Evaluating returns to postharvest research and development in the fresh-winter tomato industry


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Evaluating returns to postharvest research and development in the fresh-winter tomato industry
Physical Description:
ix, 120 leaves : ill. ; 28 cm.
Ansoanuur, James S., 1949-
Publication Date:


Subjects / Keywords:
Tomatoes -- Marketing -- Florida   ( lcsh )
Tomatoes -- Marketing -- Mexico   ( lcsh )
Tomatoes -- Postharvest technology   ( lcsh )
Tomato industry -- Harvesting -- Research   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
bibliography   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph. D.)--University of Florida, 1988.
Includes bibliographical references (leaves 110-119)
Statement of Responsibility:
by James S. Ansoanuur.
General Note:
General Note:

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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aleph - 001367156
oclc - 20658942
notis - AGM8661
sobekcm - AA00004789_00001
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Full Text








I wholeheartedly express my sincere gratitude to my chairman, Dr.

Max R. Langham, for his support, guidance and patience during the

course of my doctoral studies and the preparation of my dissertation.

At times when it was rough, his experienced and timely counsel put me

at ease. He has been my mentor, treated me like a godson and exposed

me to new knowledge, leaving me more confident as a professional

economist as I move on.

I would also like to thank Drs. Robert Emerson, Tim Taylor and

John VanSickle, the other members of my supervisory committee, for

their patience, suggestions and guidance during the course of the

preparation of my dissertation. I wish to also thank Audrey Sharp and

Lavon Mikell for their help in typing some portions of the text,

particularly the tables. I also wish to acknowledge the USDA, which

supported this research under IR-6 and the USDA/CSRS Cooperative

Agreement No. 58-32R6-2-143 entitled "Evaluation of Agricultural

Marketing Research."

Finally I would like to express my deepest appreciation to my

wife, Elizabeth, and children, Frieda, Mwitse and George, for their

support, understanding and endurance during the course of my doctoral

studies and particularly when I was preparing this dissertation.



ACKNOWLEDGEMENTS ................................................ ii

LIST OF TABLES ................................................ vi

LIST OF FIGURES.... ................................................ vii

ABSTRACT ....................................................... viii


I INTRODUCTION ......................................... 1

Problem Statement .................................... 3
Objectives ........................................... 5
Production and Marketing of Fresh-Winter Tomatoes
in Florida and Mexico .............................. 5
Tomato Production in
Florida ....................................... 6
Tomato Production in Sinaloa, Mexico ............ 10
Mexico's and Florida's Share of the Winter-
Tomato Market ................................. 13
Marketing Channels................................ 13
Fresh-Market Winter-Tomato Research .................. 18

II LITERATURE REVIEW .................................. 23

Consumers' and Producers' Surplus (CS-PS)
Approach ........................................... 24
Econometric Method ................................... 29

III THEORETICAL FRAMEWORK ............................... 36

Motivation for a Simultaneous-Equations
Approach ........................................... 36
Model Specification ................................. 37
Florida Supply ................................. 43
Mexican Export Supply .......................... 44
Marketing Margin Between the Grower
Level and the U.S. Retail Supply............. 46

Demand in the U.S. Market ...................... 46
Consumers' and Producers' Surplus
Analysis ................ .................... ... 47

IV MODEL ESTIMATED ..................................... 49

Modeling Expectation ................................ 49
The Rational Expectations Model ..................... 49
Naive Price Expectations Model ...................... 50
Extrapolative Expectations Model .................... 50
Adaptive Expectations Model ......................... 51
Revisional Price Expectations Model ................. 52
Estimates of the Model Parameters ................... 54
Estimation Method ................................... 59
Data Sources ........................................ 60
Mexican Growing Season
Temperature ................................... 60
Real Agricultural Interest Rate in Mexico........ 60
Mexican Rural Daily Wage Rate ................... 61
Quantity Shipped from Mexico
and the FOB Price in Mexico ................... 61
U.S.Population................................... 62
Mexican Fertilizer
Price Index ................................... 62
Real Per Capita National
Income in Mexico .............................. 62
Mexico's Population ............................. 62
Per Capita Quantity Shipped from Florida
and FOB Price ................................. 62
Florida Real Daily
Wage Rate ..................................... 63
Real Agricultural Interest Rate
for Florida ................................... 63
Florida Growing Season
Weather ....................................... 63
Research Expenditures ........................... 64
Total Quantity Supplied
at U.S. Retail Level .......................... 66
Real Retail Price ............................... 67
Retail Price of Substitutes ..................... 67
Real Cost Index for Fresh
Fruits and Vegetables ......................... 67
Florida Fertilizer Price ........................ 67
Weighted Average Price at the
Grower Level................................... 68

V EMPIRICAL RESULTS OF THE MODEL ...................... 69

Florida Shipping-Point Supply ....................... 69
Mexican Export Supply ............................... 75
Marketing Margin .................................... 77
U.S. Retail Demand .................................. 78

Measuring Returns of Research ....................... 79
Grower Level ................................... 82
Retail Level ................................... 83


Summary ........................................ .... 89
Results ............................................. 91
Conclusions ......................................... 92
Recommendations ..................................... 93
Area for Future Emphasis ............................ 94


A DATA USED IN THE MODEL .......................... 97

OF THE MODEL .................................. 102

REFERENCES .............................................. 110

BIOGRAPHICAL SKETCH ...................................... 120


Table Page

1 2SLS Structural Parameter Estimates................... 70

2 Discounted Values of R&D1 and R&D2 Impacts on the
Florida Supply, Mexican Export Supply, Marketing
Margin and U.S. Retail Demand (at a discount rate
of 4 percent).......................................... 80

3 Rate of Change of Surpluses with Respect
to One Unit Change in R&D Expenditure at
the Retail Level...................................... 85

4 Estimates of Marginal Rates of Return to R&D
Investments in the Fresh-Winter
Tomato Industry at the Retail Level................... 86

5 Estimates of NPV of Average Rates of
Return to R&D Investments in the
Fresh-Winter Tomato Industry.......................... 88

A.1 Data Set for Fresh-Winter Tomatoes in Florida......... 97

A.2 Data Set for Fresh-Winter Tomatoes in Mexico.......... 98

A.3 Data Set for Fresh-Winter Tomatoes in U.S.
Retail Market......................................... 99

A.4 Real Research Expenditures on Fresh-Winter
Tomatoes in Florida................................... 100

B.1 NL2SLS Structural Parameter Estimates................. 102

B.2 3SLS Structural Parameter Estimates................... 106


Figure Page

1 Major Growing Areas for Fresh-Winter Vegetables
in Florida............................................... 7

2 Growing Areas for Fresh-Winter Vegetables
in Sinaloa, Mexico....................................... 11

3 Marketing Channels for Florida Fresh
Vegetables from Grower to U.S. Consumer.................. 15

4 Marketing Channels for Mexican Fresh
Vegetables from Grower to U.S. Consumer.................. 17

5 Shift in Supply Due to Adoption of New
Improved Input.......................................... 25

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



James S. Ansoanuur

December, 1988

Chairman: Dr. Max R. Langham
Major Department: Food and Resource Economics Department

Evaluation of agricultural research has generally focused on the

effects of biological or technological improvements in production;

however, technological advancements in food and fiber processing,

quality improvements and marketing are often integral factors

affecting efficient utilization of perishable food resources, improved

marketing methods and demand shifts.

The most widely used econometric methods of evaluating returns to

agricultural research have generally focused on the impact on supply

and cost reduction. Furthermore, the returns are often expressed in

terms of internal rate of return, which does not address the

distribution of the returns to the different groups in the economic


system. A model for evaluating returns to postharvest research and

development (R&D) and preharvest marketing-related R&D, which

addresses both the supply and demand impacts of these variables and

also the distribution of the benefits to the different economic

groups, was formulated for the fresh-winter tomato industry.

Using a partial equilibrium, simultaneous-equations approach, a

Florida shipping-point supply equation, a Mexican export supply

equation and a marketing margin equation for fresh-winter tomatoes

were estimated. The estimated coefficients were then used to derive

supply and demand equations at two levels (grower and retail) in the

fresh-winter tomato market. These supply and demand equations were

used to derive consumer surplus (CS) and producer surplus (PS)

relationships as a function of the preharvest and postharvest R&D

expenditures. These CS and PS relationships enabled estimation of the

present value of marginal and average rates of return to preharvest

and postharvest R&D investments to tomato growers and distributors, to

U.S. consumers of fresh-winter tomatoes, and to society as a whole.

The results show that expenditures allocated to postharvest

activity have a very high rate of return at the margin and that

growers and distributors receive an estimated 33 percent of the

returns while consumers receive 67 percent of the returns.


Since World War II, impressive growth in productivity has been

recorded in both the agricultural and industrial sectors in the U.S.

This trend emanated from technological breakthroughs in industry and

agriculture in the form of improved and superior factors of

production, improved crop varieties, high-quality livestock breeds,

improved managerial efficiency and organization, and improved channels

of communication and information flows for the efficient utilization

of scarce resources. These improvements in technology are not

accidental but the result of investments in research and development

(R&D) programs.

Estimating the value of research and education has received

considerable attention by economists since the mid-1950s. The results

indicate that under a wide range of circumstances the economic returns

to agricultural research have been high relative to other investments

available to society (Ruttan, 1982, p.237). This research evaluation

has been largely directed towards preharvest or production-oriented

research and little on postharvest research.

Recently, there has been a growing interest in the returns to

postharvest technology and marketing economic research. Work by

Jorgenson et al. (1987, pp.198-200) indicates that growth rates in

total factor productivities of industries associated with providing



services to agriculture have been slightly negative. With food and

kindred products, and trucking and warehousing, estimates of

productivity growth rates have been less than those for production

agriculture. One hypothesis is that the U.S. has devoted too few

resources (both public and private) to basic research affecting

efficiency in industries associated with providing farm inputs and

food and fiber derived from farm products.

Freebairn et al. have developed a conceptual model which suggests

that there is no reason to believe that research opportunities are

greater or research costs less at the farm production level than at

the marketing level. White and Havlicek, in a study which focused on

farm production, concluded that underfunding of agricultural research

has serious implications on the future cost of food to consumers --

particularly if underfunding (below optimal levels) persists rather

than being made up. If the White and Havlicek conclusions hold for

research beyond the farm gate, and Freebairn et al. are correct,

consumers can expect a trend toward increased relative prices for food

as a consequence of present and past underinvestments in research on

problems beyond the farm gate.

Further studies are needed to confirm or reject these findings

and also assess the contribution of postharvest research and

development efforts in the efficient marketing of farm produce and

other postharvest processes, and the subsequent impact on consumers'

and producers' welfare. This research seeks to augment the knowledge

relating to the returns to postharvest R&D investments. Postharvest

R&D is generally geared toward technological improvements in the


packaging, processing, transportation, organizational efficiency and

information flow which are meant to enhance the market power of the

conducting industry. R&D is often an integral factor affecting demand

shifts, marketing costs and strategies, and efficient utilization of

perishable food resources to enhance profits.

Some biological or technological improvements in farm production

techniques do not only impact the production side but may also have a

bearing on the marketability of the produce. For example, genetic

research to develop varieties of tomatoes that will withstand physical

damage, which have disease resistance, and which yield fruit of a

desired size is not only production-oriented but also results in

desirable marketing qualities. The expenditures produce not only the

scientific and technological improvements at the production level, but

also at the marketing level. Such marketing-related attributes of

production-oriented R&D investments need to be recognized in the

evaluation of returns to research investments.

Problem Statement

This research is directed at evaluating the impact of postharvest

and marketing-related preharvest R&D investments on the marketing of

fresh-winter tomatoes from Florida and Mexico in the U.S. domestic

market. It is hoped that the techniques developed in this case study

will be useful for measurement of returns to research in other areas

of the food and fiber marketing channels.

Winter tomatoes were selected because they are an important

winter vegetable crop in the United States and the leading vegetable

export to the U.S. from Mexico, the major foreign supplier of winter


vegetables. Because of its climate, Florida is the leading producer

of fresh-winter tomatoes in the U.S. Tomatoes represent approximately

30 percent of the total cash farm value of the Florida vegetable

income and are grown on 11 percent of the total vegetable acreage of

Florida. The hot and dry, desert climate of northwestern Mexico

favors vegetable production in the fall, winter and spring seasons.

Over 30 percent of the total dollar value of vegetables imported from

Mexico is comprised of tomatoes. In 1983-84 the total dollar value of

imports of vegetables from Mexico was $576 million, of which $224

million (38.9 percent) was from tomatoes, 28 percent from cucumbers,

17 percent from peppers, 13 percent from squash, 2 percent from egg-

plant and 2 percent from green beans (Buckley et al.). The tomatoes

produced and exported to the U.S. must meet U.S. marketing standards

in terms of grade, size, weight, containers and maturity. The impact

of research has been paramount in the tomato industry in Florida.

Several varieties have proved outstanding. Economic and marketing

research have resulted in more efficient and low-cost methods of

handling tomatoes in the marketing channel. What impact do these

developments have on consumer and producer welfare?

The agricultural research facilities in Mexico are not able to

meet the needs of vegetable growers. Consequently the Mexican

industry imports seeds, chemicals, equipment and other technology from

the U.S. (Gutierrez). Some new technology applied in Florida and

California is almost immediately adopted by Mexican growers and new

postharvest technology also benefits Mexican growers since they use

much the same marketing procedures as U.S. growers. Thus U.S. based


R&D investments impact the Mexican fresh-winter tomato industry as

well, and this influence needs to be captured in any measurement of

returns to tomato-related research in the U.S.


The overall objective of this study is to estimate returns to

research on winter tomatoes -- especially as this research impacts

postharvest processes. Specific objectives are to:

1. Develop an econometric model describing the

interrelationship of several important variables affecting

the fresh-winter tomato industry.

2. Empirically estimate the model using data pertaining to

fresh-winter tomato production and marketing in Florida and


3. Evaluate the distributional effects (consumer and producer

surplus), and the overall returns to postharvest technology

and marketing research.

