assess the impacts of these developments on the U.S. fruit and vegetable
industry, it was essential to develop a partial spatial equilibrium model. Following on a
model developed by VanSickle et al., I modified and improved that model by simplifying
67
115
the only crop that is statistically significant at the 5% probability level in the Chicago
market. In every market, tomato has the highest absolute value of own uncompensated
quantity elasticity, while strawberry has the lowest absolute value. Own substitution
elasticities for tomato and bell pepper are higher in the Atlanta and Los Angeles markets
than they are in the Chicago and New York markets.
In Chapter 3, we investigated the economic impacts of NAFTA and the phaseout of
methyl bromide on the U.S. fruit and vegetable industry by applying the demand
elasticities from Chapter 2 into the VanSickle et al. model. The VanSickle et al. model is
a spatial equilibrium model that satisfies the profitmaximizing condition, utility
maximizing condition, and marketclearing condition. The fruit and vegetable crops that
have been identified as having the most potential for being impacted by a ban on methyl
bromide are tomatoes, bell peppers, eggplant, squash, cucumbers, strawberries, and
watermelons. Mexico is expected to become the major supplier of these crops because of
NAFTA and the Montreal Protocol.
The results from Chapter 3 show that total production of these crops in the United
States is expected to decrease by 34.22% under the third scenario (a combination of
impacts from NAFTA and a ban on methyl bromide). For example, Californias
production could decrease by 72.15% with tomato production ceasing under the second
scenario and strawberry production ceasing under the first scenario. In addition, under
the third scenario, total production in Florida is expected to decrease by 7.6%, while total
production in Mexico is expected to increase by 54.78%.
Knowing the impact these policies will have on Florida and California growers,
policy makers should develop programs that will speed the search for alternatives to
16
In g(u, q) = a0 + Zk a* In qk + (1 /2)Zk 2) ykÂ¡ In qk In qj + ufioFIk qif, (242)
where a yf, p, are the parameters. By using the derivative property of the cost function,
pÂ¡ dg I dqÂ¡ and m = g(u, q), the budget share of good i can be written as
wi= p>qÂ¡ /m
Wi = {dgl dpdpi/ g
wÂ¡ = d(ln g) / d(ln p,). (243)
Hence, from Equation 242, the logarithmic differentiation gives the budget shares as a
function of prices and utility,
wÂ¡ = a, + Zj Yij In qj + b,up0nk qkp, (244)
where yy = (1/2){yy + y,).
As an approximation, we can replace uPoiIk qk with Z, w. In q,. The differential form of
the AIIDS model is
dWi = biZiW, d(ln q,) + Zj ytJ d(ln qj),
dwÂ¡ = bÂ¡ d(ln Q) + Zj yv d(ln qj). (245)
There are four properties for the coefficients of the AIIDS model that satisfy the
neoclassical restrictions. First, the addingup conditions are
2/^ = 0, (246)
Z, bi = 0. (247)
Second, the homogeneous of degree zero is
2, Yij = 0. (248)
Third, the Slutsky symmetry is
Yij = Yj> (249)
Fourth, the negativity condition is
Z, Zj x, Yy Xj < 0 xh Xj constant. (250)
81
foreign supply line S + S/). The product would sell for price Pw. The imports are AB
(which is the difference between total desired consumption and domestic production).
Domestic production is OA, and total quantity demanded is OB. The decrease in price
causes an increase in the consumption and a decrease in domestic production.
Consumers welfare gain is area PwIEdPd, and domestic producers welfare loss is area
PwFEdPd The net gain from trade is area FIEd.
When the domestic country imposes a tariff, the foreign supply is decreased, but
the price of the product is increased. As a result, the market finds its new equilibrium at J
(which is the intersection of domestic demand line Dd and domestic supply plus foreign
supply with tariff line Sd + S/+ T). The product would sell for price Pw+r The increase
in price causes a decrease in the consumption and an increase in the domestic production.
Consumption falls to OD, and domestic production rises to OC. Imports are cut on both
accounts to CD. Consumers welfare loss is area PwIJPw+r, domestic producers welfare
gain is area PWFKPW+T, and tariff revenue effect is area GHJK.
The tariff consumption effect (BD) is related to the price elasticity of demand. A
highly elastic demand indicates that a change in price has a considerable effect on the
amount that people wish to buy. On the other hand, a relatively inelastic demand means
that a price change will lead to only a small change in the quantity demanded. If price
elasticity is zero, the quantity will not change at all, regardless of the magnitude of the
variation in the price of the product.
The effect from NAFTA (which is an agreement between the United States,
Canada, and Mexico to phaseout almost all restrictions on international trade, including
tariffs) will move the equilibrium point back to 7 and the supply line to the right (where
45
Table 21. Estimation of the RIDS model for the Atlanta market by using the mean of the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5427
0.1777
0.1911
0.0963
(0.0287)
(0.0180)
(0.0171)
(0.0106)
^Tomato
0.0763
(0.0181)
^Bell Pepper
0.0475
0.0412
(0.0107)
(0.0104)
^Cucumber
0.0254
0.0037
0.0320
(0.0107)
(0.0075)
(0.0100)
^Strawberry
0.0033
0.0025
0.0103
0.0111
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (a)
0.0600
0.0379
0.0358
0.0221
R2
0.7022
0.3433
0.3840
0.3225
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 22. Estimation of the AIIDS model for the Atlanta market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0216
0.0078
0.0088
0.0127
(0.0287)
(0.0180)
(0.0171)
(0.0106)
Tf ornato
0.1696
(0.0181)
Tbell Pepper
0.0484
0.0998
(0.0107)
(0.0104)
Ttucumber
0.0774
0.0347
0.1171
(0.0107)
(0.0075)
(0.0100)
^Strawberry
0.0438
0.0167
0.0050
0.0655
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (cr)
0.0600
0.0379
0.0358
0.0221
R2
0.3080
0.3304
0.3877
0.4842
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
105
expected to decrease from 10,518 acres to 7,659 acres (Table 33). On the other hand,
the planted acreage of strawberries in Florida is expected to increase from 4,545 acres to
4,692 acres under the first scenario. Total production of strawberries is expected to
decrease by 41.06% under the first scenario (Table 35). The production of strawberries
is expected to decrease by 51.62% in California and to increase by 3.24% in Florida.
Table 36 shows that total shipping point revenues for strawberries are expected to
decrease by $245.4 million, with California suffering a $263.3 million loss in shipping
point revenues. The average wholesale price of strawberries is expected to increase by
12.78% (Table 38). Consumer demand for strawberries in every market is expected to
decrease under the impact of the methyl bromide ban, with the highest decrease in the
Atlanta market at 66.57% (Table 39).
Aggregate impacts
Total production of the fruits and vegetables included in this model is expected to
decrease by 7.97% under the first scenario, to increase by 0.08% under the second
scenario, and to decrease by 7.26% under the third scenario (Table 34). Consequently,
consumer surplus is expected to decrease under the first and third scenarios and to
increase under the second scenario.
Total production in the United States is expected to decrease by 16.21 % under the
first scenario, by 21.93% under the second scenario, and by 34.22% under the third
scenario (Table 34). California is expected to suffer the greatest loss in production.
Tomato production in California is expected to cease under the second scenario, and
strawberry production in California is expected to cease under the first scenario. Total
production in California is expected to decrease by 31.12% under the first scenario, by
42.43% under the second scenario, and by 72.15% under the third scenario. On the other
77
equilibrium, then this allocation is Pareto optimal (which is the first fundamental theorem
of welfare economics). A differential change (dx\,..., dxÂ¡, dq\,..., dqj) in the quantities of
good g (consumed and produced) satisfies dx E, dx, = Ey dqj (since x = q, Equation 34).
The change in aggregate Marshallian surplus is then
dS = P(x) E, dx, C'(q) Ey dqj,
dS=[P(x)C'(x)]dx. (36)
It is sometimes of interest to distinguish between the two components of aggregate
Marshallian surplus that accrue directly to consumers and producers. That is, if the set of
active consumers of good g is distinct from the set of producers, then this distinction
demonstrates something about the distributional effects of the change in the level of
social welfare. There is a change in aggregate consumer surplus when consumers face
effective price p and aggregate consumption jc( p), which is
dCS(p) = [P(x)~ p]dx. (37)
There is also a change in aggregate producer surplus when firms face effective price, p,
and aggregate production q{ p), which is
dfKp) = [p C\q)] dq = [p C\x)] dx. (38)
We can see that the change in aggregate Marshallian surplus is the summation of the
change in aggregate consumer surplus and the change in aggregate producer surplus,
which can be written as
dS = dCS(p) + dn(p). (39)
We can also integrate Equation 39 to express the total value of the aggregate
Marshallian surplus, the aggregate consumer surplus, and the aggregate producer surplus.
By doing this, we get
62
Table 235. Unconstrained estimation of the RIDS model for the Chicago market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.3565
0.1354
0.2338
0.0799
(0.1251)
(0.0963)
(0.0964)
(0.0118)
^Tomato
0.0649
0.0301
0.0018
0.0049
(0.0541)
(0.0416)
(0.0416)
(0.0071)
^Bell Pepper
0.0033
0.0372
0.0111
0.0047
(0.0312)
(0.0240)
(0.0240)
(0.0066)
^Cucumber
0.0291
0.0137
0.0176
0.0165
(0.0344)
(0.0265)
(0.0265)
(0.0068)
^Strawberry
0.0074
0.0036
0.0035
0.0167
(0.0167)
(0.0129)
(0.0129)
(0.0053)
Standard Error (a)
0.0667
0.0513
0.0514
0.0316
R2
0.6306
0.4074
0.4404
0.2036
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 236. Unconstrained estimation of the RIDS model for the New York market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5173
0.2015
0.1055
0.0943
(0.0746)
(0.0486)
(0.0632)
(0.0347)
^Tomato
0.0008
0.0073
0.0306
0.0016
(0.0327)
(0.0213)
(0.0277)
(0.0152)
^Bell Pepper
0.0060
0.0288
0.0026
0.0044
(0.0223)
(0.0146)
(0.0189)
(0.0104)
^Cucumber
0.0233
0.0146
0.0803
0.0006
(0.0218)
(0.0142)
(0.0185)
(0.0101)
^Strawberry
0.0235
0.0062
0.0246
0.0192
(0.0138)
(0.0090)
(0.0117)
(0.0064)
Standard Error (a)
0.0782
0.0510
0.0662
0.0363
R2
0.7972
0.5880
0.6020
0.5386
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
U
Sickle, Chair
of Food and Resource Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequatg^in scope and quality, as a
dissertation for the degree of Doctor of Philosopf
Edward A.
Assistant Professor of Food and Resource
Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Richard N. Weldon
Associate Professor of Food and Resource
Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Aill 71^0^
Allen F. Wysocki
Assistant Professor of Food and Resource
Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Chunrong Ai
Associate Professor of Economics
85
two parts. Our study updated the VanSickle et al. model to the 2000/2001 production
season by using updated data and quantity elasticities estimated from the inverse demand
analysis. This solution provided the baseline for comparison to other solutions where the
parameters of the model were adjusted to reflect the impacts of NAFTA and the ban on
methyl bromide.
For the first part of the analysis, the model was solved with parameters that
assumed continued use of the tariff and methyl bromide. For the second part of the
analysis, three scenarios beyond the baseline were solved with the model. The first
scenario assumed the next best alternative, given projections on expected cost and yield
impacts. The second scenario gave projections on the postharvest production cost that
was reduced for Mexico from the elimination of tariffs. The third scenario combined the
impacts of NAFTA and the ban on methyl bromide. The adjustments that were made in
the parameters reflect changes in production costs and yield by switching to alternatives
to methyl bromide and changes in postproduction costs for Mexico by switching to non
tariff trade.
The VanSickle et al. model was developed by modifying the North American
winter vegetable market model developed by Spreen et al. (1995). For the demand side
of the model, the commodities were assumed to be shipped to one of four demand regions
of the United States, including the northeast, southeast, midwest, and west. These
demand regions were represented by the New York City, Atlanta, Chicago, and Los
Angeles wholesale markets, respectively. The commodities in the model were tomatoes,
bell peppers, cucumbers, squash, eggplant, watermelon, and strawberries. There is an
inverse demand equation for each commodity in each demand region with an assumption
IMPACT OF SELECTED REGULATORY POLICIES ON
THE U.S. FRUIT AND VEGETABLE INDUSTRY
By
SIKAVAS NALAMPANG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2004
Copyright 2004
by
Sikavas NaLampang
This work is dedicated to my parents and my wife.
ACKNOWLEDGMENTS
I have been very fortunate to work with my supervisory committee, whose
guidance and encouragement were essential to the completion of my research. I would
like to express my deep gratitude and appreciation to the chair of my supervisory
committee, Dr. John VanSickle, for his exceptional advice, patience, and for the financial
support through my graduate study in the Food and Resource Economics Department. I
benefited from many discussions, insightful comments, and ideas from Dr. Edward
Evans. His dedication allowed me to live up to my potential. I would also like to
acknowledge my other committee members (Dr. Allen Wysocki, Dr. Richard Weldon,
and Dr. Chunrong Ai) and Dr. Mark Brown for their concrete ideas and support. Finally,
I would like to thank my wife and my parents for their enduring love and support.
IV
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iv
LIST OF TABLES vii
LIST OF FIGURES xi
ABSTRACT xii
CHAPTER
1 INTRODUCTION 1
Overview of the Fruit and Vegetable Industry 1
Study Overview 6
2 DEMAND ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY 7
Problematic Situation 7
Hypothesis 8
Objectives 8
Conceptual Framework 9
Inverse Demand Model 9
Scale and Quantity Comparative Statics 18
Econometric Model Development 24
Methodology for Demand Analysis 28
Seemingly Unrelated Regressions Model 29
Bartens Method of Estimation 31
Unconstrained estimation 33
Estimation under the homogeneity condition 34
Estimation under the symmetry and homogeneity conditions 35
Empirical Results 37
Inverse Demand System Analysis 38
Elasticity Analysis 39
Scale effect and scale elasticity 39
Quantity effect and own substitution elasticity 41
Conclusions 43
v
3 PARTIAL EQUILIBRIUM ANALYSIS ON FRUIT AND VEGETABLE
INDUSTRY 67
Background 68
Research Problem 72
Hypotheses 73
Objectives 73
Theoretical Framework 73
Fundamental Theory of the Partial Equilibrium Model 76
Impact of the Phaseout of Methyl Bromide 78
Impact of NAFTA 79
Methodology 82
Empirical Results 97
Tomatoes 97
Bell peppers 99
Cucumbers 101
Squash 102
Eggplant 103
Watermelons 103
Strawberries 104
Aggregate impacts 105
Conclusions 106
4 SUMMARY AND CONCLUSIONS 114
Summary 114
Suggestions for Further Research and Limitation of the Study 116
LIST OF REFERENCES 117
BIOGRAPHICAL SKETCH 120
vi
LIST OF TABLES
Table
gage
21. Estimation of the RIDS model for the Atlanta market by using the mean of the
budget share 45
22. Estimation of the AIIDS model for the Atlanta market by using the mean of the
budget share 45
23. Estimation of the LaTheil model for the Atlanta market by using the mean of the
budget share 46
24. Estimation of the RAIIDS model for the Atlanta market by using the mean of the
budget share 46
25. Estimation of the RIDS model for the Los Angeles market by using the mean of
the budget share 47
26. Estimation of the AIIDS model for the Los Angeles market by using the mean of
the budget share 47
27. Estimation of the LaTheil model for the Los Angeles market by using the mean
of the budget share 48
28. Estimation of the RAIIDS model for the Los Angeles market by using the mean
of the budget share 48
29. Estimation of the RIDS model for the Chicago market by using the mean of the
budget share 49
210. Estimation of the AIIDS model for the Chicago market by using the mean of the
budget share 49
211. Estimation of the LaTheil model for the Chicago market by using the mean of
the budget share 50
212. Estimation of the RAIIDS model for the Chicago market by using the mean of
the budget share 50
213. Estimation of the RIDS model for the New York market by using the mean of
the budget share 51
vn
214. Estimation of the AIIDS model for the New York market by using the mean of
the budget share 51
215. Estimation of the LaTheil model for the New York market by using the mean
of the budget share 52
216. Estimation of the RAIIDS model for the New York market by using the mean
of the budget share 52
217. Estimation of the RIDS model for the Atlanta market by using the moving
average of the budget share 53
218. Estimation of the AIIDS model for the Atlanta market by using the moving
average of the budget share 53
219. Estimation of the LaTheil model for the Atlanta market by using the moving
average of the budget share 54
220. Estimation of the RAIIDS model for the Atlanta market by using the moving
average of the budget share 54
221. Estimation of the RIDS model for the Los Angeles Market by using the moving
average of the budget share 55
222. Estimation of the AIIDS model for the Los Angeles market by using the moving
average of the budget share 55
223. Estimation of the LaTheil model for the Los Angeles market by using the
moving average of the budget share 56
224. Estimation of the RAIIDS model for the Los Angeles market by using the
moving average of the budget share 56
225. Estimation of the RIDS model for the Chicago market by using the moving
average of the budget share 57
226. Estimation of the AIIDS model for the Chicago market by using the moving
average of the budget share 57
227. Estimation of the LaTheil model for the Chicago market by using the moving
average of the budget share 58
228. Estimation of the RAIIDS model for the Chicago market by using the moving
average of the budget share 58
229. Estimation of the RIDS model for the New York market by using the moving
average of the budget share 59
vm
230. Estimation of the AIIDS model for the New York market by using the moving
average of the budget share 59
231. Estimation of the LaTheil model for the New York market by using the moving
average of the budget share 60
232. Estimation of the RAIIDS model for the New York market by using the moving
average of the budget share 60
233. Unconstrained estimation of the RIDS model for the Atlanta market 61
234. Unconstrained estimation of the RIDS model for the Los Angeles market 61
235. Unconstrained estimation of the RIDS model for the Chicago market 62
236. Unconstrained estimation of the RIDS model for the New York market 62
237. Bartens estimation with the homogeneity condition of the RIDS model for the
Atlanta market 63
238. Bartens estimation with the homogeneity condition of the RIDS model for the
Los Angeles market 63
239. Bartens estimation with the homogeneity condition of the RIDS model for the
Chicago market 64
240. Bartens estimation with the homogeneity condition of the RIDS model for the
New York market 64
241. Elasticities for the Atlanta market 65
242. Elasticities for the Los Angeles market 65
243. Elasticities for the Chicago market 66
244. Elasticities for the New York market 66
31. Schedules of the phaseout of methyl bromide 70
32. Effect of the methyl bromide in Florida and California 84
33. Planted acreage in the baseline model, in the methyl bromide ban model, and in
the NAFTA model, by crop and area 108
34. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by area 109
35. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by crop and area 110
IX
36. Baseline revenues and changes in revenues from the methyl bromide ban effect
and the NAFTA effect, by crop and area Ill
37. Baseline revenues and changes in revenues from the methyl bromide ban effect
and the NAFTA effect, by area 112
38. Baseline average prices and percentage changes in prices from the methyl
bromide ban effect and the NAFTA effect, by crop 112
39. Baseline demand and percentage changes in demand from the methyl bromide
ban effect and the NAFTA effect, by crop and market 113
x
LIST OF FIGURES
Figure page
31. Aggregate demand and aggregate supply 76
32. Partial equilibrium under effect of the phaseout of methyl bromide 79
33. Partial equilibrium under the effect of tariff 82
34. Partial equilibrium of aggregate demand and aggregate supply 96
xi
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
IMPACT OF SELECTED REGULATORY POLICIES ON
THE U.S. FRUIT AND VEGETABLE INDUSTRY
By
Sikavas NaLampang
August 2004
Chair: John J. VanSickle
Major Department: Food and Resource Economics
The United States is one of the worlds leading producers and consumers of fruit
and vegetables. Fruit and vegetable production occurs throughout the United States, with
the largest fresh fruit and vegetable acreage in California, Florida, and Texas. Our study
used the spatial equilibrium model to determine the expected economic impacts of the
North America Free Trade Agreement (NAFTA) and the phaseout of methyl bromide in
the U.S. fruit and vegetable industry.
The first analysis relates to implementation of NAFTA. International trade is an
important component of the U.S. fresh fruit and vegetable industry. Under NAFTA, all
agricultural tariffs on trade between the United States, Mexico, and Canada will be
eliminated. As a result, Mexican growers are expected to increase shipments to the
United States as tariffs are eliminated for exports to the United States.
The second analysis relates to a ban on methyl bromide. Methyl bromide has been
a critical soil fumigant used in the production of many agricultural commodities for many
xii
years. The U.S. Clean Air Act of 1992, as amended in 1998, requires that methyl
bromide be phased out of use by 2005. While significant progress has been made in
developing alternatives to methyl bromide, no alternative has been identified that permits
a seamless transition (where comparative advantage is minimally impacted by the
elimination of methyl bromide, and the affected producers continue to compete with
other producers).
To satisfy the utilitymaximization condition, the elasticities used in the spatial
equilibrium model are calculated from the popular functional forms of the inverse
demand system. Demand analyses can be very sensitive to the chosen functional forms.
Our study addresses this concern by proposing a formulation that obviates the need to
choose among various functional forms of the inverse demand system.
Results of the spatial equilibrium analysis indicate that total production in the
United States is expected to decrease after the implementation of NAFTA and the ban on
methyl bromide. Mexico is expected to become a larger supplier of vegetables in the
United States.
xiu
CHAPTER 1
INTRODUCTION
Overview of the Fruit and Vegetable Industry
The United States is one of the worlds leading producers and consumers of fruits
and vegetables. According to the U.S. Department of Agriculture, farmers earned $17.7
billion from the sale of fruits and vegetables in 2002. Annual percapita use of fruits and
vegetables rose 7% from 19901992 to 20002002, reaching 442 pounds as fresh
consumption increased and processed consumption fell. Consumer expenditures for
fruits and vegetables are growing faster than any food group (except meats).
The United States harvested 1.4 million tons of fruits and vegetables in 1999 (a
20% increase from 1990). Even though output has been rising, aggregate fruit and
vegetable acreage has been relatively stable, indicating increasing production per acre.
The major source of higher yields has been the introduction of more prolific hybrid
varieties, many of which exhibit improved disease resistance and improved fruit set.
Shifting from lessproductive areas to higheryielding areas has also contributed to higher
U.S. yields over time. Fruit and vegetable output will likely continue to rise faster than
population growth over the next decade because of increasing consumer demand and
concerns about health and nutrition.
Fruit and vegetable production occurs throughout the United States, with the largest
fresh fruit and vegetable acreage in California, Florida, Georgia, Arizona, and Texas.
California and Florida produce the largest selection and quantity of fresh vegetables.
Climate causes most domestic fruit and vegetable production to be seasonal, with the
1
2
largest harvests occurring during the summer and fall. Imports supplement domestic
supplies, especially fresh products during the winter, resulting in increased choices for
consumers. For example, Florida produces the majority of its domestic warmseason
vegetables, such as fresh tomatoes, during the winter and spring, while California
produces the bulk of its domestic output in the summer and fall. Freshtomato imports,
primarily from Mexico, boost total supply during the first few months of the year, and
compete directly with winter and early spring production from Florida. In value terms,
Mexico supplies more than half (61%) of all the fruit and vegetable imports to the United
States, with the majority being freshmarket vegetables. Canada is the second leading
foreign supplier, with about 27% of the U.S. import market. Because of their obvious
transportation advantages, Mexico and Canada have historically been the top two import
suppliers to the United States. In value terms, fresh fruits and vegetables account for the
largest share of fruit and vegetable imports, with about $2 billion in 1999. There is a
definite seasonal pattern to U.S. fresh vegetable imports, with twothirds of the import
volume arriving between December and April (when U.S. production is low and is
limited to the southern portions of the country). Most of these imports are tender warm
season vegetables such as tomatoes, peppers, squash, and cucumbers.
The United States is one of the worlds leading producers of tomatoes, ranking
second only to China. California and Florida make up almost twothirds of the acreage
used to grow fresh tomatoes in the United States. Fresh tomatoes lead in farm value
($920 million in 1999), along with lettuce and potatoes. U.S. freshtomato production
steadily increased until 1992, when it peaked. Production then trended downward.
Declines reflected sharply rising imports, weather extremes (excessive rains, wind, and
3
frost for several years), and increased competition from rapidly expanding greenhouse
tomato growers. Peracre yields for fresh tomatoes were off substantially in 1995 and
1996 from freezes, heavy rain, and low market prices. Severe flooding in Mexico sharply
reduced its production and its exports to the United States. A smaller volume of imports
and higher prices prompted Florida growers to harvest fields more intensively, resulting
in recordhigh yields in Florida.
Although acreage has decreased over the past decade, Florida remains the leading
domestic source of fresh tomatoes. Florida produced 42% of U.S. fresh tomatoes from
1997 through 1999. Floridas season (October to June) has the greatest production in
April and May and again from November to January. The leading counties are Collier,
Manatee, and Dade. Tomatoes, one of the highestvalued crops in Florida, bring in one
third of the states vegetable cash receipts and 7% of all its agricultural cash receipts. As
a result of decreased production in the northern states, Florida was able to increase its
percentage of the U.S. domestic output from about 25% in 1960 to 42% in 1999.
Because of higher prices during the winter, Florida accounts for 43% of the total value of
the U.S. freshtomato crop.
California is the secondlargest tomatoproducing state, accounting for 31 % of the
fresh crop. Fresh tomatoes are produced across many counties in each season, except
winter, with San Diego (spring and fall) and Fresno (summer) accounting for about
onethird of the crop. Other important tomatoproducing states in 1999 included
Virginia, Georgia, Ohio, South Carolina, Tennessee, North Carolina, and New Jersey.
International trade is an important component of the U.S. freshtomato industry.
The United States imported 32% of the fresh tomatoes it consumed in 1999 (up from
4
19% in 1994), and exported 7% of its annual crop. The percentage imported rose steadily
after 1993 until low domestic prices discouraged imports in 1999. The United States, as
a net importer of fresh tomatoes, had a tomato trade deficit in 1999 of $567 million.
Mexico and Canada are important suppliers of freshtomatoes to the United States.
Freshtomato imports mostly arrive from Mexico (about 83% in 1999).
Over the past two decades, the demand for bell peppers has been rising, reaching a
record high in 2000. The United States is one of the worlds biggest producers of bell
peppers, ranking sixth behind China, Mexico, Turkey, Spain, and Nigeria. Because of
strong demand, U.S. growers harvested 12% more bell pepper acreage in 2000 than in
1999. Bell peppers are produced and marketed yearround, with the domestic market
peaking during May and June, and the import market peaking during the winter months.
Although bell peppers are grown in 48 states, the U.S. industry is largely concentrated in
California, Florida, and Texas. Trade plays an important role in the U.S. fresh bellpepper
market, with about 20% of fresh bell peppers coming from Canada and Mexico.
Originating in India, cucumbers were brought to the United States by Columbus,
and have been grown here for several centuries. The United States produces 3% of the
worlds cucumbers, ranking fourth behind China, Turkey, and Iran. U.S. freshcucumber
production reached a record high in 1999, but has trended lower since. Florida and
Georgia are the leading states in the production of freshmarket cucumbers. Fresh
cucumber prices are the highest from January through April because of limited domestic
supplies and higher production costs, and are the lowest in June when supplies are
available from many areas. As a result, imports are strongest in January and February
when U.S. production is limited by cool weather, and are the weakest in summer during
5
the height of the domestic season. Imports accounted for 45% of U.S. freshcucumber
consumption from 2001 through 2003, with most of the imports coming from Mexico and
Canada.
Cultivated for thousands of years, watermelon is thought to have originated in
Africa, and to have made its way to the United States with African slaves and European
colonists. The United States ranks fourth in the worlds watermelon production. Florida
is the leading domestic source of fresh watermelon, followed by Texas, California,
Georgia, and Arizona. Although value and production have been rising, the acreage
devoted to watermelon has been trending lower over the past few decades. During the
most recent decade, declining acreage has been due to a combination of rising peracre
yields and successive years of freeze damage in Florida and drought in Texas. Most
watermelon is consumed fresh, even though there are several processed products in the
market such as roasted seeds, pickled rind, and watermelon juice. Percapita
consumption of watermelon is highest in the West and lowest in the South.
