AN ECONOMIETRIC ANALYSIS OF
THE FLORIDA GRAPEFRUIT INDUSTRY
By
ARTHUR F. PARKER, JR.
A Dissertation Presented to the Graduate Council
of the University of Florida
in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
UNIVERSITY OF FLORIDA
1973
II1 11:1 11 1 l lill IIII1 liil il l1 11111
ACKN~OW~LEDGMENTS
The author wishes to express sincere appreciation to
his chairman, Dr. W. W\. MlcPherson, for his guidance through
out his graduate program. Also, a debt of gratitude is
owed to Dr. Lester Mlyers for his invaluable assistance dur
ing the course of the research for this study. The other
members of his committee, Dr. Max Langham and Dr. F. 0.
Goddard, are also due a special word of appreciation. The
author wishes to thank the various members of the Food and
Resource Economics Department faculty, andi especially Dr.
W. B. Lester, of the Florida Department of Citrus, for their
assistance.
The author is grateful to Mlrs. Jane Mioore for typing
the various drafts of the study and to Mlrs. Elizabeth Godey
for her typing of the final copy. Appreciation is also
extended to the Florida Department of Citrus for financing
the computer time.
Finally, the author thanks his wife, Sandy, for her
Patience and understanding during the years spent in graduate
study.
TABLE OF CONTENTS
Page
. . . . . ii
ACKNOWLEDGMENTS .....
LIST OF TABLES ...
LIST OF FIGURES .. ... .. .. .. .. .. viii
ABSTRACT .. .. ... .. .. .. . ... ix
CHAPTER
I INTRODUCTION ......
Objectives .. ....
Literature RevIiew .........
Organization of Presentation ....
II MODEL DEVELOPMENT
lo del I . . . .
Price of Grapefruit for Packing.
Price of Grapefruit for Processing..
Utilization or Pack.. ......
Storage . . .
FOB Demand
Supply to Buyers at FOB Level ...
Identities . . . . . .
Model II . . . . . .
Storage
FOB Demand . ... .
Supply to Buyers at FOB Level ...
Identities . . . . . .
III STATISTICAL CONSIDERATIONS ......
Statistical Mlodel... .....
Mo del I . . . . . .
Model II . . . . .
General Model . . . . . .
Identification ..... .....
Estimation Procedure ...... ..
Selection of Time Unit and Period..
Data . . . . .
TABLE OF CONTENTS (continued)
Page
CHAPTER
IV STATISTICAL RESULTS .. .. .. 49
Model I . . . . . . . . 49
OnTree Price Equations ........ 49
Pack Equations .. .. .. . ... 51
Storage Equations .. ... . . 53
FOB Domand . .. ... .. .. .. 55
Model II . . . . . . . . 58
Storage Equations ...... .... 58
FOB Demand . ... .. .. .. .. 59
V ECONOMIC IMPLICATIONS .. .. .. .. 61
Elasticities 61
Implications from the Derived
Reduced Forms .. .... .. .. 67
ShortTerm Forecasting .. ... .. 74
VI SUMMFARY AND CONCLUSIONS .. .. .. .. 84
Summary .. .. ... ... .. .. 84
Conclusions ....... 88
Suggestions for Further Research .... 90
APPENDIX . .... .. .. .. .. ... 92
BIBLIOGRAPHY .. .. .. . ... .. ... 120
BIOGRAPHICAL SKETCH ... .. .. .. .. .. 123
LIST OF TABLES
.ble Page
1 Percent of the Grapefruit Crop Accounted
for by Each Product Form, 196768
Through 197071 Seasons .... .. 6
2 Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefruit
in Various Forms, Computed at Mlean
Values of the Variables, Moadel I,
196471 .. .. .. ... .. . . 64
3 Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefruit
in Various Processed Forms, Computed at
Mlean Values of the Variables Mlodel II,
196470 .. .. .. ... . . 66
4 Coefficients of Derived Reduced Form
Equations for M~odel I .. .. .. .. 68
5 Coefficients of Derived Reduced Form
Equations for M~odel II .. . ... .. 71
6 Endogenous Variables : Actual Values,
Predicted Values Based on the Reduced
Form Estimated Directly and Deviations,
December, 1971, Through March, 1972 .. 78
7 Theil's Inequality Coefficients for
Predicted Yalues of the Endogeneous
Variables, Based on Reduced Form
Estimated Directly, December, 1971,
Through M~arch, 1972 ..... 8
8 Endogeneous Variables: Actual Values,
Predicted Values Based on the Derived
Reduced Form and Deviations, August
and September, 1971 . .. ... . . 82
9 OnTree and FOB Prices: Mlonthly Data
Used in Estimating the Structural
Models, 196471 ...... 93
LIST OF TABLES (continued)
Table Page
10 FOB Prices and Canned SingleStrength
Grapefruit Juice Quantities: M~onthly
Data Used in Estimating the Structural
Models, 196471 ... .. .. . 95
11 Grapefruit Sections and Frozen Concen
trated Grapefruit Juice Quantities:
Monthly Data Used in Estimating the
Structural Models, 196471 .. .. . 97
12 Inventory of Frozen Concentrated
Grapefruit Juice and Grapefruit
Quantities : Mlonthly Data Used in
Estimating the Structural Mlodels,
196471 ... .. .. .. .. .. 99
13 Exogenous Variables: Mionthly Data
Used in Estimating the Structural
Models, 196471 .. . . .. 101
14 Retail Price of Frozen Concentrated
Orange Juice and Demand Shifters:
Monthly Data Used in Estimating the
Structural Mlodels, 196471. .. .. 103
15 Coefficients, Standard Errors and
Coefficients of Determination of
Reduced Form Equations from First
Stage of TwoStage Least Squares,
Model I .. .. .. ... .. .. .. 105
16 Endogenous Variables: Actual Values,
Predicted Values Based on the Derived
Reduced Form and Deviations, December,
1971, Through Miarch, 1972 .. .. . 110
17 Theil's Inequality Coefficients for
Predicted Values of the Endogenous
Variables, Based on Derived Reduced
Form, December, 1971, 'Through Mlarch,
1972 .. .. .. .. ... .. 112
18 Data Used in Forecasting and Evalu
ating Mlodel I, by Mlonths, November,
1971, Through Mlarch, 1972.. .. . .. 113
LIST OF TABLES (continued)
Table Page
19 Coefficients, Standard Errors and
Coefficients of Determination of
Reduced Form Equations from First
Stage of TwoStage Least Squares,
Model II .. .. ... .. .. .. .. 115
20 Endogenous Variables: Actual Values,
Predicted Values Based on the Reduced
Form Estimated Directly and Deviations,
August and September, 1971 . ... .. 118
21 Data Used in Forecasting for Model II,
by Months, July, August and September,
1971 . . . 119
LIST OF FIGURES
Figure Page
1 Distribution of commercial grapefruit
acreage, by counties, as of December,
1969, and delineation of Indian River
district . ... .. .. .. .. .. 4
V111
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ANZ ECONON\ETRIC ANALYSIS OF
THE FLORIDA GRAPEFRUIT INDUSTRY
By
Arthur F. Parker, Jr.
March, 1973
Chairman: Dr. WI. W. MlcPherson
Cochairman: Dr. L. H. Myers
M~aj or Departmnent: Food and Resource Economics
The objectives of this study were (1) to quantitatively
describe, by means of a simultaneous equation model, the
Florida grapefruit industry from the grower transactions
at harvest to the FOB level for canned singlestrength juice,
canned sections, frozen concentrated juice and fresh grape
fruit, (2) to measure the effects of factors exogenous to
the Florida grapefruit industry on the production and sale
of the four products listed above, and (3) to develop a model
for forecasting values of the variables endogenous to the
Florida grapefruit industry.
Two models were developed: one for the months in which
fruit was harvested and thus available for processing and
for fresh pack (Mlodel I) and one for the months when no
fruit was available (Model II). Model I consisted of 11
behavioral equations and seven identities for the crop years
196465 to 197071. Model II consisted of six behavioral
equations and six identities for the crop years 196364 to
196970. Included in Mlodel I wJere behavioral relationships
for (1) ontree prices for grapefruit for packing and for
processing, (2) pack for each of canned sections and frozen
concentrated juice, (3) storage of each of the processed
products, and (4) FOB demand for each of the processed prod
ucts, as well as FOB demand for fresh grapefruit. The
behavioral relationships for Miodel II included (1) storage
of each of the processed products and (2) FOB demand for
eachz of the processed products. The behavioral equations
were estimated by means of twostage least squares. Monthly
data wjere used.
The supply of fruit to packers and processors was
assumed to be predetermined. In the processor and packer
ontree price equations, both the quantity available and the
prices of the products to be derived from the fruit were
shown to affect ontree prices. For fresh fruit, the margin
between the ontree price and the FOB price was found to
increase with advances in the price level.
The pack and storage equations contained price expecta
tion relationships. The results indicated that current
prices had more influence on pack and storage than did
expected prices.
The FOB demand equations w~ere each estimated with the
quantity of a product demanded as a function of its FOB
price, the prices of substitutes, disposable personal income
per capital, the FOB quantity in the previous month and the
month. In general, seasonality in demand was found to
exist, the income effects were positive and the ownprice
slopes were negative.
Average values were used to calculate elasticities.
For Model I, price elasticities of demand at the FOB level
were 0.392 for singlestrength juice, 2.101 for canned
sections, 0.163 for frozen concentrated juice and 12.268
for fresh grapefruit. For Mlodel II, the elasticities for
the first three products above were 1.254, 2.636 and
2.096, respectively. For both Model I and Model II, cross
elasticities indicated that singlestrength juice and fro
zen concentrated juice were substitutes.
Direct and derived reduced form estimates were obtained
for the two models. Implications of the derived reduced
forms were discussed.
Finally, predictions were obtained for each model using
both the direct and derived reduced form estimates. Pre
dictions were made for December, 1971, to Mlarch, 1972, for
Model I and for August and September, 1971, for Mlodel II.
Model I predictions were evaluated using Theil's inequality
coefficients. Because there w~ere only tw\o data points,
Model II predictions were not evaluated. The predictions
for Mlodel II appeared to be considerably more accurate than
were those for Mlodel I.
CHAPTER I
INTRODUCTION
During the past decade, Florida growers have produced
approximately 76 percent of the grapefruit produced in the
United States. The amount produced annually has varied from
26 to 44 million boxes, with an annual average of over 34
million boxes. California, Texas and Arizona produce average
annual quantities of 4.1, 3.9 and 2.7 million boxes, respec
tively, and are the only other states that produce grape
fruit. In terms of total value of farm production in Florida,
grapefruit ranks third, among different commodities, behind
oranges and tomatoes, with an annual average farm value of
over 44 million dollars. During the 197071 season the
value of the production of oranges, the primary agricultural
commodity in the state, was approximately 1S9 million dollars
[19, 1971 issue,p. 18].
Varieties of Florida grapefruit are classified, based
on physical characteristics, into white seedy, white seed
less and pink seedless grapefruit. The white seedless type
is primarily composed of the M~arsh variety. The Duncan
variety is the predomiinant white seedy type. In December,
1969, 26.8 percent of the bearing acreage was of the pink
seedless type, 47.8 percent was of the white seedless type
and the other 25.4 percent was white seedy [20]. The harvest
of each type usually begins in September, but it is October
before any appreciable quantity is available for market.
Harvest of the seedy type peaks in October, tapers off
through the succeeding months and ends in April or May..
The white seedless type is available in large quantities in
October; thereafter the production decreases for a month or
two and then increases. In February or March, production
neaks and then tapers off until June or July, at which time
picking ceases. The seasonal production pattern for pink
seedless fruit is similar to that for the white seedless
type.
The fact that these patterns exist tends to complicate
the decisionmaking process for processors and packers. For
example, except for a very few~ products, pink grapefruit is
not desirable for processing because of the color that it
imparts to the products. On the other hand, the Duncan
variety is preferred for use in canned grapefruit sections
because of its fairly large sections. The matter of storage
of processed products also enters the decisionmaking pro
cess, as there is no fresh fruit available during the summer
months.
Florida grapefruit production may also be categiorized
with respect to geographic location. Grapefruit is gener
ally produced in the lower twsothirdls of the state, from
Putnam, Flagler and Mlarion counties south to Collier and
Brow~ard counties (Fig. 1.). The two general areas are
referred to as the Indian River district and the Interior
district [22, p. 40]. During the crop years 196667 through
197071, 27.8 percent of the grapefruit produced in Florida
was produced in the Indian River district, while the other
72.2 percent was produced in the Interior district.~r c
Efforts to establish a differentiation between Indian
River and Interior grapefruit have been highly successful.
For years, Indian River packers have advertised fresh Indian
River fruit as being of a higher quality than fruit from the
other region. This campaign w~as successful, as shown by the
fact that, for the past five years, grapefruit from the
Indian River district has commanded an ontree price aver
aging over 75 cents per box more than Interior district
prices. However, it has been shown that product differen
tiation has decreased in the last year or two [24, p. ii].