Production and Marketing of Fresh-Winter
Tomatoes in Florida and Mexico

This section draws on material presented in Buckley et al.;

Bredahl et al.; Gutierrez; Emerson; Froman; and Zepp and Simmons.

Fresh-winter tomatoes for the U.S. market during the winter season,

December through June, come from two major production regions: Florida

in the U.S., and Sinaloa in northwest Mexico. Sinaloa has become the

only major foreign supplier of fresh market tomatoes owing to a

combination of factors, which include: favorable climate; an extensive

irrigation infrastructure; railway lines and good roads connecting


producing areas to marketing centers; proximity to western U.S.

markets; and the availability of inexpensive labor. Political factors

also contributed to the decline in other production areas. Cuba was

eliminated by the 1962 U.S. trade embargo. The termination of the

bracero program in 1964 reduced the availability of cheap labor in

the U.S. vegetable-production areas. Financial and technological

resources therefore flowed out of the United States and into Mexico in

response to these events.

Tomato Production in Florida

In Florida, winter tomatoes are the largest vegetable crop in

value, and rank second to citrus in total revenue of all Florida

agricultural commodities. According to Buckley et al.(p.15):

Tomatoes accounted for 34.7 percent of the total value of
all vegetables produced in Florida during the 1983/84
growing season.

Tomato production is concentrated around west-central and east-

central Florida during the fall and spring and moves south to

southwest Florida and around Homestead in Dade County during the

winter (Figure 1).

Tomatoes are planted between the last week in July and the third

week in March and harvested in October and November in the central

areas of the state. Production occurs further south with the approach

of winter. Technological change has played a major role in Florida's

competitive edge over Mexico in the production and marketing of fresh-

winter tomatoes, despite Mexico's lower cost of production.

Florida growers make widespread use of stake and ground culture.

In stake culture, tomato plants are supported upright with stakes and



*Plant City


Fort Pierce

Naples Pompano Beach


Major Growing Areas for Fresh-Winter Vegetables in Florida.

Zepp and Simmons (1979).

Figure 1.



string. West-central and southwest are the principal mature-green,

stake-production areas. Ground tomatoes grow without the benefit of

upright support. Dade County has the largest acreage of ground

tomatoes. The tomatoes are grown under irrigation and mostly over

plastic mulch, an improved technology wherein plastic mulch covers the

soil surface, thereby maintaining uniform soil moisture and

temperature conditions, and aiding in weed control and reducing

fertilizer leaching.

Although some vine-ripe tomatoes are marketed, the majority of

fresh- winter tomatoes produced in Florida are picked and marketed as

mature greens. Mature green tomatoes stay firm longer and have a

prolonged shelf life. Ripening can, however, be quickened with

ethylene gas after packing.

According to Buckley et al., the area planted, the yield, the

production and the total value of tomatoes produced in Florida have

shown an upward trend during the past 15 years. This has been

attributed to the adoption of staked-tomato culture, full-bed plastic

mulch, and improved disease-resistant and high-yielding varieties

developed through research. Some of the improved varieties include

FTE-12, Duke, and Sunny. They are high yielding, and produce fruits

which are much firmer and larger than traditional varieties. Laser

leveling of fields, which provides greater uniformity of soil

moisture, has also contributed to increases in tomato yields. In

order to reduce frost during the winter, most tomato growers have

acquired sprinkler irrigation systems. The tomatoes are either

transplanted or directly seeded mechanically; however, operations


such as thinning, pruning, tying plants and harvesting are performed

by hand labor.

During harvest the number of pickings depends on the market and

field conditions and the yield. Buckley et al. contend that when

production is concentrated as a result of widespread use of hybrid

varieties, fewer pickings take place. Fields once picked three to

five times, depending on market and field conditions, are now picked

two to three times.

From the field, tomatoes are sent to the packinghouse, where

they are washed, waxed, sized, artificially ripened if necessary, and

packed mechanically before being sold. The tomatoes are sold by the

packinghouses through brokers or hired salesmen.

The interests of tomato growers in Florida and Mexico are

represented by grower organizations. The Florida Tomato Committee and

the Florida Tomato Exchange support and protect the interests of

Florida tomato growers. The Florida Tomato Committee regulates the

marketing of fresh tomatoes through a federal marketing order, which

requires certain grade and size standards to be maintained during the

marketing season. Tomatoes grown in Florida and all tomatoes imported

are expected to meet these standards. The size, grade, container and

inspection requirements are set by policymakers based on the

recommendations of the Tomato Committee. All tomatoes produced in

Florida and those imported must adhere to these regulations. The

Florida Tomato Exchange, which is a nonprofit cooperative association

of first handlers of fresh tomatoes in Florida, provides collective

action with respect to the orderly marketing and distribution of fresh


tomatoes. The Tomato Exchange complements the activities of the

Tomato Committee, with major emphasis placed on production research,

promotion of tomatoes through advertising, legislative activities,

legal aid on items affecting the tomato industry, and items not

covered under the marketing order.

Tomato Production in Sinaloa. Mexico

Tomato production in Sinaloa is mainly for the export market.

However, the domestic market may be used as a secondary or residual

market for quantities and sizes that do not meet export requirements.

Market conditions determine export quantities, with more being

exported when export prices are high and exceed the export marketing

costs. Low prices can result in more being shipped to the domestic

market, fed to livestock or simply discarded.

Figure 2 depicts the major fresh-tomato-producing areas in the

state of Sinaloa, the largest producing area being Culiacan which

produces and ships primarily vine-ripe tomatoes. Planting in Culiacan

takes place in the late fall (September to November), with harvesting

peaking in the winter months of January to March. The Guasave and Los

Mochis areas produce and export roughly half vine-ripe and half mature

greens. Winter production in these areas is limited because of

frequent frost. Thus, production is directed toward two marketing

seasons -- the late fall and early spring markets. Planting time for

the fall crop is in August and September, with harvest in the months

of November and December, while the spring crop is planted during

late February and March, with harvest in the months of May and June.




Gulf of Mexico

Pacific Ocean

Mexico 0

Figure 2. Growing Areas for Fresh-Winter Vegetables in Sinaloa,

Source: Zepp and Simmons (1979).


Advances in vegetable production and harvest and postharvest

technology in the U.S., are imported and adopted by Mexican producers

with the aid of the U.S. importers of their produce. Both staked and

ground-grown tomatoes are produced. Staked tomatoes are primarily

produced around Culiacan; ground-grown tomatoes are produced around

Gausave and Los Mochis. Staked tomatoes are normally harvested as

vine-ripe tomatoes while ground-grown are harvested as mature greens.

Popular varieties such as Sunny and Contessa, as well as much of

the planting media and forms, are imported from the U.S. (Buckley, et


At harvest time, the number of pickings depends on the market

conditions (i.e., export price vis-a-vis harvesting and export costs).

From the field, tomatoes are sent to the packinghouses, where they are

dumped into a water tank to remove field heat and to clean them. After

cleaning they are waxed, sorted as export quality or domestic quality,

packed by color and size, banded in pallets, and precooled.

Like in Florida, Mexican grower associations support and protect

grower interests with regard to the production and orderly marketing

of tomatoes from Sinaloa. The Union Nacional de Productores de

Hortalizas (UNPH) and the Confederacion de Asociaciones Agricolas del

Estado de Sinaloa (CAADES) are two associations that govern tomato

production in Sinaloa. They recommend maximum planting acreages,

establish regulations governing types of containers used in shipping,

determine quality standards for exports, and issue export permits

based on acreage allotments. They adjust quality standards according

to prevailing U.S. prices. These regulations are intended to avoid


overproduction and low export prices (Froman). The acreages allotted

for planting are strictly enforced through the allocation of water by

the Agricultural Department. Excess planting may result in a

reduction in water supply, and excess export production may result in

cancellation of the export license.

In general, lower than acceptable prices result in stricter

quality requirements and, if this does not suffice to raise prices,

smaller sizes are restricted. Also, shipment of tomatoes to the U.S

market through Nogales is determined by maturity and to the rate of

movement. If movement is slow, the more mature tomatoes are

restricted. An inspection system at Nogales enforces the

restrictions. Certificates of origin are required and any truck or

rail lot that does not meet the restrictions is turned back.

Mexico's and Florida's Share of the Winter-Tomato Market

The U.S. fresh-winter tomato market is roughly split between

Florida and Mexico. Weather conditions in Florida play an important

role in the annual fluctuations in the respective market shares. In

general, supplies from Mexico dominate during the peak of the winter

season (January through April) while supplies from Florida are largest

in the early and later part of the season (Zepp and Simmons).

Florida supplies mainly the eastern United States and Mexico

supplies the west of the United States. Both areas supply the mid-

west. Domestic weather and crop conditions influence the geographic

distributions with the result that Mexico supplies more to markets in

the east and mid-west when Florida supplies are reduced by a killing


Marketing Channels

Fresh-winter tomatoes from Florida and Mexico (after clearing

Mexican and U.S. custom agents) go through the same marketing channel

before reaching the final consumer at the retail level in the U.S. In

this process, marketing services such as packing, repacking, wrapping

and transporting are provided by marketing agents.

From the field, fresh tomatoes are sent to the packing plants,

where they are washed, waxed, sized, sorted, graded, and packed. Some

degreening or ripening of mature-green tomatoes may be done at this

point by storing them in temperature controlled rooms for one to three

weeks (Buckley, et al). The degreening process is accelerated with

ethylene gas.

From the packing plants the fresh tomatoes are transported by

truck or rail depending on the distance between packing plant and

terminal or wholesale markets. Often vegetables shipped long

distances go by rail. At the terminal or wholesale markets the fresh

tomatoes are stored in warehouses and then delivered to retail

markets, restaurants, and institutions. Mature-green tomatoes may go

from the packing plants to repackers, where they are ripened, resorted

and repacked according to color before being transported to the

terminal and wholesale markets (Figure 3).

According to Buckley et al. fresh tomatoes are also marketed

through alternative routes which involve direct movement of the

vegetables from the packing plant to the warehouse of an integrated

wholesale-retail grocery chain before being distributed to retail

stores and finally to the consumer. Secondary wholesalers may also

Terminal Market

Marketing Channels for Florida Fresh Vegetables
from Grower to U.S. Consumer.

Source: Mongelli, Robert (1984).

Figure 3.


purchase the produce from primary wholesalers and then resell to

jobbers and truck jobbers.

To facilitate shipping logistics and assure marketing outlets for

the highly perishable vegetables, contractual agreements are made over

the telephone between contractual operators and local buyers or

customers in the terminal markets.

Fresh tomatoes from Mexico go from the field to the packing shed

or plant where they go through the same process as in Florida (i.e.

washing, waxing, sorting, grading and packing). From here they are

transported by truck or rail through Mexican and U.S. customs, where

they are inspected to make sure that they meet export and import

requirements. Export documentation as well as paperwork for

repatriating export earnings are processed at the Mexican side of the

border. Export fees are also collected at this point. After this,

the fresh vegetables are transported to wholesale warehouses in

Nogales, Arizona. U.S. customs agents then collect import tariffs,

process export documents and issue certificates testifying that the

produce have met U.S. import standards. These export and import

transactions are being handled by customs brokers on both sides of the

border on behalf of the Mexican producers.

Distributors in Nogales resort the vegetables according to

maturity before shipping them to terminal markets, wholesalers and

chain store warehouses. From here the vegetables go to retail

outlets, restaurants, institutions and the final consumer in the U.S.

(Figure 4). There is a partnership relationship between the

distributors and growers. Through this partnership distributors

Mexican & U.S.
Customs Brokers

Terminal Market

Marketing Channels for Mexican Fresh Vegetables from
Grower to U.S. Consumer.

Adopted from Buckley et al., and Mongelli, (1984).

Figure 4.



provide seed, other inputs, technical and market information from the

United States and preharvest and harvest financing to the growers.

According to Buckley, et al. (p.8):

approximately 60 percent of the distributors in Nogales are
partners with one or more Mexican growers. These firms handle an
estimated 60 percent of the Mexican produce.

Of the remaining 40 percent of the distributorships 20 percent are

owned outright by Mexican growers and managed by a U.S. citizen.

Independent contractors also do business with Mexican growers and they

form the remaining 20 percent of the distributorships. Chain store

buyers may also operate in Nogales, but they usually do not have

physical storage or handing facilities in the area; thus their

purchases are shipped directly to chain store warehouses. From here

the produce is then sent to retail stores for distribution to the


Fresh-Market Winter Tomato Research

In Florida, research on tomatoes began in the 1920s. Areas of

research focus have included the development of disease resistant

varieties, improved cultural practices, improved methods of preventing

postharvest decay of fruits, uniform ripening techniques, cultivars

that are amenable to machine harvest, mechanized harvesting of fresh-

market tomatoes, and handling and transportation of tomatoes to lower

the cost of marketing.

Some production-level research and development benefits both

production and marketing of tomatoes. Plant breeders have developed

varieties which have resistance to multiple diseases, concentrated

ripening of fruit, uniform maturity, and at least 90 percent


marketable yields (Villanlon and Bryan). Tomatoes have been developed

with fruits which are firm and resistant to cracking, rupturing, and

bruising during harvesting and handling (Cargill and Rossmiller).

Improved cultural practices such as plastic or paper mulching to

reduce soil temperatures and conserve soil moisture also affect the

marketability of the tomato fruits by reducing the amount of sand and

number of blemishes on them. Tomatoes for fresh market must be

relatively free of defects to meet grade requirements. Sand particles

can cause abrasions or punctures during harvest and packinghouse

handling, resulting in decay or surface defects (Ramsey et al.; Halsey

et al.).

A great amount of research has been done to develop cultivars

with characteristics that will allow machine harvesting of tomatoes.