In 1995 and 1996, fresh fruit and vegetable imports to the United States surged due
to the combined effects of the devaluation of the Mexican peso, the rising demand for
improved extended shelflife varieties, and reduced domestic output due to adverse
weather conditions. Florida and Mexico historically compete for the U.S. winter and
early spring market. For example, Mexico dominates the market in the winter (when
southern Florida is the predominant U.S. producer), and Florida dominates the market
during the spring (when Mexican production seasonally declines). Another factor has
been NAFTA. Under NAFTA, some of the tariffs on freshmarket tomatoes from
Mexico were phased out over a 5year period (19941998), while others had a 10year
6
phaseout (19942003). For those tariffs phased out over the 10year period, a tariffrate
quota (TRQ), which increased at a 3% compound annual rate, was imposed. For
example, cherry tomatoes have no TRQ because they were on the 5year phaseout
schedule. If tomato imports exceeded the quota, the overquota volume was assessed
tariffs at whichever was lower: the preNAFTA Most Favored Nation (MFN) tariff rate
or the current MFN rate in effect. The tariff on freshmarket tomato imports from
Canada fell to zero in 1998. However, a tariff snapback to the MFN rate can be triggered
by certain price and acreage conditions until 2008.
The phaseout of methyl bromide also disadvantaged U.S. fruit and vegetable
producers. Methyl bromide has been a critical soil fumigant in agricultural production
for many years. While significant progress has been made in developing alternatives to
methyl bromide, no alternative has been identified that permits a seamless transition
(where comparative advantage is minimally impacted by eliminating of methyl bromide
and the affected producers can continue to compete).
Study Overview
Our main objective of this study was to use the spatial equilibrium model to assess
both the impacts of NAFTA and the phaseout of methyl bromide on the fruit and
vegetable industry. To satisfy the utilitymaximization condition, the elasticities used in
the spatial equilibrium model were calculated from the inverse demand system.
Consequently, the second objective was to examine the method of estimation and the
method used to develop the model for the inverse demand system. The specified
objectives are satisfied in twoessay format with the first essay concentrated on the
estimation of the inverse demand system and the second essay concentrated on the spatial
equilibrium analysis.
CHAPTER 2
DEMAND ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY
Demand analyses can be very sensitive to chosen functional forms. Since no one
specification best fits all data, researchers have been preoccupied with finding ways to
select among various functional forms. Our study addresses this concern by proposing a
formulation that obviates the need to choose among the various functional forms of the
demand system. This approach was tested using four functional forms of the inverse
demand system: the Rotterdam Inverse Demand System, the Laitinen and Theils Inverse
Demand System, the Almost Ideal Inverse Demand System, and the Rotterdam Almost
Ideal Inverse Demand System.
Problematic Situation
Several studies in the past have considered the issue of how to choose among
popular functional forms when conducting demand analyses. Parks (1969) used the
average information inaccuracy concept. A relatively high average inaccuracy is taken to
be an indicator of lesssatisfactory behavior. Deaton (1978) applied a nonnested test to
compare demand systems with the same dependent variables. However, this procedure is
not suitable when comparing models with different dependent variables (as in the case of
comparing the Almost Ideal Demand System with the Rotterdam Demand System).
Barten (1993) developed a method that can deal with nonnested models with
different dependent variables. Briefly, the method starts with a hypothetical general
model as a matrixweighted linear combination of two or more basic models. A solution
is found for one of the dependent variables, followed by estimating consistently the
7
8
transformed matrix weights associated with the other models. Next, statistical tests are
carried out on the matrix weights to determine whether they are significantly different
from zero. This matrixweighted linear combination can be considered a synthetic
demandallocation system (which, under appropriate restrictions, yields different forms
of the demand system). The synthetic model can therefore be used to statistically test
which model best fits a particular data set. One drawback in applying this procedure is
that it is necessary to impose a set of restrictions for the purpose of estimating. For
example, the differentials need to be replaced by finite first differences, and the budget
share needs to be replaced by its moving average. As a result, each functional form
generates a different result.
Hypothesis
Our main hypothesis is that if the theoretical elasticities from the demand system in
the theory are the same across all functional forms, then the empirical results of the
elasticities from the demand system should also be the same across all functional forms.
Objectives
Our primary objective was to propose a formulation that obviates the need to
choose among the popular functional forms when conducting a demand analysis and to
empirically test this formulation using data on selected fruits and vegetables. The goal
was to verify that the elasticities are the same across every functional form of the demand
system. The secondary objective was to analyze the elasticities calculated from the
coefficients of the inverse demand system.
9
Conceptual Framework
Inverse Demand Model
Barten and Bettendorf (1989) investigated the demand for fish by using the
Rotterdam Inverse Demand System, which expresses relative or normalized prices as a
function of total real expenditure and quantities of all goods. The Rotterdam Inverse
Demand System is the inverse analog of the regular Rotterdam Demand System. From
an empirical viewpoint, inverse and direct demand systems are not equivalent. To avoid
statistical inconsistencies, the righthand side variables in the systems should not be
controlled by the decision maker. Therefore, it is better to use the inverse demand system
for fresh fruits and vegetables.
It will be helpful to recall the consumer theory about ordinary direct demand
functions derived from budgetconstrained utility maximization. Types of consumer
theory leading to systems of demand functions were summarized by Barten (1993),
Deaton and Muellbauer (1980), and Theil (1965). Consumers pay p,q, for the desired
amounts of commodity where p, is the price of good i and q, is the quantity of good /.
These expenditures satisfy the budget equation, I, pÂ¡qÂ¡ = m, where m is the total budget of
the consumers allocation. The consumers problem is to satisfy the budget constraint by
selecting the quantities that maximize the utility function. This consumer problem can be
stated as the utility maximization problem. It can be shown that under the appropriate
form of the utility function, there exists a unique set of optimal quantities that maximize
the utility function (subject to the budget constraint) for any set of given positive prices
and income. These optimal quantities of income and prices are the Marshallian
(Walrasian) demand functions,
qÂ¡ =f(m,pi,...,pn),
(21)
10
with Walras law: E, p,q, = m. These demand functions follow the neoclassical
restrictions, which include addingup, homogeneity of degree zero in p and m, symmetry
of the matrix of Slutsky substitution effects, and negative semidefiniteness of the matrix
of Slutsky substitution effects. The implied restrictions are most conveniently expressed
in terms of elasticities, which are derivatives of the logarithmic version of the direct
demand functions,
d(ln q,) = 7, d(ln m) + Ey ptJ d(ln pj), i,j = 1,..., n, (22)
where 7, is the income (budget, wealth, total expenditure) elasticity of demand for
commodity i and is defined as
7/ = (dqÂ¡ / dm){m / qÂ¡) = d(ln qÂ¡) / d{ln m), (23)
Py is the uncompensated price elasticity and is defined as
Mij = (dqÂ¡ / dpj)(pj / q,) = d(ln q) / d(ln Pj), (24)
dx is the derivative of variable x, and In x is the natural logarithm of variable x.
The Slutsky, or compensated price, elasticity, %, can be represented in terms of the
uncompensated price and income elasticities using the Slutsky equation,
% = My + Wp (25)
which involves the budget share,
w =PÂ¡ / m. (26)
This compensated price elasticity corresponds to the substitution effect of price changes,
keeping utility constant. These elasticities inherit certain properties from the four
neoclassical restrictions of 7,.
First, the addingup conditions are
E, WjTji = 1 (Engel aggregation),
(27)
11
X, WiHij = Wj (Cournot aggregation), (28)
X, WiSij = 0 (Slutsky aggregation). (29)
Second, the homogeneity of degree zero in p and m is
Zy Py = rÂ¡h (210)
Zy % = 0. (211)
Third, the symmetry of the matrix of Slutsky substitution effects is
W,Â£,j = WjÂ£j,. (212)
Fourth, the negativity condition is
X, Xy x, wÂ¡ Sij Xj < 0 Xj, Xj constant. (213)
From Walras law, we can show that d(ln m) = d(ln P) + d(ln 0:
m = X, p,q
dm = X, qÂ¡ dpt + X, pÂ¡ dqÂ¡,
dm / m = 'Zl (q, / m) dpÂ¡ + X, (p, / m) dqÂ¡,
d(ln m) = X, {pfti / m)(dpÂ¡ / p,) + X, (p^, / w)(^, / ^,),
c/(/ m) = X/ w, J(/ pÂ¡) + E, w, Â£/(/ Â£/,),
d{ln m) = d(ln P) + d(ln Q),
(214)
where
d(ln P) = X, Wj d(ln pÂ¡)
(the Divisia price index),
(215)
d(ln Q) = X, w, d(ln q,)
(the Divisia volume index).
(216)
An inverse demand system expresses the prices paid as a function of the total real
expenditure and the quantities available of all goods. The coefficients of the quantities in
the various inverse demand relations reflect interactions among the goods in their ability
to satisfy wants. From an empirical viewpoint, inverse and regular demand systems are
not equivalent. To avoid statistical inconsistencies, variables on the righthand side in
such systems of randomdecision rules should be the ones that are not controlled by the
12
decision maker. In most industrialized economies, the consumer is both a price taker and
a quantity adjuster for most of the products usually purchased. This is suitable with the
regular demand system. On the other hand, for certain goods like fresh vegetables,
supply is very inelastic in the short run, and the producers are virtually price takers.
Pricetaking producers and pricetaking consumers are linked by traders who select a
price they expect to clear in the market. The traders set the prices as a function of the
quantities that are suitable in the inverse demand system.
To apply consumerdemand specifications to the model, the basic results of
consumerdemand theory should be reviewed. From the utilitymaximization problem
for the consumer, we obtained a system of uncompensated inverse demand equations
from the firstorder conditions,
n, = (du / dqÂ¡) / Ey (du / dqj)qj, i = 1, 2,..., n, (217)
where nÂ¡ =pÂ¡/ m is total expenditure or income (m) = E, p,qÂ¡, u is utility, and p, and q, are
price and quantity for good respectively. The budget share (w,j can be found by using
Equation 26 and dx = x[d(ln *)],
w, = [d(ln u) / d(ln qÂ¡)] / Â£, [d(ln u) / d(ln qj)\. (218)
First, we consider the Rotterdam Inverse Demand System (RIDS) by following
Brown et al. (1995). A system of compensated inverse demand relationships can be
found by working with the distance function, which is dual to the utilitymaximization
problem. The distance function indicates the minimum expenditure necessary to attain a
specific utility level, u, at a given quality, q, which can be written as g(u, q). By
differentiating the distance function with respect to quantity, we get the compensated
13
inverse demands (which express price as a function of the quantities and specific utility
level),
Pi = dg{u, q) / dqÂ¡ = pÂ¡{u, q).
(219)
Consequently, we can also represent the compensated inverse demands for normalized
prices, Ujpi / m, where E, p,q, = m, by
7ti = p{u, q) / E, \p,(u, q).q] = nÂ¡{u, q). (220)
Next, we find the RIDS by totally differentiating this system of compensated inverse
demand relationships. As nÂ¡ is a function of u and q the total differentiate of n, is
dn, = {dn, / du) du + E7 {dn, / dqj) dqj. (221)
Consider a proportionate increase in q (i.e., dq = kq*) where & is a positive scalar. We can
then transform the term {dnjdu) du to
{dnÂ¡ / du) du = nÂ¡[d{ln n,) / d(ln w)] d(ln u),
(dn, / du) du = n,[d(ln nÂ¡) / d{ln k)){d{ln u) / [d(ln u) / d{ln A:)]},
{dn, / du) du = n,[d{ln n,) / d{ln k)\ {[E, {d{ln u) / d{ln qj) d{ln qj] /
[Ey (3(/ u) / 3(/ ^))]},
(3;r; / 3u) /m = n,[d{ln nÂ¡) / d{ln k)] E7 w7 d(ln qj. (222)
From d;r, = n, d{ln n,), we get the logarithmic version of the RIDS model,
n, d{ln n,) = n,[d{ln nÂ¡) / d{ln A)] E7 vv7 c/(/n <7y) + ^i[Ey<3(/ ^) / 3(/ <Â£,)) J(/
f(/ flÂ¡) = [3(/u ;r,) / 3(/u A:)] E7 w7 t/(/ g7) + E7 [3(/u ;r,) / 3(/ qry)] /(/ qj,
d{ln n,) = tj, d{ln Q) + E, 4 d(ln qj), (223)
where
41 d{ln n,) / 3(/ A:) (the scale elasticity), (224)
4 = d{ln n,) / 3(/ qj) (the compensated quantity elasticity). (225)
In order to satisfy thq symmetry condition, we premultiply both sides by wÂ¡. The RIDS
model now can be written as
w, d(ln n,) = w,4 d{ln Q) + E7 w&j d{ln qj,
14
w, d(ln n,) = hi d(ln Q) + Z\Â¡ h,j d(ln q^, (226)
where
h, = WtQ, (227)
hj = w&j. (228)
As dq = kq*, the scale elasticity, Q, is hÂ¡l wÂ¡. The compensated quantity elasticity
(flexibility), 4, is hy / wÂ¡ with the following properties.
First, the addingup conditions are
X,hi = \, (229)
Z, hy = 0. (230)
Second, the homogeneity condition is
Xjhy = 0. (231)
Third, the symmetry condition is
hy = hji (Antonelli symmetry). (232)
Fourth, the negativity condition is
Z, Zy Xj Wj hy Xj < 0 Xj, Xj constant. (233)
The second functional form of the inverse demand system is the Laitinen and
Theils Inverse Demand System (LaTheil). Following Laitinen and Theil (1979), we
describe the consumers preferences as g(u, q), where g(u, q) is the distance function
which is linearly homogeneous in q. The Antonelli matrix is
A = [ay], CLy = &g! d(p,qÂ¡)d{pjqj). (234)
From this Antonelli matrix, we can find the inverse demand system,
d[ln {pJP)] = Q d(ln Q) + Z7 4 d(ln qÂ¡) + ZWjd(ln qj),
d[ln (Pi/P)] = (4 +1) d(ln Q) + Z7 4 d(ln qj).
15
We also can get the logarithmic version of the LaTheil model from the logarithmic
version of the RIDS model (Equation 223) by adding d(ln Q) to both sides,
d(ln 7T,) + d(ln Q) = (4 +1) d(ln Q) + 2,Â¡ 4 d(ln qj,
d(ln pi) d{ln P) d(ln Q) + (/n 0 = (4 +1) i/(/ 0 + 2/ 4 /')>
d[ln (pt/P)\ = (4+1) i/(/ 0 + 4 4 Â£/(/ /) (235)
In order to satisfy the symmetry condition, we premultiply both sides of Equation 235 by
w so the LaTheil model is
w, d[in ipt/p)] = w,(4 +i) 4 0 + 4 4^* $y)>
W, 4/n (p,/F)] = (w,4 + w,) c/(/n 0 + 2, hydrin qj),
w, 4/n 0,/P)] = (/ij + w,) 4/n 0) + 4 h,j d(ln qj,
w, d[ln {pJP)\ = 4 4^ 0 + 4 hv d(ln
where
bÂ¡ = hi + wÂ¡. (237)
The coefficients of the LaTheil model also satisfy the neoclassical restrictions with
parameter hÂ¡j, which can be defined by Equation 227. Having the same properties as
parameter hy in the RIDS model (Equation 226), the addingup condition requires
2,6/ = 0. (238)
The third functional form of the inverse demand system is the Almost Ideal Inverse
Demand System (AIIDS), which can be obtained from the distance function,
In g(u, q) = (1 u) In a(q) u In b(q),
(239)
where
In a{q) = a0 + 2k ak In qk + (l/2)2*27 ykÂ¡ In qk In qp
(240)
In b{q) = In a(q) + pnI7k qkp.
(241)
The AIIDS cost function is written as
In g{u, q) = (1 u) In a{q) + u[ln a(q) + J3017k qk\
In g(u, q) = In a(q) + up0nk qkp,
16
In g(u, q) = a0 + Zk a* In qk + (1 /2)Zk 2) ykÂ¡ In qk In qj + ufioFIk qif, (242)
where a yf, p, are the parameters. By using the derivative property of the cost function,
pÂ¡ dg I dqÂ¡ and m = g(u, q), the budget share of good i can be written as
wi= p>qÂ¡ /m
Wi = {dgl dpdpi/ g
wÂ¡ = d(ln g) / d(ln p,). (243)
Hence, from Equation 242, the logarithmic differentiation gives the budget shares as a
function of prices and utility,
wÂ¡ = a, + Zj Yij In qj + b,up0nk qkp, (244)
where yy = (1/2){yy + y,).
As an approximation, we can replace uPoiIk qk with Z, w. In q,. The differential form of
the AIIDS model is
dWi = biZiW, d(ln q,) + Zj ytJ d(ln qj),
dwÂ¡ = bÂ¡ d(ln Q) + Zj yv d(ln qj). (245)
There are four properties for the coefficients of the AIIDS model that satisfy the
neoclassical restrictions. First, the addingup conditions are
2/^ = 0, (246)
Z, bi = 0. (247)
Second, the homogeneous of degree zero is
2, Yij = 0. (248)
Third, the Slutsky symmetry is
Yij = Yj> (249)
Fourth, the negativity condition is
Z, Zj x, Yy Xj < 0 xh Xj constant. (250)
17
In addition, from the logarithmic version of the LaTheil model (Equation 235), we can
get the logarithmic version of the AIIDS model by adding d(ln qÂ¡) d{ln Q) to both sides,
diln pi) d{ln P) + d(ln qÂ¡) d{ln Q) = (4 +1) d(ln Q) + Z7 4 d(ln qj) + d{ln qÂ¡) 
diln Q),
d(ln nÂ¡) + d(ln qj) = (4 +1) d(ln Q) + Z7 (4 + 4 wj) d{ln qÂ¡),
d(ln w,) = (Ci+1) d(ln Q) + S7 (4 + 4 ~ Wy) <7(/n qj).
We also can derive the logarithmic version of the AIIDS model by adding d(ln qÂ¡) on
both sides of the logarithmic version of the RIDS model (Equation 223),
d(ln nÂ¡) + d(ln qÂ¡) = Q d(ln Q) + Â£, 4 d(ln qj) + d(ln qÂ¡),
d{ln nj) + d(ln qÂ¡) = d(ln Q) + d(ln Q) + Z7 4 <7(/
d{ln w,) = (4 +1) d(ln Q) + S7 (4 + Sywj) d{ln qj). (251)
In order to satisfy the symmetry condition, we premultiply both sides of Equation 251 by
Wj, so the AIIDS model is
Wj d(ln wÂ¡) = {wÂ¡Q + wi) d(ln Q) + I7 (w,4 + w,S,j wÂ¡wj) d(ln qj),
dwÂ¡ = bÂ¡ d(ln Q) + Z7 yy d{ln qj),
which is the same as Equation 245 and
Yij = w<4 + w,8,j WjWj. (252)
The last functional form of the inverse demand system is the Rotterdam Almost
Ideal Inverse Demand System (RAIIDS). We can get the logarithmic version of the
RAIIDS model by subtracting d(ln Q) from both sides of the logarithmic version of the
AIIDS model (Equation 251),
diln wt) d(ln 0 = (4+1) diln Q) + Z7 (4 + 4 wj) diln qj) diln Q),
diln wÂ¡) diln Q) = Q diln Q) + Z7 (4 + 4 wj) diln qj).
We also can get the logarithmic version of the RAIIDS model by adding diln qi) d(ln Q)
to both sides of the logarithmic version of the RIDS model (Equation 223),
diln ni) + diln qi) dQn Q) = 4 d{ln Q) + Z7 4 d(ln qj) + d(ln qi) diln Q),
diln ni) + diln qi) diln Q) = 4 d(ln Q) + Z7 (4 + 4 wj) diln qj),
18
d(ln w,) d(ln Q) = Â£ d(ln Q) + I, (4 + Sy wj) d(ln qj. (253)
In order to satisfy the symmetry condition, we premultiply both sides of Equation 253 by
wÂ¡, so the RAIIDS model is
wÂ¡[d(ln Wi) d(ln 0] = w,Q d{ln Q) + S, (w,4 + w,Sy W/Wy) %),
dw, wÂ¡ d(ln Q) = h, d(ln Q) + I, /y d(ln qj). (254)
By using our new formulation, the properties of parameter h which can be defined by
Equation 227, are equivalent to the ones in the RIDS model (Equation 226), and the
properties of parameter /y, which can be defined by Equation 237, are equivalent to the
ones in the AIIDS model (Equation 245). As a result, the RAIIDS model has the RIDS
scale effects and the AIIDS quantity effects. On the other hand, the LaTheil model has
the AIIDS scale effects and the RIDS quantity effects.
Scale and Quantity Comparative Statics
We can examine relations for inverse demands by following Anderson (1980) to
express price as a function of quantities and total expenditure,
Pi =A
and normalized prices, nÂ¡ = p, / m, as a function of quantities,
*Â¡=/fo !)=/(?) (256)
As it is true about quantity elasticities of prices being equivalent to those about quantity
elasticities of normalized prices, we confine our discussion to normalized prices in what
follows. Quantity elasticities are the natural analogs for inverse demands of price
elasticities, py, in direct demands. They tell how much price i must change to induce the
consumer to absorb marginally more of good j. The quantity elasticity of good / with
respect to good j is defined as
Vij=WXq)ldqj\[qjlfXq)l
(257)
19
When dealing with inverse demands, an interesting question is: how much will
price / change in response to a proportionate increase in all commodities, or how do
prices change as you increase the scale of the commodity vector along a ray radiating
from the origin through a commodity vector? We formalize this notion for marginal
increases in the scale of consumption by defining the scale elasticity to derive restrictions
relating to quantity and scale elasticities. These restrictions show that the scale elasticity
is analogous to total expenditure elasticity, r/Â¡, in direct demands. Let q be a reference
vector in commodity space so that we can represent the consumption vector of interest as
q = kq, where k is a scalar. We can express the inverse demands as
nÂ¡ =f\kq*) = g \k, q'). (258)
The scale elasticity of good / is defined as
Ci = [dg % q ) / dk][k / g % q)l (259)
Quantity and scale elasticities obey restrictions that are directly analogous to restrictions
for direct demands. For the homogeneity of degree zero restriction, we can write
Q^jWXq) /%]<&*[* //'(*)],
Ci = 'Zj[dfi(q)/dqJ][qj/fim
Ci = 2/ Vib (260)
which is analogous to Â£, Â¡Xy = rÂ¡, in the direct demand system.
For the addingup conditions, we start by writing the budget equation, w, = n,q as
Wi=f\q)qÂ¡ (261)
From Â£, w, = 1, we get
*ifXq)q, =1
Differentiating with respect to qj, we have
2/ w\q) / dqj\qt +fXq) = 0,
(262)
20
^[df\q)ldqj\q, = f\q).
By multiplying both sides by qj, we obtain
Z, [df\q) / dqj\[qj/f\q)]f\q) q, f\q) qj.
As y/y = [df\q) / IfXq)} and w, =f\q) qÂ¡, we have
I, y/ijWt = wj, (263)
which is analogous to the Cournot aggregation, Z, WjjUy = Wj. Next, the analogous to the
Engel aggregation, Z/ w,7, =1, is obtained by
Z, W, Zy l//y = Zy Wy.
As 4/= 2y ys,j and Z, w, = 1, we get
Z, m>Q = 1. (264)
Scale and quantity elasticities are the natural concepts of uncompensated elasticities
for inverse demands. We derive the constantutilityquantity elasticities, or compensated
quantity elasticities, from the transportation function, T(q, u), which is dual to the cost
function and satisfies
U[q! T(q, u )] = (265)
for all feasible q and u. The transformation informs how much a particular
consumption vector must be divided to place the consumer on some particular
indifference curve. By differentiating with respect to goods, we get the constant utility or
compensated inverse demands,
n =f'\
These price functions give the levels of normalized prices that induce consumers to
choose a consumption bundle that is along the ray passing through q and that gives utility
u. The constant utility quantity effects, or the Antonelli substitution effects, state the
21
amounts normalized prices change with respect to a marginal change of reference
consumption qj, keeping the consumer on the same indifference level. We can express
the Antonelli substitution effects in elasticity form, which is analogous to the
compensatedprice elasticity, Sy. The constantutilityquantity elasticity of good /' with
respect to good j is defined as
4 = u ) / tyi %]{/ / W{q, u) / dq,]},
4 = (dirt / dq,)(qj / 7Ti). (267)
T(q, u) is homogeneous of degree one in q, and f* (q, ) is homogeneous of degree zero
in q. From the direct application of Eulers theorem, we get
2,4 = 0, (268)
which is analogous to the restriction, X7 Â£y = 0. From the properties of the transformation
function, which include the decrease in u, and the increase, linearhomogeneous, and
concave in q, the matrix of Antonelli effects is negative semidefinite. This implies Sy < 0
, which can be called the Law of Inverse Demand. Next, we describe the implicit
compensation scheme to derive the inverse demand equation, which is analogous of the
Slutsky equation. The total change in prices associated with an increase in one quantity
can be decomposed, as total effect equals the summation of the substitution effect and the
scale effect.
Now, consider a marginal change in the price in response to a marginal change in
relative quantity and in scale. By totally differentiating n, = g '(k, q\ we get
dnt = [dg \k, q") / dq/] dq/ + [dg (k, q*) / dk] dk. (269)
The change in scale must compensate for the change in qj* so as to leave the utility
unchanged, du = 0. With n, = (du / dq,) / X) (du/dqj)qj, we get
22
du = 2, (5m / dq*)q* dk + (du / dqj )& dqj = 0,
dk = [(5m / cty/) / 2, (5m / 5g,*)
(270)
(271)
From Equations 269, 270, and 271, we get
dnit dq/ = [5g '(*> 9*) I d%] ~ [dS '(* q*) / 5Â£]^ A:.
By multiplying both sides by (g/ / nÂ¡), we get
{dn, / dq/)(q/ / ^) = (5/r, / dq/)(q/ / nÂ¡) (dn, / 5A)^ Â£(
{dnd dq/)(q/ / itt) = (57T, / dq/)(q/ / ;r,) (5;r, / 5A)(A / ;r,)(^
(272)
As w, = ^ qh 4 = (/tt, / / nÂ¡), 4 = (Stt, / 5A)(A / ^) and ^ = (5^ / dfyXty / flÂ¡), it is
convenient to express this in elasticity terms,
(273)
4 = Wj Qwj.
This states the Antonelli substitution effects in terms of scale and uncompensated
quantity changes. It is fully analogous to the Slutsky equation (Equation 25) of standard
theory,
(5/z, / 5py)(py / /?,) = (Sft / 5^)^ / 0/) + (5^, / 5l)(w / ^,)07^/ / )
Â£,j = H\j+
where /z,(p, m) is the Hicksian compensated demand function, which allows the demand
analyst working with inverse demands to compute compensated elasticities from the
uncompensated elasticities directly (without being obliged to explicitly consider the
transformation function or compensated inverse demands). Finally, from 2, = Wj
and 2, w,Q = 1, we can derive the analog to Slutsky aggregation
2, w,4 = 2, Wjif/y 2, WiQwj,
2, w,4 = w7 (1 )\Vj,
2, w,4 = 0.
(274)
23
The symmetry of dn, / dq* implies that compensatedquantity cross derivatives
between any two goods, i and j, must satisfy dn, / dq* = dnj / dq, The symmetry
property reflects the fact that the cross derivatives of a function are equal. We also get
the symmetry of the matrix of Antonelli substitution effects from this symmetry property,
dn, / dq/ = dnÂ¡ / dq/
By multiplying by q*q/ on both sides, we get
(dm / dq/)(q,*q/) = (dn, / dq*){q*q*\
{dn, / dq/)(q,*q/)(n, / n,) = {dnj / dq*)(q,*q/){^ / nj),
{n,q*){dni / dq/){q/ / n,) = (njq/)(dnj / dq*){q* / nj).
As wÂ¡ = n, q
(275)
which is analogous to Slutsky symmetry, (Equation 212).
From the AIIDS model, we can prove for the addingup condition, Equation 246,
by using the summation of Equation 252 over /' (E, ytJ = E, w,^ + E, E, w(). As
2/ Wjgij = 0, w, = E, w/4, and E, w, = 1, we get Equation 246 (E, ytj = 0). The proof for
Equation 247 can be obtained by working with Equation 237 (E/ bÂ¡ = E, wÂ¡Q + E, wÂ¡).
As E, W& = 1 and E, w, = 1, we get Equation 247 (E, 6, = 0). Next, we prove the
homogeneity of degree zero, Equation 248, by using the summation of Equation 252
over j (Ey y,j w, Ey ^ + Ey w,S,j w, Ey Wy). As Ey Â¡,j = 0, wÂ¡ Ey WjSy and Ey Wy 1, we
get Equation 248 (Ey yÂ¡j = 0). We also prove the Antonelli symmetry, Equation 249, by
working with Equation 252 (y,j = w^y + w,Sy w,wj). As w,
get y,j = WjZjj + wjSji WjWj, which means y,} = y, (Equation 249).