Prices of grapefruit for processing in the tw~o districts
have tended to be about equal.
SThe grapefruit industry is organized along the follow
ing lines. The growJers sell the grapefruit either to packers,
for sale later as fresh fruit, or to processors for process
ing into 10 processed grapefruit products. There are at
present approximately 34 firms that process citrus. Mlost
of these firms produce at least some of the products derived
from grapefruit. Some firms produce only singlestrength
3
$;.
a
d
,,,,.
a
51,000 acres
I~] 1,00010,000 acres
6~Over 10,000 acres
II1I1ii~
'd%," '
Figure 1. Distribution of commercial girapefruit acreage,
by counties, as of Decemnber, 1969, and
delineation of Indian River district.
juices, othersproduce almost all of the products except
canned sections. During 197071, approximately 120 to 130
firms packed fresh grapefruit. The number has varied from
year to year as a number of the smaller firms have ceased
packing operations or merged with larger firms. Also, small
firms are continually being formed. During the crop years
196768 to 197071, approximately 38.3 percent of the grape
fruit crop was delivered to the packers, with the rest going
to the processors. The products that are derived from grape
fruit, as well as the relative importance of each, are shown
in Table 1. Processors pack the 10 processed products and
move them into the warehouse to be sold at a later date or
they sell them immediately to buyers (i.e., chain stores and
wholesalers). During the months w~hen grapefruit is avail
able for processing, processors build up inventories for the
summer months when fresh fruit is not available. During the
months of no grapefruit production, processed products are
moved from the warehouse and into the marketing channels for
final consumption.
Fresh grapefruit, canned juice, canned sections and
frozen concentrated juice, wJhich account annually for about
89 percent of the total crop, were included in this study.
The other seven products account for the other 11 percent,
the most important of the seven, chilled juice, accounted
for an average of less than 5 percent over the four years
included in Table 1. Although chilled juice is a relatively
*Less than .1 percent.
Source: Florida Citrus Mlutual, Annual
Report, Lakeland, Florida, 197071 issue.
Statistical
Table 1. Percent of the Grapefruit Crop Accounted
for by Each Product Form, 196768
Through 197071 Seasons
Fresh
Canned Juice
Frozen Concentrate
Chilled Juice
Canned Sections
Canned Blend
Chilled Salad
Chilled Sections
Canned Salad
Processed Concentrate
Frozen Blend
TOTAL
Percent
197071
34.8
34.0
15.7
5.5
5.4
1.6
1.5
1.1
0.2
0.2
100.0
of Total
196970
38.0
32.8
12.1
4.9
6.6
2.0
1.9
1.2
0.4
0.1
100.0
Grapefruit Crop
196869 196768
35.2 45.0
29.7 30.2
16.5 5.4
4.1 3.9
7.6 7.9
2.1 2.1
2.7 3.9
1.5 1.0
0.5 0.6
0.1 0.0
100.0 100.0
Product Form
new product, it is currently more important than canned
sections. However, a lack of data for the earlier years
included in the study precluded its use in this analysis.
The other processed products as a group, represent such a
small proportion of the total that they were omitted in this
study.
There are three main types of arrangements for the sale
of fruit to packers and processors. Cash buyers deal
directly with growers and an agreement is reached as to
price and quantity to be exchanged. The participation plan
type of contract is a hedge against a loss of markets result
ing from an oversupply of fruit. Mlost plans contain pro
visions whereby a grower binds all or a portion of his fruit
to a processor. The price of the fruit is determined at the
end of the pool period and is based upon a formula specified
in the contract. Generally, the pool periods end either at
the end of the crop year or approximately midway through it,
depending on the contract. Thus, the processor pays the
grower at the end of the year only for the fruit used, based
on the price that the processor receives for the processed
products derived from the fruit. This type of arrangement
is advantageous to growers in that they are assured of a
market for all or part of their fruit. The processor bene
fits in that he is assured, of both a source of supply and a
lockedin profit margin. The third type of arrangement is
the cooperative. Member growers pool their fruit and sell
it as a group rather than individually. At the end of the
operating year, profit received by the cooperative from the
sale of products derived from the fruit, including byproducts,
is divided among the members in proportion to the quantity
each member put into the pool. In some cases, cooperatives
have started their own processing plants. They benefit from
an assured market, even though the fruit is unpriced until
the end of the year. Also, members share in the profits of
the cooperative's processing plants. Similarly, packers and
processors that deal with the cooperative are fairly certain
of a source of rawJ fruit.
Each of the three arrangements has a different effect
on the allocation of the fruit to be packed or processed.
The participation plan member has no choice as to how his
fruit is allocated; that is, price does not play a role in
the decision to supply the fruit to a packer or to a pro
cessor. The same is true for the cooperative member. Only
the cash seller has this option. During the 197071 season,
almost 28 million boxes of grapefruit were utilized by pro
cessors for the production of various processed grapefruit
products. Of this total, nearly 10 million boxes, or almost
35 percent, were moved to the processors as priced fruit [4].
The Florida grapefruit industry is constantly faced
with the possibility of widely fluctuating supplies of fruit
combined with a more or less steadily increasing demand for
grapefruit products. This condition results in substantial
yeartoyear variations in prices and net revenues to growers.
Unlike industrial production, where the flow of raw materials
can be adjusted as conditions require, the supply of grape
fruit is a rather longterm proposition. Trees will produce
fruit for many years, so that shortrun variations in sup
plies are primarily the result of weather and basically
beyond the control of producers.
Growers, then, as well as packers and processors, are
faced with constraints on the volume of fruit available at
a particular point in time within the season as well as that
for the total season. Both of these constraints make utili
zation and marketing decisions more difficult. The more
information that is available to decision makers, the better
the industry can adjust to the factors over which it has no
control.
Objectives
Necessary inputs into the decisionmaking process
include empirical estimates of the supply and demand relation
ships at each transaction point in the system. Also needed
are estimates of economic relationships, such as price
quantity relationships and the effects of inventory levels,
which determine the allocation of grapefruit among various
products and between storage and current sales.
The objectives of this study follow:
(1) To quantitatively describe, by means of an
econometric model, the Florida grapefruit
industry from the grower transactions at
harvest to the FOB level for canned single
strength juice, canned sections, frozen
concentrated juice and fresh grapefruit.
(2) To measure the effects of factors exogenous
to the Florida grapefruit industry on the
production and sale of the four products
included in the study.
(3) To develop a model for forecasting values
of the variables endogenous to the Florida
grapefruit industry.
Literature Review
Research dealing with the Florida citrus subsector has
dealt primarily wlith the orange industry. The grapefruit
industry w~as included. only when it was necessary for the
quantification of economic relationships dealing with orange
products, such as substitutes in demand equations. This
emphasis on oranges has possibly been due to the fact that
the orange industry has historically been of much greater
economic importance than has the grapefruit industry.
Shafer has conducted several studies relating to the
annual demand for Texas grapefruit. Estimates of the demand
for Florida grapefruit were obtained as a byproduct of his
studies. In An Analysis of Season Average prices for Texas
Grapefruit, 19491967 [14], Shlafer and Gutierrez analyzed
grapefruit prices for the years fromn 1949 to 1967. They
found that the Florida crop values generally tended to move
inversely with the size of the Florida crop. A 1 percent
change in Florida production on a U. S. per capital basis
was associated with a 1.68 percent change of opposite sign
in the Florida price for fresh grapefruit. In the case of
grapefruit for processing, a 1 percent change in production
per capital was found to be associated with a 2.3 percent
change in price in the opposite direction.
A later study by Shafer [13] updated the previous study.
It was found that the quantity of Florida production allo
cated to fresh use exerted a significant negative effect on
the season average FOB price for Texas grapefruit. From
this information, it w~as concluded that fresh Florida grape
fruit and fresh Texas grapefruit w~ere substitutes for one
another.
In a study by Ward [25], detailed pricequantity rela
tionships were estimated for grapefruit from the Indian
River district. In particular, it was found that over one
third of the weekly variation in the FOB price of Indian
River grapefruit was explained by weekly changes in shipments
from Indian River, Interior Florida and Texas. Further,
Texas shipments were found to have a greater influence on
the Indian River price than did Interior shipments.
Another study by Wlard [24], conducted a year later,
generally confirmed the results of the previous study. H
found, however, that Indian River grapefruit prices had
become more responsive to Interior Florida and Texas
shipments, with the increased price responsiveness to Texas
shipments far exceeding the response to Interior shipments.
A study with objectives similar to those of the present
study was conducted by Vanderborre [23] for the soybean
economy. He described the markets for soybean oil and soy
bean meal by means of a simultaneous equation model. A pri
mary objective of that study was the estimation of the
demand relationships for both domestic and export markets
for soybean products. The model consisted of equations for
the wholesale demands for crude soybean oil and for soybean
meal, as well as equations for the export demand for those
two commodities. Pricing, margin and stock equations w~ere
also included. First differences were used in all of the
equations in an effort to reduce the possibility of auto
correlation and multicollinearity. Conclusions were reached
with respect to the effects of the ex(ogenous variables on
the endogoenous variables by algebraic manipulation of the
structural equations which were estimated by means of two
stage least squares. At the time of the publication of the
article, the model had not yet been tested for its predic
tive ability.
K'ulshreshtha and Wilson [9 ] presented a simultaneous
equation model of the Canadian beef cattle industry as a
first attempt to examine the interdependent nature of demand,
sunply and price relationships in that industry. The comn
plete system included six behavioral equations and three
identities. Behavioral equations were estimated by means
of twostage least squares and included relationships for
the demand for beef, the demand for live cattle for export,
retail prices, slaughter, dressed weight and inventory.
One of the major purposes of the study was to derive a model
for predicting changes in the beef cattle sector. For pre
dictions, the authors converted the structural equations
and the identities into reduced form equations. The pre
dictive ability of the model was evaluated with Theil's
Ucoefficient [16, p. 28, and 17, p. 32].
Another study with objectives and methodology similar
to the present one was conducted by Myers, Havlicek and
Henderson [11]. The objective was to obtain a simultaneous
equation model of the monthly structure of the hogpork
sector of the United States. The model consisted of eight
behavioral equations and two identities. The behavioral
equations represented the supply and demand relationships,
as well as margin equations, that existed within the hog
pork sector from the farm level to the retail level. Two
stage least squares was used to estimate the parameters of
the model. Then, using the secondstage structural equations
and the firststage reduced form equations, values of the
endogenous variables were predicted for 18 months for which
the data had not been used in the original estimates. The
ability of the model to predict was evaluated by several
means. As in the previously mentioned study, Theil's
Ucoefficient was calculated for each endogenous variable.
Also, the predictive ability of the model wa~s evaluated by
means of its ability to predict changes in direction in the
endogenous variables.
Organization of Presentation
The economic model of the Florida grapefruit industry
is described in the second chapter. The third chapter con
tains the statistical model, as well as a discussion of the
statistical procedures used. The statistical results of the
study are presented in the fourth chapter. The fifth chap
ter consists of implications drawn from the results of the
statistical analysis, including elasticity estimates and a
prediction model. In the final chapter the results and
conclusions are summarized.
CHAPTER II
MODEL DEVELOPMENT
At each level of exchange of fruit or processed product,
there are relationships that interact to determine price and
quantity. In addition, each level affects each other level
in that changes in orices and quantities at one level cause
repercussions in other levels. For example, a change in the
FOB price of a product affects pack decisions of that prod
uct, which in turn affects the pack of the other products.
Hence, the system was formulated as a simultaneous one.
There are several months of each year when all four
Products included in this study are produced. Model I
represents these months. However, grapefruit is not picked
year round, nor can it be stored in fresh~ form for very
long. Model II represents the months when there is no har
vest. Finally, there are months during which some, but not
all, of the products are produced. These months were dis
tributed between the two models according to the following
criteria. If canned singlestrength grapefruit juice, which
normally accounts for approximately 55 percent of all pro
cessed grapefruit, w~as produced during a month, that months
wJas placed in Mlodel I. Fresh pack usually coincides with
the months during which singlestrengith juice is produced.
On this basis, Model I included the nine months from October
to June, while Model II included July, August and September.
Retail prices were deflated by the consumer price
index, while all other prices wJere deflated by the wholesale
price index for farm products. Also, all quantities, after
the raw fruit was supplied to the packers and to the pro
cessors, wJere converted to the equivalent of gallons of
singlestrength juice. This conversion was made to facili
tate direct comparisons among products.
Model I
Price of Grapefruit for Packing
Thie quantity of grapefruit that growers are willing to
supply to packers was assumed to be determined outside of
the system. Rather than supply being a function of economic
variables, it is a function of the month of the season, with
a constant quantity being supplied in a particular month.