Mechanical harvesting is desired inorder to reduce costs and enable

Florida producers to be more competitive, and considerable effort has

been made in this direction (Everett et al.; Navarro and Locascio;

Deen et al.). Researchers from the Institute of Food and Agricultural

Sciences (IFAS) have been developing and evaluating equipment for

mechanical harvesting of mature-green tomatoes for fresh market.

Consumer acceptance tests for mechanically-harvested tomatoes handled

through commercial channels have been used to evaluate the

marketability of machine-harvested tomatoes (Hicks et al.). In these

tests, taste panel evaluations of flavor, texture, appearance and

general acceptance of newly-developed varieties compared with well-

established varieties were performed. To be feasible mechanized

systems must allow growers to deliver high quality fresh tomatoes to


market channels. To date, mechanical harvesting of fresh market

tomatoes in Florida has not proved to be economical. The machines are

designed for once-over harvesting and the varieties do not produce

fruit that ripens uniformly at one time; thus there are considerable


Research has been carried out to reduce postharvest decay

resulting from contamination by bacteria which grow in bruises and

punctures that occur during harvesting (Bartz and Crill). Ethephon

treatment of green-harvested fruit, applied at the packinghouse,

appears to have promise as a new technique for further improving the

quality of winter tomatoes. Chlorine compounds have been used

successfully for some time to control postharvest decay by reducing

bacterial inoculum during postharvest washing (Segall).

Marketing agreements and orders have been used for several

decades by various commodity groups, including tomato growers, in an

effort to stabilize and increase the level of farm income. Brooker

and Pearson evaluated the aggregate effects of these marketing orders

or supply management policies in terms of 1) the net revenue obtained

by domestic growers, 2) the volume of tomatoes marketed and consumed

in the U.S., and 3) consumer expenditures. Such information has

helped the Florida tomato industry in making marketing decisions. It

has also been of value to other commodity groups faced with similar

circumstances, and to government agencies responsible for marketing

policy. In 1979, Degner and Cubenas provided the information that, it

was hoped, would promote the development and expansion of direct

marketing of agricultural commodities from farmers to consumers on an


economically sustainable basis. Container specification is an

important factor in the marketing of tomatoes. Sherman et al.

identified suitable containers for shipping Florida tomatoes,

particularly during the warm weather.

Consumers of tomatoes prefer firm and fully-red tomatoes.

Several researchers (Ben-Yehoshua et al.; Hobson; Kittagawa et al.;

Risse et al., 1985) have studied the packing of tomatoes either in

polyethylene bags or individually wrapped in film. Mature-green

tomatoes, individually wrapped in heat-shrinkable plastic film after

ethylene treatment, had less weight loss and were firmer than non-

wrapped tomatoes stored for up to three weeks at 12.80C and held an

additional seven days at 210C. Studies have also been done to

determine the effect that film wrapping of mature-green tomatoes,

before and after ethylene treatment, has on ripening and shelf-life

(Risse, et al., 1984). Wrapping before ethylene treatment may be a

useful measure of prolonging quality and freshness of tomatoes during

export shipment or extended storage. Least-cost methods of repacking

tomatoes have been identified through research (Meyer). Mongelli

(1980), made a comparative study of handling systems for fresh

tomatoes from packinghouse to retail store. He found that a

synthesized pallet-pool system was the lowest-cost system for moving

tomatoes from packing plant to wholesaler. Pallet delivery was the

lowest-cost system for movement from wholesaler to retailer. The

lower cost of handling translated to lower prices for the consumer.

Studies on shipping alternatives for moving Florida produce to eastern

and midwestern markets were done by Klindworth and Brooks. In a 1984


study Mongelli studied methods for harvesting and handling tomatoes

from field to packinghouse and found bulk bins for handling tomatoes

from field to packinghouse, and hand stacking transport from

packinghouse to wholesale warehouse, to be the most cost-efficient


Both public and private funds are spent on tomato research at the

state and federal level. At the state level tomato research has been

conducted by IFAS. Much of the earlier research on tomatoes in

Florida was conducted at the Gulf Coast Research and Education Center

at Bradenton, Florida. At the federal level the U.S.D.A. has a

sizeable research program in tomatoes, which includes the work by

Mongelli; Meyer; Fahey; Jesse; Worthington, et al.; Zepp and Simmons

and Zepp.

The Florida tomato industry, through the Florida Tomato Exchange,

invests funds on tomato research, tomato promotion through

advertising, legislative activities and legal aid on items affecting

the fresh-market tomato industry.


This section draws on material presented in Norton and Davis,

Peterson and Hayami, and Stranahan. New technology is created through

investments in research and development (R&D) and results in

productivity increases. Economic evaluation of the returns as they

relate to investments in R&D has been an important area of study in

economics. Numerous reviews concerning technological change in

general and the productivity of research in particular have been done

(Peterson (1971), Shumway (1973, 1977), Sim and Gardner, Schuh and

Tollini, Ruttan (1980), Nelson, Norton and Davis, and Evenson (1982)).

Techniques employed to quantify and evaluate the returns to R&D

have been, primarily, the consumers' surplus (CS), the producers'

surplus (PS), and the econometric method1. The CS-PS technique has

focused on the impact of R&D on the supply of agricultural commodities

(Griliches (1958), Peterson (1967) and Evenson (1969)) and on the

social and distributional implications of R&D benefits (Schmitz and

Seckler). Econometric estimation methods have employed the production

1 Most consumers' and producers' surplus analyses have employed the
graphical approach, with some assumptions about the shape, the nature
of shift, and the elasticity of the demand and supply curves. On the
other hand, econometric estimation methods have specified a
production function relationship, or cost function, with R&D as one of
the explanatory variables, and its impact is seen as the contribution
to production or cost at the margin.



function approach or, through duality, the cost function and the

profit function approach to estimate the effect of R&D on value added

in food production (Griliches, 1964; Evenson, 1967) and manufacturing

(Mansfield, Terleckyj).

Consumers' and Producers' Surplus (CS-PS) Approach

Basically, this approach attempts to quantify the changes in

consumers' and producers' surplus which can be attributed to

technological change. Research and development generate new

knowledge which may result in resource or cost saving in the industry.

Technological change thus lowers the marginal costs of production and

shifts the supply curve to the right. This shift gives rise to

benefits as it causes changes in consumer and producer surplus. The

idea is to determine the (discounted) benefits and costs of

technological change over time and thus obtain a benefit/cost ratio

and/or an average internal rate of return to research. The cost of

technological change is reflected in the R&D expenditures.

Estimates of internal rates of return using this methodology have

ranged from 30 to 60 percent. The thrust of this method can be

illustrated as in Figure 5. The figure shows a conventional,

downward-sloping demand curve (D) and an initial supply curve (So)

which shifts to position S1 as the result of the adoption of a new

improved input developed through research. Before this shift,

consumers' surplus equaled area a; afterward, it is represented by

(a+b+c). Thus, the net gain to consumers from the research-induced

shift in supply is (b+c). Similarly, before the supply shift,

producers' surplus equaled area (b+d); afterward, the producers'

Price ($)






Shift in Supply Due to Adoption of New Improved Input.

Figure 5.


surplus equals (f+d). Their net gain from the supply shift is then

(f-b). The net gain to society (consumers' plus producers' surplus)

is (b+c+f-b c+f), which also constitutes the gross benefits of


The area under So out to Q1, minus the area under S1 out to Ql

represents the value of resources which are released after adopting

the improved technology of producing the particular good, and which

can then be employed in their next best use. Alternatively, one might

consider the effects of consequent unemployment of these resources as

in Schmitz and Seckler. The net change in economic benefits depends

upon the assumed elasticities of supply and demand and the nature of

the supply shift (Eddleman).

According to Norton and Davis the first attempt to quantify the

benefits from agricultural research investments was by Schultz in

1953. Under the special assumptions of perfectly elastic supply

curves and a perfectly inelastic demand curve, he found that 1950

techniques of production were more productive than 1910 techniques by

about at least 32 percent and that producing the same amount of 1910

output with 1950 techniques would have saved about $10 billion in

input cost.

After Schultz, Griliches (1958), under the assumption of unitary

demand elasticity and a parallel shift to the right in the supply

curve by adoption of hybrid corn, estimated returns for the case of

perfectly elastic and perfectly inelastic supply curves, and obtained

the widely quoted 743 percent rate of return to investment in hybrid

corn research. Peterson, in his 1967 evaluation of poultry research,


assumed a proportional shift in the supply curve and, relaxing

Griliches' supply and demand elasticity restrictions, found a 21 to 25

percent annual internal rate of return to investment in poultry


Ayer and Schuh estimated a demand equation and a supply equation

for improved and unimproved cotton varieties in their evaluation of

the returns to research on cotton in Brazil. Employing a similar

approach as Ayer and Schuh, Akino and Hayami estimated the social

benefits of rice breeding research in Japan together with the

distributional effects of a rice import policy.

Scobie and Posada evaluated the impact of technical change on

income distribution in Colombian rice production by the CS-PS

approach. They looked at different categories of rice producers and

consumers in various income groups and concluded that while consumers

benefited most and producers suffered overall losses, small producers

lost the most. Widmer et al., directly estimated the supply function

of beef cattle in Canada with time series data. Lagged research

expenditures were included as explanatory variables, making it

possible to estimate the rate at which research has been shifting the

aggregate supply function through time. Direct estimation of the

supply function also permitted the estimation of research benefits at

the margin. After the supply curve was estimated a new hypothetical

supply curve was generated by adding small increments to the actual

research expenditures. Then the area between this supply function and

the actual supply function, below the demand function, constitutes the

gross benefit of this incremental expenditure. Comparison of this


gross benefit with the changes in the actual research expenditures

yielded an estimate of net benefits at the margin. Widmer et al.

found an average internal rate of return of nearly 66 percent and a

marginal rate of return of 63 percent on beef cattle research in

Canada. To eliminate the biases resulting from specific assumptions

about supply shifts and elasticities, Linder and Jarrett (1978)

provided a general formula for measuring research benefits. Rose and

Wise and Fell, in comments on Linder and Jarrett's paper, suggested a

kink in the supply curve to handle the assumption of linearity in the

demand and supply curves made by Linder and Jarrett in their analysis.

The direct estimation of the supply curve as in Widmer et al. can

overcome this problem of arbitrarily assuming the nature of shift,

since the shift through time can actually be estimated if research is

one of the explanatory variables (shifters) in the supply equation

estimated. The CS-PS studies have differed in specification of supply

and demand functions and in the nature of supply function shifts. The

nature of the shift assumed affects the distribution of benefits to

producers and consumers. Producers' benefits are smaller with

divergent shifts than with either parallel or convergent shifts

(Norton and Davis).

Norton and Davis (p. 690) also contend that:

The demand elasticity is also important because the more
inelastic the demand curve, the more likely producers will lose
following technical change. Also, if the supply elasticity is
absolutely larger than the demand elasticity, consumers will tend
to receive a larger share of the benefits than producers. In
addition, those technologies which do not directly displace labor
can do so indirectly as a result of a fall in the product price
if the demand elasticity is low.


The Widmer et al. study found a supply elasticity of beef cattle

with respect to research expenditure to be 0.36, and that resulted in

90 percent of the benefits going to producers with only 10 percent

going to consumers. Their study underscores the importance of the

supply and demand elasticities in the distribution of benefits among

consumers and producers. The importance of general equilibrium

effects on factoral income distribution was stressed by Binswanger

(1980); these have been ignored in CS-PS evaluation. The basic

flexibility of the CS-PS approach can be a liability if underlying

relationships and policies are not accurately reflected in the

analysis. This approach is best for aggregate analysis because it

aggregates all consumers and producers of a given product and looks at

only those two groups. There are many types of producers of a given

commodity -- small-scale farmers, large-scale farmers, landowners,

sharecroppers, and farmers with unmechanized and mechanized units. An

aggregate producers' surplus sheds little light on how research

affects each group. To better understand the distribution of benefits

and costs, it would help to gain insights into who would benefit and

who would lose within the producing and consuming sectors. Another

problem is that of determining the costs of research and development.

Since knowledge builds on knowledge, it is difficult to know how far

in the past to consider the costs which occurred to produce a given

shift in the supply curve.

Econometric Method

The econometric method involves specifying and estimating the

relationship between supply and R&D investments and then determining


the marginal rates of return to investments in R&D. The average rates

of return can also be measured as shown in the work of Widmer et al.

Further, this method can be used to assign parts of the return to

different sources, such as scientific research and extension advice,

education and conventional inputs. The statistical significance of

the estimated returns from research can be tested. In earlier studies

the most commonly used econometric models were the production function

(PF) and productivity index models. The theory of duality has made it

possible to employ the cost function to econometrically evaluate

returns to R&D (Stranahan and Shonkwiler). Stranahan (p. 18) contends


The production function model is usually used in
cross-sectional aggregate studies whereas the productivity
index is used most often with aggregate time series or
pooled data.

Griliches (1964) used the Cobb-Douglas production function

formulation in his pioneering work to analyze cross-sectional

aggregate data of the U.S. for the years 1949 to 1959. He found that

lagged public research and extension expenditures (the average of R&D

expenditures lagged one and six years) were both significant and

important sources of aggregate output growth. His estimation showed

the elasticity of production with respect to R&D to be about .06, and

implied a very high social rate of return of about 1300 percent to

investment in agricultural R&D. Even after adjusting for private

research expenditures and their contribution to aggregate agricultural

output he still estimated a 300 percent rate of return.

Peterson (1967), found a comparable output response and a gross

return of $18.52 per dollar of public research on poultry production


when he used a similar cross-sectional model. Assuming a ten-year lag

in the impact of R&D expenditures and treating private R&D allocations

as comparable to public R&D expenditures, he estimated a substantially

smaller internal rate of return of 33 percent.

Minasian in a non-agricultural study, analyzed the contribution

of R&D to value added in a cross-sectional study of the U.S. chemical

industry. He estimated a Cobb-Douglas function with value added as

the dependent variable and capital, labor, firm constants, a time

trend and the technology of the ith firm during time period t as

independent variables. Minasian estimated an elasticity of 0.11 for

R&D, resulting in a gross return of 54 percent on investments in R&D.

