Abstract

Fresh produce growers/shippers believe that consolidations in grocery retailing may

empower retailers to act less competitively. This study evaluates the extent to which

retailers exercise market power in buying from growers and selling to consumers. Sales

data for retail chains in six U.S. metropolitan markets are used along with data on

grower prices for an analysis on apples, grapes, oranges, and grapefruit. The evidence

varies by commodity, but does consistently point to the exercise of market power by

retailers in consumer sales; less support is found on buying market power. Market power

varies over time and with produce volume. 

Keywords: Supermarket, grower-shippers, lettuce, bagged salads, tomatoes, market

power, oligopsony, oligopoly, switching regression model, fresh produce.

1Morrison School of Agribusiness and Resource Management Arizona State University.

This report was prepared under a research contract from the

Economic Research Service. The views expressed are those of the

authors and not necessarily those of ERS or USDA.

United States

Department

of Agriculture

www.ers.usda.gov

Electronic Report from the Economic Research Service

September 2003

Contractor

and

Cooperator

Report No. 1

Competition in Fresh Produce

Markets

An Empirical Analysis of Marketing

Channel Performance

Timothy J. Richards and Paul M. Patterson1
Contents

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iv

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Benefits of Retail Consolidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Evidence of Imperfect Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Buying and Selling Market Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Perishable Versus Semi-Perishable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Objectives of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

Describing Price Formation in Semi-Perishable Produce Markets . . . . . . . . .3

Importance of Understanding Price Dynamics . . . . . . . . . . . . . . . . . . . . . . .3

Three Critical Pricing Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

Existing Studies on Price Formation in Agriculture . . . . . . . . . . . . . . . . . . .3

Symmetry of Price Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

Causes of Price Fixity at Retail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

Summary of Preliminary Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

Fundamental Question: Do Retailers Have Market Power? . . . . . . . . . . . . . . .8

Rivalry in Semi-Perishable Produce Markets . . . . . . . . . . . . . . . . . . . . . . . .8

An Economic Model of Tacit Collusion Among Retailers . . . . . . . . . . . . . .8

Implications of Dynamic Model of Rivalry . . . . . . . . . . . . . . . . . . . . . . . . .9

Example of Discontinuous Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Empirical Test of Imperfect Competition in Semi-Perishable Produce . . . . .11

Empirical Implications of Trigger Model of Tacit Collusion . . . . . . . . . . .11

Data Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Sample Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Data Sources and Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Interpretation of the Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

Market Power in Grower and Retail Markets . . . . . . . . . . . . . . . . . . . . . . .14

Washington Apples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

Apple Commodity Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

Apple Retail Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Probability of Collusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Impact of Shipment Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Summary of Apple Market Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

California Fresh Grapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Grape Commodity Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Grape Retail Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Impact of Shipment Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

California Fresh Oranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Orange Commodity and Retail Markets . . . . . . . . . . . . . . . . . . . . . . . . .18

Impact of Sales Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Florida Fresh Grapefruit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Grapefruit Commodity and Retail Markets . . . . . . . . . . . . . . . . . . . . . . .19

Impact of Sales Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Summary of Market Power Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

ii ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
Conclusions and Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

Technical Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

Appendix 1. Econometric Model of Tacit Collusion . . . . . . . . . . . . . . . . . .27

Appendix 2. Finite Mixture Estimation of Switching 

Regressions Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

Appendix 3. Parameter Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● iii
Executive Summary

● Fresh produce growers, shippers, and their trade

organizations are concerned that the wave of mergers among grocery retailers may reduce the competitiveness of the retail grocery industry - both on the

buying and selling sides.

● This study represents a comprehensive analysis of

retailers’ ability to set noncompetitive prices in the

fresh apple, table grape, fresh California orange, and

Florida grapefruit markets in both their commodity

purchases and retail sales. In addition to evaluating

retailers’ price setting ability, we also evaluate other

dimensions of price performance, including where

in the marketing channel the price is set, the extent

to which changes in price are transmitted through

the channel, and the extent to which retailers hold

retail prices fixed.

● The data used in this analysis consist of two years

(1998 and 1999) of weekly retail-scanner price and

sales data from six major geographically dispersed

metropolitan markets-Albany, Atlanta, Chicago,

Dallas, Los Angeles, and Miami. Within each market,

most major retail chains are represented in the data.

At the shipper level, our data consist of shippingpoint prices and volumes obtained from either the

USDA or individual commodity commissions. These

data are supplemented with data from a variety of

other sources to account for transportation costs, marketing costs, and variations in factors that are critical

to the demand or supply of each commodity.