For example, it was found that the average quantities going
to fresh use, during the years included in this study, in
December, January, February and Mlarch were 1.555, 1.757,
1.650 and 2.102 million boxes, respectively. The correspond
ing standard deviations were 0.172, 0.143, 0.161 and 0.280,
respectively. Thus an economic supply function was not
specified for the system. The same reasoning wias applied
for the quantity of grapefruit supplied for processing.
W~hen the supply of fruit is predetermined, price becomes
the critical variable for equating supply with demand.
Therefore, the equation w~as formulated wLith ontree price as
an endogenous variable and quantities supplied as a pre
determined explanatory variable. Since the packers purchase
the fruit to vack and then sell at the FOB level, the FOB
rice was also hynothesized as influencing ontree prices.
The relationship is shown below~.
(21) PGKms = FlPFFGms,GKms)
wdh ere PGhas = deflated ontree price of grapefruit for
fresh packing in month m and year s
(dollars per 1 3/5bushiel box).
PFFGs = deflated FOB price of fresh grapefruit in
month m and year s (dollars per 1
3/5bushel box).
GKs = qua"ntity of gracefruit for packing in
msmonth m and year s (million 1 3/5
bushel boxes).
It was expected that the FOB price and the ontree
price would change in the same direction. Also, since supply
was predetermined, the price was expected to fluctuate in
versely with the quantity of fruit available in a particular
month. Therefore, aPGKms/aGKm < 0.
Price of Granefruit for Processing
The equation for the price of grapefruit for processing
was similar to that for packing in that it was derived from
the FOB level. The price that the processors pay for the
fruit was expressed as a function of, among other things,
the quantity of fruit going to the processors. Because of
the various contractual arrangements within the industry
whereby the price growers receive is determined by the FOB
prices received for the output and the processing cost, the
ontree price was also a function of the FOB prices of the
three processed products and the average cost of processing.
The year was used in other equations in the model.
Both the year and processing costs w~ere exogenous variables.
Since the system was formulated as a simultaneous one, no
predetermined variables should be highly correlated. To
violate this principle could result in a singular matrix of
exogenous variables. The correlation coefficient between
the year and procecssing costs was found to be 0.91. Because
of this close relationship, the year was used in place of
processing costs.
The equation for the price is given below.
(22) PGRms = f(PFCSms,PFCGms,PFFCms,GRms's)
where PGRms = deflated ontree price of grapefruit for
processing in nonth m and year s (dollars
per 1 3/5bushel box).
PFCSms = deflated F0B price of canned singlestrength
grapefruit juice in month m and year s
(dollars per case of twelve 46ounce cans).
PFCGms = deflated FOB price of canned grapefruit
sections in nonth m and year s (dollars
per case of 24 number 303 cans).
PFFCs = deflated FOB price of frozen concentrated
grapefruit juice in month m and year s
(dollars per case of twelve 6ounce cans).
GR = quantity of grapefruit for processing in
msmonth m and year s (million 1 3/5bushel
boxes).
s = harvest season (196465 season = 1).
Utilization or Pack
After processors have purchased the fruit, a decision
must be made with regard to allocating the fruit among alter
native products. Products produced will be either sold to
buyers immediately or stored for later sale. Thus, the
quantity packed was expected to be a function of both the
current FOB price of the product (in the event that the
product is sold during the current time period) and the
expected FOB price of the product (in the event that it is
stored for later sale). The expected price is the current
expectation of the price that the processor feels he will
receive if he sells his current output at a later date.
Since the fruit can be used in the production of more than
one product, FOB prices of alternative products were con
sidered. Further, the quantity of product currently in
storage must be considered. It w7as expected that producers
desire to reduce the pack of a particular product when inven
tories exceed certain levels. It was anticipated that the
increased popularity of frozen food products during the
years included in the study had resulted in an increase in
the production of frozen concentrated grapefruit juice. It
was also expected that the production patterns of the other
two processed products had been altered over time. To
measure these effects, time, as measured by numbering the
marketing seasons, was included as an independent variable
in the relationships.
As discussed in Chapter I, some varieties of grapefruit
are better suited for use in certain processed products,
while other varieties are best suited to other products.
Since different varieties mature during different months of
the season, the pack of a product depends somewhat upon the
month of the year. Finally, in making production decisions,
the best public information available as to crop size is the
United States Department of Agriculture (USDA) crop esti
mate. The pack relationships for canned sections and frozen
concentrated juice are shown below. The equation for canned
singlestrength juice is discussed subsequently in this
section.
(23) PCG = f(PFCS ,PFCSL ,PFCG ,PFCG" ,PFFC S,
ms ms ms ms ms m
PFFC ~,BCG ,s,S'm2m2,GE ,)
(24) PFC, = f(PFCSm ,PFCS" ,PFCG PFCGX PFFCms
PFC,BFC ,s,m,m2,GE)
ms ms ms
where PCGm = quantity of canned grapefruit sections
produced during month m in year s
(million gallons singlestrength).
PFCs = quantity of frozen concentrated grapefruit
juice produced during month m in year s
(million gallons singlestrength).
PFCSms = the expectation, during month m in year s,
of the FOB price that will be received for
canned singlestrength grapefruit juice
sold at a later date (dollars per case of
twelve 46ounce cans).
PFCGms = the expectation, during month m in year s,
of the FOB price that will be received for
canned grapefruit sections sold at a later
date (dollars per case of 24 number 303 cans).
PFFCms = the expectation, during month m in year s,
of the FOB price that will be received for
frozen concentrated grapefruit juice sold
at a later date (dollars per case of twelve
6ounce cans).
BCGms = inventory of canned grapefruit sections at
beginning of month m in year s (million
gallons singlestrength).
BFCms = inventory of frozen concentrated grapefruit
juice at beginning of month m in year s
(million gallons singlestrength).
GEms = official USDA estimate, during month mn in
year s, of the size of the grapefruit crop
for year s (million 1 3/5bushel boxes).
The other variables have been defined previously.
Since producers are assumed to be profit maximizers,
it w\as expected that they react to increased current and
expected prices by attempting to increase output, thus it
was expected that aPCG s/aPFCGm and aPCGs/aPFCG woul
be > 0. Since the three processed products are viewed by
the industry as alternatives, it was anticipated that an
increase in either the current or expected FOB price of one
of the alternative products results in a shift of productive
resources to the product withi the higher price. There fore ,
it w~as expected, a priori, that aPCG n/aPFCSs ,, 8PG/BFS
aPCGSaPFFms ms ms~m ms
BPCms/PF~msan BP~m/aPFFCs < 0. The reasoning behind
aPCGms/aBCGms < 0 was explained above. Because of the pat
tern of production whereby the quantity produced increases
one or more months and then decreases, it w\as expected that
aPCGms/am > 0 and aPCGms/am2 < 0. Finally, it was expected
that the annual size of the crop and the production of each
of the products would be directly related. The foregoing
discussion involved primarily relationship (23), but the
relationships in (24) were expected to be similar to those
in (23).
Over the past several years, the quantity of canned
sections produced annually has decreased, while the produc
tion of frozen concentrated juice has increased. This gav~e
rise to the expectation of aPCGms/3s < 0 and aPFCms/as > 0.
Expected prices appear in the above relationshiips.
However, it is difficult, if not impossible, to obtain data
relating to price expectations. The expected FOB price of
a product is the expectation, in time period ms, of the
average FOB price for that product expected for the remainder
of the year beyond time period ms and as such is a reflection
of the expected future supply and demand conditions for that
product. Future supply expectations are based on the current
crop estimate for that year. Demand expectations are based
on the current FOB price of the product. Since FOB prices
do not vary widely over the course of a crop year, the cur
rent price should reflect fairly accurately the expected FOB
price. The price expectation relationships are given below.
(25) PFCSS = g (PFCS s,GE )
(26) PFCGS = g (PFCG sG,GE
(27) PFFCs = g (PFFC G, E ))
These variables were defined previously.
Since GE, was included in relationship (25) to reflect
future supply expectations, it was expected that aPFCSms/aGEms
< 0 because a larger supply in the future would generally
lead to lower future prices. PFCSs was included to reflect
demand expectations so aPFCSk /aPFCS > 0. Similar rela
ms ms
tionships were expected for (26) and (27).
W~hen the expected price relationships w~ere substituted
into that for the pack of canned sections, the following
equation was obtained.
(28) PCGm~s = f [PF:CSms' 11gPFCSms, GEms) ,PFCGms'
82(PFCGms,GEms),PFFCms'83(PFFCms,GEm
BCGms,s,m,m2,GEms]
or
(29) PCG = h(PFCS ,PFCG ,PFFC ,GE ,BCG ,s,m,m )
ms ms ms ms' ms ms
From (28) it can be seen that PFCG has an effect
ms
both directly and indirectly through PFCGms. To determine
a priori what effect the combination will have on the quan
tity backed, it w~as necessary to examine the effects sepa
rately and then put them together. The effect through the
expected price was
aPCG BPFCGk aPCG
ms ms ms
>0Oor >0
aPFCG* aPFCG aPFCG
ms ms ms
as both partial derivatives are positive. Wvhen the direct
effect, which has a positive partial derivative, is added
to the above, the total effect is > 0. The other variables
were analyzed in a similar manner to determine if the rela
tionship (i.e., whether direct or inverse) had changed with
the introduction of the expected price. It was found that,
with the exception of the crop estimate, all sign expecta
tions were unchanged from those discussed earlier.
In the case of GEms the combined effect of the esti
mate directly and through each of the three expected prices
could not be determined a priori. Again, this relationship
can be derived from (28) above. The total effect, composed
of the sum of four parts, is
aPCG aPFCS* aPCG, aPFCGS
aPFCS* aGE aPFCG* aGE
ms ms ms ms
aPCG aPFFC~ aPCG
ms ms ms >
+ +  
aPFFCf
ms mGEs ams
The first effect is negative, while the other three are
positive. Thus the total effect depends upon the relative
magnitudes of the partial derivatives. The relationships
for the pack of frozen concentrated juice were analyzed in
an analogous manner and yielded essentially similar results.
Since the total quantity of grapefruit purchased for
processing is predetermined, it is possible to determine the
pack of canned singlestrength juice if the pack of the
other two processed products is known. Since the fruit
cannot be stored very long after it is picked, it is reason
able to assume that the sum of the quantities of the three
products that are produced is equal to the quantity of fruit
purchased for processing. Because GRs is given in boxes
and quantities packed are given in gallons singlestrength,
it was necessary to convert pack to boxes. This was done
by dividing the pack of each product by the average yield
of grapefruit used for that product times the number of
gallons per case (3.375 for singlestrength juice and canned
sections and 4.0 for frozen concentrated juice). Hence
PCSs PCGs PFCs
(210) GR + +
msYCS3.375 YCG3.375 YFC4.0
or
PCS PCG PFC
ms ms ms
(21)Gms 4.54410 4.01547 4.02932
where PCS = quantity of canned singlestrength grapefruit
ms juice produced during month m in year s
(million gallons).
YCS = average yield of canned singlestrength
grapefruit juice (cases of number 2 cans
per box of fruit).
YCG = average yield of canned grapefruit sections
(cases of number 2 cans per box of fruit).
YFC = average yield of frozen concentrated grape
fruit juice (gallons per box of fruit).
The other variables wJere defined previously.
While the yields vary slightly from year to year, the
variation is small enough so that the yields were treated as
constant. The average yields and standard deviations,
respectively, were 1.3464 and 0.0394 for singlestrength
juice, 1.2164 and 0.1436 for canned sections and 1.0198 and
0.0790 for frozen concentrated juice.
The pack of canned juice was chosen to be represented
by the identity because of the error introduced by the use of
average yields. Since the pack of the product is a residual
in the identity, the resulting percentage error is smaller
for that product since it accounts for a relatively larger
share of the processed fruit.
stores
Storage here refers to the inventory in processor ware
houses at the end of a time period. Grapefruit products
packed but not sold are placed in storage. The quantity in
storage at the end of a time period was hypothesized to be
a function of the FOB price of the product, the expected FOB
price of the product and storage costs. Als in the case of
processing costs in the pack equations, storage costs and
time w~ere highly correlated. The correlation coefficient
between storage costs and time was 0.89, so the year was
used in place of storage costs. Finally, quantities of a
product packed( should influence inventory levels since any
excess pack over current sales would move into storage. The
storage relationships are given below.
(212) SCS = f(PFCSm ,PFCS* ,PCS ,s)
(213) SCGn = f(PFCG ,PFCG ,PCG ,s)
ms ms ms ms
(214) SFC, = f(PFFC ,sPFFC ,PFC m, s)
where SCSms = quantity of canned singlestrength grapefruit
juice in storage at end of month m in year s
(million gallons).
SCGmns = quantity of canned grapefruit sections in
storage at end of month m in year s (million
gallons singlestrength).
SFCs = quantity of frozen concentrated grapefruit
juice in storage at end of month m in year s
(million gallons singlestrength).
The other variables were defined previously.
Current and expected prices of a product were expected
to have opposite effects on the quantity of that product.