Applying the PF model to commodity groups, Bredahl and Peterson and

Norton estimated the marginal internal rate of return (MIRR) to each

of four commodity groups (cash grains, dairy, poultry, and livestock)

and suggested reallocating research dollars from relatively low to

relatively high payoff commodities so as to increase the overall rate

of return.

The productivity index approach is used in time series studies.

The use of a productivity index as the dependent variable avoids the

problem of high intercorrelation problems with time-series data for

conventional production inputs and the general lack of sufficient data

for the important conventional inputs (Norton and Davis). The change

in productivity index is a suitable indicator of the effect of

research on efficiency because it measures change in efficiency, not

change in farm income or prices (Evenson, Waggoner and Ruttan).

Evenson (1978) analyzed the relationships between productivity and


investment in (a) agricultural invention, (b) education, and (c)

research and extension. There were two distinct categories of

research -- science-oriented research and technology-oriented

research. Evenson divided the U.S. into geoclimatic regions and

attempted to isolate spillover effects of research between different

states. The spillover effects were estimated by interaction of south,

north and west variables with the technology-oriented research

variable. Technology-oriented research yielded a rate of return of 95

percent; science-oriented research yielded a 110 percent rate of

return for the period of 1927 to 1950. Evenson found that 55 percent

of the change in productivity attributed to technology-oriented

research from a typical state was realized within that state, with 45

percent being realized in other states with similar soils and climate.

The spillover from science-oriented research was considerably greater.

In the econometric approach, the R&D variable enters the model

as a distributed lag. Several factors influence the lag structure

between R&D investment and the resulting increase in technology.

These include the time lag between R&D and the actual invention of a

newer and more productive process (Griliches, 1980). Previous

investigators have assumed no or little lag and no depreciation. The

lag effect is accounted for, based on the nature of the sector, by

appropriately adjusting the marginal product or internal rate of

return associated with R&D (Bredahl and Peterson; Griliches, 1964).

Lags between R&D and the realized benefits tend to be shorter in

industries where R&D focuses on development and applied issues than in


industries where efforts focus on basic research. Basic research is

longer term and more uncertain (Mansfield).

Evenson (1967) first investigated the question of lags between

R&D and realized benefits econometrically with various R&D lag

structures. Using aggregate data for U.S. agriculture he found that

an inverted V distributed lag gave the best fit, with the peak

influence coming with an average lag of six to eight years and the

total effect dying out in about ten to sixteen years.

The econometric studies cited above have generally focused on

the effects of biological or technological improvements in farm

production techniques (i.e., evaluating production-oriented or

preharvest research). In response to growing interest in returns to

postharvest R&D, Stranahan and Shonkwiler evaluated the returns to

postharvest R&D in the Florida frozen concentrated orange juice

market. Because productivity and input quantity data were either

unavailable or more difficult to obtain, while cost and price

information was more accurate in the citrus processing subsector, a

cost function in conjunction with share equations was estimated. The

indirect cost function was specified as in the following equation:

C c(Y,P,Z), (2.1)

where Y is output, P is vector of input prices, and Z is quasi-fixed

input included in the production processes. They assumed that the firm

or industry minimizes cost of producing a given output Y, with respect

to input prices and the level of the quasi-fixed input Z, where Z may

characterize the state of technical progress, degree of learning, or

contain environmental or behavioral parameters. In earlier studies


Caves, Christensen, and Swanson employed Z as a short-run fixed factor

representing capital structures in a translog cost function.

Differentiating the indirect cost function with respect to Zi (2.1)

gives the negative of the shadow price of Z (Diewert; Lau).

aC(Y,P,Z)/aZi -Wi(Y,P,Z). (2.2)

At the margin, the total cost of producing Y, given the

cost-minimizing levels of input usage, will be reduced by an amount

equal to the implicit market value (or imputed value) of input Z. In

the citrus-processing subsector study Z was taken to be the average of

expenditures on citrus-processing research, lagged one and six years,

divided by the GNP implicit price deflator, lagged one and six years.

R&D can affect input usage neutrally or can bias input levels through

time depending on the magnitude of the parameter on research in the

share equations (Binswanger, 1974). Zero parameter values imply that

research impacts input usage neutrally through time. Thus the study

also investigated the effect of R&D on input usage and found that on

average, research has had a positive effect on labor and other input

usage and a negative effect on materials usage. The rate of return to

citrus research was found to be 57.4 percent, which is somewhat higher

than those rates calculated using the productivity index approach.

All the econometric studies discussed above used R&D

expenditures as the measure of research, with considerable variation

in specific items included. Some U.S. studies have used only

commodity-specific R&D expenditures by the state experiment stations

(e.g. Bredahl and Peterson) and some have used total R&D expenditures

by experiment stations, the USDA, the Soil Conservation Service, and


private research organizations (e.g. Cline and Lu). Others (e.g.,

Evenson and Kislev 1973, 1975, and Evenson, 1974) have used the number

of scientific publications as a proxy for research. R&D expenditures

were further separated into commodity-specific applied research and

noncommodity-specific applied, agriculturally-related basic research.

Evenson and Binswanger included separate variables to measure effects

of applied research and basic science-oriented research.


Motivation for a Simultaneous-Equations Approach

The various econometric approaches to evaluating returns to R&D

outlined in the literature review, though plausible in terms of

overcoming certain data and estimation problems, do not go far enough

in evaluating the returns to research. In general, the methodology

assumes R&D affects only the supply side. However, certain kinds of

research beyond the farm gate and perhaps even some production-

oriented research, can affect the demand for the commodity, for

example, if product quality is improved or if the research leads to

more effective use of expenditures for advertising and promotion.

Such payoff to research should not be overlooked in any evaluation of

returns to R&D. Another shortcoming of approaches based on profit and

value-added functions is that they break down when prices of output

can not be taken as fixed. Such a situation normally exists in an

aggregative approach to measuring returns.

These problems provided the primary motivation for employing a

simultaneous-equations model to evaluate returns to postharvest R&D

investments in the U.S. market for fresh-winter tomatoes from Florida

and Mexico. The nature of the problem is such that we can not apply a

restricted profit function because the assumption of exogenous output

prices is invalid. The two major producing areas are considered and



the action of each can affect the output price. Simultaneity in

inputs and outputs also precludes using a direct production function

methodology. The quantity supplied and demanded and the price are

jointly determined in the system, and such joint determination

suggests the need for a structural equations model.

The cost function approach could be employed since the output

price is not one of the arguments and the endogeneity problem could be

avoided however, the approach ignores any demand-side impacts of the

R&D. Also, these duality approaches cannot adequately address the

distributional effects of the R&D investment expenditure. These

latter effects can, to a limited extent, be evaluated within a market

clearing framework.

Model Specification

The market for fresh-winter tomatoes in the U.S. is represented

here by a set of four behavioral equations, an implicit price

relationship, and four identities. Behavioral equations on a per

capital basis are specified for the Florida shipping point supply, the

export supply from Mexico, a marketing margin equation for the U.S.

market and aggregate U.S. domestic demand at the retail level.

Identities are used to define the marketing margin, as well as the

weighted average shipping point price, and the aggregate supply in the

U.S. domestic market, and to state the market clearing conditions.

Annual crop supply responses have commonly been modeled by

specifying an acreage planted equation, yield per acre equation and

the actual total production or supply as the product of the two

(Shonkwiler and Emerson; Shonkwiler; Chern and Just; Brandt and


French; and Gutierrez). Alternatively, the Nerlove model in its basic

form or a modified version which treats acreage planted as a proxy for

physical output, has been employed to model crop supply responses.

However, the variables which affect acreage and yield are those

which affect the quantity supplied. In this study supply was

estimated directly rather than indirectly through acreage and yield.

Expected and actual output prices, and prices of inputs employed in

production, and other factors such as weather are examples of

variables that affect the decisions and final supply of the profit-

maximizing farmer. The period between planting and harvesting can see

drastic dislocations in market conditions facing farmers, and result

in seemingly radical harvesting decisions. In fresh-winter tomato

production, unharvested acreages can be abandoned if output price at

harvest is less than the cost of harvesting, packing and marketing at

the shipping point.

At planting time, farmers therefore gauge what output levels

would maximize their profits based on their past experiences, physical

and technical environment, expected output prices, current prices of

inputs used for production, and other market conditions. Their plans

may of course not be realized because of weather and the influences of

other exogenous forces.

Based on the above reasoning, the supply relationships for fresh-

winter tomatoes from Florida and the export supply from Mexico were

modeled as a straightforward relationship between the physical output

and the major economic and noneconomic factors believed to affect



The marketing margin for fresh-winter tomatoes is the result of

demand and supply forces for marketing services required to move

fresh-winter tomatoes to the retail market by distributors. It is

assumed that distributors are profit-maximizers in the competitive

fresh-winter tomato market and that they employ levels of marketing

services to achieve this objective. The marketing margin for fresh-

winter tomatoes was specified as a function of the per capital total

quantity shipped from Florida and Mexico, a price index of marketing

inputs, and the preharvest and postharvest R&D expenditures

appropriately lagged.

Following the tenets of demand theory (utility maximization

subject to budget constraint), the per capital demand for fresh-winter

tomatoes at the retail level in the U.S. was postulated to depend on

the retail price, U.S. per capital disposable income, prices of

substitutes at retail level, R&D expenditures "appropriately" lagged,

and expenditures on advertisement to promote fresh-winter tomatoes.

Research affects demand for fresh-winter tomatoes by improving product

quality and increasing shelf-life, among other things.

The general structural model was specified in the following


PCQFLt f(Plt*, DWRIt, IRit, Pit, FPlt Wlt, RDlt-i, PCQMEXt)

+ ult (3.1)

PCQMEXt f(DWR2t, IR2t, P2t, FP2t, W2t, RDlt-j

RD2t-j, MPCINCt, PCQFLt) + u2t (3.2)

MMt f(PCQSUSR, MCIt, RDlt-j, RD2t-j) + u3t (3.3)

MMt RPt WAPt (3.4)


RPt f(PCQDUSRt, RPSt, IncUSt, RDlt-i, RD2t-i,

ATOMt) + u4t (3.6)


The endogenous variables in this simultaneous equations system are


to the seven equations specified in (3.1) through (3.7), WAP was

computed using the definition of weighted average price, and P2 was

eliminated from the model with an implicit function of Pl. The

Florida FOB price and the Nogales price were highly correlated. The

rest of the variables in the system were assumed to be exogenously

determined. Definitions of the individual variables are:

PCQFLt per capital quantity of tomatoes offered for shipment in
pounds in Florida at time t;

Pit real expected price per pound of tomatoes in cents at time
t in Florida;

DWRlt real daily wage rate of labor in dollars used in
production of fresh-winter tomatoes at time t in Florida;

IRlt real interest rate charged farmers during planting time
(July through January) in Florida;

Pit real season average price per pound of tomatoes in cents at
the shipping point in Florida at time t;

FPlt real price of fertilizer in Florida in dollars per ton, at
time of planting;

Wit weather index for the winter tomato-growing region in

RDlt-i real R&D expenditures on farm level technology, in
dollars, "appropriately" lagged;

PCQMEXt export supply of tomatoes from Mexico through Nogales
in pounds per capital in the U.S. market at time t;


DWR2t real daily wage rate of labor used in production of
fresh-winter tomatoes at time t in Mexico, in dollars;

IR2t real agricultural interest rate at time of planting, in

P2t real domestic supply price in Mexico (approximated by the
real FOB price in Nogales Arizona) in cents per pound at
time t;

FP2t real price index of fertilizer used in production of
fresh-winter tomatoes at time t in Sinaloa, Mexico;

W2t average temperature in Mexico's tomato-producing region;

MPCINCt real Mexican per capital national income in dollars at
time t;

MMt marketing margin for fresh-winter tomatoes in the U.S. in
cents per pound at time t;

PCQSUSRt per capital retail level supply of fresh-winter
tomatoes in the U.S. at time t in pounds;

MCIt real price index of marketing inputs (labor,
transportation charges, packaging materials) employed in
moving tomatoes from the shipping point in Florida to the
retail market at time t;

RD2t-i real postharvest research expenditures on fresh-winter
tomatoes in dollars "appropriately" lagged;

RPt real retail price of tomatoes at time t in cents per pound;

WAPt weighted average shipping point price for fresh-winter
tomatoes shipped from Florida and Mexico in cents per
pound at time t;

RPSt real retail price of substitutes (green peppers) at time t
in cents per pound;

IncUSt real U.S. per capital disposable income at time t

ATOMt real expenditures on advertisement to promote fresh-
winter tomato consumption;

ult, u2t, u3t, u4t random error terms.

The grower level supply for fresh-winter tomatoes in the U.S.

market was obtained by adding the supply from Florida and the export


supply from Mexico. By adding the marketing margin to the grower

level supply the retail supply was obtained. The grower level demand

was obtained by subtracting the marketing margin from the retail

demand. Consumers' surplus (CS) and producers' surplus (PS) at the

equilibrium quantities and prices for the different levels (grower and

retail) were estimated from the resulting demand and supply equations.

The impact of R&D on CS and PS can be evaluated by differentiating CS,

PS or (CS+PS) with respect to R&D since the CS and PS relationships

will include R&D at the farm level and marketing level as explanatory

variables. The contribution of preharvest and postharvest R&D

investments to the surplus accruing to producers and consumers was

estimated using the demand and supply equations at both the grower and

the retail levels. Estimates were derived at the equilibrium prices,

and quantities; CS, PS, and (CS+PS) relationships were derived and

then differentiated with respect to the preharvest and postharvest R&D

variables. The distributional effects among producers and consumers

and the rate of return to R&D investments were also estimated. The

rationale for the specification of the variables in the above model is

discussed below.