24
Econometric Model Development
For the purpose of estimating, operator d is the logchange operator; that is, if x is
any variable and xit is its value in year t, then
d(ln x,) = A (In x) = In xit In x, t.\ = In (x,Â¡ / xit.\). (276)
For the budget share, Barten (1993) replaced w, by the moving average, w*, where
w* = (w/,m + wit) / 2. (277)
As a result, each functional form generates different elasticities. The big disadvantage is
on the coefficients of the demand systems. To solve this problem, we proposed a new
formulation by using the mean of the budget share, w], where
w^'LtWu/T, (278)
where t = 1,T. By using this formulation, each coefficient of the demand systems is a
function of vv( instead of w and the calculated elasticities are expected to be unchanged
across the functional forms.
First, by replacing d(ln nÂ¡) with A(//? nlt), d{ln Q) with A (In Qt), and d(ln qj) with
A (In qj,) in Equation 226, the econometric model development for the RIDS model can
be written as
w, A(/n n,t) = w, Q A {In Q,) + Sy w, fo A (In qjt) + v,
w, A (In nu) hi A {In Q,) + I\Â¡ h0 A (In qj,) + vit, (279)
where
a
ll
(280)
hu = w, 4
(281)
25
Second, we get the econometric model development for the LaTheil model (which
has the RIDS scale coefficients and the AIIDS quantity coefficients) by adding vv, A {In Q,)
on both sides of the RIDS model (Equation 279),
vv, A (In 7r,i) + vv, A (In Q,) = (vv, <Â£ + iv,) A {In Q,) + X, vv, 4 A {In qjt) + vih
vv [A (In n) + A (In Q,)] = b, A (In Q,) + X, hv A (In qjt) + v,
vv, A [In ipit / Pi)] = b, A(ln Qt) + X7 htJ A(ln qJt) + v, (282)
where
vv, A[/ / P,)] = w, [A(/ /?) A(/ P,)] = vv, [ A(/ n,Â¡i) + A (In Q,)]. (283)
Next, we consider the Almost Ideal Inverse Demand System. We introduce
parameter A (In Q*) for the AIIDS model, where
A (In Q,*) = 7Lj w; A {In qJt).
(284)
By using this parameter, the coefficients of the AIIDS will be the function of vv,, not the
function of vv*,. We get the econometric model development for the AIIDS model from
Equation 245 by replacing dw, with dwlh d(ln Q) with A {In QÂ¡), and d(ln qj) with A (In q^),
dwu = (w,Â£i+ vv,) A (In Q,) + X, (vv, 4 + vv, Sy vv, w*, ) A (In qj,) + v,
dwu + X, vv, vv*, A (In qj,) X7 vv, vv, A (In qji)
= (vv, Q + vv,) A (In Qt) + X7 (vv, 4 + iv, S0 vv, vv,) A (In q) + v,
dw,,+w, [A (In Q,) A (In Q*)] = b, A (In Q,) + X, /0 A (In qj,) + v,
vv, [A (In uu) + A (In q) + A {In Q,) A {In Q*)]
= b, d(ln Q,) + X7 Yij &{ln qJt) + v, (285)
where
dwit = vv, A {In w) = vv, [A(/ n) + A {In q)],
(286)
bi = wl;i+ w,,
(287)
/y= w,4 + w, S,j w, w .
(288)
26
For the last functional form, we get the econometric model development for the
RAIIDS model that has the AIIDS scale coefficients and the RIDS quantity coefficients
by subtracting vv, A (In QÂ¡) on both sides of the AIIDS model (Equation 285),
dwu + w, [A (In Q,) A (In Q*)] w, A(ln Q,)
= w, Q A (In Q,) + Ey (w, 4 + w, Sy vv, wJ) A (In qj,) + v,
dw w, A(/ 0,*) = hi A(ln Q,) + E, A(/ qjÂ¡) + v,
w, [A(/ %) + A(/ <7f) A{ln Q*)] = hÂ¡ A (In Q,) + Ey A{ln qJt) + v. (289)
From the coefficients of each functional form of inverse demand system, we can calculate
the scale elasticity and the compensated quantity elasticity by using the following
equations:
Â£i = hi/ w, =(bi/ w,)l, (290)
4 = hV 1 = (jij / w, )+Wj Sy. (291)
The uncompensated quantity elasticity can be calculated by using the Antonelli equation,
y/y = 4 +Â£iWj. (292)
Because functional forms of the demand systems can be related to each other
theoretically, we can show that standard errors are unchanged across the functional forms
of the inverse demand system. The standard error can be calculated from the disturbance,
vu=y y = Pi xit p, xit, (293)
where yu is the estimation of the dependent or explained variable, yÂ¡h /?, is the estimation
of the coefficient, /?, ,and xit is the independent or explanatory variable. The disturbance
for the RIDS model (Equation 226) is
vu = [hi A (In Qt) + Ey hy A (In qj,)] [ h, A (In QÂ¡) + Ey htJ A {In qJt)\,
vit = (hi h,) A (In Q,) + Ey (hy htJ )A (In qJt).
(294)
27
The disturbance for the LaTheil model (Equation 236) is
v [b, A (In Q,) + Zy hy A(ln qJt)\ [b, A (In Q,) + Zy htJ A (In qjt)],
vit = (b, b, )A(In Q,) + Zy (hy hv )A(In qJt). (295)
The disturbance for the model AIIDS (Equation 245) is
v = [b, A (In Q,) +Z\y y,j A (In qJt)\ [ b, A (In Q,) +Z\Â¡ yt] A (In qJt)\,
vu = (b, b, )A(ln Q,) + Zy (y0 ytJ )A(In qJt). (296)
The disturbance for the RAIIDS model (Equation 254) is
vu = [h, A (In Q,) + Zy yv A (In qJt)] [ h, A (In Q,) + Zy ytJ A (In qJt)\,
vit = (h, h,) A (In Q,) + Zy (y0 ytJ )A (In qJt). (297)
From the coefficients of these four functional forms of inverse demand system, we
can show that
h, A, = w, Â£ w, 4' = wÂ¡ (Q 4), (298)
hy hy = w, 4 w, 4 = vv, (4 4), (299)
6, bl = (w,Ci+ w,)(vv, 4 + w,)= w,(4 4), (2100)
ft Yij= (W.$J + 4 w, ) (w, 4 + w, % w, wj) = w, (4 4), (2101)
where h, is the estimation of hÂ¡, hIJ is the estimation of hy, bt is the estimation of b yt
is the estimation of ytJ, and 4, and 4 are the estimations of 4 and 4 respectively.
Consequently, for all functional forms of the inverse demand system, we get the same
disturbance,
Vtf = W, [(4/ 4 )A(In Q,) + Z, (4 4 )A(In qJt)].
(2102)
28
Because we get the same disturbance for every functional form of the inverse demand
system, we also get the same standard error and loglikelihood value across all functional
forms.
Methodology for Demand Analysis
In following Barten (1969) to estimate the inverse demand system, we used the
maximumlikelihood method of estimation with constraints imposed. We imposed the
homogeneity and symmetry constraints by working with the concentrated loglikelihood
function. We estimated every demand equation in the system at the same time by
applying the Seemingly Unrelated Regression Estimation. GAUSS (a mathematical and
statistical software package), was used to perform the estimation.
There are four scenarios in our study. The first scenario is to estimate each
functional form of the inverse demand system by using the mean of the budget share to
multiply the logarithmic version of the inverse demand system. The second scenario is to
estimate each functional form of the inverse demand system by using the moving average
of the budget share to multiply the logarithmic version of the inverse demand system. In
addition, the first and second scenarios estimate the inverse demand system by using
Bartens estimation method with the homogeneity and symmetry constraints imposed.
The third scenario is to estimate the RIDS model by using Bartens unconstrained
estimation method. The fourth scenario is to estimate the RIDS model by using Bartens
estimation method with the homogeneity constraint imposed.
Results are based on time series data from 1994 to 1998 for four commodities of
selected vegetables and fruits, n = 4. Weekly wholesale prices and quantity unloads were
collected from the Market News Branch of the Fruit and Vegetable Division, Agricultural
Marketing Service, United States Department of Agriculture. There are 208 observations
29
of quantities and prices for each commodity in each market, T 208. The commodities
are tomatoes, bell peppers, cucumbers, and strawberries. The markets include Atlanta,
New York, Los Angeles, and Chicago.
Seemingly Unrelated Regressions Model
Following Greene (2000), the inverse demand systems can be written as
yi = XB+ Â£y,
yi = XB + Si,
yn XB + sn,
(2103)
where
e'= [s\, si,
5 Â£n ]
(2104)
E[s] = 0.
(2105)
The disturbance formulation is
anI
Gnl .
E[es\ = V=
oj
a22I .
(2106)
Vnl1
aJ_
There are n equations and T observations in the data sample. For the demand
system, we can apply Seemingly Unrelated Regressions (SUR) with identical regressors
or the Generalized Least Square (GLS) with identical regressors,
1
_
^ PS
1
_y_
X 0
0 X
0 0
o'
'By'
Â£,
0
b2
+
^2
X
A.
A.
(2107)
th
For the t observation, then xn covariance matrix of the disturbances is
30
72 =
a\2
 oi
<72\
22
^2n
?n\
2
^"nn
so, from Equation 2106, we get
V=Q1
and
T1 = QA 0 7.
We find that the GLS estimator is
B = [XVlX]A XVly
B=[X\QA I)X\A X\QA I)y
'au(XX)A
au(XX)A
.. ain(XX)A'
'(XX)
A
5 =
a2](XX)A
ct22(XX)a
.. a2n(x'xy'
(XXfo^'b,
*mX{xxy*
crn2(XX)A
nn(x'xr'_
(XX) Â£>'6,
(2108)
(2109)
(2110)
(2111)
where /= 1,... n.
After multiplication, the moment matrices cancel, and we are left with
A = T.j cr,j E/
A = 6.(2,
where j, and / = 1, ... ,n, and
bi = {XX)AXyi. (2113)
The terms in parentheses in the second line of Equation 2112 are the elements of the first
row of EE'1 = 7, so the end result is 5, = b\. Using a similar method, the same results are
true for the remaining subvectors, B, = b,. That is, in the Seemingly Unrelated
Regressions model, when all equations have the same regressors, the efficient estimator is
31
singleequation ordinary least squares (OLS is the same as GLS). Also, the asymptotic
covariance matrix of B is given by the large matrix in brackets above, which would be
estimated by
Est. Asy. Var[5]= (2114)
where
h=ai={\IT)e'ieJ, (2115)
or
Est. Asy. Cov[ B, BJ ] = (JfX)'1, (2116)
where i,j = 1,... n.
Bartens Method of Estimation
Following Barten (1969), the Maximum Likelihood (ML) method has been used to
estimate the coefficients of the demand systems. Maximumlikelihood estimators are
consistent, asymptotically efficient, and asymptotically normally distributed. The
disadvantages in using the ML procedure are the possible smallsample bias of the
estimator for the variances and covariances, the need to specify a distribution for the
random variables in the model, and the procedures computational difficulties. The
likelihood function is to be maximized with respect to the coefficient of the system and
the elements of the covariance matrix In. Derivation of the ML estimators will be done
in terms of maximizing the concentrated version of the logarithmiclikelihood function,
In L = M2(TlnnT(ji\)(\+ln2n)Tln\A\), (2117)
where
A = (1 / T) E, v,v/ (2118)
and
32
v,=y, DxÂ¡. (2119)
An alternative way of writing v, is
V= YXD', (2120)
where
V'= [vi,v2,..vr], (2121)
X'=[xux2,...,xt\, (2122)
Y'=\y\,yi,.. .,yr\. (2123)
Then
A = (1 / T) VV+ iV
A = (1/7) [Y'Y DX'Y YXD' + DXXD'] + ii\ (2124)
where
/ = (1 / Vw)i (2125)
and i is the summation vector.
The resulting estimators of the coefficients of the system are used to obtain an
estimator of variance, and hence a numerical estimate for the covariance of the
disturbances, Q. The set of equations will be estimated jointly by using a maximum
likelihood procedure (Barten, 1969). First, we estimate without the use of any restriction,
next we impose a constraint for homogeneity condition, and then we impose constraints
for both homogeneity and symmetry conditions. The assumption is made that prices and
total expenditure are stochastic and independent of the disturbance term. We also
assumed that vt are vectors of independent random drawings from a multivariatenormal
distribution with mean zero and covariance matrix, Q.
33
Unconstrained estimation
Starting from an unconstrained estimation, the estimator of h, and hÂ¡j will be
derived, which corresponds with the maximum of the concentrated likelihood function
without the use of any restriction. For the firstorder conditions for a maximum of the
concentrated likelihood function with respect to the elements of D,
d(ln L)/dD = d [1/2 (TlnnT(n 1) (1+ In 2n) Tln\A\)\ / dD,
d(ln L) / dD = (1/2)5 (Tln\A\)/ dD,
d(ln L)/dD = (M2)AA[d(TA) / dD],
from d(lnf(x)) / dx =fA(x) [df{x) / dx],
d(ln L)/dD = (1/2M'1 {d[T{MT) (FT DX'Y YXD' + DX'XD')] / dD},
from d(ax) / dx = a, If xa = (xa)' then d(xa) I dx d(xci)7 dx = d(a'x) / dx = a',
and d(x 'ax) / dx = ax + (x'a)'= ax + a'x (d(x 'ax) / dx = lax, if a = a ), then
d{ln L)/dD = (1/2)Aa [2YX2DxX'X\,
d(ln L) / dD = A'1 [YX D\X'X\. (2126)
From d In L / dD = 0 and A'1 0, we can solve for DÂ¡,
YX D\XX = 0,
D\ (X'X)A = YX,
D\ = YX(X'X)a,
Dx' = (X'X)aX'Y, (2127)
where Di is the unconstrained ML estimator. The covariance matrix of this estimator is
E[(dl d)(dx d)r\ = n (XX)A, (2128)
where dx is an n(n + 2) component vector by arranging the n columns of D\ It is
obvious that this is simply the ordinary least squares (OLS) estimator applied to each
equation separately.
34
Estimation under the homogeneity condition
The homogeneity condition states that hÂ¡j = 0. This can also be formulated in
terms of D as
Dt= 0, (2129)
where r is defined by
1*= [0,1,1, ...,l]ix(+i). (2130)
The Lagrangean expression with the homogeneity condition is
^ = lnL+ kDt, (2131)
where k is an element vector of Lagrangean multipliers. By differentiating this
Lagrangean expression with respect to the element of D,
d(ln L+ k' Dt) / dD = d(ln L)/dD+ k'(Dt) / dD,
from d(a 'xb) / dx = ab 'and d(ln L) / dD = A'1 [Y'X DX'X], then
d(ln L+ k1 Dt) / dD = A'1 [YX D2X'X\ + kY.
By premultiplying this expression by A, postmultiplying it by {X'X)A, and then using
D\ = YX(X'Xf\ we obtain
d(ln L+K'DT)/dD = AAA [YX D2X'X\ (X'X)A + A/xf(X'X)A
d{ln L+ kDt)/ dD= YX(XX)A D2 + Aicf (X'X)'1
d(ln L+ k1 Dr) / dD Di D2 + AkY (X'X)'1. (2132)
Since D2 is the ML estimator under the homogeneity condition, it has to satisfy D2t= 0.
Postmultiplying Equation 2132 by r, we get
D\t D2t+ AKi (X'X)A t= 0
Ak=DxtI[Y(X'X)at\
Ak 0D\ r, (2133)
where #is a scalar equaling 1 / f (X'X)A r. Then we get
35
D\D2 0D\ tY {X'X)A = 0
D2'= [I 0(X'X)A rf\ D\
d2' = [i e{Xxf rf] [(xxy'xY]
D2' = [(X'X)' 0{XXf t (X'X)a] X'Y
D2' = GX'Y, (2134)
where
G = [{X'X)'x 0{X'X)A tt? (X'X)'x] (2135)
and
YG = 0. (2136)
The complete covariance matrix of the ML estimator under the homogeneity condition is
E[(dld)(dld)'] = aG, (2137)
where d1 is a (+2) component vector by arranging the n columns of D2.
Estimation under the symmetry and homogeneity conditions
The symmetry condition, hÂ¡j= hjÂ¡, can also be formulated in terms of d by
rW=Atf^( = 0, (2138)
where d, the n(n + 2) component vector, is formally defined by
ClD')e = d, (2139)
with e being an n component vector of the following structure,
e'=[e\\ e2e], (2140)
and r is a row vector with one in the [(/ 1)( + 1) +j + 1]'* position minus one in the
[(/ 1)( + 1) + / + \]lh position, and otherwise consisting of zeros. There are 0.5( 1)
different symmetry conditions. These will be represented by
Rd= 0, (2141)
where R is a matrix of 0.5n(n 1) rows and n(n + 2) columns. The homogeneity
condition can also be formulated in terms of d by
36
[7 YDr]e = [7 f] [7 Â£>> = [7 r]7=0. (2142)
The Lagrangean expression to be maximized under the homogeneity and symmetry
condition is
oS = In L + k\I <]
where xTs a vector of n Lagrange multipliers for the homogeneity condition, and ^ is a
vector of 0.5n{n 1) Lagrange multipliers for the symmetry condition. The vector of
firstorder derivatives of In L with respect to d can be written as
d{ln L) / dd = I (d In L / dD\
d(ln L)/dd=[I (X'YXXDt, ) Al]e,
d(ln L)/dd= [A'' (X'YXXD^e, (2144)
and from d ax / dx = a 'then
8k\I f]d/ dd=d[id f]d/ dd,
did[I f]d/dd=[id f]',
did[I f\d/dd[K r], (2145)
and
dn'RdI dd (ju'R)' = 7?'//. (2146)
The firstorder condition with respect to d of the Lagrangean expression with the
homogeneity and symmetry conditions, Equation 2143, is
[Aa (XY XXDi')]e + [* 0 r] + Rn = 0. (2147)
Since it is required that ?D3 = 0 in view of the homogeneity condition, and we know that
D2 = GXY and fG = 0, by premultiplying Equation 2143 by [A G], we get
[A G] [Aa (X'Y XXD3)\e + [A G] [k r] + [A G\R'/d= 0
[7 (GXY GXXD3')\e + [Ak Gt\ + [A G]R'jU = 0
[I (TV [I 0{X'X)A Tf]D3')\e + [A G]R'/a = 0
[7 (TV DY)]e + [A G]R '// = 0
d2d} + \AG]R,jU=0.
(2148)
37
Since Rd3 = 0 meets the symmetry condition. By premultiplying Equation 2148 by R,
we get
Rc?R
H = lR(A GW'Ricf cP)
M = [R(A 0 ORf'RtP. (2149)
From Equation 2148 and Equation 2149, we get
cf = S (/I G^T1^ = ^ (2150)
where
H = I(AG)R\R(AG)Rr\AR. (2151)
The covariance matrix of
E[(c? d){ct d)']=H(a G)H\ (2152)
Empirical Results
The results of the estimation with the homogeneity and symmetry conditions (using
the mean of the budget share to multiply the logarithmic version of the inverse demand
system by following Bartens estimation method for each functional form in each market)
are presented in Tables 21 through 216. Next, the results of the estimation of the
homogeneity and symmetry conditions (using the moving average of the budget share to
multiply the logarithmic version of inverse demand system by following Bartens
estimation for each functional form in each market) are presented in Tables 217 through
232. The results from the unconstraint estimation for each market are presented in
Tables 233 through 236. The results from the estimation of the RIDS model with the
homogeneity condition (by following Bartens estimation method in each market) are
presented in Tables 237 through 240. The elasticities calculated from the coefficients
of the inverse demand system for each market are presented in Tables 241 through 244.
38
Inverse Demand System Analysis
The results from the estimation of the inverse demand system in every market
(Tables 21 through 216) show that by using the mean of the budget share to multiply
the logarithmic version of the inverse demand system, the RIDS has the same scale
coefficients as the RAIIDS model, and the AIIDS model has the same scale coefficients
as the LaTheil model. The quantity coefficients are the same between the RIDS model
and the LaTheil model, and are the same between the AIIDS model and the RAIIDS
model. The scale elasticity, quantity elasticity, and standard errors are unchanged across
all four functional forms of the inverse demand system.
The results from the estimation using the moving average of the budget share
(Tables 217 through 232) show that the coefficients are different from the estimation
using the mean of the budget share. We also can see that by using the moving average, a
different functional form generates a different result.
The results from the unconstrained estimation (Tables 233 through 236) show that
the relative size of the estimated asymptotic standard errors is so large that not too much
value can be attached to these results. Therefore, the unconstrained estimation results in
imprecise point estimates. Moreover, the results of the estimation with the homogeneity
constraint imposed (Tables 237 through 240) show that the homogeneity condition on it
own cannot contribute much to the precision of the estimator. Though we could have
expected smaller values for the standard errors, because of the use of a more restrictive
model, this hope is almost not realized. In this respect much more can be expected from
using the symmetry condition.
39
Elasticity Analysis
We calculated the elasticities for each market from the estimation of the RIDS
model by using Bartens method of estimation with homogeneity and symmetry
constraints imposed (Tables 21, 25, 29, and 213). The results from Tables 241
through 244 show that all elasticities in every market have the correct sign according to
theory. Tomato has the highest absolute value of the own substitution elasticity when
compared with other commodities for every market. In contrast, strawberry has the
lowest absolute value of the own substitution elasticity when compared with other
commodities for every market. The elasticities for the inverse demand system are closer
between the Atlanta and Los Angeles markets and between the Chicago and New York
markets.
Scale effect and scale elasticity
Scale effects show how much the normalized price of good i will change in
response to a proportional increase in the total quantity in all commodities. This reflects
the change in total expenditure. It denotes the change in utility, and addresses the
question of how prices change as you increase the scale of the commodity vector along a
ray radiating from the origin through a commodity vector. It measures the change in the
Divisia quantity index, showing the movement from one indifference curve to another.
Scale effects are converted into scale elasticities by dividing the scale effects by the
budget share. The scale elasticities are considered analogous to the total expenditure
(income) elasticities in the direct demand system. All the estimates for the scale effects
are statistically significant at the 5% probability level and have the expected sign.
Tomatoes. The obtained estimates for the scale effects of tomatoes in the Atlanta,
Los Angeles, Chicago, and New York markets are 0.5427, 0.5224, 0.4488, and 0.4577,
40
respectively. This showed that for a 1% increase in aggregate quantity in each market, the
wholesale price of tomatoes will fall between 0.4488% and 0.5427%. The scale elasticities
are 0.9617, 0.9075, 1.0259, and 1.0453 in the Atlanta, Los Angeles, Chicago, and New
York markets, respectively (almost unit elastic in the Atlanta market, with the highest
fluctuations in the New York market).
Bell peppers. The estimates of the scale effects of bell peppers had the expected
negative sign (which showed that as aggregate quantity increases, the normalized price
goes down). Since it is expected that the change in normalized price is proportional for
both wholesale and retail prices, the magnitude of the above change would be reflected at
both the wholesale and retail levels. As such, the obtained estimates of the scale effects
can be used to infer that if there is a 1 % increase in the quantity of the product group as a
whole, the price of bell pepper will fall by 0.1777%, 0.1885%, 0.2226%, and 0.1968% in
the Atlanta, Los Angeles, Chicago, and New York markets, respectively. The scale
elasticities range from 1.0040 to 1.0905, which are elastic in the Atlanta, Los Angeles
and Chicago markets with the scale elasticities equal to 1.0460, 1.0302, and 1.0905,
respectively (almost unit elastic in the New York market, with the scale elasticity equal to
1.0040).
Cucumbers. The estimates show that for a 1% increase in the aggregate quantity in
each market, the normalized wholesale prices will decrease by 0.1911%, 0.1517%,
0.2319%, and 0.2388% in the Atlanta, Los Angeles, Chicago, and New York markets,
respectively. The scale elasticities of cucumbers are 1.0485, 1.0365, 0.892, and 0.9438
in the Atlanta, Los Angeles, Chicago, and New York markets, respectively (inelastic in the
Chicago and New York markets and elastic in the Atlanta and Los Angeles markets).
41
Strawberries. The obtained estimates for the scale effects of strawberries in the
Atlanta, Los Angeles, Chicago, and New York markets are 0.0963, 0.1157, 0.0805,
and 0.1120, respectively. This showed that for a 1% increase in aggregate quantity, the
price for strawberries will decrease by 0.0963%, 0.1157%, 0.0805%, and 0.1120% for the
Atlanta, Los Angeles, Chicago, and New York markets, respectively. The scale
elasticities of strawberries are 1.1526, 1.2194, 0.8188, and 0.9910 in the Atlanta, Los
Angeles, Chicago, and New York markets, respectively (elastic in the Atlanta and Los
Angeles markets, elastic in the Chicago market, and almost unit elastic in the New York
market).
Quantity effect and own substitution quantity elasticity
Quantity effects represent the compensated or substitution effects of quantity
change. These effects show movement along a given indifference surface. These are
converted into quantity elasticities by dividing the quantity effects by the budget share.
The quantity elasticities are analogous to the price elasticities in the direct demand. They
reflect how much the price of good i must change to induce the consumer to absorb more
of good j. The uncompensated quantity elasticities can be calculated by using the
Antonelli equation (Equation292). In an inverse demand system, a negative quantity
effect denotes substitution and a positive quantity denotes complimentarily (the reverse
of the direct demand system). The obtained estimates of the own substitution effects
have the expected sign, and are statistically significant at the 5% probability level for all
commodities in the Atlanta, Los Angeles and New York markets. In the Chicago market,
it is statistically significant only for the own substitution effect of strawberries.
In terns of the quantity effects, in the Atlanta market, the estimate combinations of
tomato and cucumber and of tomato and bell pepper are statistically significant at the 5%
42
probability level. In the Los Angeles market, the estimate combination of tomato and
cucumber, the estimate combinations of tomato and bell pepper, and of tomato and
strawberry are statistically significant at the 5% probability level. In the New York
market, the estimate combinations of tomato and cucumber, of tomato and strawberry,
and of cucumber and bell pepper are statistically significant at the 5% probability level.
In the Chicago market, the estimate combination of cucumber and strawberry is
statistically significant at the 5% probability level.
Tomatoes. The obtained estimates for the own substitution quantity effects of
tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0763,
0.1124, 0.0220, and 0.0245, respectively. The compensated own substitution quantity
elasticities of tomatoes in the Atlanta, Los Angeles, Chicago, and New York markets are
0.1352, 0.1953, 0.0502, 0.0560, respectively. The uncompensated own substitution
quantity elasticities of tomatoes in the Atlanta, Los Angeles, Chicago, and New York
markets are 0.6778, 0.7178, 0.4990, 0.5138, respectively.
Bell peppers. The obtained estimates for the own substitution quantity effects of
bell peppers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0412,
0.0382, 0.0192, and 0.0284, respectively. The compensated own substitution quantity
elasticities of bell peppers in the Atlanta, Los Angeles, Chicago, and New York markets
are 0.2426, 0.2086, 0.0938, 0.1447, respectively. The uncompensated own
substitution quantity elasticities of bell peppers in the Atlanta, Los Angeles, Chicago, and
New York markets are 0.4204, 0.3971, 0.3165, 0.3416, respectively.
Cucumbers. The obtained estimates for the own substitution quantity effects of
cucumbers in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0320,
43
0.0366, 0.0189, and 0.0432, respectively. The compensated own substitution quantity
elasticities of cucumbers in the Atlanta, Los Angeles, Chicago, and New York markets
are 0.1754, 0.2500, 0.0726, 0.1709, respectively. The uncompensated own
substitution quantity elasticities of cucumbers in the Atlanta, Los Angeles, Chicago, and
New York markets are 0.3665, 0.4018, 0.3045, 0.4097, respectively.
Strawberries. The obtained estimates for the own substitution quantity effects of
strawberries in the Atlanta, Los Angeles, Chicago, and New York markets are 0.0111,
0.0182, 0.0186, and 0.0164, respectively. The compensated own substitution quantity
elasticities of strawberries in the Atlanta, Los Angeles, Chicago, and New York markets
are 0.1328, 0.1915, 0.1896, 0.1451, respectively. The uncompensated own
substitution quantity elasticities of strawberries in the Atlanta, Los Angeles, Chicago, and
New York markets are 0.2291, 0.3073, 0.2701, 0.2571, respectively.