● Preliminary analyses of the retail and shipping-point

price data find that: (1) prices for semi-perishable

fruits are formed at the shipping point; (2) retail

prices respond more rapidly to shipping-point price

increases than to declines, although this result was

less significant for apples than for the other commodities; (3) retail prices are fixed relative to the

variation that occurs at the shipper level. These latter two results are consistent with retailers’ possessing some control over prices in both the commodity

and retail markets, while the first suggests that

retailers determine the price they pay for fruit before

they set the price they charge to consumers.

● If retailers are able to charge noncompetitive prices

to consumers, or pay noncompetitive prices to growers, then there must be some way that they agree

among themselves, albeit tacitly, to not undercut

each other in consumer markets nor outbid each

other in product markets. We test for such agreements using a statistical model of fresh fruit pricing

based on the reasoning that rival retailers use price

thresholds (trigger prices) to instigate punishments

for those who cheat on price maintenance agreements. We estimate this model by using an approach

that allows for the possibility that prices do indeed

follow a “step-like” path over time, where retail

prices (shipper-level prices) fall (rise) during periods

of punishment and then return to the collusive path

once order is restored. 

● The results vary by commodity. For apples, we find

evidence of both buyer and seller power that is both

statistically and economically significant in virtually

all market / chain pairs. For fresh grapes, we find

strong evidence of retailers’ ability to set price in

consumer markets, but little support of this same

power in input markets. Retailers also appear to possess a considerable degree of control over the prices

consumers pay for oranges, but little control over

grower prices. Grapefruit buyers exercise a significant degree of buying power in roughly 60 percent

of the sample cases, but consistently set imperfectly

competitive prices in the output market. 

● Retailer power to set prices in both input and output

markets tends to fall with the amount of commodity

sold. We interpret this as evidence that periodic promotions serve as facilitating mechanisms for the tacitly cooperative agreement followed by rival retailers. This conclusion is supported by the fact that the

frequency of punishments is similar to the frequency

of these promotional periods and by our observation

that some chains exhibit imperfectly competitive

behavior, while others do not.

● Future research in this area should focus on areas of

specific and emerging concern among government

antitrust officials, consumer groups, and grower

associations. Specifically, data on off-invoice fees

should be gathered by appropriate government oversight agencies. 

iv ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
Introduction

Benefits of Retail Consolidation 

In 50 years, the prolonged stock market boom of the

1990s will be remembered for many things, not least

of which is the crest of the largest wave of merger and

acquisition activity in history. Virtually every sector of

the economy experienced massive consolidation as

companies used inflated share values as currency in

buyout after buyout. The retail grocery industry was

no exception. Between 1996 and 1999, there were 385

mergers in the grocery industry and the acquired firms

in these transactions had over $67 billion in annual

sales. Whereas the top eight grocery firms had a

national market share of 26 percent in 1987, their proportion of total grocery sales rose to 37 percent by

2000. In general, shareholders applauded each transaction and awarded consolidation with higher and higher

valuations, firmly believing management’s claims of

unlocking greater efficiencies in purchasing and a

larger presence in retail markets. However, few consider exactly what these “efficiencies” mean for suppliers upstream and consumers downstream from the

merged retailers. If produce retailers truly are reaping

efficiencies as a result of these mergers, then society

as a whole is better off as produce will sell for less and

stores will find that they must keep a stock of the bestquality produce or risk losing customers. However, if

consolidation facilitates imperfectly competitive

behavior, then the economic performance of the fresh

produce marketing channel may indeed be impaired. 

Evidence of Imperfect Competition

Evidence of such poor performance is, however, difficult to come by. It is now commonly recognized

among economists that a certain industry structure

does not necessarily imply a particular mode of conduct, nor a given level of performance when benchmarked against the competitive ideal (Geroski).

However, because structure is more readily observable than either conduct or performance, it is necessary to have methods of obtaining evidence from

available data that are widely accepted, rigorous, and

consistent with the way in which prices and other

decision variables are generated in the real world.

Although anecdotal evidence of unfairness nearly

always arises when an outcome is subject to negotiation and relative bargaining strength, such evidence

hardly provides a sufficient basis upon which to justify intervening in an otherwise free marketplace. The

weakness of anecdotal evidence is particularly apparent when a bargaining situation does not necessarily

result in observable outcomes, such as market prices

or shipment-orders, but rather side-payments or

incentives that are maintained as proprietary corporate information. Consequently, it is necessary to

apply statistical methods of acquiring evidence from

data that are readily observable in order to assess the

competitiveness of a given industry.