Florida Supply

The farmer is assumed to act rationally, varying levels of inputs

with the ultimate objective of profit maximization. For agricultural

crop production there is a fixed biological lag between production

efforts and the final output. For fresh-winter tomato production the

time that passes between planting and harvesting is three to four

months. Thus planting decisions must be based on the price that


producers expect to receive at harvest time, the current costs of

inputs employed in production, and the interest rate observed at

planting time reflecting tl cost of capital used for tomato


As stated earlier, the farmer may be confronted with changing

market conditions after planting decisions have been made. Thus the

farmer has to make decisions at harvest time so as to maximize

profits. The decision to harvest and the yield level are therefore

based on the prevailing product price, the harvesting, packing and

marketing cost at the shipping point, and noneconomic factors such as

weather and technology. If the product price at harvest time relative

to the harvesting, packing and marketing cost is unfavorable, planted

acreage may be abandoned. The tomato plant can be destroyed by

freezing winter temperatures, or fruit setting can be inhibited,

thereby reducing yield. Improvement in technology such as development

of high-yielding disease-resistant varieties and improved cultural

practices (e.g., plastic mulching) can affect yields. R&D expenditure

variables help to explain variations of effects such as these. The

effect of weather on yield was accounted for by including a weather


Florida and Mexico are the only two major winter-tomato-

producing regions; thus the quantity shipped from one area will affect

the other. The per capital quantities shipped from each area were

therefore included in the other's supply response relationship and

were expected to have negative impact on the competing region's


Mexican Export Supply

Since the early 1960s the Mexicans have adhered to a planned

supply program (Fliginger et al.; Goldberg; Simmons et al.; Buckley et

al.). A description of this planned supply program was given in

Chapter I.

Some macroeconomic factors also have a bearing on the production

and shipment of tomatoes to the export market. For example, the

cyclical overvaluation of the peso which in turn affects the export

price and domestic input costs has not favored tomato production and

export. Devaluation of the peso may increase net returns for Mexican

tomatoes exported to the U.S. in the short-run because it raises the

price (in pesos) Mexican producers receive relative to costs.

However, imported input costs will increase and the advantages

initially provided by increased returns are thus reduced.

Based on the structure and conduct of the fresh-winter tomato

industry the export supply from Mexico is regarded as an excess supply

to meet U.S. excess demand. The U.S. excess demand for fresh-market

winter tomatoes is the difference between the aggregate quantity

demanded in the United States during December through June and the

quantity of fresh-market winter tomatoes produced in Florida. The

Mexican export supply is the difference between the domestic supply

and the domestic demand. Thus the Mexican export supply will be a

function of the variables that enter the domestic demand and supply

relationships. The export supply from Mexico was therefore specified

as a function of the Mexican daily wage rate; the interest rate

charged Mexican vegetable farmers; the price of fertilizer;


temperature during the growing season; the price of fresh-winter

tomatoes (which was approximated by the FOB price at Nogales since the

domestic price could not be obtained); the per capital disposable

income in Mexico; external factors such as U.S. R&D expenditures on

tomato technology "appropriately" lagged; and the quantity shipped

from Florida. Acreage planted in Mexico is allocated by the

government through the recommendations of the growers' Unions, and the

quantity actually exported is based on prevailing market conditions.

Therefore, the expected price at planting time does not enter the

export supply equation; it is the current price that explains export

supply. As mentioned in Chapter I, Mexican growers depend to a great

extent on progress in the United States for technical improvement.

Technological advances are mainly acquired from U.S. technicians and

consultants and from publications of universities in the U.S. and the

U.S.D.A. Many of these publications are translated and published by

the growers' association (Firch and Young). It is therefore

appropriate to include U.S. R&D expenditures on tomato production and

marketing technology in the Mexican export supply equation. The lag

structure of the impact of R&D investments may be the same for Mexican

producers as for U.S. producers since technology developed in the

U.S. is almost immediately available to Mexican producers because of

their association with U.S. agents. A weather variable is included to

account for the effect of weather on tomato yields.

Marketing Margin Between the Grower Level and the U.S. Retail Supply

Fresh-winter tomatoes go through a marketing channel from the

shipping points in Florida and Mexico to the final consumer at the


retail level. In this process distributors are providing marketing

services. It is assumed that these distributors behave in such a way

as to maximize their profits. The marketing margin, which is the

difference between the retail price and the grower level price

(represented here as the weighted average of Florida and Mexican

supply prices), reflects the demand for the marketing services. This

was therefore specified as a function of the per capital quantity

shipped from Florida and Mexico to the retail market, the cost of the

marketing services, and the preharvest and postharvest R&D

expenditures in the U.S. The grower level demand was then obtained by

subtracting the marketing margin from the retail demand equation.

The U.S. retail supply was estimated by first horizontally

summing the grower level supplies from Florida and the export supply

from Mexico and then vertically summing this result and the marketing

margin. There were no data available to adjust quantities supplied

for any losses which may occur between the grower and the retail


Demand in the U.S. Market

The basic theory underlying the specification of the retail

demand for fresh-winter tomatoes in the U.S. is the familiar one of

utility maximization (Henderson and Quandt; Silberberg). Fresh-winter

tomatoes are mostly consumed in salads with other vegetables. It is

therefore assumed the consumers of fresh-winter vegetables strive to

maximize the utility derived from consuming a bundle of fresh-winter

vegetables (tomatoes, cucumbers, lettuce, green peppers, celery,

carrots, etc.) subject to a budget. The resulting utility-maximizing


relationship expressed in price-dependent form is a function of per

capital quantity demanded, the retail prices of substitutes and

complements, the R&D expenditures on preharvest and postharvest

technology "appropriately" lagged, the U.S. per capital disposable

income and expenditures on advertising for the promotion of fresh-

winter tomatoes. The latter five exogenous variables are demand

shifters. R&D affects demand through improved techniques that enhance

or preserve the product quality at retail, which includes increased

shelf-life and improvements in palatability. Preharvest and

postharvest R&D variables are therefore included to capture these

effects on the demand for fresh-winter tomatoes. Advertising and

promotional campaigns are information-oriented and make consumers

aware of fresh-winter tomatoes and their nutritional value in diets.

Consumers' and Producers' Surplus Analysis

Shifts in supply and demand may occur at all levels in the

marketing channel due to production-oriented R&D investments and

marketing-related R&D investments on fresh-winter tomatoes. Estimates

of the effects on consumers' and producers' surplus were obtained at

the grower level as follows:

CS DG(Q) dQ PG*QG (3.8)

f(Q, R&D1, R&D2) dQ PG.QG

where DG(Q) is the grower level demand and (QG) and (PG) are the

market clearing quantity and price respectively. Holding all


exogenous variables with the exception of the research variables

constant at their means, the consumer surplus at the grower level is a

function of the preharvest and postharvest R&D expenditures with the

lagged effects discounted to the present time.

Similarly, on the supply side, by holding the exogenous variables

constant at their means with the exception of the research variables,

the producer surplus may be expressed as a function of the preharvest

and postharvest R&D expenditures and total surplus (CS + PS)

The discounted marginal rates of returns of R&D investments were

estimated by partially differentiating CS, PS, and (CS+PS);

and, estimates of the discounted average rates of returns to R&D

investments were obtained by comparing the total returns to the total

research expenditures.

By the same procedure as in equation (3.8), alternative estimates

of CS, PS and (CS+PS) at the U.S. retail market were estimated, and

the discounted marginal and average rates of returns to U.S.-based

preharvest and postharvest R&D investments were evaluated.


A partial equilibrium, simultaneous equations model was developed

in Chapter III for the fresh-winter tomato market in the U.S. during

the months of December through June. This chapter includes a

discussion of different price expectation models, the estimation

technique and the data set.

Modeling Expectations

An expected price variable appears in the supply response

equation for Florida. Because expectations are not directly

observable, additional information is needed. Several strategies for

providing additional information have been proposed to handle this

nonobservable variable and these include: rational expectations, simple

naive expectations, extrapolative expectations, Nerlove's adaptive

expectations and revisional price expectations.

The Rational Expectations Model

The rational expectations model was first introduced by Muth in

terms of market supply and demand relationships and maintains that

participants in the market act as if they were solving the supply and

demand system in forming their price expectations. Generally, the

rational expectations interpretation of the expected price, Pt is the

mathematical expectation of Pt given all information (It-l) available

when the expectation is formed, i.e., Pt E(PtlIt-l). In a



structural econometric model this information consists of the

predetermined variables and the model's reduced-form parameters

(Wallis). Thus the model can be solved for the expected price as a

function of the expected values of the exogenous variables. This

function can then be substituted into the model, leading to a

specification which contains the original endogenous and exogenous

variables plus the expected values of the exogenous variables. In

general, following this substitution, the model will be highly non-

linear in the parameters and also have parameter restrictions across

equations. Thus a system method of estimation would be most

appropriate since a limited information method of estimation will be

less attractive because of the cross equation restrictions (Shonkwiler

and Emerson). Time series analysis is utilized to generate the

necessary forecasts of the exogenous variables.

Naive Price Expectations Model

Naive or static expectations define expectations of the current

period price as the previous period's price, i.e.,

Pt* Pt-1 (4.1)

This model has a rich history in economic analysis and has comprised

the basis for the cobweb model used in the analysis of commodity cycles

in agriculture. An advantage is that information required is simple to


Extrapolative Expectations Model

Extrapolative expectations require a longer time-series for the

variable in order to "extrapolate" how the variable changes over


time, (Moore and Meyers). There are several specifications under this


a. linear time-trend

Pt* a + bt-l (4.2a)

b. exponential growth curve

Pt* aert-1 (4.2b)

c. auto regressive trend

Pt* -a + bPt.I +....+ bpPt.p (4.2c)

Adaptive Expectations Model

The adaptive expectation model was developed by Marc Nerlove on the

premise that:

farmers react to expected price and this expected price
depends only to a limited extent on what last year's price
was (Nerlove, p. 498).

Adaptive expectations can be represented as:

Pt* P-l* b(P1 Pt-l*) 0 < b s 1 (4.3)

and stated as the revision in the expectation of Pt is proportional to

the error made in the forecast of Pt-1. We can represent adaptive

expectations as an infinite weighted-average of previous levels of the

variable, with the weights declining geometrically as the lag length


Pt bPt-I + b(l-b)Pt-2 + b(l-b)2Pt-3 + - (4.4)

Nerlove's adaptive expectations model can be empirically applied

to the case of one explanatory variable rather easily. However, when

there are several explanatory variables, the estimation procedure of

the reduced-form equation becomes complex, and the number of degrees

of freedom is reduced (Nerlove and Addison; Chern and Just).


Revisional Price Expectations Model

The revisional price expectation model which appeared in the

literature only recently reflects the situation wherein the beginning

period price expectation may be revised once during the production

process (Taylor and Shonkwiler). The other models of price

expectations outlined above are conditioned by the information

available when the production decision is made. Such definitions of

expectations are perhaps appropriate if the measure of supply is

planted acreage, a fairly common practice in agricultural supply

studies (Askari and Cummings; Shonkwiler and Emerson). However, if

supply measures are in terms of physical output (e.g., supply of

livestock or total crop production), the amount actually harvested will

depend on prevailing market conditions, thus price expectations

conditioned by the information available when the production decision

is made may be inadequate. For example, the number of pickings of

fresh vegetables or the weight at which livestock should be marketed

can all be influenced by the information acquired subsequent to the

beginning of the production period. The sequential nature of

agricultural production processes thus affects the way supply prices

are imputed. Under the assumption that additional information can be

utilized to improve the accuracy of formulating price expectations,

Taylor and Shonkwiler defined a price expectation consistent with

intended production and marketing decisions which allows unobserved1

1 It should, however, be noted that this information is not directly
observable in the data but is observed by producers (Taylor and
Shonkwiler, p. 289).

information to be utilized in obtaining a measure of price expectations

formulated by producers.

Following Taylor and Shonkwiler (pp. 289-290), let Ot-l+a be:

the information set available to the economic agent at the time t-
1+a. The a parameter being constrained on the closed interval
[0,1] indexes the information which becomes available subsequent
to period t-l up to and including period t. If the main
components of the information set are prices, a revisional
expectation may be defined by Pt' Et-l+a(PtlQt-l+a). This
revisional expectation is the conditional expectation of Pt given
information available at time t-l+a. Since a is contained in the
closed interval [0,1], the realized price Pt (a-1) and the
beginning period expectation Pt* Et-l(Ptllt-l) (c-0), are
special cases of the revisional price expectation.... If a-0, the
imputed price which yields the observed output as optimal is the
beginning period price expectation. This would imply that the
major response of supply to price rests with the decision to
commit a given set of resources to production. Conversely, if
a-1, observed price is the optimizing supply price with the
implication that economic responses in supply occur primarily
through marketing decisions.

Given the assumption that additional information can potentially

improve the ability of the economic agent to conjecture what the actual

price will be, the revisional expectation may be expressed in an

empirical framework as:

Pt' aPt + (1 a)Pt* ae[0,1] (4.5),

where Pt denotes the actual price obtained in period t and Pt* denotes

the expected price conditioned by information set available at time


Thus revisional price expectation is here defined as a convex

combination of a beginning period expectation and the observed price.

The weights assigned to the beginning period price expectation and the

observed price in imputing the optimal supply price will depend on this

value of a. If a is unconstrained and can take on any positive value

in the real number system the revisional price expectation will be an


affine combination of the beginning period price and the observed


Estimates of the Model Parameters

The highly commercial and concentrated nature of the fresh-winter

tomato industry may produce a situation more conducive to the use of

rational expectations by producers (DeCanio). Also the competition

between Florida and Mexican growers and the information collection and

dissemination service of the Florida Tomato Committee suggest that

growers take important supply and demand forces into account when

making production decisions at planting time. Thus the rationally

expected prices are informed predictions of future events and are

assumed to be based on the underlying economic forces. These forces

would be consistent with those described by appropriate economic theory

(Muth). Shonkwiler and Emerson, were able to implement the rational

expectations hypothesis in a two simultaneous equations model of fresh-

winter tomato-imports and supply. However, we could not implement

the rational expectations hypothesis in our model of four equations

because of limited observations. A revisional price expectation was

finally adopted after considerable efforts to use the rational

expectations approach.