Conclusions
To get the demand system that satisfies the neoclassical restrictions, we multiply
the budget share by the logarithmic of the demand system. On the empirical estimation,
it is better to use the mean of the budget share, vv,, instead of the moving average of the
budget share, w',, to multiply the logarithmic of the demand system. The results show
the significant effect by using the mean of the budget share on every functional form of
both direct and inverse demand systems. Moreover, by using the mean of the budget
share, we can obviate the need to choose among various functional forms. The results
also show that the estimation of the elasticity and the disturbance of the demand system
are the same across all functional forms of the inverse demand system. Overall, it is
better to use the RIDS model for fruits and vegetables to avoid statistical inconsistencies
44
(as the righthand side variables in the systems should not be controlled by the decision
maker) and to avoid the problem with the statistical significant test of the coefficients.
The elasticities were calculated from the estimation of the RIDS model by using
Bartens method of estimation with homogeneity and symmetry constraints imposed. All
the estimations of scale effects are statistically significant at the 5% probability level and
have the expected sign. In terms of own substitution quantity effects, these estimations
have the expected sign, and are statistically significant at the 5% probability level for all
commodities in the Atlanta, Los Angeles, and New York markets. In the Chicago
market, the estimation is statistically significant only for strawberry. In every market,
tomato has the highest absolute value of own uncompensated quantity elasticity while
strawberry has the lowest. In addition, own substitution quantity elasticities for tomato
and bell pepper in the Atlanta and Los Angeles markets are higher than in the Chicago
and New York markets.
45
Table 21. Estimation of the RIDS model for the Atlanta market by using the mean of the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5427
0.1777
0.1911
0.0963
(0.0287)
(0.0180)
(0.0171)
(0.0106)
^Tomato
0.0763
(0.0181)
^Bell Pepper
0.0475
0.0412
(0.0107)
(0.0104)
^Cucumber
0.0254
0.0037
0.0320
(0.0107)
(0.0075)
(0.0100)
^Strawberry
0.0033
0.0025
0.0103
0.0111
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (a)
0.0600
0.0379
0.0358
0.0221
R2
0.7022
0.3433
0.3840
0.3225
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 22. Estimation of the AIIDS model for the Atlanta market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0216
0.0078
0.0088
0.0127
(0.0287)
(0.0180)
(0.0171)
(0.0106)
Tf ornato
0.1696
(0.0181)
Tbell Pepper
0.0484
0.0998
(0.0107)
(0.0104)
Ttucumber
0.0774
0.0347
0.1171
(0.0107)
(0.0075)
(0.0100)
^Strawberry
0.0438
0.0167
0.0050
0.0655
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (cr)
0.0600
0.0379
0.0358
0.0221
R2
0.3080
0.3304
0.3877
0.4842
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
46
Table 23. Estimation of the LaTheil model for the Atlanta market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0216
0.0078
0.0088
0.0127
(0.0287)
(0.0180)
(0.0171)
(0.0106)
^Tomato
0.0763
(0.0181)
^Bell Pepper
0.0475
0.0412
(0.0107)
(0.0104)
^Cucumber
0.0254
0.0037
0.0320
(0.0107)
(0.0075)
(0.0100)
^Strawberry
0.0033
0.0025
0.0103
0.0111
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (a)
0.0600
0.0379
0.0358
0.0221
R2
0.0616
0.1278
0.0253
0.0488
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 24. Estimation of the RAIIDS model for the Atlanta market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5427
0.1777
0.1911
0.0963
(0.0287)
(0.0180)
(0.0171)
(0.0106)
Somato
0.1696
(0.0181)
Sell Pepper
0.0484
0.0998
(0.0107)
(0.0104)
Tfcucumber
0.0774
0.0347
0.1171
(0.0107)
(0.0075)
(0.0100)
Strawberry
0.0438
0.0167
0.0050
0.0655
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (a)
0.0600
0.0379
0.0358
0.0221
R2
0.6284
0.5406
0.6141
0.6190
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
47
Table 25. Estimation of the RIDS model for the Los Angeles market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5224
0.1885
0.1517
0.1157
(0.0306)
(0.0211)
(0.0189)
(0.0128)
^Tomato
0.1124
(0.0209)
^Bell Pepper
0.0348
0.0382
(0.0133)
(0.0144)
^Cucumber
0.0500
0.0003
0.0366
(0.0118)
(0.0100)
(0.0120)
^Strawberry
0.0276
0.0037
0.0131
0.0182
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.7011
0.2894
0.2223
0.2804
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 26. Estimation of the AIIDS model for the Los Angeles market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0533
0.0055
0.0053
0.0208
(0.0306)
(0.0211)
(0.0189)
(0.0128)
Yl ornato
0.1318
(0.0209)
Thell Pepper
0.0706
0.1113
(0.0133)
(0.0144)
^Cucumber
0.0342
0.0271
0.0884
(0.0118)
(0.0100)
(0.0120)
^Strawberry
0.0270
0.0137
0.0270
0.0677
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.2349
0.2186
0.1830
0.3226
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
48
Table 27. Estimation of the LaTheil model for the Los Angeles market by using the
mean of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0533
0.0055
0.0053
0.0208
(0.0306)
(0.0211)
(0.0189)
(0.0128)
^Tomato
0.1124
(0.0209)
^Bell Pepper
0.0348
0.0382
(0.0133)
(0.0144)
^Cucumber
0.0500
0.0003
0.0366
(0.0118)
(0.0100)
(0.0120)
^Strawberry
0.0276
0.0037
0.0131
0.0182
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.1338
0.0441
0.0657
0.0552
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 28. Estimation of the RAIIDS model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5224
0.1885
0.1517
0.1157
(0.0306)
(0.0211)
(0.0189)
(0.0128)
YTomato
0.1318
(0.0209)
YBell Pepper
0.0706
0.1113
(0.0133)
(0.0144)
YCucumber
0.0342
0.0271
0.0884
(0.0118)
(0.0100)
(0.0120)
YStrawberry
0.0270
0.0137
0.0270
0.0677
(0.0083)
(0.0073)
(0.0065)
(0.0071)
Standard Error (a)
0.0682
0.0479
0.0425
0.0289
R2
0.5879
0.4712
0.4171
0.5113
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
49
Table 29. Estimation of the RIDS model for the Chicago market by using the mean
the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4488
0.2226
0.2319
0.0805
(0.0246)
(0.0189)
(0.0189)
(0.0118)
^Tomato
0.0220
(0.0142)
^Bell Pepper
0.0125
0.0192
(0.0095)
(0.0105)
^Cucumber
0.0006
0.0088
0.0189
(0.0098)
(0.0081)
(0.0110)
^Strawberry
0.0101
0.0021
0.0107
0.0186
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.6287
0.4029
0.4386
0.1982
of
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 210. Estimation of the AIIDS model for the Chicago market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0113
0.0185
0.0281
0.0178
(0.0246)
(0.0189)
(0.0189)
(0.0118)
Yx ornato
0.2241
(0.0142)
Tbell Pepper
0.0769
0.1433
(0.0095)
(0.0105)
^Cucumber
0.1143
0.0443
0.1735
(0.0098)
(0.0081)
(0.0110)
^Strawberry
0.0329
0.0222
0.0149
0.0700
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.5212
0.4744
0.5653
0.4762
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
50
Table 211. Estimation of the LaTheil model for the Chicago market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0113
0.0185
0.0281
0.0178
(0.0246)
(0.0189)
(0.0189)
(0.0118)
^Tomato
0.0220
(0.0142)
^Bell Pepper
0.0125
0.0192
(0.0095)
(0.0105)
^Cucumber
0.0006
0.0088
0.0189
(0.0098)
(0.0081)
(0.0110)
^Strawberry
0.0101
0.0021
0.0107
0.0186
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.0229
0.0137
0.0163
0.0787
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 212. Estimation of the RAIIDS model for the Chicago market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4488
0.2226
0.2319
0.0805
(0.0246)
(0.0189)
(0.0189)
(0.0118)
Yl ornato
0.2241
(0.0142)
Tbell Pepper
0.0769
0.1433
(0.0095)
(0.0105)
/Cucumber
0.1143
0.0443
0.1735
(0.0098)
(0.0081)
(0.0110)
/Strawberry
0.0329
0.0222
0.0149
0.0700
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.7224
0.6100
0.6603
0.5739
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
51
Table 213. Estimation of the RIDS model for the New York market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4577
0.1968
0.2388
0.1120
(0.0190)
(0.0130)
(0.0159)
(0.0089)
^Tomato
0.0245
(0.0122)
^Bell Pepper
0.0015
0.0284
(0.0070)
(0.0079)
^Cucumber
0.0151
0.0232
0.0432
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0079
0.0036
0.0049
0.0164
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (ct)
0.0785
0.0511
0.0674
0.0364
R2
0.7956
0.5853
0.5880
0.5370
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 214. Estimation of the AIIDS model for the New York market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0199
0.0008
0.0142
0.0010
(0.0190)
(0.0130)
(0.0159)
(0.0089)
Yl ornato
0.2216
(0.0122)
Tbell Pepper
0.0843
0.1292
(0.0070)
(0.0079)
^Cucumber
0.0957
0.0264
0.1458
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0416
0.0185
0.0237
0.0839
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (a)
0.0785
0.0511
0.0674
0.0364
R2
0.6571
0.6573
0.4973
0.6015
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
52
Table 215. Estimation of the LaTheil model for the New York market by using the
mean of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0199
0.0008
0.0142
0.0010
(0.0190)
(0.0130)
(0.0159)
(0.0089)
^Tomato
0.0245
(0.0122)
^Bell Pepper
0.0015
0.0284
(0.0070)
(0.0079)
^Cucumber
0.0151
0.0232
0.0432
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0079
0.0036
0.0049
0.0164
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (a)
0.0785
0.0511
0.0674
0.0364
R2
0.0334
0.0563
0.0946
0.0589
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 216. Estimation of the RAIIDS model for the New York market by using the
mean of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4577
0.1968
0.2388
0.1120
(0.0190)
(0.0130)
(0.0159)
(0.0089)
Y\ ornato
0.2216
(0.0122)
Tfeell Pepper
0.0843
0.1292
(0.0070)
(0.0079)
Tfcucumber
0.0957
0.0264
0.1458
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0416
0.0185
0.0237
0.0839
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (a)
0.0785
0.0511
0.0674
0.0364
R2
0.7536
0.8456
0.7560
0.6830
Note: Asymptotic standard error of each estimated parameter is shown in parentheses
53
Table 217. Estimation of the RIDS model for the Atlanta market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5421
0.1706
0.1871
0.1014
(0.0276)
(0.0199)
(0.0165)
(0.0116)
^Tomato
0.0856
(0.0179)
^Bell Pepper
0.0490
0.0428
(0.0112)
(0.0112)
^Cucumber
0.0291
0.0009
0.0372
(0.0102)
(0.0077)
(0.0099)
^Strawberry
0.0075
0.0053
0.0091
0.0112
(0.0069)
(0.0054)
(0.0051)
(0.0052)
Standard Error (a)
0.0574
0.0422
0.0346
0.0244
R2
0.7264
0.2814
0.3916
0.2906
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 218. Estimation of the AIIDS model for the Atlanta market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0157
0.0048
0.0004
0.0118
(0.0277)
(0.0200)
(0.0167)
(0.0124)
ornato
0.1601
(0.0180)
Thell Pepper
0.0432
0.0912
(0.0112)
(0.0113)
^Cucumber
0.0807
0.0314
0.1137
(0.0103)
(0.0077)
(0.0100)
^Strawberry
0.0362
0.0166
0.0016
0.0545
(0.0073)
(0.0057)
(0.0054)
(0.0056)
Standard Error (a)
0.0577
0.0424
0.0349
0.0260
R2
0.2907
0.2653
0.3773
0.3170
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
54
Table 219. Estimation of the LaTheil model for the Atlanta market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0231
0.0044
0.0090
0.0108
(0.0276)
(0.0200)
(0.0163)
(0.0114)
^Tomato
0.0765
(0.0179)
^Bell Pepper
0.0472
0.0397
(0.0112)
(0.0112)
^Cucumber
0.0244
0.0017
0.0322
(0.0102)
(0.0076)
(0.0097)
^Strawberry
0.0050
0.0058
0.0095
0.0087
(0.0068)
(0.0054)
(0.0051)
(0.0051)
Standard Error (a)
0.0574
0.0424
0.0342
0.0240
R2
0.0758
0.1008
0.0287
0.0301
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 220. Estimation of the RAIIDS model for the Atlanta market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5493
0.1709
0.1786
0.1024
(0.0278)
(0.0200)
(0.0171)
(0.0128)
TTomato
0.1507
(0.0181)
The 11 Pepper
0.0415
0.0885
(0.0112)
(0.0113)
Ttucumber
0.0756
0.0308
0.1087
(0.0106)
(0.0079)
(0.0104)
^Strawberry
0.0336
0.0161
0.0022
0.0519
(0.0075)
(0.0058)
(0.0056)
(0.0058)
Standard Error (a)
0.0578
0.0423
0.0359
0.0270
R2
0.6493
0.4549
0.5789
0.4635
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
55
Table 221. Estimation of the RIDS model for the Los Angeles Market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5534
0.1794
0.1674
0.1031
(0.0309)
(0.0208)
(0.0203)
(0.0138)
^Tomato
0.1184
(0.0213)
^Bell Pepper
0.0425
0.0432
(0.0133)
(0.0147)
^Cucumber
0.0520
0.0008
0.0370
(0.0127)
(0.0106)
(0.0134)
^Strawberry
0.0239
0.0015
0.0141
0.0113
(0.0088)
(0.0078)
(0.0072)
(0.0078)
Standard Error (cr)
0.0687
0.0471
0.0456
0.0309
R2
0.7200
0.2743
0.2378
0.2170
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 222. Estimation of the AIIDS model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0300
0.0006
0.0137
0.0190
(0.0300)
(0.0208)
(0.0196)
(0.0141)
/T ornato
0.1279
(0.0207)
/bell Pepper
0.0639
0.1010
(0.0133)
(0.0150)
/Cucumber
0.0353
0.0255
0.0872
(0.0123)
(0.0105)
(0.0129)
/Strawberry
0.0286
0.0116
0.0263
0.0665
(0.0090)
(0.0080)
(0.0073)
(0.0081)
Standard Error (ct)
0.0668
0.0473
0.0439
0.0317
R2
0.2123
0.1954
0.1721
0.2682
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
56
Table 223. Estimation of the LaTheil model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0429
0.0083
0.0163
0.0216
(0.0297)
(0.0205)
(0.0194)
(0.0133)
^Tomato
0.1076
(0.0204)
^Bell Pepper
0.0355
0.0364
(0.0131)
(0.0146)
^Cucumber
0.0480
0.0011
0.0314
(0.0122)
(0.0103)
(0.0128)
^Strawberry
0.0241
0.0019
0.0155
0.0104
(0.0085)
(0.0076)
(0.0070)
(0.0076)
Standard Error (a)
0.0660
0.0465
0.0435
0.0298
R2
0.1277
0.0435
0.0545
0.0491
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 224. Estimation of the RAIIDS model for the Los Angeles market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5663
0.1717
0.1649
0.1004
(0.0315)
(0.0213)
(0.0208)
(0.0148)
YTomato
0.1171
(0.0217)
YBell Pepper
0.0570
0.0942
(0.0136)
(0.0151)
YCucumber
0.0312
0.0254
0.0815
(0.0130)
(0.0109)
(0.0137)
YStrawberry
0.0289
0.0118
0.0249
0.0656
(0.0094)
(0.0083)
(0.0077)
(0.0085)
Standard Error (a)
0.0701
0.0482
0.0467
0.0332
R2
0.6159
0.4073
0.3806
0.3984
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
57
Table 225. Estimation of the RIDS model for the Chicago market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4441
0.2316
0.2487
0.0758
(0.0248)
(0.0203)
(0.0209)
(0.0130)
^Tomato
0.0246
(0.0148)
^Bell Pepper
0.0164
0.0220
(0.0100)
(0.0113)
^Cucumber
0.0019
0.0109
0.0196
(0.0105)
(0.0088)
(0.0120)
^Strawberry
0.0101
0.0054
0.0107
0.0154
(0.0066)
(0.0057)
(0.0059)
(0.0057)
Standard Error (a)
0.0674
0.0553
0.0568
0.0348
R2
0.6201
0.3872
0.4250
0.1583
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 226. Estimation of the AIIDS model for the Chicago market by using the moving
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0221
0.0224
0.0223
0.0219
(0.0233)
(0.0196)
(0.0203)
(0.0140)
Y\ ornato
0.2188
(0.0141)
TheII Pepper
0.0762
0.1421
(0.0096)
(0.0110)
Tfcucutnber
0.1089
0.0418
0.1685
(0.0100)
(0.0086)
(0.0117)
/Strawberry
0.0337
0.0241
0.0178
0.0756
(0.0068)
(0.0059)
(0.0061)
(0.0062)
Standard Error (a)
0.0632
0.0533
0.0552
0.0377
R2
0.5404
0.4506
0.5111
0.4199
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
58
Table 227. Estimation of the LaTheil model for the Chicago market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0210
0.0217
0.0231
0.0193
(0.0231)
(0.0198)
(0.0201)
(0.0129)
^Tomato
0.0234
(0.0138)
^Bell Pepper
0.0143
0.0215
(0.0096)
(0.0111)
^Cucumber
0.0014
0.0111
0.0190
(0.0099)
(0.0086)
(0.0116)
^Strawberry
0.0104
0.0040
0.0092
0.0157
(0.0064)
(0.0057)
(0.0058)
(0.0057)
Standard Error (a)
0.0627
0.0539
0.0546
0.0345
R2
0.0267
0.0191
0.0141
0.0630
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 228. Estimation of the RAIIDS model for the Chicago market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4453
0.2322
0.2496
0.0732
(0.0250)
(0.0201)
(0.0210)
(0.0143)
fl ornato
0.2177
(0.0151)
Thell Pepper
0.0741
0.1415
(0.0100)
(0.0111)
^Cucumber
0.1094
0.0420
0.1678
(0.0105)
(0.0087)
(0.0120)
^Strawberry
0.0341
0.0254
0.0164
0.0759
(0.0071)
(0.0060)
(0.0062)
(0.0063)
Standard Error (a)
0.0679
0.0545
0.0569
0.0383
R2
0.7096
0.5853
0.6146
0.4957
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
59
Table 229. Estimation of the RIDS model for the New York market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4646
0.2118
0.2208
0.1066
(0.0182)
(0.0135)
(0.0169)
(0.0100)
^Tomato
0.0294
(0.0119)
^Bell Pepper
0.0003
0.0255
(0.0072)
(0.0084)
^Cucumber
0.0177
0.0212
0.0406
(0.0095)
(0.0072)
(0.0113)
^Strawberry
0.0120
0.0046
0.0017
0.0184
(0.0058)
(0.0050)
(0.0054)
(0.0054)
Standard Error (a)
0.0745
0.0527
0.0720
0.0413
R2
0.8176
0.6108
0.5146
0.4475
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 230. Estimation of the AIIDS model for the New York market by using the
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0041
0.0152
0.0230
0.0076
(0.0186)
(0.0138)
(0.0165)
(0.0103)
/Tomato
0.2047
(0.0124)
/bell Pepper
0.0772
0.1256
(0.0074)
(0.0086)
/Cucumber
0.0879
0.0234
0.1353
(0.0094)
(0.0073)
(0.0110)
/Strawberry
0.0396
0.0251
0.0241
0.0887
(0.0060)
(0.0050)
(0.0054)
(0.0055)
Standard Error (a)
0.0761
0.0545
0.0700
0.0427
R2
0.6377
0.6319
0.4528
0.5514
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
60
Table 231. Estimation of the LaTheil model for the New York market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.4646
0.2118
0.2208
0.1066
(0.0182)
(0.0135)
(0.0169)
(0.0100)
^Tomato
0.0294
(0.0119)
^Bell Pepper
0.0003
0.0255
(0.0072)
(0.0084)
^Cucumber
0.0177
0.0212
0.0406
(0.0095)
(0.0072)
(0.0113)
^Strawberry
0.0120
0.0046
0.0017
0.0184
(0.0058)
(0.0050)
(0.0054)
(0.0054)
Standard Error (ct)
0.0728
0.0506
0.0671
0.0386
R2
0.0414
0.0542
0.0660
0.0584
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 232. Estimation of the RAIIDS model for the New York market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4568
0.2273
0.2080
0.1117
(0.0188)
(0.0149)
(0.0178)
(0.0108)
/Tomato
0.2030
(0.0124)
/Sell Pepper
0.0818
0.1268
(0.0078)
(0.0093)
/Cucumber
0.0814
0.0224
0.1296
(0.0098)
(0.0080)
(0.0121)
/Strawberry
0.0398
0.0226
0.0258
0.0882
(0.0062)
(0.0054)
(0.0058)
(0.0058)
Standard Error (a)
0.0768
0.0591
0.0758
0.0444
R2
0.7525
0.8237
0.6596
0.6025
Note: Asymptotic standard error of each estimated parameter is shown in parentheses
61
Table 233. Unconstrained estimation of the RIDS model for the Atlanta market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5868
0.0225
0.2231
0.0993
(0.1905)
(0.1209)
(0.1151)
(0.0715)
^Tomato
0.0548
0.0576
0.0395
0.0004
(0.1120)
(0.0710)
(0.0676)
(0.0420)
^Bell Pepper
0.0154
0.0715
0.0183
0.0006
(0.0366)
(0.0232)
(0.0221)
(0.0137)
^Cucumber
0.0603
0.0640
0.0247
0.0181
(0.0418)
(0.0265)
(0.0252)
(0.0157)
^Strawberry
0.0299
0.0251
0.0032
0.0123
(0.0194)
(0.0123)
(0.0117)
(0.0073)
Standard Error (cr)
0.0588
0.0373
0.0355
0.0221
R2
0.7137
0.3648
0.3947
0.3276
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 234. Unconstrained estimation of the RIDS model for the Los Angeles market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.3980
0.2997
0.0717
0.0846
(0.1786)
(0.1262)
(0.1110)
(0.0749)
^Tomato
0.1874
0.1039
0.0908
0.0928
(0.1079)
(0.0763)
(0.0671)
(0.0452)
^Bell Pepper
0.0073
0.0171
0.0370
0.0330
(0.0394)
(0.0279)
(0.0245)
(0.0165)
^Cucumber
0.0632
0.0102
0.0765
0.0511
(0.0370)
(0.0261)
(0.0230)
(0.0155)
^Strawberry
0.0048
0.0172
0.0245
0.0342
(0.0249)
(0.0176)
(0.0154)
(0.0104)
Standard Error (a)
0.0676
0.0478
0.0420
0.0283
R2
0.7059
0.2931
0.2409
0.3061
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
62
Table 235. Unconstrained estimation of the RIDS model for the Chicago market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.3565
0.1354
0.2338
0.0799
(0.1251)
(0.0963)
(0.0964)
(0.0118)
^Tomato
0.0649
0.0301
0.0018
0.0049
(0.0541)
(0.0416)
(0.0416)
(0.0071)
^Bell Pepper
0.0033
0.0372
0.0111
0.0047
(0.0312)
(0.0240)
(0.0240)
(0.0066)
^Cucumber
0.0291
0.0137
0.0176
0.0165
(0.0344)
(0.0265)
(0.0265)
(0.0068)
^Strawberry
0.0074
0.0036
0.0035
0.0167
(0.0167)
(0.0129)
(0.0129)
(0.0053)
Standard Error (a)
0.0667
0.0513
0.0514
0.0316
R2
0.6306
0.4074
0.4404
0.2036
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 236. Unconstrained estimation of the RIDS model for the New York market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5173
0.2015
0.1055
0.0943
(0.0746)
(0.0486)
(0.0632)
(0.0347)
^Tomato
0.0008
0.0073
0.0306
0.0016
(0.0327)
(0.0213)
(0.0277)
(0.0152)
^Bell Pepper
0.0060
0.0288
0.0026
0.0044
(0.0223)
(0.0146)
(0.0189)
(0.0104)
^Cucumber
0.0233
0.0146
0.0803
0.0006
(0.0218)
(0.0142)
(0.0185)
(0.0101)
^Strawberry
0.0235
0.0062
0.0246
0.0192
(0.0138)
(0.0090)
(0.0117)
(0.0064)
Standard Error (a)
0.0782
0.0510
0.0662
0.0363
R2
0.7972
0.5880
0.6020
0.5386
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
63
Table 237. Bartens estimation with the homogeneity condition of the RIDS model for
the Atlanta market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5378
0.1879
0.1881
0.0927
(0.0283)
(0.0181)
(0.0171)
(0.0106)
^Tomato
0.0835
0.0658
0.0190
0.0035
(0.0185)
(0.0118)
(0.0112)
(0.0069)
^Bell Pepper
0.0069
0.0350
0.0122
0.0005
(0.0164)
(0.0105)
(0.0099)
(0.0061)
^Cucumber
0.0505
0.0217
0.0318
0.0168
(0.0177)
(0.0113)
(0.0107)
(0.0067)
^Strawberry
0.0261
0.0091
0.0005
0.0128
(0.0131)
(0.0084)
(0.0079)
(0.0049)
Standard Error (a)
0.0588
0.0376
0.0355
0.0221
R2
0.7136
0.3553
0.3944
0.3275
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 238. Bartens estimation with the homogeneity condition of the RIDS model for
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5184
0.1912
0.1456
0.1159
(0.0305)
(0.0216)
(0.0191)
(0.0130)
^Tomato
0.1150
0.0386
0.0399
0.0278
(0.0209)
(0.0148)
(0.0131)
(0.0089)
^Bell Pepper
0.0146
0.0369
0.0027
0.0035
(0.0229)
(0.0162)
(0.0143)
(0.0098)
^Cucumber
0.0840
0.0085
0.0390
0.0165
(0.0210)
(0.0149)
(0.0132)
(0.0090)
^Strawberry
0.0164
0.0068
0.0036
0.0149
(0.0182)
(0.0129)
(0.0114)
(0.0078)
Standard Error (a)
0.0677
0.0479
0.0424
0.0289
R2
0.7052
0.2905
0.2264
0.2813
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
64
Table 239. Bartens estimation with the homogeneity condition of the RIDS model for
the Chicago market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4457
0.2194
0.2349
0.0799
(0.0249)
(0.0192)
(0.0191)
(0.0118)
^Tomato
0.0271
0.0054
0.0023
0.0049
(0.0151)
(0.0116)
(0.0116)
(0.0071)
^Bell Pepper
0.0170
0.0181
0.0114
0.0047
(0.0140)
(0.0107)
(0.0107)
(0.0066)
^Cucumber
0.0064
0.0077
0.0173
0.0165
(0.0144)
(0.0111)
(0.0111)
(0.0068)
^Strawberry
0.0165
0.0049
0.0036
0.0167
(0.0111)
(0.0086)
(0.0086)
(0.0053)
Standard Error (a)
0.0668
0.0514
0.0514
0.0321
R2
0.6296
0.4051
0.4404
0.1752
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 240. Bartens estimation with the homogeneity condition of the RIDS model for
the New York market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4678
0.2022
0.2320
0.1147
(0.0204)
(0.0133)
(0.0175)
(0.0095)
^Tomato
0.0216
0.0075
0.0224
0.0102
(0.0127)
(0.0083)
(0.0109)
(0.0059)
^Bell Pepper
0.0067
0.0286
0.0350
0.0008
(0.0128)
(0.0083)
(0.0109)
(0.0059)
^Cucumber
0.0109
0.0148
0.0487
0.0057
(0.0125)
(0.0081)
(0.0107)
(0.0058)
^Strawberry
0.0173
0.0063
0.0087
0.0166
(0.0104)
(0.0068)
(0.0089)
(0.0049)
Standard Error (a)
0.0783
0.0510
0.0669
0.0364
R2
0.7967
0.5880
0.5936
0.5377
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
65
Table 241. Elasticities for the Atlanta market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
0.9617
1.0460
1.0485
1.1526
%Tornato
0.1352
0.2795
0.1396
0.0401
<3Bell Pepper
0.0842
0.2426
0.0205
0.0302
Â£Cucumber
0.0451
0.0220
0.1754
0.1229
Strawberry
0.0059
0.0148
0.0563
0.1328
ornato
0.6778
0.3108
0.4520
0.6103
y^Bell Pepper
0.0793
0.4204
0.1987
0.2260
y/Cucumbex
0.1302
0.2126
0.3665
0.0872
^Strawberry
0.0744
0.1022
0.0313
0.2291
Note: <^is scale elasticity, Â£ is compensated elasticity, and y/ is uncompensated
elasticity.