Buying and Selling Market Power 

Unlike traditional agricultural commodities such as

grain, cotton, or cattle, fresh fruits and vegetables are

generally not used as inputs to further processing by

their buyer. Rather, because the channel is commonly

more direct between the grower-shipper and the ultimate consumer, deviations from perfectly competitive

behavior may appear on either (or both) of two levels:

on the supplier/buying side or on the output/retail selling side.2 In either case, market power may be evident

in either prices that are higher (lower) to consumers

(shippers) than in competition or through some form

of a rent extraction mechanism such as side or offinvoice payments. While evidence of the former lies in

readily observable market prices, evidence of the latter

tends to be of a weaker, anecdotal form. Indeed, one of

the most important implications of this work is that if

government antitrust agencies are truly concerned with

these practices, they need to develop some method of

acquiring the appropriate data on their use. With

regard to the former question, however, pricing strategies by produce buyers are likely to depend critically

upon the nature of the specific commodity in question.

Perishable Versus Semi-Perishable 

If retailers with market power can either offer noncompetitive prices or offer competitive prices but with

some form of off-invoice payment expected from the

grower, then we must examine the motives and posit

the likelihood of both strategies if real-world pricing

data are to have any resonance. Because a buyer’s

incentive to pay competitive per-unit prices and levy

an off-invoice fee (the latter strategy) rises the more

responsive is supply to price changes, we expect to see

imperfectly competitive or monopsony pricing the less

responsive is industry supply. Clearly, with a relatively

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 1

2 Typically, 43 percent of fresh produce is marketed directly from

growers to retailers; larger retailers (those with annual sales greater

than $1.5 billion) may obtain 66 percent of their supplies directly

from growers.
fixed (inelastic) supply, retailers can reduce the prices

they pay by a relatively large amount before suppliers

are no longer willing to bring their goods to market. If

supply is highly responsive (elastic), on the other

hand, then a similar pricing strategy will mean that

retailers are left with little to sell to consumers and

their total profit falls accordingly. 

In fact, the distinction between elastic and inelastically

supplied fruits and vegetables underlies the two distinctly different modeling strategies that appear in

other studies of imperfect competition in fresh produce

markets (see also Sexton, Zhang, and Chalfant).

Whereas we are more likely to see evidence of some

degree of monopsony pricing among the highly perishable commodities (tomatoes and lettuce, for example),

the opposite is true for goods that are semi-storable

and, hence, more elastic in supply.3 Apples, oranges,

grapefruit, and table grapes can each, to a differing

extent, be kept on hand until prices are more favorable.

In this case, buyers may be more likely to offer competitive prices, but then extract producer profits

through some form of a fixed fee. From a social perspective, this outcome is more desirable than the first

because consumers are not deprived of a commodity

that they would have otherwise bought at market

prices. Empirical evidence of either competitive or

noncompetitive pricing in fresh produce is, however,

virtually nonexistent. 

Objectives of Study

We hope to determine whether retailers are able to

exercise market power in either their produce buying

or selling activities. Because produce markets typically

differ substantially on the basis of both geography and

commodity, our empirical example considers a number

of products and retail markets. Namely, we examine

the markets for apples, grapes, fresh oranges, and fresh

grapefruit in six regionally disparate retail markets -

Albany, Atlanta, Chicago, Dallas, Los Angeles, and

Miami. Prior to describing the logic underlying the

empirical approach we apply, however, the report

begins with a consideration of three key issues in any

analysis of commodity pricing: (1) the locus of price

determination, (2) the symmetry of retail price adjustment to upward and downward farm price movements,

and (3) the “fixity” of retail prices. These issues concern exactly who “sets” fruit prices in the U.S. and

how responsive they are to changes in underlying

forces of supply and demand. This section also

describes in some detail the data used in this study,

and the possible limitations it presents for the study of

market power. 

The next section uses the results of this preliminary

data analysis to develop an economic model of retail

and grower-level fresh fruit pricing that allows for the

possibility that retailers exercise market power in both

their buying and retail selling activities. By allowing

the degree of market power to vary with supply, we

test hypotheses regarding the relative importance of

scarcity and retailer marketing strategies such as category management and periodic price promotions. 

The report concludes by drawing some implications

for the conduct of retail buyers and suppliers of fresh

fruit. This section also identifies some of the key

issues that remain to be resolved in understanding the

efficiency with which produce prices are formed and

whether or not retail concentration—if it, in fact, contributes to the exercise of market power—is necessarily to be feared on the basis of pricing evidence alone.

2 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

3 As a reviewer notes, the relationship between storability and elasticity is not one-to-one, but it is clear that on a weekly basis suppliers have far more alternatives for their output if it is potentially

storable, exportable or otherwise withheld from the market.
Describing Price Formation in

Semi-Perishable Produce

Markets

Importance of Understanding 

Price Dynamics 

Understanding the way prices are formed in an industry first requires thorough knowledge of both the institutions that surround the price formation process and

the price dynamics that arise as a result. With respect

to retail produce sales, marketers both at the retail and

shipper levels are becoming increasingly sophisticated.