An increase in the current price should cause more of the
product to be sold in the current time period, whereas a
rise in the expected price should cause more of the product
to be stored for sale at a later date at the expected
higher price. Thus aSCSms/aPFCSs < 0, while aSCSms/aPFCSm
and aSCSms/as > 0. Relationships for (213) and (214) were
expected to be similar to those described for (212).
Relationships for the expected prices were substituted
into the equation of the storage of canned singlestrength
juice to obtain
(215) SCSms = f[PFCSms'81(PFCSms ,GEms) ,PCSms,s]
(216) SCSmIs = f(PFCSmsGEms ,PCSms,s)
Again the expected effect of the FOB price was both
direct and indirect.
aSCS aPFCS aSCS
ms ms ms>
i< 0
aPFCSm aPFCSm aPFCSm
since the product was positive and aSCSms/aPFCSms < 0. The
relative magnitudes of the partial derivatives determine
the sign. aSCSms/aGEms was expected to be < 0. The other
sign expectations were unchanged. Similar reasoning was
applied to (213) and (214), with similar results.
FOB Demand
FOB demand is directly related to retail demand.
While the FOB level was hypothesized to be the critical
pricing point throughout the industry, demand for a product
at the FOB level is derived from the demand at the retail
level. Therefore,
(217) QFCSmsI = f(PFCSms, retail demand for canned
singlestrength grapefruit juice)
(218) QFCGms = f(PFCGms, retail demand for canned
grapefruit sections)
(219) QFFCm = f(PFFCms retail demand for frozen
concentrated grapefruit juice)
The formlulationn for the FOB demand for fresh grapefruit
was somewhat different. Since the quantity of fresh
grapefruit going to packers was hypothesized to be predeter
mined, the quantity at the FOB level was also predetermined.
Consequently, the relationship was formulated with the FOB
price of the product as a function of the FOB quantity and
the retail demand.
(220) PFFGms = f(QFFGms,realdmnfofes
Grapefruit)
where QFCSms = quantity of canned singlestrength grapefruit
juice demanded by buyers at the FOB level
during month m of year s (million gallons).
QFCGms = qu~antity of canned grapefruit sections
demanded by buyers at the FOB level during
month m in year s (million gallons single
,fstrength).
QFFCms = quantity oE frozen concentrated grapefruit
juice demanded by buyers at: the FOB level
during month m in year s (million gallons
singlestrength).
QFFGms = quantity of fresh grapefruit available at
the FOB level during month m in year s
(million gallons singlestrength).
Retail demand for each of the processed, products wdas
reflected by the retail quantity of the product, per capital
disposable personal income and the retail prices of each of
the products thought to be substitutes for the product.
Also, to reflect seasonality in the demand for the product,
the month and the month squared were included. For fresh
grapefruit, retail. quantities, rather than retail prices,
w~ere included. In the absence of retail quantity data, the
preceding month's FOB sales for processed products, were
included as an approximate estimate of retail sales. A
comparison of the turning points for FOB movement with those
for household purchases, as reported by the Mlarket Research
Corporation of Amnerica [11], revealed approximately a one
month lag between FOB and retail sales. Income and retail
price of substitutes wjere included as demand shifters.
Texas grapefruit has been shown to be a substitute for
Florida grapefruit [25]. The quantity of Texas grapefruit
shipped was used, rather than the retail price, because
there were no data available on retail prices of Texas grape
fruit. Since retail prices w~ere not available for the var
ious grapefruit products the corresponding FOB prices were
used in place of the retail prices of the substitute products.
Dummy variables were added to the equations after a
graphical analysis of prices and quantities revealed that
there may have been a shift in demand for three of the prod
ucts. If a shift had actually occurred, and this shift w~as
not accounted for, erroneous results could be generated.
For example, a shift may have occurred during the time period
under consideration which would require two demand curves,
one reflecting the demand before the shift and the other
reflecting the demand after the shift. To ignore this
shift would lead to a demand equation which did not reflect
reality.
The FOB demand equations are given below.
(221) QFCSms = f(PFCSms,QFCSm1,s,I~msPO~ms'
PFFC ms~mm2
(222) QFCGm = f(PFCGmsQCGmsINms,PFFGms
TGms,m,m2,D1)
[223) QFFCm = f(PFFCms,QFFCm1~'I,sImsPFCSms'
POJ S,m,m ,D2)
(224) PFFG = f(QFFG ,IN :QFCG ,TG ,m,m ,D3)
ms ms' ms ms ms
w~h ere INm = deflated per capital disposable personal
income in month m and year s (thousands
of dollars).
POJs = deflated retail price of frozen concentrated
orange juice during month m in year s
(dollars per case of 6ounce cans).
TGms = shipments of Texas grapefruit during month m
of year s (million cartons).
s1 0 ( ~~;8,""" '""if otherwise
D ={1 if 196566 or 196667
s 0 if otherwise
D ={1 if 196768
s 0 if otherwise
The other variables w~ere defined previously.
For each of the products the income effect was expected
to be positive. The ownprice slopes were expected to be
negative for the processed products, as was the ownquantity
slope for fresh grapefruit. Since the lagged quantities
were introduced as proxy variables for retail sales, they
wcere expected to have positive slopes. There were no
complementary relationships hypothesized, so each cross
product w~as viewed as a substitute product. As such, the
crossprice slopes were expected to be positive. In equa
tion (224), the crossquantity slopes were expected to be
negative. The expectations for the slopes of the dummy
variables were aQFCGms/3D1s and aPFFGms/aD3s > 0 and
aQFFCms/3D2s < 0.
Supply to Buyers at FOB Level
If the quantity of a product produced and the storage
of that product are known, then the quantity supplied by
processors for sale at the FOB level can be derived by
tying together the three quantities via an identity. Thus,
for each product there would be three equations with three
unknowns, from which a solution can be obtained. The supply
for each product is shown below~ to be equal to the inventory
at the beginning of time period ms plus the pack of the
product during time period ms minus the quantity in storage
at the end of time period ms.
(225) SUCSm = BCSs + PCSm SCSs
(226) SUCGm = BCGs + PCGm SCGm
(227) SUF'C = BFCs + PFC SFC
where SUCS = quantity of canned singlestrength grapefruit
msjuice supplied to buyers at the FOB level
during month m in year s (million gallons)
SUCGm = quantity of canned grapefruit sections
supplied to buyers at the FOB level during
month m in year s (million gallons single
strength).
SUFCms = quantity of frozen concentrated grapefruit
juice supplied to buyers at the FOB level
during month m in year s (million gallons
singlestrength).
BCSms = inventory of canned singlestrength grape
fruit julce at beginning of month m in
year s (million gallons).
The other variables were defined previously.
Identities
To assume that, at the FOB level, supply equals demand,
identities are nooded in order to equate the two.
(228) QFCSms = SUCSms
(229) QFCGs = SUCGm
(230) QFFCs = SUFCm
Model II
During the months included in Mlodel II, there is no
grapefruit available for supply to packers or processors.
Since fresh grapefruit cannot be stored, there can be no
production of any of the products being considered in this
study. Therefore, grower supply, processor demand, pack
and fresh relationships that are part of Mlodel I are no
longer appropriate. Model II includes only the behavioral
equations for storage and FOB demand plus the necessary
identities.
Storage
The storage equations in Mlodel I were formulated with
the quantity of a product stored as a function of the FOB
price of the product, the expected FOB price of the prod
uct, the quantity of the product packed and the storage
cost. The quantity stored for Mlodel II was hypothesized to
be a function of the FOB price of the product, the expected
FOB price of the product, storage cost and the month. As
in Model I, the year was used in place of storage cost.
Processors must insure that they are able to supply products
at all times of the year, despite the fact that there is no
production with which to replenish inventories. Therefore,
the month becomes very important. The storage relation
ships are shown below.
(231) SCSm = f(PFCSmsPFCSms,s,m)
ms ms ms
(233) SFC = f(PFFCn ,PFFCh ,s ,m)
The variables are as defined previously.
The anticipated signs were similar to those for the
storage equations for M~odel I. The fact that some of each
product is sold each month implied that aSCSms/am,
aSCGms/am and BSF~Cms/3m < 0.
As in Mlodel I, the expected price relationships were
substituted into the storage equations. However, for Mlodel
II, the USDA crop estimate in the expected price equations
was replaced by the actual size of the grapefruit crop, for
the harvest period had ended. After the substitution,
storage for canned singlestrength juice became
(234) SCSms = f(PFCSms,s,Qs,m)
where Q5 = size of the Florida grapefruit crop in year s
s(million 1 3/5bushel boxes).
It was not possible to determine the sign of
aSCms /aPFCSm a priori for the sam~e reasons given in Model I.
The other three coefficients were expected to be negative.
FOB Demand
The reasoning for the FOB demand relationships during
the months when there is no production was similar to that
in Model I. There were only the three processed products ,
because of the nonavailability of fresh grapefruit during
this period. The FOB demand equations are given belowv.
(235) QFCSms = f(PFCSmsPFFmFCsQFSm1s'~m,s msPOm
(236) QFCGms = f(PFCGmsQFCGm1,sINms)
(237) QFFCms = f(PFFCmsQFFCm1,sINmsPFCSmsPOJms)
The variables have been defined Dreviously. The expected
signs of the coefficients were similar to those for the
respective equations in Mlodel I.
36
Supply to Buyers at FOB Level
The FOB supply identities were similar to those in
Model I. However, there was no new pack in the months of
Model II.
(238) SUCSs BCSm SCSm
(239) SUCG =BCG SCS
msms ms
(240) SUFCm = BFC SFC
msms ms
Identities
The following three identities show~ that FOB supply
equals FOB demand.
(241) QFCSs = SUCSm
(242) QFCG =SUCG
ms ms
(243) QFFC, = SUFCm
CHAPTER III
STATISTICAL CONSIDERATIONS
Statistical Model
The statistical models that w~ere estimated are given
below~. The variables were defined in Chapter II. Endo
genous variables are those variables whose values are deter
mined jointly within the system. These variables are pre
ceded by "6" coefficients. Exogenous variables, those whose
values are determined outside of the system, are preceded by
"y" coefficients.
M\o del I
FOB Price Equations:
(31) 611PGKm 12BPFFGm 10 yl 11GKms 1 ~ms
(32) 821PGRms C 22PFCSms + 23PFCGms 2 B4PFFCms
+ 20 + 21s + Y22GRms = 2ms
Pack:
PCSs PCG PFC
(3)Gms 4.5 4;1 4.01547 4.0m932=0
(34) 831PCSms + 632PFCSms 33aPFCGm 34BPFFCm
f 30 + 31GEms + 32BCSms Y33s + Y34m
SY35m2 =3ms
(35) 641PCGms + 42PFCSms + 43PFCGms + 44PFFCms
+ 40 + 41GEms + 42BCGms Y43s + Y44m
SY45m2 = 4ms
Storage:
(36) B51SCSms + 52PFCSms + 53PCSms + 50
51YSGEms + 52s = v5ms
(37) B61SCGms 6 B2PFCGms + 63PCGms + 60
+ 61GEms + 62s = v6ms
(38) B71SFCms + 72PFFCms 7 B3PFCms 70Y?
+ 71GEms 7 Y2s = v7ms
FOB Demand:
(39) 881QFCSs + 682PFCSm 835PFFCm 80YQ
SY81QFCSm1,s 8 Y2INms f 83POJms Y84m
SY85m 2 8ms
(310) B91QFCGms 9 a2PFCGms + 93PFFGms 9g0
SY91QFCGm1,s 9 Y2INms Y93TGms 94Ygm
79Y5m2 9 Y6D1s = 9ms
39
(11 101QFFms 102PFFms 103PFCms 100
C 101QFFCm1,s + 102INms + 103POJms C 104m
10m2 106D~ 10ms
(2 111PFFms 112QFCms 110 Y111QFFms
112IITGms r 113I~ms t 114m + Yll5m2
+ 116D3s 11ms
Identities :
(313) SUCSS BCS, PCSs + SCSS = 0
(314) SUCG BCG PCG + SCG = 0
ms ms ms ms
(315) SUFC BFC PFC + SFC =0
ms mns ms ms
(316) QFCSs SUCSm = 0
(317) qFCG SUCG = 0
ms ms
(318) QFFCms SUFCms = 0
Model II
Storage:
(319) 8121SCSms + 122PFCSms + 120 +121 s
+ 122s + Yl23m = 1l2ns
(320) B 3 SCG m 132 PFCGms 130j 131 Q s
13s+y33m = 3ms
40
(321) B141SFms 6142PFm 14 11s
+ 142s + Yl43m = pl4ms
FOB Demand:
(322) B151QFCSms + 152PFCSms + 153PFFCms + 150
f 151QFCSmls 1 s 152INms Y153POJms 1 ~5ms
(323) Bl61QFCGms + 162PFCGms + 160 161QFCGm1,s
+ 162INms = 16ms
(324) B171QFFCms + 172PFFCms + 173PFCSms + 170
+ 171QFFCm 1,s + 172INms + 173POJms = 17ms
Identities:
(325) SUCS BCSS + SCS =0
(326) SUCGm BCG + SCG = 0
(327) SUFCS BFCs + SFCS = 0
(328) QFCS, SUCS = 0
(329) QFCG SUCG = 0
(330) QFFCS SUFCm = 0
General Mlodel
The two models can each be stated in matrix notation as
BY + TX = p
where B is the JxJ matrix of coefficients of the J endo
genous variables,
Y is the Jx1 vector of endogenous variables,
r is the JxK; matrix of coefficients of the K
exogenous variables,
X is the Kx1 vector of exogenous variables, and
v is the Jx1 Vector of disturbance terms.