Preliminary estimation using different lag structures

(geometrically and linearly declining lags, second-degree Almon lag and

the inverted V) and different lag lengths of the two R&D expenditure

variables were tried. These trials provided a basis for specifying the

lag length and structure for the preharvest and postharvest R&D

expenditure variables in the model estimated.


The lag structure between R&D investments, which is a proxy for

the resulting increase in technology and the subsequent impact on

output, is influenced by several factors. These factors include: the

time lag between R&D expenditures and the development of a new variety

or production process; between research and commercial development and

adoption of the technique or variety; and the depreciation rate of the

new technology.

In the agricultural sector, technology depreciates because of the

biological environment. The lags between R&D investments and the

realized benefits in agriculture will thus vary with the type of

technology forthcoming from the research and the commodity involved.

Evenson (1967) found the impact of R&D on aggregate agriculture was

best described by an inverted V lag with a mean lag of 5 to 7 years.

Lags of longer lengths have been used. There is evidence that quite

long lags, at least 30 years, must be allowed if it is hoped to capture

all of the impact of research on agricultural output (Pardey and

Craig). A very long series of data would be required to measure the

impact of research with such long lags in benefits. The present value

of benefits in the distant future would be low.

Lags of 4,5,6, 7, 8, 9, 10 and 11 years for the R&D expenditure

variable, following a second-degree Almon polynomial with zero end-

point restrictions, were tried in the preliminary runs of the model

with the two different price expectation models (i.e., the naive price

expectation and the revisional price expectation). Lags of 6, 8 and 10

years following the inverted V lag with zero end-point restrictions

were also tried. The revisional price expectation was implemented by


including both the current and lagged prices in the supply equation

(i.e., beginning period expectation was taken to be the price lagged

one period) and then restricting the sum of their coefficients to be

between 0 and 1; i.e., a convex combination of the two prices (Taylor

and Shonkwiler). The coefficient estimates for both the current price

and the lagged price were negative. The model was reestimated without

any restrictions on the current and lagged price coefficients (i.e.,

affine combination of the two prices). The input prices and output

price were also deflated by the interest rate, i.e., homogeneity of

degree zero was imposed on the Florida and Mexican excess supply

equations. The parameter estimates of the deflated current and lagged

price were positive as expected. A 10-year lag following a second-

degree Almon polynomial-distributed lag was believed most appropriate

for the preharvest research expenditure variable affecting the supply

in Florida. An 11-year lag following a second-degree Almon polynomial-

distributed lag had the smallest estimated standard error relative to

the respective estimated coefficient for both the preharvest and

postharvest research expenditure variables affecting the Mexican excess

supply, the marketing margin and the retail demand in the U.S.

Generally the impact of research on output could be described by

the following lagged relationship:

Yt a + bOXt + blXt.- + + bkXt.k + Ut, (4.6)

where Yt is a measure of output at time t and Xt.i i 0,1,......,k

the values of the R&D expenditures during the current and past k years

respectively. Ut is the disturbance term which satisfies the usual

assumptions (Kelejian and Oates). A degree-of-freedom problem and


multicollinearity would be encountered if the model were estimated as

specified in equation (4.6)). The Almon and the inverted V lag both

provide ways to reduce the number of parameters to be estimated. The

Almon lag assumes that the pattern of the impact of R&D on output (the

b's in equation (4.6) follow a polynomial which shows that the b's are

expected to increase at first and then decrease. In this study the

impact of R&D on output was approximated by a second-degree polynomial,


bi +0 + ali + a2i2 i 0,1,....,k, (4.7)

where ao, al and a2 are constants to be determined. If we replace the

b's in (4.6) by their expressions in (4.7), we have:

Yt a + a0Xt +(a0 + al + Q2 )Xt-l +(aO +2al + 4a2)Xt-2 + ...(4.8)

+ (aO +kal + k2a2)Xt.k + Ut.

Rearranging terms in (4.8) gives us:
k k k
Yt a + 00 X Xt-i + l0 ZiXt-i + a2 Zi2Xt-i + Ut. (4.9)
i-0 i-1 i-1
To simplify further, define
k k k
Zlt Xt-i., Z2t ZiXt-i and Z3t Ei2Xti. (4.10)
i-0 i-1 i-1
(4.10) is substituted into (4.9) to give:

Yt a + a0Zlt + alZ2t + a2Z3t + Ut. (4.11)

This equation can be simplified by assuming b-1 and bk+1 are zero

(zero-end point restrictions), i.e., now

i -1, 0, 1, m, m+1 and

b-1 aQ al + a2 0 and

bk+l a0 + al(k+l) + a2(k+l)2 0.

These expressions can be solved in terms of a0 and al and substituted

back into (4.11) to eliminate two parameters, i.e.,

(k+2)al + a2[(k+1)2 1] 0

al -a2 [(k+1)2 1]/(k+2) Q2B

=0 a2 [-[(k+l)2 1]/(k+2) -1] a2A

Yt a + a2AZit + a2BZ2t + a2Z3t + Ut (4.12)


Yt a + a2[AZlt + BZ2t + Z3t] + Ut (4.13)

Yt a + a2Zt + Ut. (4.14)

After estimating (4.14) 0o and al are obtained from the relationships

above, then estimators for the b's are obtained as follows:

bo a0 (4.15)
bl 00 + 1a + "2
b2 a0 + 2al + 402

bk a0 + kal + k2a2.

The inverted V lag was suggested and used by DeLeeuw. The technique

assumes zero end-point restrictions and an even lag length. That is,

for an even lag length k, bo 0 and bk 0. Then

bi ib for 0 s i s k/2 (4.16)

(k-i)b for k/2 s i s k.

Substituting these values into (4.6), we get

Yt bZt + Ut (4.17)

k/2 k
Zt Z iXt-i + Z (k-i)Xt-i.
i-0 (k/2)+l


After estimating b from (4.17) and using (4.16) one can obtain

estimates of bi.

Estimation Method

The model was estimated in the linear form and the natural logarithmic

form. The model in the natural logarithm form was estimated by non-

linear two-stage least squares (NL2SLS) using all the exogenous

variables in the system as instruments. The marketing margin and

retail demand equations which contain a nonlinear variable (InQSUSR)

were estimated by Amemiya's (1974) nonlinear two-stage least squares

estimator, where the instruments are low-order polynomials of all the

exogenous variables in the system. A second-degree polynomial of all

the exogenous variables was used. For all the other equations the

instruments were all the exogenous variables in the system. There was

a degree-of-freedom problem with the nonlinear approach due to the

fact that the number of observations was fewer than the number of

parameters in the second-degree polynomial used in the first stage of

the estimation of the marketing margin and retail demand.

The linear model was estimated by linear two-stage least squares

and as a system by 3SLS. The system of equations contain endogenous

variables as explanatory variables and since there could be correlation

of the stochastic disturbance terms across structural equations because

of the simultaneous nature of the model, these endogenous variables

would be correlated with the stochastic disturbance terms across

equations. The 3SLS uses estimated information on the correlation of

the stochastic disturbance terms of the structural equations from 2SLS

residuals in order to improve asymptotic efficiency. The 3SLS


estimates are consistent and are asymptotically efficient but are

recognized as being sensitive to specification errors which may exist

in the model. The results using 2SLS were more consistent with

expectations than those obtained with 3SLS -- perhaps due to

sensitivity to specification errors.

Data Sources

Mexican Growing Season Temperature

The major production of fresh-winter tomatoes in Mexico occurs

around Culiacan, which lies on latitude 250N and longitude 80W, and

Los Mochis, lying between latitude 250 30'N and longitude 820 12'N in

the State of Sinaloa; thus the average temperature data that should

enter the model would be that prevailing in these areas during the

growing season. The closest location from which temperature data were

available was for Guadalajara, lying between 270N and 760 30'W. These

average temperature data in degrees Fahrenheit were obtained from the

U.S. National Weather Data Center.2

Real Agricultural Interest Rate in Mexico

The data on interest rate charged farmers in Mexico were obtained

from various sources. The figures for 1964-1970 were obtained from

Commission Nacional Bancaria, Boletin Estadistico Secretaria de

Hacienda Y Credito Publico, Mexico 1964-1970 and those for 1971-1984

were obtained from FIRA, Banco Nacional de Mexico. The interest rate

was then deflated by the CPI in Mexico to give the real agricultural

interest rate. The CPI data for Mexico were obtained from the

International Monetary Fund, International Financial Statistics (1964-

2 Paul Dyke provided diskettes containing temperature data.


1984). The Mexican agricultural interest rate was very highly

correlated with the interest rate charged farmers in Florida, so the

U.S. interest rate was used in place of the Mexican interest rate in

the Mexican supply equation to reduce the number of exogenous variables

in the model.

Mexican Rural Daily Wage Rate

The Mexican rural daily wage rate data for the 1964/65-1980/81

seasons were obtained from Gutierrez, and for the 1981/82-1983/84

seasons from Buckley et al. These were deflated with the Mexican CPI

for the season to give the real Mexican rural daily wage rate.

Quantity Shipped from Mexico and the FOB Price in Mexico

The quantity shipped for the 1964/65-1983/84 seasons (December-

June) in millions of pounds were obtained from various issues of the

Florida Tomato Committee, Annual Report. The FOB price is the

weighted average price per pound for generally good quality tomatoes,

including duty and crossing charges at Nogales, Arizona. These were

also obtained from various issues of the Florida Tomato Committee,

Annual Report and were deflated by the CPI to give the real FOB price.

The FOB price was used as a proxy for the Mexican domestic supply price

since the domestic price could not be obtained. The Mexican FOB price

was very highly correlated with the Florida FOB price, therefore the

latter was used in the Mexican export supply equation; i.e., an

implicit relationship among these two prices was used to eliminate an

endogenous variable from the Mexican export supply equation.


The total quantities shipped were divided by the U.S. total

population as of July 1 of each year to obtain the per capital quantity

shipped to the U.S. The U.S. population data were obtained from

U.S.D.A. Statistical Bulletin No.713.

Mexican Fertilizer Price Index

The indices of fertilizer prices for Mexico were obtained from the

World Bank through personal communication.

Real Per Capita National Income in Mexico

Personal income data were not available for Mexico. Consequently,

Mexico's national income deflated by Mexico's CPI and the population

were used in the Mexican export supply equation. Data were obtained

from the U.N. Department of International Economic and Social Affairs,

Monthly Bulletin of Statistics (1965-1984).

Mexico's Population

Mexico's mid-year population for each year was used. The population

data were taken from the U.N. Department of International Economic and

Social Affairs, Monthly Bulletin of Statistics (1965-1984).

Per Capita Quantity Shipped from Florida and FOB Price

The total quantity shipped from Florida in million of pounds for

the 1964/65-1983/84 seasons (December-June) and the seasonal weighted

average shipping-point price, or FOB price, for generally good-quality

tomatoes were obtained from various issues of the Florida Tomato

Committee, Annual Report. The CPI for all commodities in the U.S. for

each season were obtained from various issues of the Survey of Current

Business and used to deflate the FOB price to give the real deflated


FOB price in Florida. The total quantities shipped from Florida were

divided by the total U.S. population to give the per capital quantity


Florida Real Daily Wage Rate

The Florida real daily wage rate was obtained by multiplying the

hourly wage rate for field workers during the first week in October of

each year by 8 and then deflating by the CPI for all commodities. The

labor wages for 1966-1981 were obtained from Gutierrez; the daily wage

rate for 1983 was obtained from Buckley et al. The wage rates for

1964 and 1965 were obtained from U.S.D.A. Farm Labor, 1964, 1965.

There were no data available for 1982 and 1984. The missing values

were filled by running a simple regression of the log of data against

time with intercept (i.e., InWRt a + rt). The estimates of a and r

were then used to forecast the missing values of the wage rate.

Real Agricultural Interest Rate for Florida

The interest rate charged tomato farmers was represented by the

interest on non-real-estate debt which was obtained from U.S.D.A.

Statistical Bulletin No.740. The interest rate was then deflated by

the U.S., CPI for all commodities to give the real interest rate.

Florida Growing Season Weather

The weather variable for Florida was represented by the number of

days below freezing at Homestead. The largest production of fresh-

winter tomatoes in Florida occurs in the Dade County area and the area

around Immokalee in Collier County. Since winter production is

concentrated in the southern part of the state, freezing temperatures

in Homestead should provide a good proxy for cold weather in the


growing area. Number of days below freezing point was selected because

of the devastating effect of freezing temperatures on the tomato plant

and consequently on the production. The Florida weather data were

obtained from various issues of the U.S. Weather Bureau, Climatological

Data, Monthly and Annual Summary Florida Section.

Research Expenditures

Much of the preharvest agricultural research expenditures data were

obtained from the Current Research Information Service (CRIS) of the

U.S.D.A. Preharvest research expenditures for 1953-1964 and 1970-1984

were obtained from this source. Some preharvest research expenditures

for 1976 to 1984 were obtained from the Florida Tomato Exchange.

Postharvest research expenditures for 1970-1984 were obtained from CRIS

and the Florida Tomato Exchange. Some postharvest research expenditures

on fresh tomatoes in Florida were obtained from Inventory of

Agricultural Research of SAES Forestry Schools, Research Agencies of

the U.S.D.A. Vol.11 (Tables II,III,IV) 1966-1983 and from various

issues of Funds for Research at State Agricultural Experiment Stations

CSRS-U.S.D.A. Postharvest research expenditures from these sources

were determined by looking at the Research Problem Area Classification

Code. There are different classification codes for different research

activities ( i.e., production, breeding, efficient marketing activity,

quality improvement and consumer acceptance activities). The missing

values for the preharvest research expenditures from 1965-1969 were

obtained by a simple regression of the log of the current expenditures

on the log of the expenditures lagged one period with no intercept


(i.e., InR&Dt alnR&Dt-l). The estimate was then used to forecast the

missing values.