As a result, they are relying less and less on open markets and arms-length transactions to buy and sell fruit,

and are instead developing institutions that reflect the

greater efficiencies and certainty of longer term trading relationships, such as contracts, preferred-supplier

agreements, and participation in automatic inventory

replenishment systems. In fact,

56 percent of all produce shippers used retail contracts

for at least 10 percent of their shipments in 1997

(McLaughlin et al.). Whereas fundamental issues of

price determination and causality were once thought to

be well understood, they are less clear now with the

proliferation of various retail pricing strategies driven

by category management, efficient consumer response,

periodic promotions, or everyday-low-price policies.

Central to the development of any model of retail and

supplier price determination, therefore, is an understanding of how pricing strategies influence how, and

where, prices are determined.

Three Critical Pricing Issues 

There are essentially three issues to be determined: (1)

the locus of price determination, (2) the symmetry of

price determination from the locus to the market, and

(3) the ability or apparent tendency of prices to adjust

to fluctuations in supply and demand, or to move

toward equilibrium. Empirically, the locus of price

determination is found indirectly, by inferring from the

co-movement of prices at different levels of the marketing channel the direction of causality. If price is

determined at the shipper level, then shipping-point

prices cause retail or wholesale prices and vice versa. 

Commonly, tests of causality are used for this purpose

and, in general, tend to show that prices are formed in

the middle market. However, with the declining importance of the traditional middleman and transactions

increasingly conducted between buyers for large

regional grocery chains and large, vertically integrated

grower-packer-shippers, the locus of price discovery is

not only uncertain, but is likely to be changing over

time. Because this study investigates the performance of

the entire marketing channel, the locus of price discovery is of more than notional interest, with implications

for the well being of producers and consumers as well.

Existing Studies on Price Formation 

In Agriculture 

Given the current low rate of inflation, growers fear that

retailers’ inability to pass cost increases onto consumers

will mean that shipping-point prices will reflect higher

marketing costs by being pushed below competitive levels. This fear depends upon where prices are first

formed, or the “locus of price determination.” Among

empirical studies, this locus of price discovery is not

necessarily found to be at the shipper level as is commonly assumed. In fact, Hahn shows that price discovery

in beef and pork markets can occur at either wholesale

or retail. Similarly, Wohlgenant and Mullen show that

retail beef prices do not “cause” or lead to farm prices in

a statistical sense, so the retail level cannot be the point

of discovery. Ward argues that price discovery occurs at

the level that is best able to assimilate information

regarding either changes in demand or supply. 

Because the wholesale sector tends to have fewer 

firms than either the farm or retail sectors, the cost of

obtaining price information is lower and information

moves within firms more readily than between them

(Salop and Stiglitz), so price discovery is more likely

to occur at wholesale. Ward finds support for this argument using data on farm, wholesale, and retail prices

for a group of fresh vegetables. Heien, on the other

hand, finds that wholesale and retail prices are independent for apples, tomatoes, and lettuce, but influence each other for canned tomatoes and fresh orange

juice. These indeterminate results for fruits and vegetables are supported by Lamm and Westcott, who find

shipper and retail produce prices to be independent.

However, Bernard and Willett’s study of price spreads

in the broiler industry provides support both for

Ward’s theoretical and empirical results. Others, such

as Powers, Wohlgenant and Clary, and Pick et al.,

instead merely assume that farm prices drive retail

prices. Pick et al. do not even consider wholesale citrus prices because, as is the case for many fruits,

retailers buy directly from shippers and do not use

wholesalers. Understanding who is responsible for

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 3
determining prices is a logical starting point for further

investigation into how efficient the price determination

process is, and how competitive the result may be.

Symmetry of Price Adjustment 

Another indirect indicator of the competitiveness of

price adjustment is whether upward and downward

price movements at the locus are translated to the

other market with equal speed and completeness. The

speed with which retail prices adjust to price changes

originating at the shipping point is often interpreted as

an indicator of either retailers using their control over

price to temporarily widen margins, or of the competitiveness of the retail sector. For example, Pick et al.

provide evidence of lags of up to 3 weeks for retailers

to adjust to farm price changes, while Ward finds no

lag in tomato price adjustment. Others find evidence of

significant adjustment lags in dairy products

(Kinnucan and Forker), lettuce (Powers), groups of

food products (Heien), frozen orange juice

(Shonkwiler and Taylor), beef products (Wohlgenant;

Schroeder and Goodwin; Bailey and Brorsen), broilers

(Bernard and Willet), and rice (Brorsen et al.).

If there are indeed significant costs of adjusting retail

prices in response to upstream changes in supply or

demand, or if prices are inherently uncertain and

retailers have irreversible investments in maintaining

price points (Dixit and Pindyck), then these lags may

be perfectly consistent with a competitive equilibrium.