For Model I, J = 18 and K; = 19. For Mlodel II, J = 12 and
K= 11.
The following assumptions were made regarding the model.
(1) The matrix 6 is assumed to be nonsingular,
so that the system can be solved for the
endogenous variables.
(2) Plm 1 X'X = Ex where Ex is the non
singular contemporaneous covariance matrix.
(3) The p's are random variables w~ith E(vjms) = 0
(for j=1,..., JL; s=1,..., S; for each value
of s ,m=1,..., MI). L is defined as the number
of identities, S is the number of years and
M is the number of months per year. The L
identities are excluded because the coeffi
cients are known.
(4) ~pjs9 n) =0 ,if and only if i=j m=n
and s=t tfor 1,j=1.. ;st1..
and m,n=1,..., M for each s).
(5) E(lsjms9 int) = 0 wjhen ifj or mfn or sft
(for i,3=1,..., JL, s,t=1,..., S and
m,n=1,..., Mi for each s).
Identification
The problem of identification must be considered prior
to estimation of the structural coefficients of the model.
If the parameter values in a relationship can be uniquely
estimated, the relationship is said to be identified.
Consider one equation from a system of equations. The
necessary or order condition for identifiability is that the
number of exogenous variables excluded from the equation
must be at least as great as the number of endogenous vari
ables included minus one. This can be calculated as
H h g 
where H = the number of exogenous variables in the system,
h = the number of exogenous variables in the equation,
and g = the number of endogenous variables in the equation.
If Hh = g1, the equation is said to be justidentified.
If Hh > g1, the equation is overidentified. In the event
that Hh < g1, the equation is not identified and the
parameters cannot be uniquely estimated. The necessary con
ditions for identification indicate that each of the equa
tions in M~odel I and Mlodel II is overidentified.
Trhe necessary and sufficient condition for identifica
tion is known as the rank condition. For an equation to be
identified, it must be possible to form at least one nonzero
determinant of rank J1 from the coefficients of the
variables excluded from the equation of interest, but which
occur elsewhere in the system. J is the number of endo
genous variables in the system.1
Estimation Procedure
Estimation of the coefficients of overidentified equa
tions by ordinary least squares yields biased and inconsis
tent estimates. Estimates obtained by twostage least
squares (2SLS) are biased but consistent. Threestage
least squares (3SLS) is superior to 2SLS in its asymptotic
efficiency because 3SLS incorporates restrictions associated
with the specification of the structural equations in the
system. Since the whole system of equations is estimated
simultaneously, 3SLS estimates are more subject to specifi
cation errors. The list of all variables in the equation
of interest plus the list of all exogenous variables in the
system is needed for 2SLS. However, 3SLS requires the
specification of all zero elements of the parameter matrix
[T'B'], not just the row of that matrix corresponding to the
par ti cular equation. Thus, if an element is hypothesized to
be zero when it is actually nonzero, this affects the 2SLS
estimates of that particular equation only. In the case of
3SLS, estimates in all equations are affected [21, pp.528529].
For a more detailed discussion of identification in the
case of simultaneous equations, see Johnston [8, pp. 240
252].
However, the overriding consideration in the choice of
estimation Drocedure was the unavailability of a 3SLS com
puter program capable of handling a model as large as that
specified in Chapter II. Therefore, 2SLS was used to esti
mate the parameters in the two models.
Selection of Time Unit and Period
The time unit selected for this study was a month. At
the FOB level, processors generally announce price increases
two weeks in advance of the actual change. This gives
buyers time to make their adjustments within the month.
Also, the nature of the production pattern for grapefruit
ruled out time units of less than a month. The quantity of
grapefruit available in a particular month can be predicted
more reliably than can the quantity available in a particu
lar week. In other words, the production pattern over time
is more constant from month to month than from weiek to week.
An additional consideration was the availability of
data. Several data series are published on a monthly basis.
While it w~as possible to sum the weekly data series to obtain
monthly observations it w~as not possible to convert the
monthly observations to a weekly basis.
Data
Most of the data used in this study hiad to be trans
formed in some way before it could be used. The monthly
data, after transformations, are given in Tables 9 to 14.
All prices, w~ith the exception of the retail price of frozen
concentrated orange juice, were deflated by the wholesale
price index (195759 = 100). Ontree prices and shipment
data for grapefruit for fresh use are reported on a monthly
basis by the Growers Administrative Committee and Shippers
Advisory Committee [7]. Retail prices of frozen concen
trated orange juice are reported monthly by Florida Citrus
Mutual [6]. All other prices are reported weekly. Prices
for seedy, white seedless and pink seedless grapefruit
going to processors are reported by the United States Depart
ment of Agriculture (19], while the corresponding shipment
data are reported by the Grow~ers Administrative Committee
and Shippers Advisory Committee [7]. To obtain a single
price, the price of each of the three types of grapefruit
was multiplied by its respective shipment quantity and the
re sults were summe d. This sum was then divided by the sum
of the shipments for that month to yield a weighted average
price.
FOB prices of processed products are published weekly
by various processors in the form of price cards [1,2,12].
The prices for the different size containers and the various
product forms, such as sugar added or sugarless, are reported.
For this study, the largestselling container size and form
w~as chosen as the representative one. Since the prices are
reported, on a weekly basis, it w~as necessary to weight the
weekly prices by the respective FOB sales to obtain a single
price for each month. FOB prices for fresh grapefruit are
published as prices for Interior fruit and for Indian River
fruit on a weekly basis by the Growers Administrative Com
mittee and Shippers Advisory Committee [7]. To obtain a sin
gle price for each month, the product of the weekly prices
times their quantities were summed and then divided by the
total quantity for the month. After the monthly FOB prices
and ontree prices were derived, they were deflated by the
monthly wholesale price index to convert them to constant
dollars. The retail price of frozen concentrated orange
juice was deflated by the consumer rice index (195759
= 100).
The measure used for income was disposable personal
income per capital, which is not reported directly. The
series wJas obtained by subtracting reported personal taxes
and nontax payments from personal income each month and
then dividing this by the population of the United States.
Both population and personal income are reported monthly by
the United States Department of Commerce [21], while per
sonal income per capital was deflated by the consumer price
index to adjust for the effect of inflation on income.
Data on pack, FOB movement and inventories for pro
cessed products are published in weekly series by the Florida
Canners Association [3,5]. Beginning inventories and quanti
ties in storage can be taken directly from the series. Pack
and movement figures must be summed over the weeks in the
month. The quantities of canned singlestrength grapefruit
juice and canned grapefruit sections, as reported, were in
cases of 24 number 2 cans. Frozen concentrated grapefruit
juice quantities are reported in gallons of 400 brix con
centrate. To make all of the quantities comparable, they
wvere converted to gallons of singlestrength equivalent by
multiplying singlestrength juice and canned sections quan
tities by 3.375 and frozen concentrate juice quantities by
4.0. The conversion factor 3.375 converts cases of 24
number 2 cans to gallons of singlestrength juice. The
factor 4.0 converts concentrated juice to singlestrength
juice.
The quantities of fresh grapefruit at the FOB and grove
levels are published as a monthly series by Florida Citrus
MIutual [6] as boxes shipped. To convert boxes of fresh
grapefruit to cases of 24 number 2 cans of singlestrength
juice, it was necessary to multiply the number of boxes
times the yield of canned singlestrength grapefruit juice.
The yield for each month is available in published form from
the Florida Canners Association [4]. To convert the cases
of 24 number 2 cans to gallons it was necessary to multiply
by a factor of 3.375.
The quantity of grapefruit going to processors is the
sum of thle grapefruit, in boxes used in each of the pro
cossed products. The quantity going to each product is
published by Florida Canners Association [4] on a weekly
basis in terms of cases of 24 number 2 cans. To get a
monthly series, the weekly quantities were summed over the
period of each month. The number of boxes were then ob
tained by dividing the number of cases packed by the respec
tive yield for each product.
The shipments of Texas grapefruit are reported monthly
by the Growers Administrative Committee and Shippers Advi
sory Committee [7].
Finally, the monthly United States Departmnent of A~gri
culture's estimate of the size of the crop is published in
the weekly report of the Florida Canners Association (3,5].
CHAlPTER IV
STATISTICAL RESULTS
The results of the estimation of the coefficients are
presented in this chapter. The standard errors are given
in parenthesis below the respective coefficients. Consider
ation of the statistical significance of more than one
coefficient in a particular equation requires a joint
hypothesis. In the absence of a joint hypothesis, the test
ing of more than one coefficient results in a change in the
probability of a Type I error. Therefore, no statistical
tests were made.
Model II
OnTree Price Equations
(41) PGK = 1.639 + 0.906 PFFG 0.173 GKs
ms ~(0.046) m (0.127) m
(42) PGR =1.797 + 0.665 PFCS 0.039 PFCG
ms (0.067) ms (0.109) ms
+ 0.117 PFFCS + 0.067 GR 0.039 s
(0.088) ms(0.028) ms (0.018)
The equations for the prices of grapefruit for packing
and for processing were normalized on the ontree price of
grapefruit. The signs of the coefficients were in keeping
with a priori expectations.
The coefficient of the FOB price of fresh grapefruit
(PFFG) indicates that the ontree price and the FOB price
tend to move together. The importance of the FOB price in
the relationship is shownm by the fact that its estimated
coefficient w~as more than 19 times as large as its standard
error. The coefficient of the FOB price w\as 0.906. The
margin between prices can be examined using the estimated
equation above. K~ere the coefficient to be 1.0, margins
would be unaffected by price levels, for a rise in the FOB
price would correspond to an equal rise in the price that
the growers receive. The coefficient of 0.906 implies that,
as the price level increases, the absolute margin between
the ontree price and the FOB price increases slightly.
Miore than half of the grapefruit that is processed goes
into the packing of canned singlestrength grapefruit juice.
Thus, it was expected that the ontree price that the pro
cessors are willing to pay for grapefruit would be affected
more by the canned singlestrength juice FOB price than by
the FOB prices of the other two processed productscanned
sections and frozen concentrated juice. This w~as indeed the
case. The coefficient of the F~OB price of singlestrength
juico (PFCS) was over 17 times as large as that for the
price of canned sections (PFCG), and almost six times as
large as that for frozen concentrated juice (PFFC). The
signs of the FOB price coefficients were as expected, with
the exception of the FOB price of canned sections.
The year (s) was included as a proxy variable for pro
cessing costs, which were assumed to increase steadily from
year to year. However, since the coefficient of the year
was opposite of expectations, it may also represent other
variables that have not been included but that also change
steadily over time. One such variable might be changes in
technology that reduce the cost of producing frozen concen
trated grapefruit juice. Since the ontree price is
derived from the FOB prices of the three products, a cost
reducing change in technology would affect the price of the
input, that input being grapefruit.
Pack Equations
(43) PCG
ms
(44) PFC
ms
= 0.166 0.411 PFCS + 0.755 PFCG
(0.265) ms(0.452) m
0.133 PFC + 0.184 BCG 0.199 s
(0.346) ms (0.182) ms (0.087)
+ 0.121 m 0.133 m2 + 0.079 GE
(0.929) (0.079) (0.033) m"s
=16.100 + 0.807 PFCS 1.931 PFCG
(1.030) ms (2.235) ms
+ 1.447 PFFC 0.304 BFCm + 0.575 s
(1.389) m"s (0.246) ms 0.366)
5.821 m + 0.886 m2 0.148 GEm
(2.892) (0.307) (0.139) m
While the signs of the coefficients of the prices in
equation (43) were as expected, equation (44) was less
satisfactory in this respect. FOB prices entered the equa
tions to measure tw\o effects. One was the effect that the
current FOB prices have on the pack of the products. The
other was the effect on pack of the FOB prices that the
processor expects to obtain for the products at a later
date. It was shown earlier that the ownprice slope should
be positive whilee the crossprice slopes should be negative.
In equation (44), the coefficient of the price of canned
singlestrength juice (PFCS) had a sign opposite from
expectations. However, its coefficient wias relatively
small compared to its standard error.
Since canned sections is a product of declining impor
tance and frozen concentrated juice an emerging one, the
negative and positive, respectively, annual trends were in
keeping with a priori expectations.