The research expenditure figure for 1965 was obtained from this

simple model; the model was run again with the 1965 estimated missing

value as a new data point and a new estimate for the coefficient (a)

was obtained and used to forecast the value for 1966. This stepwise

procedure was repeated until all the missing values were obtained. The

figure for 1970 was forecasted by this procedure and the forecasted

value was compared with the actual figure for 1970. The ratio of the

actual to the forecasted value was about 0.40 which was then used to

scale all the forecasted values for the other years.

The preharvest research data for 1953 to 1964 were for vegetable

research in general and not specifically for tomatoes. The amount

devoted to tomato research was obtained by multiplying the research

expenditures times the ratio of the total value of fresh-winter

tomatoes to the total value of vegetables produced in Florida. This

ratio was crosschecked by finding the proportion of fresh-tomato-

related research projects among all vegetable research projects in

Florida, from various issues of the Florida Agricultural Experiment

Station, Annual Reports. This proportion was almost the same as the

ratio of the value of fresh tomatoes to the value of all vegetables in

Florida (about 0.35). The research expenditures for 1961-1964 showed

a big jump in spending between this period and the earlier period

(1953-1960). Considerable effort was made to attempt to smooth the

data across this apparent flaw in the data. However, the resulting

smoothed data gave results with several estimated coefficients


inconsistent in sign. As a consequence, the original preharvest

research data were used in the final estimation of the model.

The preharvest and postharvest research expenditure data series

were then deflated with the U.S. agricultural research deflator series

constructed from factor level price indices weighted with time varying

weights which capture the shifting factor mix of research spending by

the State Agricultural Experiment Stations (SAES) (Pardey et al.).

Many analytical studies of agricultural research have deflated the R&D

expenditure figures with single-price indices based on the implicit GDP

deflator and have assumed all of the appropriate price series move as

one. Generally, total research expenditures have been deflated by a

salaries-based price series; some have used the federal implicit GDP

deflator and others the CPI

Most of the other commonly-used deflator series use two expenditure

categories, labor and nonlabor, with either fixed or variable index

weights. These single factor price index deflators have tended to

overstate or understate the amount of research expenditures. In this

study the deflator used was a four factor research deflator constructed

by Pardey et al. The four factors in the deflator are: labor expenses,

operating expenses, expenditures for land and building, and

expenditures for equipment. The deflated research expenditures were

used to construct series of varying lag lengths. These series were

then used in the trial runs of the model to specify the length of lags.-

Total Quantity Supplied at U.S. Retail Level

The total supply at the U.S. retail level was obtained by summing

the quantity shipped from Florida and Mexico and then dividing by the


total U.S. population as of July 1 of each year to get the per capital

retail supply. Data on marketing losses were not available to adjust

the series.

Real Retail Price (RP)

The retail price for fresh-winter tomatoes in cents per pound were

obtained from U.S.D.A. Fresh Market Vegetables Statistics 1949-80 and

later issues. Prices were deflated with the U.S., CPI for all


Retail Price of Substitutes

The retail price in cents per pound for green peppers, which were

treated as a substitute for fresh tomatoes, was obtained from U.S.D.A.,

ERS-Statistical Bulletin No.688, and U.S.D.A., Fresh Market Vegetable

Statistics, 1949-80, and later issues. These prices were also deflated

with the U.S., CPI for all commodities.

Real Cost Index for Fresh Fruits and Vegetables

The retail cost index for marketing fresh fruits and vegetables was

obtained from U.S.D.A. Statistical Bulletin No.713.

Data on expenditures for advertisement and promotion of fresh-winter

tomatoes were obtained from the Florida Tomato Exchange. U.S.

disposable income data were obtained from the U.S. Department of

Commerce, Survey of Current Business. These were deflated with the

U.S., CPI and the total U.S. population to estimate the real per

capital disposable income.

Florida Fertilizer Price

Florida fertilizer prices in dollars per ton were obtained from

U.S.D.A., Statistical Bulletin No.750.


Weighted Average Price at the Grower Level

A weighted average price series at the grower level was constructed

by multiplying the quantities shipped from Florida and Mexico by the

respective FOB prices for each season and then divided by the total

quantity shipped from the two supply areas. This weighted average

price was then subtracted from the retail price, which is also a

weighted average price, to obtain the marketing margin.

The final data set used is presented in appendix A.


The model was fitted to data for the 1964/65-1983/84 seasons

(December-June). Table 1 shows the 2SLS parameter estimates for the

model in linear form. These were used in the final analysis and are

discussed below. N2SLS parameter estimates for the model in log form

and 3SLS parameter estimates for the model in linear form are reported

in appendix B, tables B.1 and B.2 respectively. There were more

instruments than number of observations for the first stage of the

N2SLS estimation and therefore there was a linear dependency in the

estimation of the instrument for the quantity supplied at retail


Florida Shipping-Point Supply

Parameter estimates for the Florida shipping-point supply all

carry the signs suggested by theory, except the deflated fertilizer

price (deflated with the interest rate charged farmers in Florida),

which was positive instead of negative. The deflated wage rate had a

negative impact on supply as expected. The deflated current price

parameter was positive (1.055), i.e., an elasticity of supply with

respect to deflated current price of 0.698. The deflated lagged price

parameter estimate was 0.037, which translated into a long-run

1 The expected sign is shown in parentheses by the name of the
variables in column 2 of Table 1.


Table 1 2SLS Structural Parameter Estimatesa

Equation Variable Coeff. t- Elast.
Estim. Stat.

Florida Shipping
Point Supply
(per capital

intercept(- +)

wage rate(-)



-0.499 -0.291 -0.315


number of
days below
point in

current price(+)

lagged price(+)

per capital
quantity from

-0.166 -1.097







-0.935 -3.117 -0.752

R&D expenditure

Mexican Export


wage rate(-)

fertilizer price(-)














Table 1 cont.

current price(+)

average growing-
season tempera-

per capital quant.
from Florida(-)

per capital
national income(-)

R&D expenditures

R&D expenditures







-3.265 -1.148

-0.227 -0.763






Marketing Margin

intercept(- +)

per capital
quantity at

cost index(+)

-6.118 -0.297

-0.074 -0.071

-0.114 -0.033

Table 1 cont.
R&D expenditures
t(+) 3.747 1.446
t-1(+) 6.870 1.446
t-2(+) 9.369 1.446
t-3(+) 1.242 1.446
t-4(+) 12.492 1.446
t-5(+) 13.116 1.446
t-6(+) 13.116 1.446
t-7(+) 12.492 1.446
t-8(+) 11.242 1.446
t-9(+) 9.369 1.446
t-10(+) 6.870 1.446
t-ll(+) 3.747 1.446

R&D expenditures
t(+) 3.796 2.544
t-l(+) 6.960 2.544
t-2(+) 9.491 2.544
t-3(+) 11.389 2.544
t-4(+) 12.654 2.544
t-5(+) 13.287 2.544
t-6(+) 13.287 2.544
t-7(+) 12.654 2.544
t-8(+) 11.389 2.544
t-9(+) 9.491 2.544
t-10(+) 6.960 2.544
t-ll(+) 3.796 2.544

U.S. Retail intercept(+-) 5.981 0.407
US retail per capital -1.768 -1.011 -6.320
price) quantity at

price of 0.115 0.732 0.777
green peppers

per capital 0.101 0.127 0.052
US disposable

expenditures 0.297 1.151
on advertising
to promote

Table 1 cont.
R&D expenditures
t(+) 3.956 4.895
t-1(+) 7.253 4.895
t-2(+) 9.890 4.895
t-3(+) 11.868 4.895
t-4(+) 13.187 4.895
t-5(+) 13.846 4.895
t-6(+) 13.846 4.895
t-7(+) 13.187 4.895
t-8(+) 11.868 4.895
t-9(+) 9.890 4.895
t-10(+) 7.253 4.895
t-11(+) 3.956 4.895

R&D expenditures
t(+) 4.351 4.000
t-l(+) 7.976 4.000
t-2(+) 10.877 4.000
t-3(+) 13.052 4.000
t-4(+) 14.502 4.000
t-5(+) 15.227 4.000
t-6(+) 15.227 4.000
t-7(+) 14.502 4.000
t-8(+) 13.052 4.000
t-9(+) 10.877 4.000
t-10(+) 7.976 4.000
t-11(+) 4.351 4.000

a. Expected signs of coefficients are indicated by the
b. Deflated with the interest rate.


elasticity of supply with respect to price of 0.722. These results

suggest that current price carries more weight than the lagged price

in supply decisions. From an economic standpoint, this suggests that

supply response to price occurs primarily through yield variations

rather than planting decisions in the case of fresh-winter tomatoes.

This result can be interpreted as the revisional price expectation,

where price expectations formed at the beginning of the production

period (lagged price is beginning period expected price) do not affect

shipping decisions considerably. As more information becomes

available price expectations are being revised, resulting in current

price carrying most of the weight regarding supply decisions. The

weights to be attached to the beginning period expected price and the

current price were not restricted to the interval (0,1) before

estimation, as in Taylor and Shonkwiler, it could be any value on the

real positive number system, i.e., an affine combination of the

planting time and marketing time price.

The preharvest research variable entered the Florida supply

equation as a 10-year second-degree Almon polynomial-distributed lag.

Coefficient estimates had the right signs, with the impact rising to a

peak and then declining. The elasticity of the total undiscounted

impact was (0.277). Increases in the per capital quantity shipped from

Mexico were associated with a decline in the Florida supply as

expected. A 1 percent increase in per capital quantity shipped from

Mexico was associated with a 0.752 percent decline in the per capital

quantity shipped from Florida.


The weather was proxied by the number of days below freezing in

Homestead, the major winter-tomato producing area. Thus, this

variable was expected to have a negative impact on supply since tomato

plants are quite sensitive to freezing temperatures.

Mexican Export Supply

The Mexican supply specified as an excess supply relationship has

as arguments production input prices, output price, demand-related

variables (e.g., per capital income), per capital quantity shipped from

Florida, and the preharvest and postharvest R&D expenditures on tomato

research in Florida. The FOB price in Florida and Mexico were highly

correlated, as were the U.S. and the Mexican agricultural interest

rates. As a consequence, the Florida FOB price and the U.S. interest

rate were used in the Mexican export supply equation. As in the

Florida supply equation, output price and input prices on the supply

side of the Mexican market were relative to the interest rate. The

parameter estimates for the daily wage and fertilizer price, both

relative to the interest rate, were positive 5.131 and 0.167,

respectively. Since interest costs are an important component of

cost, it is not clear whether these signs are inconsistent; however,

the estimate of the coefficient for the wage rate is opposite in sign

to that estimated in the Florida supply equation. The impact of

temperature on supply was negative (-0.092), which was inconsistent

because rises in temperature between the ranges of 650F and 850F are

conducive to tomato production. The average temperatures were

observed in the low 60s. The tomato plant does best in moderately

dry areas with temperatures ranging between 650F and 850F. Foliage


diseases are induced by high temperature coupled with humidity (Ware

and McCollum) but high temperatures were not observed in Mexico.

The parameter estimate for the supply price was 1.153 with a

small standard error. The lagged price was not specified to enter the

supply relationship because the Mexican government imposes

restrictions on acreage planted, so beginning period price

expectations of farmers is not an important factor in planting

decisions. The parameter estimate for per capital national income was

negative (0.227) as expected, because an increase in per capital

national income will result in increased domestic consumption and,

since tomato is a normal good, less for export. The parameter

estimate for the per capital quantity shipped from Florida was negative

(-0.924), with a small standard error, and consistent with theory.

Since the quantities shipped from Mexico are to meet the U.S. excess

demand, they were expected to be negatively associated with quantities

supplied from Florida.

The estimated coefficients of the preharvest and postharvest U.S.

based R&D expenditure variables in the Mexican export supply equation

represented by an 11-year second-degree Almon polynomial-distributed

lag were negative. Implying the U.S. based R&D investments had

negative impact on export supply, which is inconsistent with

expectation. Considering the fact that much of the technology

employed in the production and marketing of fresh-winter tomatoes in

Mexico comes from the U.S., one would expect a positive impact on

Mexican supply and consequently on the excess supply. However, since


Mexico controls shipments based on quantities shipped from Florida,

the effect may be theoretically indeterminant.

Marketing Margin

The parameter estimates for the marketing margin equation all had

the expected signs except the marketing cost index represented by the

price of marketing services. Tomek and Robinson define the marketing

margin as the price of a collection of marketing services, which is

the outcome of the demand for and the supply of such services. Hence

higher input prices for a service ceteris paribus would result in a

decrease in supply and a higher margin. It is therefore expected that

the estimate for the parameter for the marketing cost index should be

positive in sign. The estimated coefficient was (-0.114) with a large

standard error (3.480), indicating the marketing cost index did not

significantly affect the marketing margin. The per capital quantity

shipped had an estimated parameter of (-0.0743), with a large standard

error (1.051), indicating nonsignificant impact on the marketing

margin. From a conceptual point of view, this sign may be positive or


Preharvest R&D investments increased supply at the farm level

thereby increasing demand for marketing services to move the produce

to the retail level. This will increase the price of the marketing

services and thus the marketing margin. There should therefore be a

positive relationship between the preharvest R&D expenditure variable

and the marketing margin. The parameter estimate for this variable

was positive (0.312), with a standard error of (0.216). The

postharvest R&D parameter estimate in the margin equation was positive


(0.316), with a standard error of (0.124). This sign is consistent

with expectations since it was believed that research in postharvest

activities increases the number and level of services in the marketing

channels and hence the margin.

U.S. Retail Demand

The retail demand parameter estimates all had the expected signs.

The estimated own price elasticity of demand was (-6.32) and falls

within the upper range of elasticities obtained in previous studies.

The demand price elasticities in previous studies varied from -0.181

(Hamming and Mittelhammer) to -0.79 (Shonkwiler and Emerson) to -1.07

and -3.25 to -5.5 (Simons and Pomareda) and -6.4 (Firch and Young).