Many, however, interpret such behavior as imperfect

competition (Hahn), especially when sluggish adjustment is accompanied by asymmetrical price changes.

For this reason, studies that investigate the rate of

price adjustment often also consider the symmetry of

response of affected prices to changes in causal

prices.4 Defining retail prices as affected and shippingpoint or wholesale prices as causal, symmetrical retail

price response means that retailers pass prices changes

downstream equally irrespective of whether the change

is an increase or a decrease. 

Asymmetry in price adjustment is often interpreted as

poor pricing performance, where retailers are either

absorbing price increases to avoid losing market share

or failing to expeditiously pass through price reductions in order to temporarily raise their margins.

Among studies of produce industries, Powers provides

evidence of the former case in fresh lettuce and Ward

for various fresh vegetables, while Pick et al. find that

citrus retailers are more likely to raise margins in

response to shipping-point price changes, although

their results vary by both product and market. This

issue is also considered at length in other industries by

Kinnucan and Forker (dairy products), cattle (Bailey

and Brorsen), pork (Boyd and Brorsen), and broilers

(Bernard and Willett). Of course, concern over the

speed of price transmission is moot if retail prices are

found to be essentially fixed and the retail level is the

locus of price determination.

Causes of Price Fixity at Retail 

Many argue that the ability to set and maintain retail

price points amid considerable variation in shippingpoint prices is itself evidence of market power.

Moreover, our interviews with shippers and brokers

suggest that retail price fixity is seen as the most visible and egregious embodiment of market power

because fixed price strategies mean that supply and

demand cannot function properly to clear the market

during times of oversupply. Indeed, there is little argument that retail prices move very little relative to shipping-point prices. Shonkwiler and Taylor show that

desired produce prices must change by a significant

amount before prices change in actuality. Powers

develops a model based on similar logic to show that

price-adjustment costs are largely responsible for the

apparent fixity of retail lettuce prices, while Slade

(1998) shows the same in a dynamic model of price

behavior by retailers selling wheat crackers.

Explanations for price fixity, however, go far beyond

these “menu cost” rationales and, in fact, go to the

heart of what we see as the source of imperfect competition in the retail grocery industry.

In the past, macroeconomists used the notion of costly

price adjustments (menu costs) to explain aggregate

price rigidity in inflationary environments. However,

they now recognize that there are many potential

explanations. In fact, Blinder et al. surveyed firms in

several different industries in order to find which

explanations are the most common in an empirical

sense. Among the many potential explanations for

price rigidity, only a few were found to be relevant to

firms engaged in retail trade. By far, the most common

response by firms of all types in the survey, and particularly those in retail trade, is that sticky prices are

caused by a “failure to coordinate,” in the words of

Ball and Romer. This explanation, which Ball and

Romer attribute to the notion of “strategic complemen4 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

4 Bernard and Willett's general terminology of affected and causal

prices is appropriate as there is some question as to the locus of

price determination in many industries.
tarity” developed by Cooper and John, recognizes that

rivals respond to one another’s price increases by

increasing their own price. Once the competing firms

reach a stable price, they are reluctant to move away

from this equilibrium. 

However, the question posed to survey respondents

(Blinder et al.) reflects a concept more akin to Okun’s

notion of a kinked demand curve in that firms merely

expressed a reluctance to be the first to raise prices for

fear of losing market share, or to lower prices for fear of

instigating a price war. If they could coordinate their

price changes, clearly it would be optimal for them all

to move together to a new desired price level. Although

considered distinct explanations, this notion is very similar to the idea that prices are fixed by “implicit contracts” between a firm and its customers—maintaining

relatively constant prices to loyal customers benefits

firms through higher average prices that result from

loyal customers’ inelastic demand, but also benefits customers by allowing them to save on search costs. Still,

these explanations ignore the fact that retailers interact

with each other, and with their customers, repeatedly

over time in a complex strategic way.

Following this line of reasoning, Mischel develops a

conceptual model to show that sticky prices can be

the result of a successful rather than a failed coordination in an environment where firms interact repeatedly over time. Indeed, the notion that strategic

complementarity alone is responsible for price fixity

is inconsistent with the price-reaction models of

Gasmi et al. or Slade (1990). Ball and Romer’s

explanation is also at odds with other empirical

research - based in econometric analysis of secondary

price data rather than survey responses. In particular,

the notion of coordination failure is inconsistent with

Stiglitz’s affirmation of Green and Porter’s explanation for rigid or “fixed” prices in which oligopolistic

firms enforce tacitly collusive price setting arrangements through punishment strategies based on the

shared recognition of trigger prices. 