The net influence of the USDA crop estimate was com
posed of a negative component from the expected price rela
tionship and a positive direct component. Since the coeffi
cient of GEm in equation (43) was positive it was con
cluded that the expected FOB price of the product had a
less important impact on the production decisionmaker than
did the current USDA crop estimate. However, the sign of
the coefficient in equation (44) wjas negative, implying
the opposite relationship of that above.
Storage Equations
(45) SCS =1.458 + 0.280 PFCS + 1.749 PCS
ms ~(2.044) ms(0.325) m
+ 0.117 s 0.101 GE
(0.690) (0.240) m
(46) SCG = 17.280 1.538 PFCG 0.397 PCGs
ms (0.752) ms (0.186) m
+ 0.161 s 0.083 GE
(0.161) (0.058) ms
(47) SFC =14.600 0.430 PFFC + 1.008 PFC
ms (11.272) ms(0.141) m
+ 1.014 s 0.369 GE
(0.332) (0.130) m
In equations (45) and (47), the coefficients for
pack (PCS and PFC) are greater than one. It may appear
unrealistic for inventory to increase by more than the
quantity packed. It becomes much more reasonable w\hen the
meaning of the variables is made clear. A change in inven
tory, of course, refers to a change in the total quantity
of the product in storage. However, a change in the pack
refers to a change in the rate of pack, and not the change
in the cumulative quantity packed in the year. Consider
the case of canned singlestrength juice for December, 1964,
to January, 1965. The pack in December was 1,450,937 cases
of number 2 cans while the pack in January was 1,756,995.
The inventory at the end of each month was 1,618,112 and
2,643,230 cases, respectively. From December to January,
the inventory increased by 1,025,118 cases, the rate of pack
increased by 306,058 cases, and the cumulative pack in
creased by 1,756,995 cases. Thus, an increase of 306,058
cases in the rate of pack corresponded to an increase of
1,025 ,118 cases in inventory. Thus, it is not unreasonable
for the inventory to increase by more than the rate of
change in pack.
As in the pack equations above, FOB prices of the prod
ucts were both a reflection of the FOB prices in the current
time period and the expected FOB prices of the products.
The direct effect was expected a priori to be negative,
while it wans expected that producers would respond to
changes in expected prices by adjusting inventories in the
same direction as the price changes. The fact that the FOB
price of canned singlestrength juice (PFCS) had a positive
coefficient, while the other twJo FOB prices (PFCG and PFFC)
had negative coefficients implies that the expected FOB
price is relatively more important to processors w~hen making
storage decisions concerning singlestrength juice, but
that current prices are more important in decisions con
cerning the other two products.
The year was included as a proxy for storage costs.
One normally expects storage costs and quantity stored to
move in opposite directions. However, the coefficient of
the year w~as positive in each equation. This indicates that
the variable was possibly measuring the effect of one or
more other variables, in addition to storage costs. One
possible effect in the case of canned sections might be a
declining sales trend and a failure to fully coordinate
production with sales, with a resulting buildup of inven
tories. For the other two products, it is possible that
the year variable was also measuring the increase in storage
needed to meet increased demand.
The USDA crop estimate (GE) was found to have a negative
relationship with storage. This was expected. Since the
crop estimate entered the relationship via the expected
price equation with an expected negative coefficient in that
equation, the variable was also measuring the effect of the
expected price on storage. An increase in the crop esti
mate would presumably affect storage decisions through the
expectation of a fall in the whole spectrum of grapefruit
product prices. This would cause a desire on the part of
producers to sell more of the products in the current time
period and put less into storage for sale at a later date
when prices are expected to be low~er.
FOB Demand
(48) QFCS = 10.380 0.549 PFCS + 0.456 PFFC
ms ~(0.509) ms(0.856) m
+ 6.590 IN 0.085 POJ
(4.097) ms (0.161) ms
+ 0.092 QFCS 0.338 m 0.027 m
(0.274) m1,s (1.350) (0.138)
(49) QFCG
ms
(410) QFFC
ms
(411) PFFG
ms
=0.335 0.554 PFCG 0.080 PFFG
(0.358) ms (0.099) ms
+ 0.643 INs + 0.334 D1 0.272 TG
(1.066) ms(0.216) s(0.216) ms
+ 0.607 QFCG + 0.898 m 0.105 m
(0.149) m1,s (0.409) (0.042)
= 6.382 + 0.290 PFCS + 0.076 PFFC
(0.221) ms (0.420) ms
1.531 IN 0.063 POJ 0.284 D25
(1.605) m (0.070) ms (0.321)
+ 0.212 QFFC 1.109 m +0.149 m
(0.240) m1,s (0.526) (0.055)
=8.257 0.042 QFFG 0.368 QFCG
(0.075) ms 0.234) m
+ 0.441 TG 2.346 IN + 0.817 m
(0 .418) ms(181 ms(06)
0.094 m2 + 1.963 D3s
(0.679) (0.394)s
The estimation of the FOB demand equations yielded
very acceptable results. The ownprice slopes for single
strength juico, canned sections and fresh grapefruit (PFFG)
were negative, as theory would lead one to expect. The own
price slope of frozen concentrated juice (PFFC), however,
was positive, indicating that there is possibly an identifi
cation problem whereby supply has not been completely iso
lated from demand. However, the estimated coefficient for
the FOB price of frozen concentrated juice was considerably
smaller than its estimated standard error.
In equations (48) and (410), the signs of the coeffi
cients of two products hypothesized as competing were posi
tive as expected, implying that singlestrength juice and
frozen concentrated juice are indeed substitutes. In both
equations, the coefficient of the price of concentrated
orange juice (POJ) w~as negative. However, the estimated
coefficient in each case was less than its estimated stan
dard error.
It was anticipated that fresh grapefruit and canned
grapefruit sections would be substitutes for one another.
Also, since it has been shown that fresh Texas grapefruit
(TG) and fresh Florida grapefruit substitute for one another
to some extent [25], it was expected that canned sections
and fresh Texas grapefruit would also substitute for one
another. While the signs of the coefficients for fresh
grapefruit in equation (49) and Texas grapefruit in (411)
were the opposite of expectations, Texas grapefruit was
found to substitute for canned sections.
Seasonality in the demand for each of the products
was found to exist. For singlestrength juice and canned
sections, there is a tendency for demand to first increase
and then decrease as the season progresses. The opposite
seasonal effect was found for concentrated juice and fresh
grapefruit with the demand increasing later in the season.
Disposable personal income (IN), as expected, exerts a
positive influence on the demand for the first two products.
The negative coefficient for income in equation (410) was
unexpected. However, the estimated coefficient of the dis
posable personal variable was less than the estimated stan
dard error for that variable.
The coefficient of income in equation (411) was also
negative. It is possible that consumers shift away from
fresh grapefruit in favor of the more convenient processed
grapefruit products as their income increases. Weisenborn,
M~cPherson and Polopolus found that consumption of fresh
oranges decreases with increases in income [26, pp. 1920].
Since the value of the dummy variable (D2) in the con
centrated juice equation was 1 in the early years of the
study, the negative coefficient was as expected for an emerg
ing product. The coefficient indicates that the demand has
shifted upward during the later years of the study. Though
canned sections has declined in importance, the sign of the
coefficient of the dummy variable (DI) indicates that the
demand for that product has also shifted upwdards. The value
of this variable was 0 in the earlier years of the study.
This shift after the 196667 crop year possibly resulted
from the large crop in 196667 and the resulting low prices.
With the low prices, consumers may hiave become attached to
the products and continued buying them in succeeding years.
The demand for fresh grapefruit shifted upw~ards during
the 196768 crop year. This possibly w~as caused by the fact
that the quality of the citrus crop in that year was
especially good, resulting in consumers demanding more of
the product at each price.
Model II
Storage Equations
(412) SCS
ms
(413) SCG S
(414) SFC
ms
= 43.142 6.235 PFCSm + 0.980 s
(3.517) ms(0.925)
S0.390 Q 0.770 m
(.619) s(1.931)
=4.060 0.530 PFCG + 0.142 s
(0.762) ms(0.119)
+ 0.076 Q 0.952 m
(0.041) s (0.194)
=36.765 + 3.474 PFFC 1.262 s
(1.476) ms(0.312)
+ 1.094 Q_ 0.940 m
(0.166) s (0.483)
In theory, the storage equations for M~odel II were
similar to those for Mlodel I. The primary difference w~as
that there was no pack during the months in Mfodel II.
In the first two equations, the negative coefficients
for the prices of the products imply that the current FOB
price is a more important consideration in the decision
making process than is the expected price of the product.
However, since M[odel II covered only the last three months
of each season, it is possible that producers assume that
the current price is the expected price.
As explained earlier, the positive trend for sections
is possibly due to the fact that the processors have not
fully coordinated their storage decisions with the declining
importance of the product. The negative coefficient for the
year in equation (414) was consistent with theory, since
the year was included as a proxy variable for storage costs.
In each equation, the month had a negative coefficient,
as expected. Since there is no pack, all of the sales must
come from inventory, so it is expected to decrease from
month to month. The coefficients of the quantity of grape
fruit in a year were as expected in the latter two equations.
FOB Demand
(415) QFCS
ms
=1.088 1.018 PFCSm + 0.769 PFFCm
(0.841) ms 2.064) m
+ 0.148 QFCS + 2.017 INmS
(0.74) m1,s (7.695) s
0.121 POJ
(0.307) m
(416) QFCGmIs = 2.0988 0.554 PFCGm 0.581 QFCGm,
(0.173) (0.227)
+ 0.879 IN
(0.338) m
(417) QFFCms
= 9.320 0.718 PFFCS + 0.327 PFCSm
(0.996) ms(0.365) m
+ 0.200 QFFC + 4.224 INs
(0.92) m1,s (4.004) m
+ 0.092 POJ
(0.1.54) m
61
The estimated coefficients in the equations for FOB
demand for both singlestrength juice and canned sections
for Model II were very similar to those for Mlodel I, especi
ally with respect to signs. However, the equation for
frozen concentrated juice was closer to expectations than
was the equation in Model I. The ownprice slope for con
centrated grapefruit juice was found to be negative. The
resulting demand elasticities for Model I and M~odel II are
compared in the next chapter.
CHAPTER V
ECONOMIIC IMPLICATIONS
This chapter is divided into three sections. In the
first section, estimates of elasticities and implications
based on these estimates are presented. The second section
deals with an analysis of the derived reduced forms for the
two models. Finally, in the third section, the results of
shortterm forecasting based on the reduced forms are pre
sented.
Elasticities
The estimates of the demand elasticities and cross elas
ticities for grapefruit products at the FOB level for Mlodel I
are presented in Table 2.1 The elasticities for processed
grapefruit products at the FOB level were calculated directly
from the demand equations as estimated. Since the FOB demand
equation for fresh grapefruit was estimated with price as a
function of quantity, it w~as necessary to solve it for the
quantity demanded in terms of prices and income.
1Elasticity estimates should be interpreted with caution
in the case of simultaneous equation models. Elasticities
are based on the assumption of ceteris paribus. However, in
a simultaneous equation model, a change in an endogenous
variable would result in changes in other endogenous variables
wJithin the system to restore the equilibrium. Hence, the
assumption that all other endogenous variables remain con
stant is not fulfilled.
62
Table 2. Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefru~it
in Various Forms, Computed at Mrean V'alues
of the Variables, Mlodel I, 196471
Elasticities or Cross Elasticities
Normaizedwith Resp3ect to:
Variable PFCS PFCG PFFC PFFG POJ IN
QFCS 0.392  0.309 0.268 3.216
qFCG  2.101  0.270  1.219
QFFC 0.654  0.163  0.622 2.357
QFFG  2.874a  12.268a  1.667a
aComputed by solving the estimated demand function
for the quantity in terms of prices and income.
The cross elasticity estimates presented in Table 2
indicate that none of the products are very strong substi
tutes for one another at the FOB level. A positive cross
elasticity is required for substitute goods and a negative
one for complementary goods. Based on the measures given in
Table 2, frozen concentrated grapefruit juice and canned
singlestrength juice are substitutes for each other. This
is really not surprising since they are simply two forms of
the same product.
The cross elasticity measures for canned sections and
fresh grapefruit conflict somewhat. One elasticity measure
indicates that the two products are substitutes, while the
other indicates that they are complementary.
Based on the cross elasticity estimates, concentrated
orange juice is shown to be complementary to both single
strength juice and frozen concentrated juice. However, as
indicated earlier, the estimated coefficients for concen
trated orange juice were less than their respective esti
mated standard errors.
The income elasticities given in Table 2 show~ that in
a period of rising income, the quantity demanded of canned
singlestrength juice and canned sections would increase,
while the quantity demanded of frozen concentrated juice
and fresh granefruit would decrease. An increase in dis
posable personal income per cavita of 1 percent would result
in increases in the FOB demand of singlestrength juice and
canned sections of slightly over 3 percent and 1 percent,
respectively. Also, the FOB demand for frozen concentrated
juice and fresh grapefruit would decrease by more than 2
percent and 1.5 percent, respectively.