Table 242. Elasticities for the Los Angeles market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
c
0.9075
1.0302
1.0365
1.2194
Â£Tomato
0.1953
0.1901
0.3418
0.2910
Bell Pepper
0.0604
0.2086
0.0021
0.0389
^Cucumber
0.0869
0.0017
0.2500
0.1384
4Strawberry
0.0480
0.0202
0.0897
0.1915
I//T,ornato
0.7178
0.4030
0.2549
0.4110
y^Bell Pepper
0.1056
0.3971
0.1917
0.1842
y^Cucumbex
0.0459
0.1525
0.4018
0.3169
tyStraw berry
0.0382
0.0776
0.1881
0.3073
Note: Â£is scale elasticity, ^is compensated elasticity, and y/'\s uncompensated
elasticity.
66
Table 243. Elasticities for the Chicago market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
z
1.0259
1.0905
0.8920
0.8188
Â£Tomato
0.0502
0.0610
0.0022
0.1026
Â£>Bell Pepper
0.0285
0.0938
0.0338
0.0212
Â£Cucumber
0.0013
0.0431
0.0726
0.1083
4Strawberry
0.0231
0.0102
0.0410
0.1896
^Tomato
0.4990
0.4161
0.3925
0.2556
y^Bell Pepper
0.1810
0.3165
0.1483
0.1884
tyCucumber
0.2681
0.2404
0.3045
0.1046
Strawberry
0.0778
0.1175
0.0468
0.2701
Note: C, is scale elasticity, is compensated elasticity, and (// is uncompensated
elasticity.
Table 244. Elasticities for the New York market
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
1.0453
1.0040
0.9438
0.9910
%Tomato
0.0560
0.0079
0.0598
0.0696
^Bell Pepper
0.0035
0.1447
0.0917
0.0320
Â£Cucumber
0.0345
0.1184
0.1709
0.0435
Â£Strawberry
0.0180
0.0185
0.0194
0.1451
y^Tornato
0.5138
0.4317
0.3535
0.3644
y^Bell Pepper
0.2014
0.3416
0.0933
0.1622
y^Cucumbex
0.2300
0.1357
0.4097
0.2072
tyStrawberrv
0.1002
0.0950
0.0872
0.2571
Note: C, is scale elasticity, Â£ is compensated elasticity, and iff is uncompensated
elasticity.
CHAPTER 3
PARTIAL EQUILIBRIUM ANALYSIS ON FRUIT AND VEGETABLE INDUSTRY
This chapter concentrates on the potential impact of two major developments on
the U.S. fruit and vegetable industry. The first development is the proposed phasing out
of using methyl bromide. Methyl bromide is a critical soil fumigant that has been used in
the production of several fresh fruits and vegetables grown in the United States. The U.S.
Clean Air Act of 1992 requires that methyl bromide be phased out of use by 2005. The
problem is that while significant progress has been made towards developing alternatives
to methyl bromide, a suitable alternative has not been identified. The second
development is the elimination of all tariff and trade restrictions on exports of fruits and
vegetables from Mexico as a result of the implementation of the North American Free
Trade Agreement (NAFTA). Under NAFTA, all agricultural tariffs on goods traded
between the United States and Mexico will be eliminated by 2008. Some of the tariffs
were eliminated in 1994, while others were to be phased out over 5, 10, or 15 years. In
addition, negotiations of trade agreements within the World Trade Organization (WTO)
or as part of the Free Trade Area of the Americas (FTAA) could significantly affect these
tariffs. The elimination of tariffs means that U.S. domestic production of fresh fruits and
vegetables is likely to face increased competition from imports.
To assess the impacts of these developments on the U.S. fruit and vegetable
industry, it was essential to develop a partial spatial equilibrium model. Following on a
model developed by VanSickle et al., I modified and improved that model by simplifying
67
68
regional effects and changing the objective function so that the model can simulate all
fruits and vegetables at the same time.
Background
Methyl bromide has been a critical soil fumigant in the agricultural production for
many years. Methyl bromide is a broad spectrum pesticide that can be used to control
pest insects, nematodes, weeds, pathogens, and rodents. Under normal conditions,
methyl bromide is a colorless and odorless gas. About 21,000 tons of methyl bromide are
used annually in agriculture in the United States and about 72,000 tons are used globally
each year. When used as a soil fumigant, methyl bromide gas is injected into the soil at a
depth of 12 to 24 inches before a crop is planted. This procedure effectively sterilizes the
soil, and kills a majority of soil organisms. In addition, commodities may be treated with
methyl bromide as part of a quarantine requirement of an importing country. Some
commodities are treated several times during both storage and shipment.
Methyl bromide was assigned a 0.4 ozonedepletion potential (methyl bromide has
contributed about 4% to the current ozone depletion and may contribute 5% to 15% to
future ozone depletion if it is not phased out). Methyl bromide is 40 times more efficient
at destroying the ozone than chlorine (which should be phased out as well). The
degradation of the ozone layer leads to higher levels of ultraviolet radiation reaching the
Earths surface, which could reduce crop yields and could cause health problems (e.g.,
skin cancer, eye damage, and impaired immune systems).
The impact of methyl bromide on ozone depletion led to the development of the
Montreal Protocol in 1987. According to the U.S. Environmental Protection Agency
(EPA), the Montreal Protocol was designed to help revise methyl bromide phaseout
schedules on the basis of periodic scientific and technological assessments. The U.S.
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Clean Air Act of 1992, as amended in 1998, requires that methyl bromide be phased out
of use on the basis of separate schedules prepared for developed and developing countries
who are party to the Montreal Protocol (Table 31). The phaseout of methyl bromide use
is being implemented by restricting the volume of methyl bromide that can be produced
and sold. So far, efforts to phase out methyl bromide have resulted in a 50% reduction in
use (the first two 25% reductions have already occurred in the United States). Table 31
shows the schedule for phasing out methyl bromide. Developing countries can still use
methyl bromide until 2015 (10 years after the phaseout in the developed countries).
There is concern that developed countries could be placed at a disadvantage (compared to
developing countries) if suitable alternatives cannot be found. This is highlighted by the
fact that in 2005, when the developed countries should have completed the phaseout of
methyl bromide, the developing countries would still be permitted to use methyl bromide
on 80% of the base level. Unfortunately, there are very few viable alternatives that are
technically and are economically feasible and also acceptable from a public health
standpoint. Therefore the Montreal Protocol allowed for exemptions to the phaseout
(e.g., the critical use exemption). In March of 2004, a meeting of the Parties to the
Montreal Protocol was held in Montreal, Canada, during March 2426, 2004 to address
problems related to the methyl bromide phaseout such as nominations and granting
conditions for Critical Use Exemptions (CUES). For examples, the United States made a
CUE request after a thorough and comprehensive review process. The U.S. EPA will
work with the USDA to fully support the U.S. nomination.
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Table 31. Schedules of the phaseout of methyl bromide
Developed Countries
Developing Countries
1991: Base level
199598 average: Base level
1995: Freeze
2002: Freeze
1999: 75% of base
2003: Review of reductions
2001: 50% of base
2005: 80% of base
2003: 30% of base
2005: Phaseout
2015: Phaseout
Source: U.S. Environmental Protection Agency
Four factors need to be considered when selecting and evaluating suitable
alternatives to methyl bromide. The first factor is technical. Methyl bromide is quite
versatile, fairly easy to apply, and can be effective against a wide range of pests (unlike
most other pesticide, fumigant, or pest control methods). U.S. producers may consider
using Integrated Pest Management (IPM) as an alternative to using methyl bromide. IPM
is based on pest identification, and monitoring and establishing pest injury levels.
However, a successful IPM program requires more information, analysis, planning, and
knowhow than does using methyl bromide.
The second factor is economic (the impact of alternatives on the profitability of the
enterprise). While some alternatives may involve a high initial investment cost,
especially considering the operating costs of new equipment, they might actually be more
costeffective in the long run. This is true because the cost for using methyl bromide is
expected to rise in the future. A less effective alternative could be as profitable as using
methyl bromide if the costs for using the alternative are sufficiently lower. For the
economic factor, profitability needs to be examined.
The third factor is health and safety, and the fourth factor is environmental
concerns. Given the heightened awareness of safety and environmental concerns (from
both marketing and environmental perspectives), it is advisable to select alternatives that
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are considered environmental friendly and pose no or minimal risks to users. For
example, an alternative should not cause ozone depletion and global warming.
Turning our attention to the potential trade impact, it should be noted that
international trade is an important component of the U.S. fruit and vegetable industry. In
1999, imports accounted for 11.6% of total U.S. fruit and vegetable consumption. The
United States imposed ad valorem tariffs on imports of fresh vegetables. The U.S. ad
valorem tariffs were 3.1% to 4.6% on fresh tomatoes, 3.0% on fresh bell peppers, and
2.1% to 10.6% on fresh cucumbers. Negotiations of trade agreements within the World
Trade Organization (WTO) or as part of the Free Trade Area of the Americas (FTAA)
could significantly lower these tariffs. As stated earlier, NAFTA has had a considerable
impact on the levels of these tariffs. NAFTA, which went into force on January 1,1994,
is an agreement by the United States, Canada, and Mexico to phase out almost all
restrictions on international trade and investment among the three countries. The United
States and Canada were already well on the way to eliminating the barriers to trade and
investment between them when NAFTA went into effect. The main new feature of
NAFTA was the removal of most of the barriers between Mexico and the United States.
Fresh vegetable imports have been under scrutiny since before the implementation
of NAFTA in 1994. During the first year of NAFTA, the import share of consumption
for fresh fruits and vegetables remained at the preNAFTA level of about 10%.
However, following the devaluation of the Mexican peso in December of 1994, U.S.
imports of Mexican vegetables rose sharply. Mexican growers increased shipments to
the United States because of poor domestic demand and more attractive prices in the
United States. As a result of measured exports of fresh vegetables from Mexico, the
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import share of U.S. domestic consumption of vegetables grew steadily from 10% in
1994 to 15% in 1998. In 1999 and into early 2000, low U.S. domestic prices slowed
import volume and pushed the import market share down to 14%.
Several empirical studies in the literature on the analysis of internationaltrade
issues have focused on partial equilibrium analysis. For example, spatial price
equilibrium analysis attempts to predict changes in future trade flows, prices,
consumption, and production for a commodity under governmental policies. The results
allow the estimation of welfare benefits and costs by using the concept of economic
surplus to individual countries from specific trade policies.
Under the partial equilibrium analysis, the assumption is that producers maximize
their profits, consumers maximize their utilities, and marketing activities are competitive.
Distortions come about only through governmental policies. There is no world price in
this model because the price differs among regions by transportation costs, tariffs, and
market imperfections. The amounts of consumption, production, exports, imports, and
equilibrium prices in each region are determined simultaneously.
Research Problem
With an increase in the number of U.S. sponsored trade agreements and general
trends toward opening the market, U.S. producers of fruits and vegetables may face
increased competition from foreign sources. Changes in competitiveness could affect
trade flows, which could change the structure and geographic distribution of the
agricultural industries. Internationaltrade agreements and competition among fruit and
vegetable industries have increased. Also, the phaseout of methyl bromide places the
United States at a disadvantage in trade with Mexico. Our study analyzes the impacts of
internationaltrade agreements and the ban on methyl bromide by estimating the change
73
in location of agricultural production and by determining which countries will benefit and
which countries will lose.
Hypotheses
Our main hypotheses were as follows:
If a ban on methyl bromide is imposed without viable economic alternatives, then
the production of these crops will decrease. Therefore the decrease in production
causes the prices of fruits and vegetables in the United States to increase.
The impact of NAFTA will decrease fruit and vegetable prices in the United States.
Afterwards, the decrease in prices will cause an increase in the quantity demanded
and a decrease in the domesticquantity supplied.
Objectives
The first objective of our study is to estimate the impact of the phaseout of methyl
bromide on consumers, producers, prices, productions, and revenues. The second
objective of our study is to investigate the impact of NAFTA on the fruit and vegetable
industry. By investigating the impacts of the internationaltrade issues, the model is
expected to replicate the evolution of the fruit and vegetable industry.
Theoretical Framework
Following MasColell (2000), in a competitive economy, consumers and producers
act as price takers by regarding market prices as unaffected by their own actions.
Building on a spatial equilibrium model developed by VanSickle et al., we conducted an
investigation of the fruit and vegetable industry. This spatial equilibrium model satisfies
a profitmaximizing condition, a utilitymaximizing condition, and a marketclearing
condition. These three conditions must be met for a competitive economy to be
considered in equilibrium. The profitmaximizing condition states that each firm will
choose a production plan that maximizes its profits, given the equilibrium prices of its
outputs and inputs. The utilitymaximizing condition requires that each consumer choose
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a consumption bundle that maximizes utility, given the budget constraint imposed by the
equilibrium prices and wealth. The marketclearing condition requires that at the
equilibrium prices, the aggregate supply of each commodity equals the aggregate demand
for that commodity. If excess supply or demand exists for a good at the going prices, the
economy would not be at a point of equilibrium. At the equilibrium price that equates
demand and supply, consumers do not wish to raise prices, and firms do not wish to
lower them.
The partial equilibrium analysis assumes that the market for one good (or several
goods), represents a small part of the overall economy. It is also assumed that the wealth
effects in a small market will also be small, as the expenditure on the good is a small
portion of a consumers total expenditure. Moreover, given the small size of the market,
any changes in this market are expected to have no or negative impact on prices in other
markets. In terms of the partial equilibrium interpretation, we consider good g as the
good whose market is being investigated, and denote the composite of all other goods as
the numeraire. We normalize the price of the numeraire to equal one, and let p denote the
price of good g. Each firm j = 1,..Jis able to produce good g from good k. The
amount of the numeraire required by firm j to produce qj units of good g is given by the
cost function c/jqj). Given equilibrium price p for good g, the profitmaximizing
condition implies that firm f s equilibrium output level qj must satisfy the profit
maximizing problem,
Max pqj c(qj).
(31)
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Likewise the utilitymaximizing condition implies that given the equilibrium price
p for good g, consumer f s equilibrium consumption level x, must satisfy the utility
maximizing problem, subject to the budget constraint,
Max u,{Xj), (32)
subject to
I i pxi = m, (33)
where m is the budget share.
Because of the market clearing condition assumed, the equilibrium price of good g
will be price p at which the aggregate demand equals the aggregate supply,
x = q, (34)
where x is an aggregate demand (x = Â£, xÂ¡) and q is an aggregate supply (q = Â£, qj).
Because consumers and producers are price takers, the inverses of the aggregate
demand and supply functions are of interest. The inverse demand function, P{x) = X'(x),
gives the price that results in the aggregate demand of x. That is, when each consumer
optimally chooses a consumer demand for good g at this price, total demand exactly
equals x. At these individual demand levels, each consumers marginal benefit from an
additional unit of good g is exactly equal to P(x). Moreover, given that the aggregate
quantity x is efficiently distributed among the consumers, the value of the inverse demand
function, P(x), can also be viewed as the marginal social benefit of good g.
Likewise, inverse supply function,/? = Q'\q), gives the price that results in the
aggregate supply of q. That is, when each firm chooses its optimal output level facing
this price, the aggregate supply is exactly q. The inverse of the industry supply function
can be viewed as the industry marginal cost function, which can be denoted by
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C\q) = a\q). (35)
We get the inverse supply function (or the industry marginal cost function) from
the profitmaximizing condition and the inverse demand function from the utility
maximizing condition. Then we can find the equilibrium price at whichp(x) =p(q),
Xx{x) = Q'\q), or P{x) = C'(x) as x = q (Equation 34). Figure 31 represents the partial
equilibrium analysis using the Marshallian graphical technique with the equilibrium price
at the point of intersection of the aggregate demand and aggregate supply curves.
Figure 31. Aggregate demand and aggregate supply
Fundamental Theory of the Partial Equilibrium Model
In the partial equilibrium model, it is relatively easy to measure the change in the
equilibrium outcome of a competitive market or the change in the level of social welfare,
resulting from a change in underlying market conditions such as an improvement in
technology, a new government internationaltrade policy, or the elimination of some
existing market imperfection. The partial equilibrium model turns out the optimal
consumption and production levels for good g that maximize the Marshallian aggregate
surplus. Moreover, if price p and allocation (*i, ..., x q\, ...,qj) constitute a competitive
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equilibrium, then this allocation is Pareto optimal (which is the first fundamental theorem
of welfare economics). A differential change (dx\,..., dxÂ¡, dq\,..., dqj) in the quantities of
good g (consumed and produced) satisfies dx E, dx, = Ey dqj (since x = q, Equation 34).
The change in aggregate Marshallian surplus is then
dS = P(x) E, dx, C'(q) Ey dqj,
dS=[P(x)C'(x)]dx. (36)
It is sometimes of interest to distinguish between the two components of aggregate
Marshallian surplus that accrue directly to consumers and producers. That is, if the set of
active consumers of good g is distinct from the set of producers, then this distinction
demonstrates something about the distributional effects of the change in the level of
social welfare. There is a change in aggregate consumer surplus when consumers face
effective price p and aggregate consumption jc( p), which is
dCS(p) = [P(x)~ p]dx. (37)
There is also a change in aggregate producer surplus when firms face effective price, p,
and aggregate production q{ p), which is
dfKp) = [p C\q)] dq = [p C\x)] dx. (38)
We can see that the change in aggregate Marshallian surplus is the summation of the
change in aggregate consumer surplus and the change in aggregate producer surplus,
which can be written as
dS = dCS(p) + dn(p). (39)
We can also integrate Equation 39 to express the total value of the aggregate
Marshallian surplus, the aggregate consumer surplus, and the aggregate producer surplus.
By doing this, we get
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x X(p) q(p)
So+ f [P(s)C'(s)]ds={ J [P(s)~ p]ds} + {n0+ \ [pC\s)}ds),
0 0 0
x oo q(p)
S0+ J [P(s) C'(s)] ds= J x(s) ds+{n0+ j [p C'(j)] ds, (310)
0 p 0
where So is a constant of integration equal to the value of the aggregate surplus. When
there is no consumption or production of good g, 17o is a constant of integration equal to
the value of the profits when qj = 0 for all j and So = /70 (which is equal to 0 if c,(0) = 0
for all j). In Figure 31, the aggregate consumer surplus is depicted by area A and the
aggregate producer surplus is depicted by Area B. The maximized aggregate Marshallian
surplus is depicted by area A plus area B, which is exactly equal to the area lying
vertically between the aggregate demand and supply curves for good g, up to equilibrium
quantity x.
Impact of the Phaseout of Methyl Bromide
Since currently available alternatives of methyl bromide are more expensive, it can
be postulated that in the absence of methyl bromide, cost of production is likely to
increase. This can be represented in the model by an upwards shift in the aggregate
supply curve, C'm(Z). Figure 32 shows that the new supply curve is Zm(P) = C'(Z) +
C'm(Z), where C'm(Z) is the addition marginal cost resulting from the phaseout of the
methyl bromide. Figure 32 shows that the upward shift of the supply curve results in an
increase in the equilibrium price (from P* to P**) and a decrease in the aggregate
shipment quantity (from X* to X**).
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Figure 32. Partial equilibrium under effect of the phaseout of methyl bromide
Impact of NAFTA
The most important effect of trading with another nation is the economic gains that
accrue to both parties as a result of trade. Without trade, each country has to make
everything it needs, including those products it is not efficient at producing. On the other
hand, when trade is permitted, each country can concentrate its efforts on producing
exports in exchange for imports. Gains from trade arise from being able to purchase
desired commodities or services from abroad cheaper than it would cost to produce them
at home.
As pointed out by SchiavoCampo (1978), countries trade among themselves
because of differences in factor endowments. An analysis of the impact of different
national endowments of production factors have upon international trade is summarized
in the HeckscherOhlin Theorem. This theorem states that a country has a comparative
advantage in producing commodities with a relatively abundant factor and importing
commodities with a relatively scarce factor. However, there are many barriers to
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international trade, including natural obstacles like the geographic distance between
countries and the resulting costs of transport.
The bestknown, and most frequently used, instrument of commercial policy
(which is a manmade obstacle to international trade) is the tariff. Tariffs may be
expressed in absolute dollarsandcents terms (a specific tariff) or in relative terms as a
percentage tax (ad valorem tariff). A tariff is an instrument that is used to economically
separate the national market from the world economy by increasing the import price of a
commodity over its world price (i.e., a tariff causes an increase in the domestic price,
which is the main consequence of tariffs on production, consumption, income
distribution, and trade).
The several effects of a tariff can be shown by means of supplyanddemand
diagrams that are expanded to include import supply in addition to domestic supply.
Figure 33 shows the market situation for a homogeneous product in the importing
country. In the complete absence of foreign trade, the market would find its equilibrium
at Ed, which is the intersection of domestic demand line Dj and domestic supply line S.
The product would sell for price Pd. Consumers surplus under the absence of trade
(which is the differences between the market price and the maximum they would be
willing to pay) is area PdEdL. Producers surplus under the absence of trade (which is the
difference between the market price and the minimum the producers would be willing to
accept) is area MEdPw.
When trade is allowed, the imports increase product supply (S + S/) and decrease
the product price to consumers. Consequently, the market would find its new equilibrium
at I (which is the intersection of domestic demand line Dd and domestic supply plus
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foreign supply line S + S/). The product would sell for price Pw. The imports are AB
(which is the difference between total desired consumption and domestic production).
Domestic production is OA, and total quantity demanded is OB. The decrease in price
causes an increase in the consumption and a decrease in domestic production.
Consumers welfare gain is area PwIEdPd, and domestic producers welfare loss is area
PwFEdPd The net gain from trade is area FIEd.
When the domestic country imposes a tariff, the foreign supply is decreased, but
the price of the product is increased. As a result, the market finds its new equilibrium at J
(which is the intersection of domestic demand line Dd and domestic supply plus foreign
supply with tariff line Sd + S/+ T). The product would sell for price Pw+r The increase
in price causes a decrease in the consumption and an increase in the domestic production.
Consumption falls to OD, and domestic production rises to OC. Imports are cut on both
accounts to CD. Consumers welfare loss is area PwIJPw+r, domestic producers welfare
gain is area PWFKPW+T, and tariff revenue effect is area GHJK.
The tariff consumption effect (BD) is related to the price elasticity of demand. A
highly elastic demand indicates that a change in price has a considerable effect on the
amount that people wish to buy. On the other hand, a relatively inelastic demand means
that a price change will lead to only a small change in the quantity demanded. If price
elasticity is zero, the quantity will not change at all, regardless of the magnitude of the
variation in the price of the product.
The effect from NAFTA (which is an agreement between the United States,
Canada, and Mexico to phaseout almost all restrictions on international trade, including
tariffs) will move the equilibrium point back to 7 and the supply line to the right (where
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the supply of the product is domestic supply plus foreign supply line + Sj). The
product would sell for price Pw.
Methodology
A partial equilibrium model can be used to evaluate the effects of a change in the
industry on the production and marketing of various crops in various regions. In the
VanSickle et al. model, these crops were modeled in a monthly model, considering
production from each of the major producing regions in Florida and from other regions in
the United States and Mexico. The model was developed to characterize crop production
from these regions for the winter months in which Florida ships these commodities.
The VanSickle et al. model allocates crop production across regions based on
delivered cost to regional markets, productivity, and regional demand structure in the
United States. Inverse demand equations were used in the model based on work by Scott
(1991) for squash, eggplant, and watermelons and from Chapter 2 for tomatoes, bell
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peppers, cucumbers, and strawberries. Preharvest and postharvest cost production costs
were estimated for each production system and area by Smith and Taylor (2002). The
cost budgets were constructed using a computerized budget generator program, AGSYS.
Technical coefficients used in constructing the budgets were obtained by consultation
with individual growers, county agents, and UF/IFAS researchers. Florida uses several
doublecropping systems in which a primary crop is followed by a different (secondary)
crop on the same unit of land. Transportation costs were included for delivering these
products to each of the regional markets based on mileages determined by the Automap
software and an estimation for a fullyloaded refrigerated truck carrying 40,000 pounds at
$1.3072 per mile (VanSickle, et al., 1994).
The constrained optimization model was solved using GAMS software. After
solving the VanSickle et al. model for a base solution for the 2000/2001 season, the
budgets and yields were changed to reflect the costs of growing the crops using an
alternative to methyl bromide. The results were compared to determine the impact that
the phaseout of methyl bromide may have on the production and marketing of these
crops.
In our study, we investigated the effect of the phaseout of methyl bromide on
tomatoes, bell peppers, and eggplant in Florida and on strawberries grown in both Florida
and California. Estimates of the impacts on production costs and yields from using
alternatives to methyl bromide were determined from discussions with scientists
attending USDA meetings (Carpenter and Lynch, 1998). For strawberries, California
growers were assumed to have switched to Chloropicrin (with additional hand weeding)
as a replacement to methyl bromide. Strawberry producers in West Central Florida were
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assumed to have switched to a Telone C17/Devrinol herbicide combination. For
tomatoes, Florida growers were assumed to have switched to a Telone C17/Chloropicirin/
Tillam herbicide combination. For eggplant and bell peppers, Florida growers were
assumed to have switched to a Telone C17/Devrinol herbicide combination. Using
Telone requires additional protective equipment that must be worn by applicators and
field workers. Table 32 shows the impact of these alternatives to methyl bromide on
preharvest cost and yield in each region in Florida and California. Other regions
included in the model were assumed to be producing crops without using methyl
bromide, and therefore would have no effect on costs and yields from the phaseout.
Table 32. Effect of the methyl bromide in Florida and California
State
Region
Preharvest Cost
Impact
($/acre)
Percentage of Yield
Reduction
(%)
Florida
Dade County
(291)
10
Palm Beach County
(115)
5
Southwest Florida
(74)
10
West Central
(139)
5
California
Northern California
653
20
Southern California
653
20
Source: USDA
Next we investigated international trade by changing the production costs for
Mexico to reflect the effect of NAFTA. Our baseline assumed a fixed tariff of S0.1 per
unit of imported commodity, which was added to the postharvest cost of production. We
found that the impact of NAFTA would be the elimination of all such tariffs.
The VanSickle et al. model was solved using GAMS programming software. The
analysis of the impacts from NAFTA and the ban on methyl bromide were conducted in
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two parts. Our study updated the VanSickle et al. model to the 2000/2001 production
season by using updated data and quantity elasticities estimated from the inverse demand
analysis. This solution provided the baseline for comparison to other solutions where the
parameters of the model were adjusted to reflect the impacts of NAFTA and the ban on
methyl bromide.
For the first part of the analysis, the model was solved with parameters that
assumed continued use of the tariff and methyl bromide. For the second part of the
analysis, three scenarios beyond the baseline were solved with the model. The first
scenario assumed the next best alternative, given projections on expected cost and yield
impacts. The second scenario gave projections on the postharvest production cost that
was reduced for Mexico from the elimination of tariffs. The third scenario combined the
impacts of NAFTA and the ban on methyl bromide. The adjustments that were made in
the parameters reflect changes in production costs and yield by switching to alternatives
to methyl bromide and changes in postproduction costs for Mexico by switching to non
tariff trade.
The VanSickle et al. model was developed by modifying the North American
winter vegetable market model developed by Spreen et al. (1995). For the demand side
of the model, the commodities were assumed to be shipped to one of four demand regions
of the United States, including the northeast, southeast, midwest, and west. These
demand regions were represented by the New York City, Atlanta, Chicago, and Los
Angeles wholesale markets, respectively. The commodities in the model were tomatoes,
bell peppers, cucumbers, squash, eggplant, watermelon, and strawberries. There is an
inverse demand equation for each commodity in each demand region with an assumption
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that the slope of the demand function is constant over quantities. The model calculates
total production costs by summing preharvest and postharvest costs. The preharvest
cost is the product of the number of acres planted and the peracre preharvest costs. The
postharvest cost is the product of the number of acres planted, yield, and perunit harvest
and postharvest costs. Alternatives are expected to have impacts on both yield and per
unit cost. Moreover, the model can calculate the transportation cost that is the product of
the quantity of commodity shipped and the perunit transportation cost.
The VanSickle et al. model can be characterized as a spatial equilibrium problem.
By using the following indices the model can be mathematically stated as
region: i = 1index the 12 production points,
crops: k = 1 index the seven crops being considered,
market: j = 1index the four market centers,
production systems: ks = index the 16 production systems,
time: m =1 ,...,M index the 12 months when the crop may be sold.