When firms have complete, yet imperfect, information

regarding their rivals’ behavior, Green and Porter

assume firms begin in a state of collusion, but punish

rivals for a single-period defection from the (tacitly)

agreed price by reverting to less profitable, noncooperative prices until rivals again fall in line and set the

same, imperfectly competitive price (Friedman). If

rivals are aware of each other’s strategies and are sufficiently patient, then such a tacit cartel can survive

threats to “cheat” and undercut the agreed price

again.5

When information is less than perfect, however, a firm

does not know whether a low price (in the case of output market rivalry) represents a defection by a rival or

simply results from adverse market conditions.

Employing the harsh punishment strategy envisioned

by Friedman results in a step-like pattern of behavior,

with prices varying between low, noncooperative levels and somewhat less than the perfectly collusive

level.6 This explanation, while not originally intended

as a rationale for fixed prices, has found empirical support in 19th century railroads (Porter (1994), Lee and

Porter, Hajivassiliou), the airline industry (Brander and

Zhang), beef packing (Koontz et al.) and processing

potatoes (Richards et al.). If this explanation is correct,

then fixed prices may be a direct artifact of strategic

behavior in imperfectly competitive industries. On the

other hand, fixed prices are also consistent with many

models of competitive pricing behavior, whether in

response to the high cost of physically changing prices

(Slade), not wanting to cause confusion among consumers (Bils), constant selling costs (Blinder et al.), or

the possibility that consumers become very price sensitive during recessions (Rotemberg and Saloner).

Whether price fixity forms the basis for a more complete model of fresh produce pricing by retailers—

both upstream to their suppliers and downstream to

their customers—depends upon whether its predictions

are consistent with the price data from our sample

commodities and markets.

Summary of Preliminary Data Analysis

While we leave an extended discussion of the econometric methods used to analyze the fresh produce data

elsewhere (Richards and Patterson, 2001), we summarize our results here before moving to the central issue

of the behavior of fresh fruit margins. Essentially, we

find that: (1) fresh fruit prices tend to be formed at the

shipping point rather than at retail; (2) retail price

adjustment in response to a shock at the shipping point

is fundamentally asymmetrical, with retail price

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 5

5 This is by no means the only effective punishment strategy.

Abreu et al. show that, in a more general model than Green and

Porter, optimal punishments are less benign than a reversion to

Nash strategies and can last for only a single period.

6 Green and Porter develop their model assuming Cournot rivalry,

while Porter (1983) considers the same example from a Bertrand

perspective. As Porter notes, the models differ very little.
increases occurring far more rapidly and completely

than price reductions; and (3) retail prices, while not

fixed in an absolute sense, appear to be relatively stable compared to shipping-point prices.

Despite this study’s concern with a broad set of commodities (apples, fresh oranges, fresh grapes, and fresh

grapefruit), it is necessary to direct the analysis to a

more specific set of goods in order to avoid problems

of aggregation across products that may be viewed as

imperfect substitutes by consumers.7 Consequently,

our data consist of retail and shipping-point prices for

Red Delicious apples (Washington FOB prices), fresh

oranges (California FOB prices), green seedless grapes

(California Thompson and Perlette varieties), and fresh

Florida grapefruit. The retail scanner data are from a

private data vendor and include the weekly average

price and total quantity sold from several grocery

chains in six regional markets. Further details of these

data are reported in the data description section below,

but we describe the specific results on an issue-byissue basis here. 

First, for each product, we find that shipping-point

prices “cause” retail prices. In other words, our statistical models show that variation in shipping-point prices

explains subsequent changes in retail prices, but there

is no evidence that the opposite occurs as well. This

implies that the locus of price discovery is apparently

at the grower or shipper level—a result that is consistent with much of the prior research discussed above

regarding the commodity price discovery process.

When the locus of price discovery is at the shipping

point, as in our case, this means that expectations of

future supply and demand conditions are largely

formed at the source of the commodity. It does not

mean, however, that only supply conditions cause

prices to change. Rather, it may mean that retailers set

their buying prices based on their expectations of retail

demand and their observations on supply conditions.

Further, due to the geographic isolation of many markets for farm products, the fact that prices are determined at the source of the product does not imply that

these changes occur instantaneously, nor are they

likely to occur at the same rate for price increases and

decreases. What remains to be determined is the extent

and speed with which these price changes are transmitted from shipping point to retail.

Second, we find considerable, but variable, evidence of

asymmetry in price adjustment. For this test, we divide

the data into periods of rising and falling prices and,

accounting for other factors that may explain the

process of price adjustment, estimate the rate at which

prices return to their ideal levels in each regime. In this

case, the results are mixed across commodities. While

we are very confident, in a statistical sense, that prices

adjust at different rates, depending on whether they are

rising or falling, for grapes, oranges, and grapefruit, we

are less certain of this finding for apples. However, we

are more certain of our finding that retail prices do not

adjust instantaneously for any commodity. The fact that

prices do not adjust immediately in response to changes

in market fundamentals is perhaps not surprising, however, and is not necessarily due to any imperfection in

the price transmission process. Rather, if prices are

costly to adjust, or are fixed by contract or consumer

expectations, then we would expect to observe prices

that are relatively constant. 