The elasticities and cross elasticities of demand for
the three products in MIodel II are given in Table 3. In
each case, the equation was normalized on the quantity
variable for estimation, making the pricequantity slope,
as estimated, appropriate for computing elasticities
directly.
The elasticities for M~odel II are much closer to the
oretical expectations than were those for M~odel I in that
all elasticity measures have the expected signs. In
Table 3. Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefruit
in Various Processed Forms, Computed at
Mean Values of the Variables, Mlodel II,
1964170
Elasticities or Cross Elasticities
Normalized with Respect to:
Variable PFCS PFCG PFFC IN
QFCS 1.254  .825 1.532
QFCG  2.636  2.094
QFFC 1.097 2.096 8.734
contrast to Mlodel I, all of the products have negative
demand elasticities.
The demand for each of the products is shown to be more
elastic during the months of M~odel II. During these months,
the demand for canned sections and frozen concentrated
juice is more responsive to changes in income. The demand
for singlestrength juice responds about half as much as
during the months of Mlodel I.
As in Model I, canned singlestrength juice and frozen
concentrated juice are shown to be substitutes. Both elas
ticity measures are larger than their respective measures
in Model 1, implying that, during the months in M~odel II,
consumers respond more readily to changes in the prices of
the substitutes.
The elasticities of the two models can be compared.
In general, consumers are more responsive to changes in
prices and income during July, August and September th~an
during the other nine months of the year. This possibly
results from the importance that consumers place on the cold
preventing properties inherent in citrus products. During
the summer months, consumers are less interested in prevent
ing colds than they are in the winter months, so they may
choose to substitute carbonated beverages and other fruit
drinks for the grapefruit beverages as thirst quenchers.
Thereforec, during the months of M~odel II, there are more
substitute prIoducts available, which typically has the
effect of making consumers more responsive to price.
Implications fr~om th~e
Derived Reduced Form Estimates
Reduced form equations describe each endogenous variable
in terms of all exvogenous variables in the system. The
direct reduced form is identical to the first stage of the
twostage least squares procedure. It is obtained from
Y = X + 9
where r is the matrix of direct estimates of the reduced
form. The derived reduced form estimates are obtained from
Yi = B yX + D
where B y = is the matrix of derived reduced form esti
The derived and direct reduced form estimates for
Model I are given in Tables 4 and 15, respectively. Those
for Mlodel II are given in Tables 5 and 19, respectively. In
this section, implications based on the derived reduced form
are discussed for M~odel I. A similar discussion follows for
Model II, at which time the two models are compared.
In Model I, increases in personal disposable income
per capital would increase the FOB demand for each of the
products, with the exception of canned sections. For single
strength juice and frozen concentrated juice, the FOB prices
and quantities demanded would increase. Also, the FOB3 price
of fresh grapefruit would increase. For canned sections,
the FOB price would increase, but there would be a corre
sponding decrease in the quantity demanded.
The increases in revenue would not be restricted to
processors. Growers would also benefit. Whereas the quan
tity of grapefruit going to processing and to packing is
predetermined, increased ontree prices would mean increased
returns for the growers. Thus, in a period of rising in
come, such as has consistently occurred in recent years, the
Florida grapefruit industry as a whole would receive in
creased revenues.
The effect of beginning inventories can also be exam
ined. If the industry w~ere to initiate a program to in
crease inventories, perhaps to be able to provide more of
the products during the months of Mlodel II or to provide a
cushion in the event of a freeze, the result would be an
Exogenous Endogenous Variablea
Variable PGR PGK PFCS PFCG PFFC PFFG
Table 4. Coefficients of Derived Reduced Form
Equations for M~odel I
IN
BCS
BCG
BFC
m
m2
TG
POJ
GE
Dl
D2
D3
QFCSb
qF~cb
QFFCb
GR
GK
QFFG
7.149
0.810
0.437
1.285
5.585
0.684
1.187
0.078
0.002
0.315
0.085
0.305
0.040
0.075
0.154
0.227
2.823
0.000
0.001
1.959
0.047
0.102
0.062
0.806
0.085
0.027
0.481
0.001
0.002
0.089
0.014
1.820
0.004
0.161
0.011
0.160
0.173
0.039
10.208
1.072
0.600
2.143
7.911
0.972
1.962
0.109
0.025
0.577
0.119
0.529
0.055
0.100
0.216
0.394
3.647
0.000
0.001
57.386
2.372
0.248
0.535
0.325
1.852
0.172
0.142
0.125
0.005
0.009
0.136
0.074
0.064
0.023
0.247
0.055
0.845
0.000
0.001
4.263
4.262
0.918
0.496
1.090
3.392
0.378
1.286
0.089
0.161
0.583
0.097
0.375
0.045
0.085
0.176
0.280
3.122
0.000
0.001
12.216
2.163
0.052
0.112
0.068
0.889
0.093
0.030
0.532
0.001
0.002
0.098
0.016
2.009
0.005
0.178
0.012
0.177
0.000
0.043
7.855
Constant 38.353 5.141
Exogenous Endogenous Variablea
Variable PCS QFCS,SUCS SCS PCG QFCG,SUCG
Table 4. (continued)
IN
BCS
BCG
BFC
m
m2
s
TG
POJ
GE
D1
D2
D3
QFCSb
QFC~b
QFFCb
GR
GK
QFFG
7.723
1.508
0.086
1.433
0.327
0.083
1.643
0.015
0.221
0.670
0.016
0.418
0.008
0.139
0.029
0.312
0.589
0.000
0.001
2.924
0.171
0.104
1.674
2.462
0.335
1.664
0.019
0.172
0.583
0.021
0.461
0.010
0.077
0.038
0.344
0.581
0.000
0.001
10.647
2.338
0.018
3.107
2.789
0.418
3.307
0.005
0.393
1.279
0.005
0.880
0.002
0.216
0.009
0.656
0.009
0.000
0.000
2.968
0.375
0.092
0.490
2.181
0.187
0.329
0.038
0.007
0.074
0.041
0.112
0.019
0.035
0.075
0.083
1.275
0.000
0.000
0.499
0.142
0.305
0.185
0.198
0.002
0.081
0.245
0.003
0.005
0.266
0.042
0.125
0.013
0.484
0.031
0.482
0.000
0.003
Constant 16.136 26.708
42.884 18.564 2.101
ExognousEndogenous Variablea
Variable SCG PFC QFFC,SUFC SFC
a~,ariables are as defined in Chapter II.
bQuantity lagged one month.
Table 4. (continued)
2.469
0.233
0.787
0.305
1.982
0.190
0.248
0.207
0.005
0.068
0.225
0.069
0.105
0.022
0.410
0.052
0.793
0.000
0.002
16.464
9.826
1.713
0.169
0.779
1.898
0.114
1.127
0.025
0.203
0.544
0.027
0.259
0.013
0.158
0.049
0.193
5.830
0.000
0.001
4.315
1.753
0.381
0.212
0.538
1.443
0.162
0.470
0.038
0.068
0.123
0.042
0.159
0.020
0.035
0.076
0.119
1.296
0.000
0.000
9.314
8.073
1.333
0.043
0.317
0.454
0.047
1.597
0.063
0.135
0.667
0.069
0.100
0.032
0.123
0.125
0.074
4.535
0.000
0.001
4.999
IN
BCS
BCG
BFC
m
m2
s
TG
POJ
GE
Dl
D2
D3
QFCSb
QFCcb
QFFCb
GR
GK
QFFG
Constant
CO U
UUL
m m 0
SOL4CA
uoECV ACTCYC
increase in the level of pack. Also, FOB sales would be
increased. However, perhaps because the impetus would come
from the supply side, the FOB prices of each of the prod
ucts would decrease. The price of singlestrength juice,
which accounts for about 55 percent of the grapefruit pro
cessed, would decrease by approximately onethird, while
the movement would increase by less than 4 percent. In
addition, though not given in the reduced forms, there would
likely be increases in the cost of storing the increased
inventories. Therefore, during the months of Mlodel I, it
appears that revenue to producers would decrease. However,
as shown later, revenues during the months represented by
Modell II would increase.
Increases in Texas grapefruit is shown to adversely
affect the Florida industry. Increases in Texas grapefruit
shipments would depress prices for all three processed
grapefruit products and, consequently, the price that
growers receive for grapefruit going to processing would
decline. Also, the price of grapefruit for fresh sales
would decrease. Fortunately for the Florida industry, Texas
shipments are annually only about 3 percent as large as the
Florida crop.
Based on the coefficients for the FOB prices in the
reduced form equations, increases in the price of frozen
concentrated orange juice would adversely affect the prices
of canned sections and frozen concentrated grapefruit juice.
The fresh market for grapefruit would be unaffected by
changes in the price of frozen concentrated orange juice.
Finally, changes in the FOB quantity of fresh grapefruit
would have virtually no effect on the other products in the
study. The effect of a decrease in the FOB quantity, per
haps caused by a freeze, would be an increase in both the
ontree and FOB price for fresh grapefruit.
For Model II, increases in income would result in in
creased demand for singlestrength juice and canned sections,
with prices anid quantities both increasing. Income increases
would result in an increased volume of sales of frozen con
centrated juice; however, there would be a net decrease in
price. Since frozen concentrated juice represents a rela
tively small share of the grapefruit market, rising income
would clearly result in increased revenues to the industry.
Whereas in Mlodel I, singlestrength juice w~as shown to
be a substitute for frozen concentrated orange juice, the
reduced form for M~odel II tends to substantiate the findings
based on the cross elasticity for the tw\o products. The
cross elasticity was negative, indicating complementarity.
Were the price of the orange product to increase, both the
quantity and the price of singlestrength juice would de
crease while the storage of the product would increase.
Further, the price of frozen concentrated grapefruit juice
would decline while the FOB movement would increase.
In Model I, it w~as shown that the gains from increased
inventories would be questionable. However, if they were
to be increased during the months in Mlodel I and w\ere carried
over to give higher inventory levels during the months of
Model II, net revenue to producers would increase. For
singlestrength juice and canned sections, sales would be
increased, while prices would decline. However, based on the
elasticity estimates decreases in the prices would be more
than offset by increases in sales.
ShortTerm Forecasting
Forecasts of the values of the variables endogenous to
the Florida grapefruit industry can prove invaluable to the
growers, packers and processors wiithin the industry by
reducing uncertainties. Based on the expected values of the
exogenous variables, the decision makers within the industry
could determine the economic consequences of following their
established decision criteria. For example, once the size
of the grapefruit crop for the coming year is predicted, the
values of all of the endogenous variables can be forecast.
This assumes that it is possible to obtain acceptable pre
dictions for the other exogenous variables.
To avoid the necessity of having to actually simultane
ously solve the equations in the model to determine the
values of the endogenous variables each time a change occurs
in the exogenous variables, the reduced form of the system
is used. The forecasts based on these reduced form equa
tions are only for the short term. W\hen forecasting w~ith
a static model, the assumption is made that the structure
of the system will remain as it was during the period of
data used for estimation of the structure. Thus, a model
that yields satisfactory forecasts for the short term may
be inadequate for longterm predictions because of changes
in the structure.
There are several methods that can be used to evaluate
the resulting forecasts. Each method requires that pre
dictions be made for a period in which the values for both
the endogenous and exogenous variables are known, so that
the model's predicted values can be compared with the actual
values that occurred. To avoid biasing the comparison, data
used in testing the model should not have been used in the
estimation of the model. One test involves the ability of
the model to predict turning points. The turning points
that are predicted are compared with the turning points that
actually occurred. This test w~as inappropriate to the pros
ent study because of the lack of turning points over the
range of the data for each production season.
Another test attempts to give an objective measure of
how close the predictions are to the actual values by con
sidering the magnitude of the predictions relative to the
actual values. In addition, the ability of the model to
predict changes in the endogenous variables is also included.
This measure is known as Theil's inequality coefficient
[16, p. 28 and 17, p. 32].
C(PA)
U. = v
(Aj 1 TjAj0)
C(P A )
2 (A jQ
where P. is the predicted value of the endogenous variable
and A. is the actual value.2
U1 is confined to values between 0 and 1. A value of
0 imlie tht P = A.j for all j, so that the forecasts are
perfect. A value of U1 = 1 implies the extreme case where
nonzero predictions are made of actual values that are 0 or
viceversa (i.e., P. = 0 for all j or A. = 0 for all j).
Or it means that there is a nonpositive proportionality
between the P's and the A's.
A value of 0 for U2 likewise denotes perfect forecast
ing. If a nochange extrapolation is applied (i.e., that
the value in time period j is predicted to be the same as
occurred in time period j1), then P = Aj1. In thzat case,
the numerator and the denominator are equal and UZ = 1. The
The coefficients, U1 and U2, are typically given as
1 i 1 V
and
U2 iA )2 (A )
where the Ai and Pi refer to changes in the actual value
and the predicted value, respectively. The A and P that
annear in the formulations in the text are ac ual va ues,
rather than changes. For the derivation of the formulations
in the text, see Stekler [15, p. 4139].
coefficient has no upper bound, so a value greater than 1
implies that the forecast is worse than could be obtained
by using a nochange extrapolation.