The demand for these crops is divided into four different markets. The inverse
demand curve is represented for the markets as
Pjkm ~ Qjkm ~ bjkm Qjkmi (31 1)
where Pjkm is the wholesale price per ton for crop k in market j in month m,
Qjkm is the quantity of tons of crop k that is sold in market j in month m,
jkm is the demand curves intercept,
bjkm is the slope of the demand function.
This formulation assumes that the slopes of the demand functions are constant over all
quantities. The model assumes that each regions production is a perfect substitute for
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that of any other region. Moreover, the model assumes that the price of each commodity
is a function of its own quantity alone and that the price is not affected by other crop
prices and quantities that may be sold in that market in that month.
To compute the inverse demand function, demand flexibilities were based on
wholesale price and arrival data for the various crops. The flexibilities are the
uncompensated own quantity elasticities calculated from the Rotterdam Inverse Demand
System (RIDS). The RIDS model satisfies the utilitymaximizing condition. Using this
information, the parameters for the slope and intercept of the demand equation can be
calculated.
Let = the demand flexibilities for crop k in market j in month m, where
Wjkm = (dPjkm / dQjkm)(Qjkm / Pjkm) (312)
The slope of the inverse demand equation is
 bjkm = (dPjkm / dQjkm),
 bjkm Vjkm (Pjkm / Qjkm) (313)
After bjkm had been calculated, aÂ¡km can be estimated from
Qjkm = Pjkm + bjkm Qjkm (314)
For the supply side, the production points are Florida, California, Mexico, Texas,
South Carolina, Virginia, Maryland, Alabama, and Tennessee. Florida was separated into
four producing areas: Dade County, Palm Beach County, Southwest Florida, and West
Central Florida. Mexico was separated into two producing areas: the states of Sinaloa
and Baja California. California was separated into two producing areas: Southern
California and Northern California. Also, there are 16 cropping systems, which include
both single and double cropping systems. The single cropping systems include tomatoes,
fall tomatoes, spring tomatoes, bell peppers, fall peppers, spring peppers, cucumbers,
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squash, eggplant, and strawberries. The double cropping systems include tomatoes and
cucumbers, tomatoes and squash, tomatoes and watermelons, bell peppers and
cucumbers, bell peppers and squash, and bell peppers and watermelons. The model
assumes that all producers in a particular region use the same production technology
(with the same yields and costs), and that crops are produced with fixedproportion
production functions.
The production costs in this model include preharvest cost, harvest cost, post
harvest cost, and transportation cost. The model calculates total production costs by
summing preharvest and postharvest costs. The preharvest cost is the product of the
number of acres planted and the peracre preharvest cost (in which we can apply the
alternative effect). The postharvest cost is the product of the number of acres planted,
yield, and perunit harvest and postharvest costs. The preharvest cost includes both
operating costs and fixed costs. The operating costs include fertilizer, fumigant,
fungicide, herbicide, insecticide, labor, surfactant, transplants, machinery, machinery
labor, scouting, stakes, plastic string, plastic mulch, farm vehicles, and interest on
working capital. The fixed costs include land rent, machinery fixed cost, supervision
cost, and overhead cost. Harvest and postharvest costs include harvesting, cooling,
packing, transportation to shipment point, and marketing costs. These costs for Mexico
also include transportation to the U.S. border and all tariffs and fees to cross the border
into the United States. An average permile transportation cost of $ 1.31 was calculated
using information from the USDA Agricultural Marketing Service. These costs include
truck brokers fees for shipments in truckload volume to a single destination, based on
costs of shipping from the point of origin to the point of destination, and do not include
89
any costs of returning the truck to the point of origin. Perunit transportation cost can be
calculated from the product of the distance between supply region i to demand region j
and the transportation cost of perunit, permile.
The VanSickle et al. model can determine which regions and which production
systems will achieve the most profit from producing each crop in each month (up to the
point where growers have used all the available land). The model attempts to maximize
producers return and consumers benefits while taking into account the constraint on the
amount of land available in each region (i.e., a demand constraint) and that the amount
sold to consumers cannot be greater than the amount supplied (i.e., a supply constraint).
Therefore, the model finds the equilibrium consumption of each commodity in each
demand region. On the supply side, the model calculates the optimal production in
acreage and the quantity of each commodity produced. This model also finds the optimal
level of shipments. By using these optimal solutions, price, production, and revenue can
be calculated. Altogether, the impacts on consumers, producers, price, production, and
revenue can be investigated using this model.
By assuming that all producers in a particular region use the same production
technology, it also can be assumed that they will have the same yields and costs. The
model uses data on each regions crops, yields, constraints, and marketing windows to
determine which regions and which production systems are best for achieving the most
profit from producing each crop in each month (up to the point where the growers have
used all the available land). The model allows growers to choose which of the four
demand market areas to use, given the different market prices and transportation costs for
each market. The model seeks to maximize producers returns and consumers benefits
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while taking into account that there are constraints on the amount of land available in
each region and that the amount sold to consumers cannot be greater than the amount
supplied.
The optimal solution to this model provides the equilibrium consumption of each
commodity in every month for each demand region; the optimal level of shipments
between each supply area and each demand region; the optimal production of each
cropping system, by production area; and the quantity of each commodity produced in
each supply region, by month.
The VanSickle et al. model is simulated by using the profitmaximizing problem to
find the optimal production that satisfies the competitive equilibrium market, given the
inverse demand equation, supply constraint, and demand constraint. From the firstorder
condition, the profitmaximizing condition is satisfied, as the inverse demand equation
equals the total marginal cost (which includes both the marginal cost of production and
the marginal cost of transportation). This model applies elasticities calculated from an
inverse demand system that solves the utilitymaximizing problem (so that the utility
maximizing condition is satisfied). Moreover, the market clearing condition is satisfied
as both supply and demand constraints are binding.
To simplify the model, the VanSickle et al. model is simulated by using the profit
maximizing problem to find the optimal production that satisfies the competitive
equilibrium, Equation 31. The quadratic programming model can be written as
J K 12 I KS
Max Y Y Y \ajkmQjkm(\/2)bjkmQ*jkm\ Â£ Â£ C\iks Wih
j = lk = \m = l i = lks = l
I KS K 12 I J K 12
~ Y Y Y Y C2iksk Zikm Y Y Y Y C3ijianXjjkm
i = \ks = \k = \m = \ z = 1 j = \k \m \
(315)
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subject to
Z/km X djkskm ^iks>
(316)
ks = 1
(317)
/
X Xylan Qjkmi
1 = 1
(318)
Qjkm, wik, Zikm, Xijkm > 0 for all of i,j, k, m, and ks,
where d^km = peracre yield of commodity k in month m from cropping system ks in
supply region i,
Wiks = number of acres planted of cropping system ks in supply region i,
Ukskm = the production of commodity k in supply region i and month m for cropping
system ks,
Cl iksk= per acre preharvest production cost of commodity k using cropping system ks in
supply region i,
Zikm ~ the total supply of commodity k from supply region / in month m,
Qjkm = the total demand of commodity k at demand region j in month m,
C2jksk = perunit harvest and postharvest costs associated with commodity k using
cropping system ks in supply region i,
Xijkm = quantity of commodity k shipped from supply region / to demand region j in
month m,
C3 jkm = perunit transportation cost of commodity k shipped from supply region i to
demand region j in month m.
The inverse demand equation, Equation 311, Price = aÂ¡km bÂ¡km Qjkm
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I KS I KS K 12
Total cost of production = Â£ Â£ Cl/fo W,ks + X X X X C2,&* 2,to. (319)
/ = 1 fcs = 1 / = 1 As = 1 Â£ = 1 /w = 1
I J K 12
Cost of transportation = X X X X CljjkmXykm (320)
i = iy = U = lw = l
We can derive the VanSickle et al. model from the Lagrangean equation
J K 12 ^ I KS
L= X X X Qjkm{m)bjkm Â£?jkm] ~ X X Cl/to IC/fo
y = 1 & = 1 w = 1 = 1 As = 1
/ KS K 12 I J K 12
 X X XX ClikskZikm X X X X C'iijkmXijkm
i = \ks = \k = \m = \ i = 1 j = \k = \m = 1
I K \2 KS
+ X X X ( X 4h 1C/*s 2",to)
/ = 1 Â£ = 1 w = 1 As = 1
I K \2 j
+ X X X gi/tm (2,to X Kyto)
i = 1 k =1 m = 1 y = l
J 12 /
+ X X X Ujkm ( XijkmQjkm), (3*21)
j = \k = \m = \ i = 1
where gikm and Ujkm are the Lagrange multipliers.
Both constraints satisfy the regularity condition of the KuhnTucker Theorem as they are
linear. From the firstorder condition with Qjkm, the KuhnTucker condition is
d L I d Qjkm Qjkm ~ bjkm Qjkm ~ 0; Qjkm ^ 0(d L / d Qjkm)Qjkm ~ 0. (322)
Let Qjkm > 0, so that d LI d Qjkm = 0. Therefore,
Qjkm Qjkm ~ bjkm Qjkm (323)
The Lagrange multiplier for the demand constraint is the market price, ujkm = Pjkm
Consequently, we can see that this model satisfies the utilitymaximizing condition.
From the firstorder condition with Wiks, the KuhnTucker condition is
93
KS KS
d L / 5 Wiks Sjian Â£ diiiskm J] Cl iks 0?
ks = 1 ks = 1
^>0; (dL/dWiks)Wiks = 0.
Let > 0 to get a trial solution, so that d LI d Wlks = 0. Therefore,
KS KS
Sikm~ X Cl Â¡ks/ X djkskn,.
ks = 1 ks = 1
(324)
(325)
The Lagrange multiplier for the acreage equation, sikm, is the marginal cost of preharvest
production.
From the firstorder condition with Z,km, the KuhnTucker condition is
d L / d Zikm = gikm C2* ikm ~ sikm < 0; Zikm >0;(dL/ d Zikm)Zikm = 0, (326)
KS
where C2*ikm = d( Â£ C2iksk Zikm) / d Zikm, for m = 1 12.
ks = 1
Let Zikm > 0, so that d L / d Z,km = 0. From Equation 325, we get
gikm ~ C2 Â¡km + SÂ¡km
KS KS
gikm ~ C2 Â¡km + ( Â£ C\,ks / Â£ dikskm) (327)
As = 1 As = 1
The Lagrange multiplier for the supply equation, g(*OT, is the total marginal cost of
production.
From the firstorder condition with gikm, the KuhnTucker condition is
J
d L / d gikm Zjkm ~ X Xjjkm 0; gikm > 0\ {d L / d gikm)gikm = 0, (328)
7 = 1
Let gikm > 0, so that d L / d gikm = 0. Therefore,
Zikm jr Zijkm
7 = 1
(329)
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Equation 329 implies that the total supply of commodity k from supply region i in month
m equals the aggregate for all demand regions of the quantity of commodity k shipped
from supply region / to demand region j in month m.
From the first order condition with Ujkm, the KuhnTucker condition is
d L / d Ujkm = XiJkm Qjkm > 0; uJkm > 0; (d L / d ujkm)ujkm = 0; (330)
i = l
Let Ujkm > 0, so that d L / d Ujkm = 0. Therefore,
Qjkm = S Xijkm (331)
/ = 1
Equation 331 implies that the total demand of commodity k at demand region j in month
m equals the aggregate for all supply regions of the quantity of commodity k shipped
from supply region i to demand region j in month m.
From Equations 329 and 331, we can prove that the marketclearing condition is
satisfied,
Xijkm Xjjkm
I J 1 J
X X Xjjkm = X X Xjjkm
/=iy=i i=ij=i
j i i j
Z X Xjikm = Z X Xjjkm
y=1/=i / = i y = i
j i
X Qjkm X Zjkm
j = 1 1 = 1
(332)
So the firstorder condition of this model satisfies the marketclearing condition of the
competitive equilibrium at which aggregate demand equals aggregate supply.
From the firstorder condition with we get
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d LI d sikm = I dikskm Wta Zikm = 0. (333)
ks = 1
From Equation 329, we get
I
KS J
I dikskmWiks= x Xijkm (334)
fcv = 1 y = l
From the firstorder condition with Xykm, the KuhnTucker condition is
dLl d Xijkm = UjJkm g ijh C3ijkm < 0; Xijkm > 0 ;(dL/d Xljkm)X,jkm = 0, (335)
where u jkm = ujkm for /'= 1and g* ljkm = gikm for j = 1,..., J.
To get a trial solution, we let Xijkm > 0, so that dLl d X,jkm = 0. By using Equations 323,
327, and 331, where ujkm is the same for all of we get
I
Qjkm ~ bjlcm ( X Xijkm) ~ C2 ,km + ( C1 Â¡ksk / ^ dikskm) C3ykm (336)
/ = 1 ks 1 ks = 1
Equation 336 ensures the profitmaximizing condition where price equals the marginal
cost.
From Equation 334, the firstorder condition of this model satisfies the profit
maximizing condition of the competitive equilibrium. This model solves the competitive
equilibrium problem by simulating Xykm and fV/ks, which satisfies Equation 332, 334,
and 336. By using the optimal solution of X'ykm, we can find the total demand, Qjkm, by
using Equation 331. We can find the total supply, Zikm, by using Equation 329, and
price, Pjkm, by using Equation 323.
This model can be represented by using the Marshallian graphical technique with
the equilibrium price as the point of intersection of the aggregate demand and aggregate
supply curves. In addition, this model is Pareto optimal because the aggregate
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Marshallian surplus is maximized. From Figure 34, demand curve X(P) can be defined
by using the inverse demand function,
X(P) = P( i Qjkm) (337)
7 = 1
The supply curve Z(P) for each production region can be defined by using the
marginal cost function,
Z{P) = C\ { Zikm). (338)
i = \
From the point of intersection of the aggregate demand and aggregate supply
curves, we can find the equilibrium price, P*, and the level of the aggregate shipment
I J
quantity, X, where X= Â£ Â£ Xijkm.
i = 1 7 = 1
7 = 1 i = 1
Figure 34. Partial equilibrium of aggregate demand and aggregate supply
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Empirical Results
The solution to the VanSickle et al. model included shipments, by month and crop,
from each producing area to each market; the planted acreage, production, and revenues
to each cropping system in each production area; and the equilibrium prices and quantity
consumed, by month and crop, in each of the four market areas. The baseline solution
performed reasonably well in replicating the observed pattern of shipments and acres
planted for the 2000/2001 production season.
The baseline acreage planted to each crop in each of the major producing areas is
shown in Table 33, which includes estimates of the expected inputs from the ban on
methyl bromide alone (first scenario), NAFTA alone (second scenario), and the
combination of the ban on methyl bromide and NAFTA together (third scenario).
Percentage changes in production and revenues, compared with the baseline for each crop
in each area, are shown in Table 35. Changes in production, compared with the
baseline, by area, are shown in Table 34. Changes in revenues, compared with the
baseline, by crop, in each area, are shown in Table 36. Changes in production and
revenues, compared with the baseline, by area, are shown in Table 37. Changes in
average prices, compared with the baseline, by crop, are shown in Table 38. Results
show that significant effects may be expected across producing areas for all crops.
Percentage changes in consumer demand for each commodity in each market, compared
with the baseline, are shown in Table 39.
Tomatoes
Tomato production in Dade and Palm Beach Counties in Florida and in the
Alabama/Tennessee region is expected to cease in every scenario. California is expected
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to cease tomato production under the second scenario. Mexico is expected to increase its
tomato producing acreage significantly, especially as a result of NAFTA. For example,
the planted acreage of tomatoes in Baja is expected to increase from 5,369 acres to
27,583 acres (Table 33). The results for Mexico in the third scenario (under both
NAFTA and the ban on methyl bromide) are not significantly different from the second
scenario, since Mexico already enjoys significant gains from NAFTA. South Carolina,
West Central Florida, and Southwest Florida are the only U.S. domestic producers that
are expected to gain under the third scenario.
Results from Table 35 show that total production of tomatoes across all areas in
the United States is expected to decrease by 7.11%, 41.88%, and 42.77% in the first,
second, and third scenarios, respectively. On the other hand, tomato production in
Mexico is expected to increase by 13.42%, 64.10%, and 68.50% in the first, second, and
third scenarios, respectively.
The total revenues that growers receive for tomatoes are expected to decrease by
$1.1 million under the first scenario, to decrease by $3.6 million under the second
scenario, and to increase by $1.6 million under the third scenario (Table 36). Florida
will suffer the greatest loss in tomato shipping point revenues under the first scenario,
with a loss of $56.9 million. California will suffer the greatest loss in tomato shipping
point revenues under the second scenario, with a loss of $286 million. On the other hand,
Mexico will increase their shipping point revenues by $67.2 million under the first
scenario, by $332.7 million under the second scenario, and by $353.7 million under the
third scenario. Two significant conclusions to draw from these results for tomatoes are
that the impact from NAFTA in Mexico is more significant than the impact from the ban
99
on methyl bromide and that Mexico will gain market share and shipping point revenues.
The average wholesale price of tomatoes is expected to increase by 1.46% under the first
scenario, to decrease by 0.52% under the second scenario, and to increase by 0.82%
under the third scenario (Table 38).
On the demand side, Table 39 shows that consumer demand of tomatoes in every
market is expected to decrease under the first scenario with the highest decrease in the
Chicago market (1.44%) and the lowest decrease in the Los Angeles market (0.82%).
The increase in the percentage change in the consumer demand of tomatoes under the
second scenario is highest in the Atlanta market (1.26%) and is lowest in the New York
market (0.51%). In the third scenario, the consumer demand of tomatoes is expected to
increase in the Atlanta and Los Angeles markets and to decrease in Chicago and New
York markets because the impact of the methyl bromide ban is higher than the impact of
NAFTA in the Chicago and New York markets.
Bell peppers
Banning methyl bromide will have a negative impact on Florida. For example, the
planted acreage of bell peppers is expected to decrease from 7,175 acres to 6,986 acres in
Palm Beach County and to decrease from 10,997 acres to 9,499 acres in West Central
Florida (Table 33). On the other hand, methyl bromide ban is expected to have a
positive impact on Texas and Mexico, offsetting some of the loss experienced in Florida.
The planted acreage of bell peppers is expected to increase from 12,680 acres to 14,458
acres in Texas and to increase from 13,600 acres to 13,901 acres in Mexico.
Under the first scenario, total production of bell peppers is expected to decrease by
1.04% (Table 35). Total shipping point revenues for bell peppers are expected to
decrease by $6.6 million, with Florida suffering a $17.1 million loss in shipping point
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revenues (Table 36). Shipping point revenues in Texas and Mexico are expected to
increase by $8.2 million and $2.3 million, respectively. The average wholesale price of
bell peppers under the first scenario is expected to increase by 1.35% (Table 38).
Consumer demand of bell peppers in every market is expected to decrease with the
highest percentage change of consumer demand for bell peppers will be in the New York
market, which is expected to decrease by 5.91% (Table 39).
Under second scenario, bell pepper production in Mexico is expected to increase by
2.67%, while bell pepper production in Florida is expected to decrease by only 0.78%
(Table 35). Table 38 shows that the average wholesale price of bell peppers under the
second scenario is expected to decrease by 0.24%. Table 39 shows that consumer demand
of bell peppers under the second scenario is expected to increase in every market.
Under the third scenario, the planted acreage of bell peppers in Mexico is expected
to increase significantly from 13,600 acres to 14,551 acres (Table 33). As a result,
production of bell peppers in the United States is expected to decrease by 2.85% (Table
35). The impact of NAFTA is expected to reduce the impact of the methyl bromide ban
in the U.S. domestic market (e.g., production of bell peppers is expected to increase by
10.12% in Texas and to decrease by 8.37% in Florida). In addition, the total shipping
point revenues for bell peppers are expected to decrease by $4.3 million, with shipping
point revenues for bell peppers in Mexico increasing by $6.1 million and shipping point
revenues for bell peppers in the United States decreasing by $10.4 million (Table 36).
The average wholesale price of bell peppers under the third scenario is expected to
increase by 0.90% (Table 38). Consumer demand of bell peppers in every market is
expected to decrease, except in the Los Angeles market, which is expected to increase by
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0.84% (Table 39), due to the greater impact of NAFTA as opposed to the lower impact
of the methyl bromide in the Los Angeles market.
Cucumbers
Floridas 6,693 baseline acreage of cucumber production in Palm Beach County is
expected to increase to 6,986 acres under the first scenario, to 6,769 acres under the
second scenario, and to 6,829 acres under the third scenario (Table 33). Double
cropping of cucumbers and bell peppers can increase total production of cucumbers in
Florida. Cucumber production in Florida is expected to increase by 4.38% under the first
scenario, by 1.14% under the second scenario, and by 2.04% under the third scenario
(Table 35). Cucumber production in Mexico is expected to increase by 2.26% under
scenario one and to increase by 2.83% under scenarios two and three.
Total shipping point revenues for cucumbers are expected to increase under all
three scenarios; that is, by S917,980 under the first scenario, by $1.4 million under the
second scenario, and by $941,490 under the third scenario (Table 36). Floridas
shipping point revenues for cucumbers are expected to decrease by $79,510 under the
first scenario, to increase by $104,430 under the second scenario, and to decrease by
$302,210 under the third scenario. Table 38 shows that the average wholesale price of
cucumbers is expected to decrease by 0.40%, 0.65%, and 0.36% under these three
scenarios, respectively.
Table 39 shows that the consumer demand of cucumbers is expected to increase in
every market under the first scenario because of the decrease in the price of cucumbers.
Under the second scenario, the consumer demand of cucumbers is expected to increase in
every market. Under the third scenario, the consumer demand of cucumbers in every
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market, except the Los Angeles market, is expected to decrease, as the Los Angeles
market receives more benefits from NAFTA than do the other markets.
Squash
The 3,637 planted baseline acres of squash in Southwest Florida are expected to
increase to 4,423 acres under the first scenario, to 4,286 acres under the second scenario,
and to 4,568 acres under the third scenario (Table 33). On the other hand, the planted
acreage of squash in Dade County is expected to decrease in every scenario from 8,081
acres to 7,880 acres under the first scenario, to 7,647 acres under the second scenario, and
to 7,749 acres under the third scenario.
Squash production in Mexico is expected to decrease by 0.76% under the first
scenario, but is expected to increase by 1.46% under the second scenario and by 1.85%
under the third scenario (Table 35). Squash production in Florida is expected to increase
by 4.99%, 1.83%, and 5.11% under these three scenarios, respectively. Floridas total
shipping point revenues for squash are expected to increase by $327,680 under the first
scenario, by $322,760 under the second scenario, and by $185,970 under the third
scenario, while Mexicos shipping point revenues are expected to decrease by $145,080
under the first scenario, to increase by $125,260 under the second scenario, and to
increase by $198,630 under the third scenario (Table 36).
Table 38 shows that the average wholesale price of squash is expected to decrease
by 0.18% under the first scenario, by 0.50% under the second scenario, and by 0.41%
under the third scenario. Table 39 shows that the consumer demand of squash is
expected to increase under these three scenarios in every market. The highest percentage
change in the consumer demand of squash is in the New York market.
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Eggplant
The 5,327 baseline acres of eggplant planted in Palm Beach County are expected to
decrease to 5,132 acres under the first scenario, to 5,247 acres under the second scenario,
and to 5,075 acres under the third scenario (Table 33). On the other hand, eggplant
production in Mexico is expected to increase by 4.69% under the first scenario, by 5.96%
under the second scenario, and by 9.75% under the third scenario to offset the loss of
production in Florida (Table 35).
Total shipping point revenues for eggplant are expected to decrease by $2.5 million
under the first scenario and by $2.1 million under the third scenario (Table 36). On the
other hand, under the second scenario, the total shipping point revenues for eggplant are
expected to increase by $340,060, as Mexico gains $1.2 million and Florida loses
$847,960 in shipping point revenues. The average wholesale price of eggplant is
expected to decrease by 0.36% under the second scenario, but is expected to increase by
1.26% under the first scenario and by 0.87% under the third scenario (Table 38).
The consumer demand of eggplant in every market is expected to decrease under
the first scenario with the highest decrease in the Atlanta market (11.55%) and to increase
under the second scenario with the highest increase in the Los Angeles market (2.34%).
Under the third scenario, the consumer demand of eggplant in every market is expected
to decrease, except in the Los Angeles market, which is expected to increase by 1.90%
(Table 39), due to the greater impact of NAFTA as opposed to the impact of the methyl
bromide ban.
Watermelons
Table 33 shows that the 1,812 planted baseline acres of watermelon in West
Central Florida are expected to decrease to 593 acres under the first scenario, to 1,694
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acres under the second scenario, and to 923 acres under the third scenario. This occurs
because of the decrease in the production of double cropped of watermelons and bell
peppers. The 17,338 baseline acres of watermelon in Southwest Florida are expected to
increase to 18,340 acres under the first scenario, to 18,002 acres under the second
scenario, and to 17,899 acres under the third scenario as a result of the increase in the
production of double cropped of watermelons and tomatoes.
Total production of watermelons is expected to decrease by 0.76% under the first
scenario and by 1.44% under the third scenario (Table 35). Consequently, the average
wholesale price of watermelons is expected to increase by 5.13% under the first scenario
and by 5.39% under the third scenario (Table 38). In contrast, under the second
scenario, total production of watermelons is expected to increase by 2.91%, and the
average wholesale price of watermelons is expected to decrease by 1.42%.
Total shipping point revenues for watermelons are expected to decrease by $7.9
million under the first scenario, by $976,981 under the second scenario, and by $5.7
million under the third scenario (Table 36). Consumer demand of watermelons is
expected to increase in the first and third scenarios in every market (Table 39). On the
other hand, the consumer demand of watermelons is expected to increase in every market
under the second scenario, with the highest impact in the Atlanta market.
Strawberries
The model only estimates the impact of the methyl bromide ban for strawberries
since tariffs are not currently collected on imports. The impact on California is
significant because of the high cost and high productivity of the current production
systems in California. Strawberry production in Northern California is expected to cease
under the first scenario, and the planted acreage of strawberries in Southern California is
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expected to decrease from 10,518 acres to 7,659 acres (Table 33). On the other hand,
the planted acreage of strawberries in Florida is expected to increase from 4,545 acres to
4,692 acres under the first scenario. Total production of strawberries is expected to
decrease by 41.06% under the first scenario (Table 35). The production of strawberries
is expected to decrease by 51.62% in California and to increase by 3.24% in Florida.
Table 36 shows that total shipping point revenues for strawberries are expected to
decrease by $245.4 million, with California suffering a $263.3 million loss in shipping
point revenues. The average wholesale price of strawberries is expected to increase by
12.78% (Table 38). Consumer demand for strawberries in every market is expected to
decrease under the impact of the methyl bromide ban, with the highest decrease in the
Atlanta market at 66.57% (Table 39).
Aggregate impacts
Total production of the fruits and vegetables included in this model is expected to
decrease by 7.97% under the first scenario, to increase by 0.08% under the second
scenario, and to decrease by 7.26% under the third scenario (Table 34). Consequently,
consumer surplus is expected to decrease under the first and third scenarios and to
increase under the second scenario.
Total production in the United States is expected to decrease by 16.21 % under the
first scenario, by 21.93% under the second scenario, and by 34.22% under the third
scenario (Table 34). California is expected to suffer the greatest loss in production.
Tomato production in California is expected to cease under the second scenario, and
strawberry production in California is expected to cease under the first scenario. Total
production in California is expected to decrease by 31.12% under the first scenario, by
42.43% under the second scenario, and by 72.15% under the third scenario. On the other
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hand, total production in Mexico is expected to increase by 11.01%, 50.74%, and 54.78%
under the first, second, and third scenarios, respectively.
Under the first scenario, shipping point revenues are expected to decrease by $70.9
million in Florida, by $272.7 million in California, by $20.5 million in Alabama and
Tennessee, and by $700,600 in Virginia and Maryland (Table 37). In contrast, shipping
point revenues are expected to increase by $8.3 million in Texas, by $19.2 million in
South Carolina, and by $71.5 million in Mexico. However, these gains do not offset the
loss expected under the first scenario. As a result, total revenues are expected to decrease
by $265.9 million. Under the second scenario, Mexicos shipping point revenues are
expected to increase by $336.9 million, while U.S. total shipping point revenues are
expected to decrease by $354.1 million. Under the third scenario, U.S. total shipping
point revenues are expected to decrease by $623.4 million, with California shippers
losing $549.3 million. Mexicos shipping point revenues are expected to increase by
$363.4 million.
Table 39 shows that consumer demand for tomatoes, bell peppers, eggplant,
watermelon, and strawberries is expected to decrease under the first scenario. The
consumer demand of every commodity, except strawberries, is expected to increase under
the second scenario. The highest impacts on the consumer demand for eggplant,
watermelon and strawberries will be in the Atlanta market.