Asymmetry in price adjustment is often viewed as less

innocuous. In fact, if retailers are intent on profiting

from price volatility, then we would expect to observe

retail prices responding more quickly to a rise in shipping-point prices than to a fall. This is exactly what we

find. Specifically, a rise in grape shipping-point prices

causes retail prices in the subsequent week to rise only

63 percent of the original price increase. On the other

hand, only 54 percent of a fall in grape shipping-point

prices is passed through to retail in the first week.

Although this difference may appear to be small, it does

mean that retailers are relatively quick to pass along

cost increases to consumers compared with price reductions. This result implies that retail grape prices take

approximately 1.5 weeks to completely adjust to a rise

in shipping-point prices, but adjust completely to a fall

in shipping-point prices after approximately 2 weeks. 

Among other commodities, apples and oranges exhibit

significantly asymmetric price adjustment, but the difference between upward and downward adjustment

rates is smaller for oranges than it is for apples. Retail

orange prices also appear to adjust more rapidly than

either apples or grapes, while grapefruit prices adjust

6 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

7 Nonetheless, some product aggregation was inevitable due to the

lack of specific shipping-point price data on fruit of a particular

size, grade, or source description. While existing USDA - AMS

price data do indeed cover a range of sizes and varieties for many

fruits, these were deemed inadequate due to holes in reporting

periods, reports of biases in the price gathering procedure, wide

ranges between the high and low price quotes for a given week,

and their seeming fixity despite evidence from other sources to the

contrary. Therefore, FOB price data were obtained from each of

the relevant commodity commissions or grower-sponsored price

reporting agencies.
the slowest of all. Further, all adjustment rates fall in

the quantity moving to market each week—a result

that is consistent with either adjustment costs that rise

in the amount sold, or an increase in market power

during periods of oversupply. 

Third, we find that retail prices are sticky relative to

shipping-point prices. Similar to the empirical

approach adopted by Slade (1998) for this purpose, we

construct a simple statistical model that is intended to

explain the probability of a change in retail prices

(where a change is defined by a movement of more

than $0.01) as a result of changes in shipping-point

prices. As expected, we find that the likelihood of a

change in the retail price is unrelated to changes in

shipping-point prices. Thus, as a first approximation,

we can conclude that retail prices are fixed in the face

of fluctuations in underlying supply and demand for

the product. Consequently, growers are likely to be

worse off because demand for their output is not

allowed to respond to changes at the consumer level. 

Although these preliminary empirical results, taken

together, seem to imply that retailers do enjoy a certain

measure of control over the determination of shippingpoint prices, the extent to which prices deviate from

purely competitive levels requires a more detailed

analysis of price behavior. Specifically, we must

account for variations in commodity supply, retailing

costs, consumer demand and strategic behavior by rival

retailers if we are to gain a better understanding of

fluctuations in retail margins. Of these factors affecting

retail margins, the potential for strategic behavior is

perhaps the most difficult, yet important, to identify.

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 7
Fundamental Question: Do

Retailers Have Market Power?

Rivalry in Semi-Perishable 

Produce Markets

Sweeping generalizations of how buying and selling

prices are determined in produce markets are invalid if

not impossible. Each fruit and vegetable market is distinct. However, to be useful, economic models of price

determination must separate which market differences

are important from those that may be plausibly

assumed to be constant. The commodity markets considered here are all semi-perishable—each can be

stored either on the tree or in cold storage for a significant amount of time. 

Other studies concerning produce price determination

explicitly consider the extreme perishability of fresh

farm products (Sexton and Zhang). In cases of extreme

perishability, supply is fixed when price is above marginal harvesting costs, but supply falls to zero for

prices below the cost of harvesting. When prices make

harvesting feasible, any surplus returns above the cost

of harvesting are divided among buyers and sellers

according to their relative bargaining power in the

market, which is largely influenced by the amount of

supply. If the product is storable for a significant

amount of time (grapes, apples, oranges, or grapefruit)

or is manufactured (bagged salads), this type of pricing mechanism does not apply. However, it is still true

that the grower price for nonmanufactured fresh fruits

is likely influenced by the relative bargaining power of

retail buyers on one side and grower-shippers on the

other. Given that growers are often separated by large

distances and do not have a history of effective coordination, retail buyers are more likely able to set prices. 