Thus, in the cases of both U1 and U2, values close to
0 are indicative of accuracy in forecasting, whereas values
approaching 1 indicate that a nochange extrapolation would
have performed about as well. If U2 > 1, a nochange
extrapolation would have been preferable.
The predicted values of the endogenous variables for
Model I, based on the estimated reduced form, are given in
Table 6. Table 6 also includes the actual values for the
variables and the deviations of the predicted values from
the actual values. Predictions based on the estimated
reduced forms rather than on the derived reduced forms are
presented in the text because, evaluated on the basis of the
inequality coefficients, they were closer to the actual
values. The calculated inequality coefficients, U1 and U2'
are given in Table 7. While the discussion in the text is
based on the results presented in Tables 6 and 7, predicted
values and inequality coefficients based on the derived
reduced forms are presented in Tables 16 and 17. Data used
in forecasting are given in Table 18.
Based on the inequality coefficients, the model pre
dicted the storage of canned singlestrength juice fairly
well. Also, the values for storage and FOB quantity of
frozen concentrated juice were fairly accurate. However,
Table 6. Endogenous Variables: Actual Values,
Predicted Values Based on the Reduced
Form Estimated Directly and Deviations,
December, 1971, Through Mlarch, 1972
Month
Variable December January February Mlarch
.92
.41
.51
1.54
1.61
.07
.92 .88
.23 .16
.69 1.04
Actual
Predicted
Deviationb
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
.93
.24
.69
1.49
1.60
.11
1.44
2.00
.56
1.34
2.13
.79
4.72
3.85
.87
5.46
5.01
.45
3.97
3.37
.60
5.40
3.22
2.18
10.007
11.264
1.256
5.494
8.539
3.044
10.511
8.753
1.759
2.706
3.073
0.367
4.58
3.30
1.28
5.30
5.28
.02
3.85
3.61
.24
5.24
3.10
2.14
11.853
14.476
2.624
5.087
10.109
5.022
17.277
14.910
2.367
2.064
3.979
1.915
4.51
3.15
1.36
5.37
5.42
.05
3.80
4.07
.27
5.10
3.45
1.65
13.202
14.866
1.664
4.978
10.629
5.651
25.501
21.546
3.954
1.361
3.317
1.956
4.07
2.38
1.69
5.41
5.80
.39
3.83
4.27
.44
4.90
3.35
1.55
15.416
21.338
5.923
6.728
13.892
7.164
34.188
32.984
1.204
0.448
3.622
3.174
gal.)
PFCS, SUCS Actual
(mil. gal.) Predicted
Deviation
SCS Actual
(mil. gal.) Predicted
Deviation
PCG Actual
(mil. gal.) Predicted
Deviation
Month
Variablea December January February March
QFCG, SUCG Actual 0.935 0.824 0.978 0.948
(ml.ga.)Predicted 0.599 0.301 0.853 0.945
Deviation 1.535 0.523 0.126 0.003
SCG Actual 4.610 5.850 6.233 5.732
(mil. gal.) Predicted 6.496 8.265 8.292 8.887
Deviation 1.885 2.415 2.059 3.155
PFC Actual 4.528 3.495 4.043 13.891
(mil. gal.) Predicted 0.172 2.479 0.121 4.518
Deviation 4.356 5.974 4.164 9.373
QFFC, SUFC Actual 2.248 1.265 1.389 2.867
(mil. gal.) Predicted 2.328 1.583 1.839 1.884
Deviation 0.080 0.319 0.451 0.984
SFC Actual 6.871 9.102 11.756 22.779
(mil. gal.) Predicted 2.437 2.817 7.154 14.406
Deviation 4.434 6.284 4.601 8.373
aVariables are as defined in Chapter II.
Actual value minus predicted value.
Table 6. (continued)
Table 7. Theil's Inequality Coefficients for
Predicted V'alues of the Endogenous
Variables, Based on Reduced Form
Estimated Directly, December, 1971,
Through Mlarch, 1972
U~b
33.5867
7.931.8
5.3877
2.1762
4.2819
10.6775
2.1020
5.7869
0.3466
3.1768
2.7952
3.2185
1.1968
0.6337
0.9896
Ula
0.9520
0.9919
0.7407
0.5946
0.7445
0.8440
0.5168
0.7851
0.2034
0.9978
0.6495
0.6858
0.6662
0.4045
0.6817
Endogenous Variable
PR
PK
PFCS
PFCG
PFFC
PFFG
PCS
QFCS, SUCS
SCS
PCG
QFCG, SUCG
SCG
PFC
QFFC, SUFC
SFC
aUI = PA) 4C (AAj >2
j=2 j=2
where A. = actual value (j = 2, 3, 4)
P. = predicted value (j = 2, 3, 4]
bU2 =~ j ~ ~ 4 P A 2 (A Aj
j=2 j=2
+4 (P Aj1 2c
;=7
81
for all the other variables, the values of U~2 w~ere > 1. :
This implies that a nochange extrapolatiopn~would have beenrk
preferable to the predicted values.
If evaluated with respect to the values of UI, the
model performs somewhat better. The clcosr the..value;EiF. oE
is to 1, the closer the predictions get to th~e ;ro chang~e
extrapolation value. Eight of the 18 variables had U1
values less than 0.7, indicating that the predictions may
not be as bad as indicated by the U2 values. Th7iS isno~t` '
to imply that 0.7 is the value below which the predictive
ability of the model is acceptable; there is no.test.to : .
indicate how much better a particular value of U1 is thaa r
another. Overall, with the few exceptions noted, it appears
that the predictive ability of Mlodel I is not very sharp..:
The predicted values based on the derived reduced forms,
actual values and deviations for Mlodel II are presen~ted.ia> .
Table 8, while the predictions based on thze,cs;sinrtted1..
reduced form are presented in Table 20. The data used in
obtaining the predictions are given in Table:2"p.; :No ingrt.
equality coefficients wecre calculated foS.Medell II becasuse
there w~ere only tw~o months of data available that were ,not ..
used in the estimation. Any attempts to draw~ conclusions
as to the predictive ability of the model would be sus.pect,
However, several observations can be made. In general, the
predictions based on the two reduced forms did not.dItEfes
widely, though, based on observation alone, the precdictions
Month
Variable August September
aActual value minus predicted value.
Table 8. Endogenous Variables: Actual
Predicted Values Based on the
Reduced Forms and Deviations,
and September, 1971
Values,
Derived
August
4.51
3.53
0.98
5.22
5.90
.68
3.80
3.09
0.71
3.875
3.953
0.078
0.751
0.594
0.157
2.099
1.831
0.268
9.798
9.719
0.078
3.100
3.257
0.157
8.899
10.167
1.268
4.68
3.88
0.80
5.42
5.72
.30
3.941
2.56
1.38
4.454
3.042
1.412
0.987
0.703
0.284
2.710
2.504
0.206
5.343
6.756
1.412
2.113
2.397
0.284
7.189
7.395
0.206
Actual
Predicted
Deviations
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
Actual
Predicted
Deviation
PFCG
($/gal.)
QFCS, SUCS
(mil. gal.)
QFCG, SUCG
(mil. gal.)
QFFC, SUFC
(mil. gal.)
SCS
(mil.
gal.)
gal.)
gal.)
SFC
(mil.
83
using the derived reduced form were slightly more accurate.
Also, both reduced forms for Model II predicted better than
did either reduced form for Model I.
CHAPTER VI
SUMMEARY AND CONTCLUSIONTS
The first part of the present chapter consists of a
summary of the objectives and findings of the study. Con
clusions based on the findings are presented in the second
section. Finally, suggestions are made as to further
research that is needed for a fuller understanding of the
Florida grapefruit indus try.
Summary
The objectives of this study were (1) to quantitatively
describe, by means of an econometric model, the Florida
grapefruit industry from the grower transactions at harvest
to the FOB level for canned singlestrength juice, canned
sections, frozen concentrated juice and fresh grapefruit;
(2) to measure the effects of factors exogenous to the
Florida grapefruit industry on the production and sale of
the four products listed above; and (3) to develop a model
for forecasting values of the variables endogenous to the
Florida grapefruit industry.
Twio models were developed: one for the months in which
fruit was harvested and thus available for processing and
for fresh pack (Mlodel I) and one for the months when no
fruit was harvested (Mlodel II). Model I consisted of 11
behavioral equations and 7 identities for the crop years
from 196465 to 197071. Model II consisted of six behav
ioral equations and six identities for the crop years
196364 through 196970. Included in Mlodel I were behav
ioral relationships for (1) ontree prices for grapefruit
for packing and for processing, (2) pack for each of canned
grapefruit sections and frozen concentrated grapefruit
juice, (3) storage of each of the processed products, and
(4) FOB demand for each of the processed products, as well
as FOB demand for fresh grapefruit. The behavioral rela
tionships for Mlodel II include (1) storage of each of the
processed products and (2) FOB demand for each of the pro
cessed products. All of the behavioral equations were over
identified and w~ere estimated using twostage least squares.
Monthly data w~ere used.
The processor and packer ontree price equations were
each formulated w~ith the ontree price as a function of thle
other variables. All of the other equations were normalized
on quantity. Both the quantity demanded and the prices of
the products to be derived from the fruit were shown to
affect the prices that the buyers were willing to pay, Also,
for fresh fruit, the margin between the ontree and FOB
price was found to increase with advances in the price
level. The year was also included in the equation for the
price of fruit for processing.
The packs of canned sections and frozen concentrated
juice were hypothesized to be a function of the FOB price
of the product and the FOB price of the other two products
that compete for the fruit, as well as the inventory level
of the product and the USDA estimate of the size of the
grapefruit crop for the year. The year was included to cap
ture the effects of the emergence and decline of frozen con
centrated juice and canned sections, respectively. Included
in each equation w~ere price expectation relationships con
sisting of the USDA crop estimate (to reflect expected
supply) and the FOB price of the product (to reflect
expected demand). The results did not indicate that expected
prices influence pack decisions.
The storage equations also contained expected price
relationships. Generally, the results did not indicate
that expected prices influence storage decisions. Not sur
prisingly, the quantity of each of the products that was
packed wvas found to affect the storage of the products in
Model I. Also, the equations included the year and the USDA
estimate. In Mlodel II there was no pack, so the pack vari
ables were omitted.
In Model I, the FOB demand for each of the products
was estimated with the quantity of a product demanded as a
function of its FOB price, the prices of substitutes, dis
posable personal income per capital, the FOB quantity in the
previous month and the month. In Mlodel II, the month
variable dropped out because it covered such a short period
of tine. Seasonality in the demand for the products wvas
found to exist. Also, generally, income had a positive
effect on demand. W~ith the exception of frozen concentrated
juice, the ownprice slopes were negative. It was suggested
that the positive ownprice slope for concentrated juice
resulted from an identification problem.
The estimates of the structural coefficients, average
prices and average quantities were used to calculate price
elasticities. Also, measures of average disposable personal
income per capital were used to calculate income elasticities.
For M~odel I, the price elasticities of demand obtained at
the FOB level were 0.392 for singlestrength juice, 2.101
for canned sections, 0.163 for frozen concentrated juice
and 12.268 for fresh grnpefruiit. The income elasticities
for the first two products listed above were positive, while
they wecre negative for the other twao products. Based on the
cross elasticities, singlestrength juice and frozen concen
trated juice were found to be substitutes. Cross elastici
ties for singlestrength juice and concentrated grapefruit
juice with respect to frozen concentrated orange juice were
0.268 and 0.622, respectively. For Mlodel II, the demand
elasticities were 1.254, 2.636 and 2.096 for single
strength juice, canned sections and frozen concentrated
juice, respectively. The income elasticities for the prod
ucts were all positive. Cross elasticities indicated that
singlestrength juice and frozen concentrated grapefruit
juice were substitutes.
Direct and derived reduced form estimates were obtained
for the two models. Implications of the derived reduced
form estimates were discussed.
Finally, predictions were obtained for each of the
models using both the estimated and derived reduced forms.
Predictions were made for December, 1971, to March, 1972,
for Model I and for August and September, 1971, for Mlodel II.
Model I predictions were evaluated using Theil's inequality
coefficients. The reduced form estimated directly produced
more accurate predictions that did the derived reduced form
estimates. Because there wrere only tw\o data points, the
predictions for Mlodel II were not evaluated. Based on
observations, however, the derived reduced form estimates
appeared to give more accurate predictions that did the
reduced form estimated directly. Also, the predictions for
Model II appeared to be considerably more accurate than
those for M~odel I.
Conclusions
Based on the results obtained in the study, the follow~
ing conclusions were drawn.
(1) During periods of rising disposable personal
income per capital, such as has occurred in
the years included in the study, both growers
and processors experience increased returns
through increases in prices and sales.