Conclusions
An economic model of the fruit and vegetable industry was used to determine the
projected impacts of NAFTA and the methyl bromide ban. Methyl bromide has been a
critical soil fumigant in the production of many agricultural commodities. Tomatoes, bell
peppers, eggplant, squash, cucumbers, strawberries, and watermelons are the crops with
107
the greatest potential of being impacted under the first scenario. Florida is a major
supplier of these products, and the methyl bromide ban would adversely affect the
competitive position of Florida in these markets. Much of the lost production would
move to Mexico. In addition, Texas could benefit from increased production of bell
peppers, and South Carolina could benefit from increased production of tomatoes.
The production of strawberries in California would be expected to decrease under
the first scenario, and the production of tomatoes in California would be eliminated under
the second scenario. Even though Texas does not use methyl bromide in the production
of bell peppers, its production of bell peppers would not increase much.
The main new feature of NAFTA was the removal of most of the trade barriers
between Mexico and the United States. As a result, total production in Mexico could
increase by more than 50%. For example, production of tomatoes in California could be
eliminated, while production of tomatoes in Baja could increase by more than 400%.
These losses could devastate U.S. agriculture because much of the lost production would
move to Mexico, especially the production of tomatoes. The consumer demand in every
commodity in every market would increase from the benefit of increased imports from
Mexico under the second scenario.
Mexico would become the major supplier of fresh vegetables because of NAFTA
and the Montreal Protocol agreements, which allow Mexico an additional 10 years to use
methyl bromide. Overall, with the advantage from NAFTA, Mexico will be the primary
beneficiary of the ban on methyl bromide because they will likely use methyl bromide to
increase production. This could cause a large shift in production away from the United
States to Mexico.
108
Table 33. Planted acreage in the baseline model, in the methyl bromide ban model, and
in the NAFTA model, by crop and area
Crop/
Acreage
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
(
Acres
)
Tomatoes
Florida
Dade
4,408
0
0
0
Palm Beach
2,798
0
0
0
West Central
11,077
12,020
12,761
11,804
Southwest
20,975
22,763
22,288
22,467
California
36,408
35,206
0
0
Alabama/Tennessee
3,448
0
0
0
South Carolina
6,923
8,823
8,595
8,677
V irginia/Maryland
6,282
6,179
6,249
6,195
Mexico
Sinaloa
34,951
39,235
38,583
40,468
Baja
5,369
6,497
27,583
27,472
Total
132,641
130,723
116,060
117,082
Bell Penners
Florida
Palm Beach
7,175
6,986
7,131
6,829
West Central
10,997
9,499
10,900
9,821
Texas
12,680
14,458
12,727
13,963
Mexico/Sinaloa
13,600
13,901
13,963
14,551
Total
44,452
44,845
44,721
45,165
Cucumbers
Florida/Palm Beach
6,693
6,986
6,769
6,829
Mexico/Sinaloa
10,076
10,304
10,361
10,361
Total
16,769
17,290
17,130
17,190
Squash
Florida
Dade
8,081
7,880
7,647
7,749
Southwest
3,637
4,423
4,286
4,568
Mexico/Sinaloa
7,265
7,210
7,371
7,399
Total
18,984
19,513
19,304
19,716
Note: MB is abbreviated for Methyl Bromide.
109
Table 33. Continued
Crop/
Acreage
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
(
Acres
)
Eggplant
Florida/Palm Beach
5,327
5,132
5,247
5,075
Mexico/Sinaloa
2,734
2,862
2,897
3,000
Total
8,060
7,994
8,143
8,075
Watermelons
Florida
West Central
1,812
593
1,694
923
Southwest
17,338
18,340
18,002
17,899
Total
19,149
18,933
19,697
18,822
Strawberries
Florida/West Central
4,545
4,692
4,545
4,692
California
Southern
10,518
7,659
10,518
7,659
Northern
9,217
0
9,217
0
Total
24,280
12,351
24,280
12,351
Note: MB is abbreviated for Methyl Bromide.
Table 34. Baseline production and percentage changes in production crops in the methyl
bromide ban effect and in the NAFTA effect, by area
Area
Production
Baseline
MB Ban
NAFTA MB Ban and NAFTA
(Units)
(
%.
)
Florida
103,851
(6.91)
(7.61)
(7.60)
California
92,674
(31.12)
(42.43)
(72.15)
Texas
7,735
14.02
0.37
10.12
V irginia/Maryland
4,272
(1.64)
(0.52)
(1.38)
South Carolina
6,854
27.44
24.14
25.34
Alabama/Tennessee
2,138
(100.00)
(100.00)
(100.00)
United States
217,524
(16.21)
(21.93)
(34.22)
Mexico
94,509
11.01
50.74
54.78
Total
312,033
(7.97)
0.08
(7.26)
Note: MB is abbreviated for Methyl Bromide.
110
Table 35. Baseline production and percentage changes in production crops in the methyl
Crop/
Production
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
(Units) (
%
)
Tomatoes
Florida
56,506
(10.86)
(10.35)
(12.16)
California
39,321
(3.30)
(100.00)
(100.00)
Alabama/T ennessee
2,138
(100.00)
(100.00)
(100.00)
South Carolina
6,854
27.44
24.14
25.34
V irginia/Maryland
4,272
(1.64)
(0.52)
(138)
United States
109,091
(7.11)
(41.87)
(42.77)
Mexico
73,786
13.42
64.10
68.50
Total
182,876
1.17
0.89
2.13
Bell PeDDers
Florida
18,172
(9.28)
(0.78)
(8.37)
Texas
7,735
14.02
0.37
10.12
United States
25,907
(2.33)
(0.44)
(2.85)
Mexico
10,282
2.22
2.67
6.99
Total
36,189
(1.04)
0.45
(0.06)
Cucumbers
Florida
4,016
4.38
1.14
2.04
Mexico
5,572
2.26
2.83
2.83
Total
9,588
3.15
2.12
2.50
Squash
Florida
4,395
4.99
1.83
5.11
Mexico
1,518
(0.76)
1.46
1.85
Total
5,913
3.51
1.73
4.27
Eeenlant
Florida
7,457
(3.65)
(1.50)
(4.73)
Mexico
3,352
4.69
5.96
9.75
Total
10,809
(1.07)
0.81
(0.24)
Watermelon
Florida
6,475
(0.76)
2.91
(1.44)
Strawberries
Florida
12,725
3.24
0.00
3.24
California
53,354
(51.62)
0.00
(51.62)
Total
66,079
(41.06)
0.00
(41.06)
Note: MB is abbreviated for Methyl Bromide.
Ill
Table 36. Baseline revenues and changes in revenues from the methyl bromide ban
effect and the NAFTA effect, by crop and area
Crop/
Revenue($)
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
Tomatoes
Florida
448,227,870
(56,878,770)
(46,798,270)
(62,753,470)
California
286,004,000
(9,442,000)
(286,004,000)
(286,004,000)
Alabama/T ennessee
20,477,170
(20,477,170)
(20,477,170)
(20,477,170)
South Carolina
71,270,950
19,210,230
17,207,920
17,712,950
V irginia/Maryland
42,736,960
(700,600)
(222,390)
(591,470)
United States
868,716,950
(68,288,310)
(336,293,910)
(352,113,160)
Mexico
496,178,430
67,177,520
332,710,470
353,716,970
Total
1,364,895,380
(1,110,790)
(3,583,440)
1,603,810
Bell Peppers
Florida
171,026,490
(17,069,120)
(994,830)
(16,315,310)
Texas
58,828,370
8,248,660
218,480
5,954,450
United States
229,854,860
(8,820,460)
(776,350)
(10,360,860)
Mexico
102,449,600
2,269,300
1,678,200
6,061,900
Total
332,304,460
(6,551,160)
901,850
(4,298,960)
Cucumbers
Florida
26,579,760
(79,510)
104,430
(302,210)
Mexico
64,228,410
997,490
1,243,710
1,243,700
Total
90,808,170
917,980
1,348,140
941,490
Squash
Florida
51,107,510
327,680
322,760
185,970
Mexico
19,105,090
(145,080)
125,260
198,630
Total
70,212,600
182,600
448,020
384,600
Eggplant
Florida
56,568,750
(3,663,070)
(847,960)
(4,254,770)
Mexico
25,895,360
1,214,100
1,188,020
2,155,720
Total
82,464,110
(2,448,970)
340,060
(2,099,050)
Watermelon
Florida
11,799,539
(7,874,013)
(976,981)
(5,667,189)
Strawberries
Florida
93,912,080
17,912,420
0
17,912,420
California
466,867,600
(263,289,100)
0
(263,289,100)
Total
560,779,680
(245,376,680)
0
(245,376,680)
Note: MB is abbreviated for Methyl Bromide.
112
Table 37. Baseline revenues and changes in revenues from the methyl bromide ban
effect and the NAFTA effect, by area
Revenue($)
MB Ban and
Area
Baseline
MB Ban
NAFTA
NAFTA
Florida
853,322,230
(70,941,450)
(64,809,740)
(76,712,610)
California
752,871,600
(272,731,100)
(286,004,000)
(549,293,100)
Texas
58,828,370
8,248,660
218,480
5,954,450
V irginia/Maryland
42,736,960
(700,600)
(222,390)
(591,470)
South Carolina
71,270,950
19,210,230
17,207,920
17,712,950
Alabama/T ennessee
20,477,170
(20,477,170)
(20,477,170)
(20,477,170)
United States
1,799,507,280
(337,391,430)
(354,086,900)
(623,406,950)
Mexico
707,856,890
71,513,330
336,945,660
363,376,920
Total
2,507,364,170
(265,878,100)
(17,141,240)
(260,030,030)
Note: MB is abbreviated for Methyl Bromide.
Table 38. Baseline average prices and percentage changes in prices from the methyl
bromide ban effect and the NAFTA effect, by crop
Price
Crops
Baseline
MB Ban
NAFTA
MB Ban and NAFTA
Tomatoes
($/unit) (
8.69
1.46
%
(0.52)
)
0.82
Bell Peppers
6.14
1.35
(0.24)
0.90
Cucumbers
7.71
(0.40)
(0.65)
(0.36)
Squash
6.96
(0.18)
(0.50)
(0.41)
Eggplant
4.81
1.26
(0.36)
0.87
Watermelon
1.15
5.13
(1.42)
5.39
Strawberries
11.77
12.78
0.00
12.78
Note: MB is abbreviated for Methyl Bromide.
113
Table 39. Baseline demand and percentage changes in demand from the methyl bromide
ban effect and the NAFTA effect, by crop and market
Crop
Market
Baseline
MB Ban
NAFTA
MB Ban
and NAFTA
(Units)
(
%
)
Tomatoes
Atlanta
41,080
(1.05)
1.26
0.39
Los Angeles
33,871
(0.82)
0.86
0.18
Chicago
38,744
(1.44)
0.96
(0.24)
New York
66,763
(1.33)
0.51
(0.75)
Bell Peppers
Atlanta
9,955
(3.37)
0.06
(2.60)
Los Angeles
5,529
(1.15)
1.56
0.84
Chicago
11,399
(2.19)
0.79
(1.32)
New York
9,305
(5.91)
0.21
(5.26)
Cucumbers
Atlanta
2,077
1.07
2.81
(0.01)
Los Angeles
1,988
1.60
2.00
2.00
Chicago
2,943
0.72
1.97
(0.07)
New York
2,580
0.66
1.84
(0.11)
Squash
Atlanta
1,808
0.58
1.10
0.81
Los Angeles
1,690
0.42
2.19
1.98
Chicago
1,686
0.61
1.15
0.84
New York
728
1.92
3.58
2.60
Eggplant
Atlanta
1,673
(11.55)
0.17
(11.15)
Los Angeles
2,991
(0.13)
2.34
1.90
Chicago
3,983
(2.68)
0.16
(2.12)
New York
2,162
(7.89)
0.41
(7.74)
Watermelon
Atlanta
468
(59.90)
16.55
(62.93)
Los Angeles
1,348
(6.28)
1.73
(6.60)
Chicago
1,484
(11.64)
3.22
(12.23)
New York
3,174
(4.55)
1.26
(4.78)
Strawberries
Atlanta
11,088
(66.57)
0.00
(66.57)
Los Angeles
16,215
(43.99)
0.00
(43.99)
Chicago
17,554
(49.56)
0.00
(49.56)
New York
20,649
(47.09)
0.00
(47.09)
Note: MB is abbreviated for Methyl Bromide.
CHAPTER 4
SUMMARY AND CONCLUSIONS
Summary
The purpose of an economic impact analysis is to help planners, analysts, and
interested individuals estimate the total economic effect of a change in a particular sector
or industry on a regions output, income earnings, and employment. Our study used a
spatial equilibrium model to investigate the economic impact of NAFTA and the ban on
methyl bromide for fruits and vegetables produced in the United States. Our spatial
equilibrium model satisfies the utilitymaximization condition by using the elasticities
from the inverse demand system (we investigated the method to estimate the inverse
demand system in Chapter 2). The results from Chapter 2 showed that by using the mean
of the budget share to develop the inverse demand model, the estimation of the
elasticities is the same across all functional forms of the inverse demand system. We
estimated the inverse demand system by using Bartens method of estimation with
homogeneity and symmetry constraints imposed. Overall, Chapter 2 provided the
method to estimate the elasticities for selected fruits and vegetables in the U.S. market by
using a model that can obviate the need to choose among the popular functional forms.
Based on the results of the estimated coefficients, the scale effects of all
commodities in every market are statistically significant at the 5% probability level and
they have the expected sign. In terms of own substitution, they all have the expected
sign, according to theory, and they are statistically significant at the 5% probability level
for all commodities in the Atlanta, Los Angeles, and New York markets. Strawberry is
114
115
the only crop that is statistically significant at the 5% probability level in the Chicago
market. In every market, tomato has the highest absolute value of own uncompensated
quantity elasticity, while strawberry has the lowest absolute value. Own substitution
elasticities for tomato and bell pepper are higher in the Atlanta and Los Angeles markets
than they are in the Chicago and New York markets.
In Chapter 3, we investigated the economic impacts of NAFTA and the phaseout of
methyl bromide on the U.S. fruit and vegetable industry by applying the demand
elasticities from Chapter 2 into the VanSickle et al. model. The VanSickle et al. model is
a spatial equilibrium model that satisfies the profitmaximizing condition, utility
maximizing condition, and marketclearing condition. The fruit and vegetable crops that
have been identified as having the most potential for being impacted by a ban on methyl
bromide are tomatoes, bell peppers, eggplant, squash, cucumbers, strawberries, and
watermelons. Mexico is expected to become the major supplier of these crops because of
NAFTA and the Montreal Protocol.
The results from Chapter 3 show that total production of these crops in the United
States is expected to decrease by 34.22% under the third scenario (a combination of
impacts from NAFTA and a ban on methyl bromide). For example, Californias
production could decrease by 72.15% with tomato production ceasing under the second
scenario and strawberry production ceasing under the first scenario. In addition, under
the third scenario, total production in Florida is expected to decrease by 7.6%, while total
production in Mexico is expected to increase by 54.78%.
Knowing the impact these policies will have on Florida and California growers,
policy makers should develop programs that will speed the search for alternatives to
116
methyl bromide. In the interim, policy makers should consider programs that can help
growers survive over the short run from these impacts.
Suggestions for Further Research and Limitation of the Study
This study provides useful information for discussion about competition in the
market for tomatoes, bell peppers, cucumbers, squash, eggplant, watermelons, and
strawberries. Other commodities could also benefit from a similar study. Other areas of
research would likely enhance the investigation of competition between Florida and
Mexico and of production results from both areas on the vegetable market.
The primary limitation of the study is the assumption regarding finding alternatives
to using methyl bromide as a preplant fumigant. The development of economically
viable alternative fumigants or alternative nonfumigant production systems would alter
the empirical results of this study. Another limitation of the study is that alternative crops
were not extensively analyzed. The assumption was made that current market conditions
limit the potential for expanding the production of these crops. The process of
identifying and developing successful production systems and markets could be difficult.
In addition, the methodology used to estimate the economic impact of the methyl
bromide ban is deterministic based on average yield and cost of production data. In
reality, there is significant yeartoyear variation in harvested production per acre in fresh
fruit and vegetable production. Variation in crop yields is a result of both weather and
economic factors. The uncertainty faced by fresh fruit and vegetable producers is ignored
in this study.
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119
VanSickle, J.J., and S. NaLampang. The Impact of the Phase Out of Methyl Bromide
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BIOGRAPHICAL SKETCH
Sikavas NaLampang is a native of Thailand. He earned his Bachelor of
Engineering degree in mechanical engineering, from Chulalongkom University,
Thailand. He later held a design engineer position at the environmental engineering
consulting firm where he designed heating, ventilation, and air conditioning systems for
many commercial and government buildings. In 1996, he enrolled in the Engineering
Management program at the University of Florida. He was awarded his Master of
Engineering degree in industrial and systems engineering, with a specialization in
engineering management, in 1998. In 2000, he began pursuing a Ph.D. in food and
resource economics at the University of Florida. His areas of interest are international
trade and econometrics. While studying in the Food and Resource Economics
Department, he served as a Graduate Research/Teaching Assistant.
120
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
U
Sickle, Chair
of Food and Resource Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequatg^in scope and quality, as a
dissertation for the degree of Doctor of Philosopf
Edward A.
Assistant Professor of Food and Resource
Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Richard N. Weldon
Associate Professor of Food and Resource
Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Aill 71^0^
Allen F. Wysocki
Assistant Professor of Food and Resource
Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Chunrong Ai
Associate Professor of Economics
This dissertation was submitted to the Graduate Faculty of the College of
Agricultural and Life Sciences and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.,
August 2004
a.
Dean, College of Agricultural ancKLi
Sciences \ )
ife
Dean, Graduate School
This dissertation was submitted to the Graduate Faculty of the College of
Agricultural and Life Sciences and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
August 2004
CL
Dean, College of Agricultural ancFLife
Sciences V )
Dean, Graduate School
15
We also can get the logarithmic version of the LaTheil model from the logarithmic
version of the RIDS model (Equation 223) by adding d(ln Q) to both sides,
d(ln 7T,) + d(ln Q) = (4 +1) d(ln Q) + 2,Â¡ 4 d(ln qj,
d(ln pi) d{ln P) d(ln Q) + (/n 0 = (4 +1) i/(/ 0 + 2/ 4 /')>
d[ln (pt/P)\ = (4+1) i/(/ 0 + 4 4 Â£/(/ /) (235)
In order to satisfy the symmetry condition, we premultiply both sides of Equation 235 by
w so the LaTheil model is
w, d[in ipt/p)] = w,(4 +i) 4 0 + 4 4^* $y)>
W, 4/n (p,/F)] = (w,4 + w,) c/(/n 0 + 2, hydrin qj),
w, 4/n 0,/P)] = (/ij + w,) 4/n 0) + 4 h,j d(ln qj,
w, d[ln {pJP)\ = 4 4^ 0 + 4 hv d(ln
where
bÂ¡ = hi + wÂ¡. (237)
The coefficients of the LaTheil model also satisfy the neoclassical restrictions with
parameter hÂ¡j, which can be defined by Equation 227. Having the same properties as
parameter hy in the RIDS model (Equation 226), the addingup condition requires
2,6/ = 0. (238)
The third functional form of the inverse demand system is the Almost Ideal Inverse
Demand System (AIIDS), which can be obtained from the distance function,
In g(u, q) = (1 u) In a(q) u In b(q),
(239)
where
In a{q) = a0 + 2k ak In qk + (l/2)2*27 ykÂ¡ In qk In qp
(240)
In b{q) = In a(q) + pnI7k qkp.
(241)
The AIIDS cost function is written as
In g{u, q) = (1 u) In a{q) + u[ln a(q) + J3017k qk\
In g(u, q) = In a(q) + up0nk qkp,
94
Equation 329 implies that the total supply of commodity k from supply region i in month
m equals the aggregate for all demand regions of the quantity of commodity k shipped
from supply region / to demand region j in month m.
From the first order condition with Ujkm, the KuhnTucker condition is
d L / d Ujkm = XiJkm Qjkm > 0; uJkm > 0; (d L / d ujkm)ujkm = 0; (330)
i = l
Let Ujkm > 0, so that d L / d Ujkm = 0. Therefore,
Qjkm = S Xijkm (331)
/ = 1
Equation 331 implies that the total demand of commodity k at demand region j in month
m equals the aggregate for all supply regions of the quantity of commodity k shipped
from supply region i to demand region j in month m.
From Equations 329 and 331, we can prove that the marketclearing condition is
satisfied,
Xijkm Xjjkm
I J 1 J
X X Xjjkm = X X Xjjkm
/=iy=i i=ij=i
j i i j
Z X Xjikm = Z X Xjjkm
y=1/=i / = i y = i
j i
X Qjkm X Zjkm
j = 1 1 = 1
(332)
So the firstorder condition of this model satisfies the marketclearing condition of the
competitive equilibrium at which aggregate demand equals aggregate supply.
From the firstorder condition with we get
3 PARTIAL EQUILIBRIUM ANALYSIS ON FRUIT AND VEGETABLE
INDUSTRY 67
Background 68
Research Problem 72
Hypotheses 73
Objectives 73
Theoretical Framework 73
Fundamental Theory of the Partial Equilibrium Model 76
Impact of the Phaseout of Methyl Bromide 78
Impact of NAFTA 79
Methodology 82
Empirical Results 97
Tomatoes 97
Bell peppers 99
Cucumbers 101
Squash 102
Eggplant 103
Watermelons 103
Strawberries 104
Aggregate impacts 105
Conclusions 106
4 SUMMARY AND CONCLUSIONS 114
Summary 114
Suggestions for Further Research and Limitation of the Study 116
LIST OF REFERENCES 117
BIOGRAPHICAL SKETCH 120
vi
36
[7 YDr]e = [7 f] [7 Â£>> = [7 r]7=0. (2142)
The Lagrangean expression to be maximized under the homogeneity and symmetry
condition is
oS = In L + k\I <]
where xTs a vector of n Lagrange multipliers for the homogeneity condition, and ^ is a
vector of 0.5n{n 1) Lagrange multipliers for the symmetry condition. The vector of
firstorder derivatives of In L with respect to d can be written as
d{ln L) / dd = I (d In L / dD\
d(ln L)/dd=[I (X'YXXDt, ) Al]e,
d(ln L)/dd= [A'' (X'YXXD^e, (2144)
and from d ax / dx = a 'then
8k\I f]d/ dd=d[id f]d/ dd,
did[I f]d/dd=[id f]',
did[I f\d/dd[K r], (2145)
and
dn'RdI dd (ju'R)' = 7?'//. (2146)
The firstorder condition with respect to d of the Lagrangean expression with the
homogeneity and symmetry conditions, Equation 2143, is
[Aa (XY XXDi')]e + [* 0 r] + Rn = 0. (2147)
Since it is required that ?D3 = 0 in view of the homogeneity condition, and we know that
D2 = GXY and fG = 0, by premultiplying Equation 2143 by [A G], we get
[A G] [Aa (X'Y XXD3)\e + [A G] [k r] + [A G\R'/d= 0
[7 (GXY GXXD3')\e + [Ak Gt\ + [A G]R'jU = 0
[I (TV [I 0{X'X)A Tf]D3')\e + [A G]R'/a = 0
[7 (TV DY)]e + [A G]R '// = 0
d2d} + \AG]R,jU=0.
(2148)
46
Table 23. Estimation of the LaTheil model for the Atlanta market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0216
0.0078
0.0088
0.0127
(0.0287)
(0.0180)
(0.0171)
(0.0106)
^Tomato
0.0763
(0.0181)
^Bell Pepper
0.0475
0.0412
(0.0107)
(0.0104)
^Cucumber
0.0254
0.0037
0.0320
(0.0107)
(0.0075)
(0.0100)
^Strawberry
0.0033
0.0025
0.0103
0.0111
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (a)
0.0600
0.0379
0.0358
0.0221
R2
0.0616
0.1278
0.0253
0.0488
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 24. Estimation of the RAIIDS model for the Atlanta market by using the mean of
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.5427
0.1777
0.1911
0.0963
(0.0287)
(0.0180)
(0.0171)
(0.0106)
Somato
0.1696
(0.0181)
Sell Pepper
0.0484
0.0998
(0.0107)
(0.0104)
Tfcucumber
0.0774
0.0347
0.1171
(0.0107)
(0.0075)
(0.0100)
Strawberry
0.0438
0.0167
0.0050
0.0655
(0.0064)
(0.0049)
(0.0049)
(0.0047)
Standard Error (a)
0.0600
0.0379
0.0358
0.0221
R2
0.6284
0.5406
0.6141
0.6190
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
38
Inverse Demand System Analysis
The results from the estimation of the inverse demand system in every market
(Tables 21 through 216) show that by using the mean of the budget share to multiply
the logarithmic version of the inverse demand system, the RIDS has the same scale
coefficients as the RAIIDS model, and the AIIDS model has the same scale coefficients
as the LaTheil model. The quantity coefficients are the same between the RIDS model
and the LaTheil model, and are the same between the AIIDS model and the RAIIDS
model. The scale elasticity, quantity elasticity, and standard errors are unchanged across
all four functional forms of the inverse demand system.
The results from the estimation using the moving average of the budget share
(Tables 217 through 232) show that the coefficients are different from the estimation
using the mean of the budget share. We also can see that by using the moving average, a
different functional form generates a different result.
The results from the unconstrained estimation (Tables 233 through 236) show that
the relative size of the estimated asymptotic standard errors is so large that not too much
value can be attached to these results. Therefore, the unconstrained estimation results in
imprecise point estimates. Moreover, the results of the estimation with the homogeneity
constraint imposed (Tables 237 through 240) show that the homogeneity condition on it
own cannot contribute much to the precision of the estimator. Though we could have
expected smaller values for the standard errors, because of the use of a more restrictive
model, this hope is almost not realized. In this respect much more can be expected from
using the symmetry condition.
9
Conceptual Framework
Inverse Demand Model
Barten and Bettendorf (1989) investigated the demand for fish by using the
Rotterdam Inverse Demand System, which expresses relative or normalized prices as a
function of total real expenditure and quantities of all goods. The Rotterdam Inverse
Demand System is the inverse analog of the regular Rotterdam Demand System. From
an empirical viewpoint, inverse and direct demand systems are not equivalent. To avoid
statistical inconsistencies, the righthand side variables in the systems should not be
controlled by the decision maker. Therefore, it is better to use the inverse demand system
for fresh fruits and vegetables.
It will be helpful to recall the consumer theory about ordinary direct demand
functions derived from budgetconstrained utility maximization. Types of consumer
theory leading to systems of demand functions were summarized by Barten (1993),
Deaton and Muellbauer (1980), and Theil (1965). Consumers pay p,q, for the desired
amounts of commodity where p, is the price of good i and q, is the quantity of good /.
These expenditures satisfy the budget equation, I, pÂ¡qÂ¡ = m, where m is the total budget of
the consumers allocation. The consumers problem is to satisfy the budget constraint by
selecting the quantities that maximize the utility function. This consumer problem can be
stated as the utility maximization problem. It can be shown that under the appropriate
form of the utility function, there exists a unique set of optimal quantities that maximize
the utility function (subject to the budget constraint) for any set of given positive prices
and income. These optimal quantities of income and prices are the Marshallian
(Walrasian) demand functions,
qÂ¡ =f(m,pi,...,pn),
(21)
years. The U.S. Clean Air Act of 1992, as amended in 1998, requires that methyl
bromide be phased out of use by 2005. While significant progress has been made in
developing alternatives to methyl bromide, no alternative has been identified that permits
a seamless transition (where comparative advantage is minimally impacted by the
elimination of methyl bromide, and the affected producers continue to compete with
other producers).
To satisfy the utilitymaximization condition, the elasticities used in the spatial
equilibrium model are calculated from the popular functional forms of the inverse
demand system. Demand analyses can be very sensitive to the chosen functional forms.
Our study addresses this concern by proposing a formulation that obviates the need to
choose among various functional forms of the inverse demand system.
Results of the spatial equilibrium analysis indicate that total production in the
United States is expected to decrease after the implementation of NAFTA and the ban on
methyl bromide. Mexico is expected to become a larger supplier of vegetables in the
United States.
xiu
83
peppers, cucumbers, and strawberries. Preharvest and postharvest cost production costs
were estimated for each production system and area by Smith and Taylor (2002). The
cost budgets were constructed using a computerized budget generator program, AGSYS.