As in Shonkwiler and Emerson, the price of substitutes was

proxied by the price of green peppers and this variable had an

estimated coefficient of (0.115) or an elasticity of (0.777). A

positive elasticity of less than 1 between the retail price of fresh

tomatoes and its substitute, green peppers, is consistent with Buse's

conclusion that the elasticity of the price of good "j" with respect

to changes in the price of good "i" is usually positive and less than

1 for substitute commodities. The elasticity of demand with respect

to real per capital disposable income was positive but near zero

(0.052). Fresh tomatoes are a normal good and one would expect its

demand to increase as income increases, though one would expect a

stronger effect on retail demand than was estimated. The preharvest

R&D expenditures variable, which was represented by an 11-year second-

degree Almon polynomial-distributed lag in the retail demand, had a

positive impact which is consistent with the earlier argument that


some preharvest research will affect the demand since breeding

programs and cultural practices to produce tomato fruit of good

quality, taste and longer shelf-life would be expected over time to

increase the demand. The postharvest R&D expenditure variable, which

is geared toward preservation and improving the quality in the

marketing process, would impact demand positively. This variable was

also represented by an 11-year second-degree Almon polynomial-

distributed lag and the parameter estimates all had the correct signs.

Lastly, the impact of advertisement and promotional activity on

the retail demand of fresh tomatoes was positive (0.279) as expected

because advertisement and promotion are supposed to increase the

demand for fresh tomatoes. However, the estimated effect was quite


Measuring Returns to Research

Estimates of parameters reported in Table 1 were used to define

supply and demand functions at the grower and retail levels. The

lagged effects of the preharvest and postharvest R&D variables were

discounted at a real rate of 4 percent to obtain the present value of

the impact of the research expenditures. The discounted, lagged

effects of the research expenditures are reported in table 2. The sum

of the discounted, lagged effects were then used in place of the

undiscounted research expenditure variable coefficient estimates in

the model.

The Florida shipping-point supply function was added to the

Mexican excess supply function to give the grower level supply

function. The supply of fresh-winter tomatoes at the retail level is

Table 2. Discounted Values of R&D1 and R&D2 Impacts on the Florida
Supply, Mexican Export Supply, Marketing Margin and U.S.
Retail Demand (at a real discount rate of 4 percent)

R&D1 R&D2

Year FL Mex. Market. U.S. Mex. Market U.S.
Margin Margin

t 0.392 -0.451 3.748 3.956 -1.180 3.796 4.351
t-l 0.686 -0.794 6.606 6.974 -2.080 6.692 7.669
t-2 0.890 -1.042 8.662 9.144 -2.727 8.775 10.056
t-3 1.014 -1.202 9.995 10.551 -3.147 10.124 11.603
t-4 1.067 -1.284 10.678 11.272 -3.362 10.817 12.396
t-5 1.055 -1.297 10.781 11.381 -3.394 10.921 12.516
t-6 0.986 -1.247 10.366 10.943 -3.264 10.501 12.034
t-7 0.867 -1.142 9.493 10.021 -2.989 9.616 11.020
t-8 0.704 -0.988 8.215 8.672 -2.586 8.322 9.537
t-9 0.501 -0.792 6.582 6.949 -2.072 6.668 7.642
t-10 0.265 -0.558 4.641 4.900 -1.461 4.702 5.388
t-ll -0.293 2.434 2.570 -0.766 2.466 2.826

8.428 -11.089 92.200 97.331

-29.027 93.398 107.038


the supply at the grower level plus the marketing cost expended to

move them to the retail level; and the marketing cost is the marketing

margin. Thus the retail level supply was obtained by adding the

marketing margin to the grower level supply.

There was a very high correlation between the Florida FOB price

(which was used in both the Florida supply and Mexican excess supply

equations) and the weighted average grower level price. A simple

linear regression of the Florida FOB price on the weighted average

price was run without an intercept, resulting in a coefficient

estimate of 0.9282 with a t-statistic of 33.034 for the weighted

average price. This simple linear relationship between the Florida

FOB price and the weighted average price was substituted for the FOB

price in the grower level supply equation. This resulted in a

weighted average price in both the marketing margin equation and the

grower level supply equation, i.e., the same grower level price in

both equations. When the marketing margin was then added to the

grower level supply the weighted average price dropped out, leaving

the retail price in the retail supply equation.

The demand at the grower level is a derived demand for the raw

product less the demand for marketing services; thus the marketing

margin was subtracted from the retail demand for fresh-winter tomatoes

to give the grower level demand. Holding all other variables in the

model constant at their means, except the weighted average grower

level price, the total quantity supplied at the grower level and the

preharvest and postharvest research variables, the grower level and

retail level supply and demand equations were:

WAP -7.8123 + 0.9449PCQSUSR + 0.5566RD1 + 13.1046RD2 (5.1)
(grower level supply)

WAP 17.7811 1.6941PCQSUSR + 5.1313RD1 + 13.6401RD2 (5.2)
(grower level demand)

RP -14.14 + 0.8706PCQSUSR + 92.7562RD1 + 106.5028RD2 (5.3)
(retail level supply)

RP 11.4534 1.7684PCQSUSR + 97.3309RD1 + 1007.0383RD2 (5.4)
(retail level demand)

Equations (5.1) to (5.4) were used to derive the consumers' and

producers' surplus relationships at the grower and retail levels in

the U.S. These surplus measures were used to estimate the benefits of

research on tomatoes.

The approach used was to estimate the effect of changing the

level of R&D expenditures and then letting the full effect work itself


Grower Level

Equations (5.1) and (5.2) were solved for the equilibrium

quantity and price at the grower level as:

PCQSUSRE 9.6981 + 1.7335RD1 + 0.2029RD2 and (5.5)

WAPE 1.3515 + 2.1946RD1 + 13.2963RD2 (5.6)

Following the procedure in (3.8) the consumers' and producers' surplus

relationships at the grower level were obtained as follows:

CSG 79.668 + 28.4801RD1 + 3.3339RD2 + 2.5453RD12 +

0.0349RD22 + 0.5959RD1RD2 (5.7)

PSG 44.4357 + 15.8854RD1 + 1.8588RD2 + 1.4197RD12 +

0.0194RD22 + 0.3323RD1RD2 (5.8)


Differentiating (5.7) and 5.8) with respect to R&D1 and R&D2 we obtain

the change in the consumers' and producers' surplus at the grower

level per unit change in these variables.2 These derivatives were

evaluated at the mean values of the R&D1 and R&D2 expenditures for the

period 1965-84.

Retail Level

Following a procedure similar to that used for the grower level,

the retail level consumers' and producers' surplus relationships were

obtained by first solving equations (5.3) and (5.4) for the

equilibrium quantity and price as follows:

PSQSUSRE 9.6981 + 1.7335RD1 + 0.2029RD2 (5.9)

RPE -5.6969 + 94.2667RD1 + 106.681RD2; (5.10)

and, then, by using equation (3.8) the consumers' and producers'

surplus relationships at the retail level were obtained as:

CSR 83.1631 + 29.7168RD1 + 3.4652RD2 + 2.6547RD12 +

0.0361RD22 + 0.6191RD1RD2 (5.11)

PSR 40.9405 + 14.6488RD1 + 1.7284RD2 + 1.3104RD2 +

0.0182RD22 + 0.3092RD1RD2. (5.12)

By differentiating (5.11) and (5.12) with respect to R&D1 and R&D2 the

per unit change in the consumers' and producers' surplus with respect

to these variables at the retail level was obtained. These first

derivatives were then evaluated at the means of the research


2 1 unit for R&D1 $10 million and 1 unit for R&D2 $1 million.


The rate of change of the surpluses with respect to a one unit

change in R&D expenditures in cents per capital3 are reported in

Table 3. Estimates of the marginal rates of returns to R&D

investments in the fresh-winter tomato industry are reported in

Table 4. These were obtained by adjusting the values in Table 3 by

the U.S. population and units of research expenditures ($10 million

in the case of preharvest and $1 million in the case of postharvest).

Using estimates at the retail level, marginal rates of return to

R&D investments indicate that for every additional dollar of

investment made in preharvest R&D on tomato research, a gross return

of $10.85 was realized by society, of which $3.58 or 33 percent

accrued to distributors and growers, and $7.27 or 67 percent to U.S.

consumers. Similarly, an additional unit of investment made in

postharvest R&D on tomato research yielded a gross return of $12.70

to society (table 4). The percentage distribution of these returns

between producers and consumers was nearly identical to that for

preharvest research. Thus, benefits from both preharvest and

postharvest research investments on fresh tomatoes were estimated to

accrue mostly to consumers as a group. Economic theory would suggest

that to maximize surplus, additional dollars of research should be

added until the present value of marginal return was $1. The

estimates indicate that additional dollars of both preharvest and

postharvest research are needed to reach the social optimum.

3 The grower and retail level prices were in cents per pound and
the quantities were measured on per capital basis, so the
surpluses were in cents per capital.


Table 3. Rate of Change of Surplus with Respect to a One Unit Change
in R&D Expenditures at the Retail Level (cents per capital)

Preharvest R&D (1 unit-Sl mil.) Postharvest R&D (1 unit-Sl mil.)
Change Change Change Change Change Change
in in in in in in
total producer consumer total producer consumer
surplus surplus surplus surplus surplus surplus

4.52042 1.4926 3.0278 5.2918 1.7611 3.5306


41 tW

00 w
0 0 0

4) 0

0 w

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Sc4 z c
0 :1 1
w 41 > 41 1 0 <1

1 >w w-
a0 4 C 0
0-1 0 41
0 > 0

C >
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to- 4-4 30W 0

r-C -3 Q
041 41 0 CN

o >C

0 00
20 X


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0 0 40

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A0 C 1

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d) 0.4 o r 4 c

4) B in 0 0 3


4 4 A

4) 4


Estimates of the net present value of average rates of returns to

preharvest and postharvest research investments on fresh winter

tomatoes are presented in table 5. They show higher rates of return

on average to postharvest research than preharvest and indicate that

society is being very well rewarded for its research investments in

both preharvest and postharvest research. These values were obtained

by evaluating equations (5.11) and (5.12) at the means of the

research expenditures and adjusting for population and the units of

research expenditures.

It had been hoped to measure the impact on Mexican producers

(spillover effects) of U.S.-based preharvest and postharvest research

investments, however, the model did not permit separate estimation of

benefits on the Mexican side.






0 0

0 4)




4 )
u 0




0) U


4) M

4) 4J



4 U
4) 41 0
> 4) W
co wu



Considerable effort has been devoted in the past to evaluating

returns to R&D investments in agriculture and manufacturing. Most of

these studies, however, have been directed at production level R&D

investments, with little emphasis on postharvest and marketing-related

R&D investments. Lately there has been an increased interest in

measuring the returns to postharvest R&D investments.

The studies that have been done thus far have largely ignored the

impact of both preharvest and postharvest R&D expenditures on the

demand side. They tend to focus on the impact on productivity and

cost saving. Producers' and consumers' welfare analyses have been

done assuming shifts in the supply curve and supply elasticities

resulting from the R&D-induced productivity and cost changes. The

supply shift is the net effect of a combination of factors, including

R&D expenditures. Thus, by attributing the shift in supply only to

R&D expenditures leads to overestimation of the benefits of research

investments. The impact of R&D investments needs to be separated from

that of other factors. Also, the returns have often been expressed in

terms of internal rates of return, which does not reveal much about

the distribution of benefits. Impacts on producers and consumers

provide useful information to policymakers.



This study has attempted to address these problems by specifying

a simultaneous equations model which encompasses a shipping-point

supply equation for tomato producers in Florida, a Mexican export

supply equation, a marketing margin equation and the U.S. retail

demand equation for fresh-winter tomatoes. Both preharvest and

postharvest R&D expenditures entered the retail demand equation, the

marketing margin equation and the Mexican export supply equation.

This specification provides a basis for measuring the impact of

research expenditures on demand. It also enabled estimation of the

separate impact of research expenditures on supply and demand.

Supply and demand elasticities were also estimated as well as the

nature of shift in the supply curve, in the analysis of consumers' and

producers' welfare.

The model was estimated in linear form by 2SLS, by nonlinear 2SLS

in log form and by 3SLS. The 2SLS estimates were used in estimating

the benefits from pre and postharvest R&D. The research expenditures

entered the estimated model as 10- and 11-year Almon polynomial-

distributed lags. The supply price was a combination of current and

lagged prices reflecting the sequential nature of supply decisions,

i.e., the decision to plant and then the decision to harvest and

market. The model was fitted to seasonal (December-June) winter-

tomato data from Florida and Mexico from 1965-1984. The parameter

estimates were then used to define both grower- and retail-level

supply and demand equations. The grower-level supply was the sum of

the Florida and the Mexican export supply equations; the grower-level

demand was obtained by subtracting the marketing margin from the


retail demand. The retail supply was obtained by adding the marketing

margin to the grower-level supply.


The estimates of some of the structural parameters were not consistent

with the expected sign, and estimated standard errors of some were

large relative to the size of the coefficient estimated. Most

parameter estimates in the Florida shipping-point supply equation had

the correct signs, but a number of them had large estimated standard

errors, indicating a weak impact on supply. However, important

variables such as current own price, Mexican shipments and the

research variables had quite significant influence on the supply. The

Mexican excess supply equation had several coefficient estimates which

seemed incorrect in sign and had large standard errors. The research

variables had negative signs in the Mexican excess supply equation and

these results reduced the total impact of research variables in the

final equations used in the analysis. Key variables such as the

supply price and the shipments from Florida were very significant,

however. In the marketing margin equation all coefficients had the

correct signs but the per capital quantity and marketing cost index had

very weak impact. The parameter estimates for the research variables

were significant. Overall, the retail demand equation had much

sounder parameter estimates than all the others. Per capital income

and the price of substitutes seemed from the results to have the

weakest influence on retail price. The research variables coefficient

estimates were quite significant.