Technical coefficients used in constructing the budgets were obtained by consultation
with individual growers, county agents, and UF/IFAS researchers. Florida uses several
doublecropping systems in which a primary crop is followed by a different (secondary)
crop on the same unit of land. Transportation costs were included for delivering these
products to each of the regional markets based on mileages determined by the Automap
software and an estimation for a fullyloaded refrigerated truck carrying 40,000 pounds at
$1.3072 per mile (VanSickle, et al., 1994).
The constrained optimization model was solved using GAMS software. After
solving the VanSickle et al. model for a base solution for the 2000/2001 season, the
budgets and yields were changed to reflect the costs of growing the crops using an
alternative to methyl bromide. The results were compared to determine the impact that
the phaseout of methyl bromide may have on the production and marketing of these
crops.
In our study, we investigated the effect of the phaseout of methyl bromide on
tomatoes, bell peppers, and eggplant in Florida and on strawberries grown in both Florida
and California. Estimates of the impacts on production costs and yields from using
alternatives to methyl bromide were determined from discussions with scientists
attending USDA meetings (Carpenter and Lynch, 1998). For strawberries, California
growers were assumed to have switched to Chloropicrin (with additional hand weeding)
as a replacement to methyl bromide. Strawberry producers in West Central Florida were
20
^[df\q)ldqj\q, = f\q).
By multiplying both sides by qj, we obtain
Z, [df\q) / dqj\[qj/f\q)]f\q) q, f\q) qj.
As y/y = [df\q) / IfXq)} and w, =f\q) qÂ¡, we have
I, y/ijWt = wj, (263)
which is analogous to the Cournot aggregation, Z, WjjUy = Wj. Next, the analogous to the
Engel aggregation, Z/ w,7, =1, is obtained by
Z, W, Zy l//y = Zy Wy.
As 4/= 2y ys,j and Z, w, = 1, we get
Z, m>Q = 1. (264)
Scale and quantity elasticities are the natural concepts of uncompensated elasticities
for inverse demands. We derive the constantutilityquantity elasticities, or compensated
quantity elasticities, from the transportation function, T(q, u), which is dual to the cost
function and satisfies
U[q! T(q, u )] = (265)
for all feasible q and u. The transformation informs how much a particular
consumption vector must be divided to place the consumer on some particular
indifference curve. By differentiating with respect to goods, we get the constant utility or
compensated inverse demands,
n =f'\
These price functions give the levels of normalized prices that induce consumers to
choose a consumption bundle that is along the ray passing through q and that gives utility
u. The constant utility quantity effects, or the Antonelli substitution effects, state the
60
Table 231. Estimation of the LaTheil model for the New York market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.4646
0.2118
0.2208
0.1066
(0.0182)
(0.0135)
(0.0169)
(0.0100)
^Tomato
0.0294
(0.0119)
^Bell Pepper
0.0003
0.0255
(0.0072)
(0.0084)
^Cucumber
0.0177
0.0212
0.0406
(0.0095)
(0.0072)
(0.0113)
^Strawberry
0.0120
0.0046
0.0017
0.0184
(0.0058)
(0.0050)
(0.0054)
(0.0054)
Standard Error (ct)
0.0728
0.0506
0.0671
0.0386
R2
0.0414
0.0542
0.0660
0.0584
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 232. Estimation of the RAIIDS model for the New York market by using the
moving average of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4568
0.2273
0.2080
0.1117
(0.0188)
(0.0149)
(0.0178)
(0.0108)
/Tomato
0.2030
(0.0124)
/Sell Pepper
0.0818
0.1268
(0.0078)
(0.0093)
/Cucumber
0.0814
0.0224
0.1296
(0.0098)
(0.0080)
(0.0121)
/Strawberry
0.0398
0.0226
0.0258
0.0882
(0.0062)
(0.0054)
(0.0058)
(0.0058)
Standard Error (a)
0.0768
0.0591
0.0758
0.0444
R2
0.7525
0.8237
0.6596
0.6025
Note: Asymptotic standard error of each estimated parameter is shown in parentheses
100
revenues (Table 36). Shipping point revenues in Texas and Mexico are expected to
increase by $8.2 million and $2.3 million, respectively. The average wholesale price of
bell peppers under the first scenario is expected to increase by 1.35% (Table 38).
Consumer demand of bell peppers in every market is expected to decrease with the
highest percentage change of consumer demand for bell peppers will be in the New York
market, which is expected to decrease by 5.91% (Table 39).
Under second scenario, bell pepper production in Mexico is expected to increase by
2.67%, while bell pepper production in Florida is expected to decrease by only 0.78%
(Table 35). Table 38 shows that the average wholesale price of bell peppers under the
second scenario is expected to decrease by 0.24%. Table 39 shows that consumer demand
of bell peppers under the second scenario is expected to increase in every market.
Under the third scenario, the planted acreage of bell peppers in Mexico is expected
to increase significantly from 13,600 acres to 14,551 acres (Table 33). As a result,
production of bell peppers in the United States is expected to decrease by 2.85% (Table
35). The impact of NAFTA is expected to reduce the impact of the methyl bromide ban
in the U.S. domestic market (e.g., production of bell peppers is expected to increase by
10.12% in Texas and to decrease by 8.37% in Florida). In addition, the total shipping
point revenues for bell peppers are expected to decrease by $4.3 million, with shipping
point revenues for bell peppers in Mexico increasing by $6.1 million and shipping point
revenues for bell peppers in the United States decreasing by $10.4 million (Table 36).
The average wholesale price of bell peppers under the third scenario is expected to
increase by 0.90% (Table 38). Consumer demand of bell peppers in every market is
expected to decrease, except in the Los Angeles market, which is expected to increase by
22
du = 2, (5m / dq*)q* dk + (du / dqj )& dqj = 0,
dk = [(5m / cty/) / 2, (5m / 5g,*)
(270)
(271)
From Equations 269, 270, and 271, we get
dnit dq/ = [5g '(*> 9*) I d%] ~ [dS '(* q*) / 5Â£]^ A:.
By multiplying both sides by (g/ / nÂ¡), we get
{dn, / dq/)(q/ / ^) = (5/r, / dq/)(q/ / nÂ¡) (dn, / 5A)^ Â£(
{dnd dq/)(q/ / itt) = (57T, / dq/)(q/ / ;r,) (5;r, / 5A)(A / ;r,)(^
(272)
As w, = ^ qh 4 = (/tt, / / nÂ¡), 4 = (Stt, / 5A)(A / ^) and ^ = (5^ / dfyXty / flÂ¡), it is
convenient to express this in elasticity terms,
(273)
4 = Wj Qwj.
This states the Antonelli substitution effects in terms of scale and uncompensated
quantity changes. It is fully analogous to the Slutsky equation (Equation 25) of standard
theory,
(5/z, / 5py)(py / /?,) = (Sft / 5^)^ / 0/) + (5^, / 5l)(w / ^,)07^/ / )
Â£,j = H\j+
where /z,(p, m) is the Hicksian compensated demand function, which allows the demand
analyst working with inverse demands to compute compensated elasticities from the
uncompensated elasticities directly (without being obliged to explicitly consider the
transformation function or compensated inverse demands). Finally, from 2, = Wj
and 2, w,Q = 1, we can derive the analog to Slutsky aggregation
2, w,4 = 2, Wjif/y 2, WiQwj,
2, w,4 = w7 (1 )\Vj,
2, w,4 = 0.
(274)
CHAPTER 1
INTRODUCTION
Overview of the Fruit and Vegetable Industry
The United States is one of the worlds leading producers and consumers of fruits
and vegetables. According to the U.S. Department of Agriculture, farmers earned $17.7
billion from the sale of fruits and vegetables in 2002. Annual percapita use of fruits and
vegetables rose 7% from 19901992 to 20002002, reaching 442 pounds as fresh
consumption increased and processed consumption fell. Consumer expenditures for
fruits and vegetables are growing faster than any food group (except meats).
The United States harvested 1.4 million tons of fruits and vegetables in 1999 (a
20% increase from 1990). Even though output has been rising, aggregate fruit and
vegetable acreage has been relatively stable, indicating increasing production per acre.
The major source of higher yields has been the introduction of more prolific hybrid
varieties, many of which exhibit improved disease resistance and improved fruit set.
Shifting from lessproductive areas to higheryielding areas has also contributed to higher
U.S. yields over time. Fruit and vegetable output will likely continue to rise faster than
population growth over the next decade because of increasing consumer demand and
concerns about health and nutrition.
Fruit and vegetable production occurs throughout the United States, with the largest
fresh fruit and vegetable acreage in California, Florida, Georgia, Arizona, and Texas.
California and Florida produce the largest selection and quantity of fresh vegetables.
Climate causes most domestic fruit and vegetable production to be seasonal, with the
1
50
Table 211. Estimation of the LaTheil model for the Chicago market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0113
0.0185
0.0281
0.0178
(0.0246)
(0.0189)
(0.0189)
(0.0118)
^Tomato
0.0220
(0.0142)
^Bell Pepper
0.0125
0.0192
(0.0095)
(0.0105)
^Cucumber
0.0006
0.0088
0.0189
(0.0098)
(0.0081)
(0.0110)
^Strawberry
0.0101
0.0021
0.0107
0.0186
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.0229
0.0137
0.0163
0.0787
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 212. Estimation of the RAIIDS model for the Chicago market by using the mean
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4488
0.2226
0.2319
0.0805
(0.0246)
(0.0189)
(0.0189)
(0.0118)
Yl ornato
0.2241
(0.0142)
Tbell Pepper
0.0769
0.1433
(0.0095)
(0.0105)
/Cucumber
0.1143
0.0443
0.1735
(0.0098)
(0.0081)
(0.0110)
/Strawberry
0.0329
0.0222
0.0149
0.0700
(0.0061)
(0.0052)
(0.0053)
(0.0052)
Standard Error (a)
0.0668
0.0515
0.0515
0.0317
R2
0.7224
0.6100
0.6603
0.5739
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
69
Clean Air Act of 1992, as amended in 1998, requires that methyl bromide be phased out
of use on the basis of separate schedules prepared for developed and developing countries
who are party to the Montreal Protocol (Table 31). The phaseout of methyl bromide use
is being implemented by restricting the volume of methyl bromide that can be produced
and sold. So far, efforts to phase out methyl bromide have resulted in a 50% reduction in
use (the first two 25% reductions have already occurred in the United States). Table 31
shows the schedule for phasing out methyl bromide. Developing countries can still use
methyl bromide until 2015 (10 years after the phaseout in the developed countries).
There is concern that developed countries could be placed at a disadvantage (compared to
developing countries) if suitable alternatives cannot be found. This is highlighted by the
fact that in 2005, when the developed countries should have completed the phaseout of
methyl bromide, the developing countries would still be permitted to use methyl bromide
on 80% of the base level. Unfortunately, there are very few viable alternatives that are
technically and are economically feasible and also acceptable from a public health
standpoint. Therefore the Montreal Protocol allowed for exemptions to the phaseout
(e.g., the critical use exemption). In March of 2004, a meeting of the Parties to the
Montreal Protocol was held in Montreal, Canada, during March 2426, 2004 to address
problems related to the methyl bromide phaseout such as nominations and granting
conditions for Critical Use Exemptions (CUES). For examples, the United States made a
CUE request after a thorough and comprehensive review process. The U.S. EPA will
work with the USDA to fully support the U.S. nomination.
68
regional effects and changing the objective function so that the model can simulate all
fruits and vegetables at the same time.
Background
Methyl bromide has been a critical soil fumigant in the agricultural production for
many years. Methyl bromide is a broad spectrum pesticide that can be used to control
pest insects, nematodes, weeds, pathogens, and rodents. Under normal conditions,
methyl bromide is a colorless and odorless gas. About 21,000 tons of methyl bromide are
used annually in agriculture in the United States and about 72,000 tons are used globally
each year. When used as a soil fumigant, methyl bromide gas is injected into the soil at a
depth of 12 to 24 inches before a crop is planted. This procedure effectively sterilizes the
soil, and kills a majority of soil organisms. In addition, commodities may be treated with
methyl bromide as part of a quarantine requirement of an importing country. Some
commodities are treated several times during both storage and shipment.
Methyl bromide was assigned a 0.4 ozonedepletion potential (methyl bromide has
contributed about 4% to the current ozone depletion and may contribute 5% to 15% to
future ozone depletion if it is not phased out). Methyl bromide is 40 times more efficient
at destroying the ozone than chlorine (which should be phased out as well). The
degradation of the ozone layer leads to higher levels of ultraviolet radiation reaching the
Earths surface, which could reduce crop yields and could cause health problems (e.g.,
skin cancer, eye damage, and impaired immune systems).
The impact of methyl bromide on ozone depletion led to the development of the
Montreal Protocol in 1987. According to the U.S. Environmental Protection Agency
(EPA), the Montreal Protocol was designed to help revise methyl bromide phaseout
schedules on the basis of periodic scientific and technological assessments. The U.S.
36. Baseline revenues and changes in revenues from the methyl bromide ban effect
and the NAFTA effect, by crop and area Ill
37. Baseline revenues and changes in revenues from the methyl bromide ban effect
and the NAFTA effect, by area 112
38. Baseline average prices and percentage changes in prices from the methyl
bromide ban effect and the NAFTA effect, by crop 112
39. Baseline demand and percentage changes in demand from the methyl bromide
ban effect and the NAFTA effect, by crop and market 113
x
52
Table 215. Estimation of the LaTheil model for the New York market by using the
mean of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
b
0.0199
0.0008
0.0142
0.0010
(0.0190)
(0.0130)
(0.0159)
(0.0089)
^Tomato
0.0245
(0.0122)
^Bell Pepper
0.0015
0.0284
(0.0070)
(0.0079)
^Cucumber
0.0151
0.0232
0.0432
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0079
0.0036
0.0049
0.0164
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (a)
0.0785
0.0511
0.0674
0.0364
R2
0.0334
0.0563
0.0946
0.0589
Note: Asymptotic standard error of each estimated parameter is shown in parentheses.
Table 216. Estimation of the RAIIDS model for the New York market by using the
mean of the budget share
Parameter
Tomato
Bell Pepper
Cucumber
Strawberry
h
0.4577
0.1968
0.2388
0.1120
(0.0190)
(0.0130)
(0.0159)
(0.0089)
Y\ ornato
0.2216
(0.0122)
Tfeell Pepper
0.0843
0.1292
(0.0070)
(0.0079)
Tfcucumber
0.0957
0.0264
0.1458
(0.0092)
(0.0067)
(0.0103)
^Strawberry
0.0416
0.0185
0.0237
0.0839
(0.0053)
(0.0045)
(0.0048)
(0.0048)
Standard Error (a)
0.0785
0.0511
0.0674
0.0364
R2
0.7536
0.8456
0.7560
0.6830
Note: Asymptotic standard error of each estimated parameter is shown in parentheses
112
Table 37. Baseline revenues and changes in revenues from the methyl bromide ban
effect and the NAFTA effect, by area
Revenue($)
MB Ban and
Area
Baseline
MB Ban
NAFTA
NAFTA
Florida
853,322,230
(70,941,450)
(64,809,740)
(76,712,610)
California
752,871,600
(272,731,100)
(286,004,000)
(549,293,100)
Texas
58,828,370
8,248,660
218,480
5,954,450
V irginia/Maryland
42,736,960
(700,600)
(222,390)
(591,470)
South Carolina
71,270,950
19,210,230
17,207,920
17,712,950
Alabama/T ennessee
20,477,170
(20,477,170)
(20,477,170)
(20,477,170)
United States
1,799,507,280
(337,391,430)
(354,086,900)
(623,406,950)
Mexico
707,856,890
71,513,330
336,945,660
363,376,920
Total
2,507,364,170
(265,878,100)
(17,141,240)
(260,030,030)
Note: MB is abbreviated for Methyl Bromide.
Table 38. Baseline average prices and percentage changes in prices from the methyl
bromide ban effect and the NAFTA effect, by crop
Price
Crops
Baseline
MB Ban
NAFTA
MB Ban and NAFTA
Tomatoes
($/unit) (
8.69
1.46
%
(0.52)
)
0.82
Bell Peppers
6.14
1.35
(0.24)
0.90
Cucumbers
7.71
(0.40)
(0.65)
(0.36)
Squash
6.96
(0.18)
(0.50)
(0.41)
Eggplant
4.81
1.26
(0.36)
0.87
Watermelon
1.15
5.13
(1.42)
5.39
Strawberries
11.77
12.78
0.00
12.78
Note: MB is abbreviated for Methyl Bromide.
IMPACT OF SELECTED REGULATORY POLICIES ON
THE U.S. FRUIT AND VEGETABLE INDUSTRY
By
SIKAVAS NALAMPANG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2004
Ill
Table 36. Baseline revenues and changes in revenues from the methyl bromide ban
effect and the NAFTA effect, by crop and area
Crop/
Revenue($)
Area
Baseline
MB Ban
NAFTA
MB Ban and
NAFTA
Tomatoes
Florida
448,227,870
(56,878,770)
(46,798,270)
(62,753,470)
California
286,004,000
(9,442,000)
(286,004,000)
(286,004,000)
Alabama/T ennessee
20,477,170
(20,477,170)
(20,477,170)
(20,477,170)
South Carolina
71,270,950
19,210,230
17,207,920
17,712,950
V irginia/Maryland
42,736,960
(700,600)
(222,390)
(591,470)
United States
868,716,950
(68,288,310)
(336,293,910)
(352,113,160)
Mexico
496,178,430
67,177,520
332,710,470
353,716,970
Total
1,364,895,380
(1,110,790)
(3,583,440)
1,603,810
Bell Peppers
Florida
171,026,490
(17,069,120)
(994,830)
(16,315,310)
Texas
58,828,370
8,248,660
218,480
5,954,450
United States
229,854,860
(8,820,460)
(776,350)
(10,360,860)
Mexico
102,449,600
2,269,300
1,678,200
6,061,900
Total
332,304,460
(6,551,160)
901,850
(4,298,960)
Cucumbers
Florida
26,579,760
(79,510)
104,430
(302,210)
Mexico
64,228,410
997,490
1,243,710
1,243,700
Total
90,808,170
917,980
1,348,140
941,490
Squash
Florida
51,107,510
327,680
322,760
185,970
Mexico
19,105,090
(145,080)
125,260
198,630
Total
70,212,600
182,600
448,020
384,600
Eggplant
Florida
56,568,750
(3,663,070)
(847,960)
(4,254,770)
Mexico
25,895,360
1,214,100
1,188,020
2,155,720
Total
82,464,110
(2,448,970)
340,060
(2,099,050)
Watermelon
Florida
11,799,539
(7,874,013)
(976,981)
(5,667,189)
Strawberries
Florida
93,912,080
17,912,420
0
17,912,420
California
466,867,600
(263,289,100)
0
(263,289,100)
Total
560,779,680
(245,376,680)
0
(245,376,680)
Note: MB is abbreviated for Methyl Bromide.
78
x X(p) q(p)
So+ f [P(s)C'(s)]ds={ J [P(s)~ p]ds} + {n0+ \ [pC\s)}ds),
0 0 0
x oo q(p)
S0+ J [P(s) C'(s)] ds= J x(s) ds+{n0+ j [p C'(j)] ds, (310)
0 p 0
where So is a constant of integration equal to the value of the aggregate surplus. When
there is no consumption or production of good g, 17o is a constant of integration equal to
the value of the profits when qj = 0 for all j and So = /70 (which is equal to 0 if c,(0) = 0
for all j). In Figure 31, the aggregate consumer surplus is depicted by area A and the
aggregate producer surplus is depicted by Area B. The maximized aggregate Marshallian
surplus is depicted by area A plus area B, which is exactly equal to the area lying
vertically between the aggregate demand and supply curves for good g, up to equilibrium
quantity x.
Impact of the Phaseout of Methyl Bromide
Since currently available alternatives of methyl bromide are more expensive, it can
be postulated that in the absence of methyl bromide, cost of production is likely to
increase. This can be represented in the model by an upwards shift in the aggregate
supply curve, C'm(Z). Figure 32 shows that the new supply curve is Zm(P) = C'(Z) +
C'm(Z), where C'm(Z) is the addition marginal cost resulting from the phaseout of the
methyl bromide. Figure 32 shows that the upward shift of the supply curve results in an
increase in the equilibrium price (from P* to P**) and a decrease in the aggregate
shipment quantity (from X* to X**).
39
Elasticity Analysis
We calculated the elasticities for each market from the estimation of the RIDS
model by using Bartens method of estimation with homogeneity and symmetry
constraints imposed (Tables 21, 25, 29, and 213). The results from Tables 241
through 244 show that all elasticities in every market have the correct sign according to
theory. Tomato has the highest absolute value of the own substitution elasticity when
compared with other commodities for every market. In contrast, strawberry has the
lowest absolute value of the own substitution elasticity when compared with other
commodities for every market. The elasticities for the inverse demand system are closer
between the Atlanta and Los Angeles markets and between the Chicago and New York
markets.
Scale effect and scale elasticity
Scale effects show how much the normalized price of good i will change in
response to a proportional increase in the total quantity in all commodities. This reflects
the change in total expenditure. It denotes the change in utility, and addresses the
question of how prices change as you increase the scale of the commodity vector along a
ray radiating from the origin through a commodity vector. It measures the change in the
Divisia quantity index, showing the movement from one indifference curve to another.
Scale effects are converted into scale elasticities by dividing the scale effects by the
budget share. The scale elasticities are considered analogous to the total expenditure
(income) elasticities in the direct demand system. All the estimates for the scale effects
are statistically significant at the 5% probability level and have the expected sign.
Tomatoes. The obtained estimates for the scale effects of tomatoes in the Atlanta,
Los Angeles, Chicago, and New York markets are 0.5427, 0.5224, 0.4488, and 0.4577,
This dissertation was submitted to the Graduate Faculty of the College of
Agricultural and Life Sciences and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
August 2004
CL
Dean, College of Agricultural ancFLife
Sciences V )
Dean, Graduate School
33
Unconstrained estimation
Starting from an unconstrained estimation, the estimator of h, and hÂ¡j will be
derived, which corresponds with the maximum of the concentrated likelihood function
without the use of any restriction. For the firstorder conditions for a maximum of the
concentrated likelihood function with respect to the elements of D,
d(ln L)/dD = d [1/2 (TlnnT(n 1) (1+ In 2n) Tln\A\)\ / dD,
d(ln L) / dD = (1/2)5 (Tln\A\)/ dD,
d(ln L)/dD = (M2)AA[d(TA) / dD],
from d(lnf(x)) / dx =fA(x) [df{x) / dx],
d(ln L)/dD = (1/2M'1 {d[T{MT) (FT DX'Y YXD' + DX'XD')] / dD},
from d(ax) / dx = a, If xa = (xa)' then d(xa) I dx d(xci)7 dx = d(a'x) / dx = a',
and d(x 'ax) / dx = ax + (x'a)'= ax + a'x (d(x 'ax) / dx = lax, if a = a ), then
d{ln L)/dD = (1/2)Aa [2YX2DxX'X\,
d(ln L) / dD = A'1 [YX D\X'X\. (2126)
From d In L / dD = 0 and A'1 0, we can solve for DÂ¡,
YX D\XX = 0,
D\ (X'X)A = YX,
D\ = YX(X'X)a,
Dx' = (X'X)aX'Y, (2127)
where Di is the unconstrained ML estimator. The covariance matrix of this estimator is
E[(dl d)(dx d)r\ = n (XX)A, (2128)
where dx is an n(n + 2) component vector by arranging the n columns of D\ It is
obvious that this is simply the ordinary least squares (OLS) estimator applied to each
equation separately.
119
VanSickle, J.J., and S. NaLampang. The Impact of the Phase Out of Methyl Bromide
on the U.S. Vegetable Industry. International Agricultural Trade and Policy Center
IW 023, University of Florida, Gainesville, April 2002.
VanSickle, John J., Daniel Cantliffe, Emil Belibasis, Gary Thompson, and Norm Oebker.
Competition in the U.S. Winter Fresh Vegetable Industry. Economic Research
Service, U.S. Department of Agriculture, Agricultural Economic Report 691,
Washington, D.C., July 1994.
103
Eggplant
The 5,327 baseline acres of eggplant planted in Palm Beach County are expected to
decrease to 5,132 acres under the first scenario, to 5,247 acres under the second scenario,
and to 5,075 acres under the third scenario (Table 33). On the other hand, eggplant
production in Mexico is expected to increase by 4.69% under the first scenario, by 5.96%
under the second scenario, and by 9.75% under the third scenario to offset the loss of
production in Florida (Table 35).
Total shipping point revenues for eggplant are expected to decrease by $2.5 million
under the first scenario and by $2.1 million under the third scenario (Table 36). On the
other hand, under the second scenario, the total shipping point revenues for eggplant are
expected to increase by $340,060, as Mexico gains $1.2 million and Florida loses
$847,960 in shipping point revenues. The average wholesale price of eggplant is
expected to decrease by 0.36% under the second scenario, but is expected to increase by
1.26% under the first scenario and by 0.87% under the third scenario (Table 38).
The consumer demand of eggplant in every market is expected to decrease under
the first scenario with the highest decrease in the Atlanta market (11.55%) and to increase
under the second scenario with the highest increase in the Los Angeles market (2.34%).
Under the third scenario, the consumer demand of eggplant in every market is expected
to decrease, except in the Los Angeles market, which is expected to increase by 1.90%
(Table 39), due to the greater impact of NAFTA as opposed to the impact of the methyl
bromide ban.
Watermelons
Table 33 shows that the 1,812 planted baseline acres of watermelon in West
Central Florida are expected to decrease to 593 acres under the first scenario, to 1,694
5
the height of the domestic season. Imports accounted for 45% of U.S. freshcucumber
consumption from 2001 through 2003, with most of the imports coming from Mexico and
Canada.
Cultivated for thousands of years, watermelon is thought to have originated in
Africa, and to have made its way to the United States with African slaves and European
colonists. The United States ranks fourth in the worlds watermelon production. Florida
is the leading domestic source of fresh watermelon, followed by Texas, California,
Georgia, and Arizona. Although value and production have been rising, the acreage
devoted to watermelon has been trending lower over the past few decades. During the
most recent decade, declining acreage has been due to a combination of rising peracre
yields and successive years of freeze damage in Florida and drought in Texas. Most
watermelon is consumed fresh, even though there are several processed products in the
market such as roasted seeds, pickled rind, and watermelon juice. Percapita
consumption of watermelon is highest in the West and lowest in the South.
In 1995 and 1996, fresh fruit and vegetable imports to the United States surged due
to the combined effects of the devaluation of the Mexican peso, the rising demand for
improved extended shelflife varieties, and reduced domestic output due to adverse
weather conditions. Florida and Mexico historically compete for the U.S. winter and
early spring market. For example, Mexico dominates the market in the winter (when
southern Florida is the predominant U.S. producer), and Florida dominates the market
during the spring (when Mexican production seasonally declines). Another factor has
been NAFTA. Under NAFTA, some of the tariffs on freshmarket tomatoes from
Mexico were phased out over a 5year period (19941998), while others had a 10year
214. Estimation of the AIIDS model for the New York market by using the mean of
the budget share 51
215. Estimation of the LaTheil model for the New York market by using the mean
of the budget share 52
216. Estimation of the RAIIDS model for the New York market by using the mean
of the budget share 52
217. Estimation of the RIDS model for the Atlanta market by using the moving
average of the budget share 53
218. Estimation of the AIIDS model for the Atlanta market by using the moving
average of the budget share 53
219. Estimation of the LaTheil model for the Atlanta market by using the moving
average of the budget share 54
220. Estimation of the RAIIDS model for the Atlanta market by using the moving
average of the budget share 54
221. Estimation of the RIDS model for the Los Angeles Market by using the moving
average of the budget share 55
222. Estimation of the AIIDS model for the Los Angeles market by using the moving
average of the budget share 55
223. Estimation of the LaTheil model for the Los Angeles market by using the
moving average of the budget share 56
224. Estimation of the RAIIDS model for the Los Angeles market by using the
moving average of the budget share 56
225. Estimation of the RIDS model for the Chicago market by using the moving
average of the budget share 57
226. Estimation of the AIIDS model for the Chicago market by using the moving
average of the budget share 57
227. Estimation of the LaTheil model for the Chicago market by using the moving
average of the budget share 58
228. Estimation of the RAIIDS model for the Chicago market by using the moving
average of the budget share 58
229. Estimation of the RIDS model for the New York market by using the moving
average of the budget share 59
vm