As such, retail industry members must consider how

each rival uses their own power in setting prices to

growers. Given the relative inelasticity of supply at

any point in time, and the fact that category management and efficient consumer response methods rely on

using price as a strategic tool, it is more likely that this

rivalry takes the form of competing on offered prices

on both the buying and selling sides rather than on

quantities purchased. Similarly, these same buyers

often interact in common retail markets as produce

sellers. With the amounts that they sell determined by

their buyers often weeks ahead of time, amounts that

are in turn determined by the prices paid to growers,

rivalry at this stage is again in prices rather than quantities. This assumption is supported by survey evidence

that finds almost 70 percent of produce sellers set

prices according to their rivals’ behavior (McLaughlin

et al.). However, this simple model of retailer interaction considers only their single-period or static rivalry.

Reality is far more complex and dynamic, with rivals

learning from one another and revising strategies to

allow for cooperation and mutual benefit. 

An Economic Model of Strategic Pricing

Among Retailers 

The fact that retail produce prices remain fixed for

long periods of time, despite wide swings in shippingpoint prices, supports Stiglitz’s notion that retail price

fixity derives from a fundamental success in coordination among retailers, rather than a failure as suggested

by Ball and Romer. Indeed, arguments that retailers

cannot possibly share information efficiently enough

to support an implicitly cooperative outcome similar to

that described by Green and Porter fail to recognize

the popularity of “food pages” in the weekend paper,

the proximity of retail grocery stores within U.S.

cities, and the fact that most metropolitan areas are

effectively served by only three or four major chains.

Clearly, to sustain noncompetitive pricing, there must

be some means by which rivals do not formally cooperate with one another to fix prices.

By interacting on a daily basis, the repeated nature of

rival firms’ decisions can lead to tacit, or implicit,

coordination. Moreover, other studies explain similar

price patterns that we observe here as resulting from

factors unrelated to market power - consumer search

costs (Bils; Lal and Matutes), fixed or “menu costs” of

price adjustment (Slade 1998; Sheshinski and Weiss)

or simply cyclical fluctuations in supply and demand

(Rotemberg and Saloner; Warner and Barsky; Sexton

and Zhang). Indeed, ours is but one among several

explanations of observed price patterns in the retail

produce industry. 

There is a large body of research that attempts to

explain price wars as outcomes arising from repeated

interactions between firms. Slade (1990) categorizes

these theories into three groups: learning models

where firms use price wars to cause rivals to reveal

their costs (Slade, 1987), cyclical models wherein the

strength of industry demand influences the incentives

to cooperate or not (Rotemberg and Saloner;

Haltiwanger and Harrington; Hajivisilliou), or “imperfect monitoring” models (Green and Porter; Abreu et

8 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
al.). Because the grocery industry is relatively stable,

its members often next to one another in shared markets, and capable of only imperfect competitive monitoring due to the multi-product nature of their format

permits, it is clear that the “trigger price” model is the

most plausible. 

Using the logic of Green and Porter and Porter (1983),

Lee and Porter explain the episodic price wars engendered by the Joint Executive Committee (JEC) in the

U.S. rail industry of the late 1800s. Porter (1983), however, assumes that the punishment strategy is carried out

in quantities, much like dumping product on the market

to lower prices, while Brander and Zhang allow for

either price cutting or dumping supply on the market.

Using firm-specific data on duopoly airline routes,

Brander and Zhang find considerable support for this

type of trigger model in quantity. Koontz et al. find support for a trigger price specification in the U.S. meat

packing industry - an industry with supply conditions

very similar to what we see in fresh produce. Further,

Hajivassiliou, using the JEC data, tests a trigger price

model against one in which behavior is explained by

cyclical changes in demand and rejects the latter, but

can not reject the implications of the former. 

Consequently, there is considerable empirical support

for imperfect monitoring models in general, but less

for other dynamic oligopoly models. More important,

the way in which fresh produce is bought and sold is

highly conducive to the type of information flow

required for an imperfect monitoring model to function. First, imperfect price signals are likely to exist in

relatively thin markets, such as the market for fresh

produce, because buyers deal with hundreds of suppliers where formal price announcements are logistically

impossible (Koontz et al.). Second, most markets are

seasonal so buyers are likely to interact with different

sellers at various times during the year. Third, the supply facing one retail buyer is likely to be influenced by

both rival behavior and the inherent randomness of

supply. Finally, retail buyers form a small group within

each region, so they can easily share information

among each other (implicitly) through negotiations

with large sellers or selling groups. Ultimately, however, the true test of which model is most appropriate

is found in the data itself.

Our description of the imperfect monitoring model

should make it clear that, although the best outcome

from the perspective of buyers is to cooperate in all

periods, thus earning a share of monopoly profits

throughout, this is not a realistic description of what

we observe given the uncertainty inherent in market

prices and rivals’ strategies. Rather, it is more likely

that retail produce buyers, if they are able to tacitly

cooperate with each other, do so by cooperating when

market prices are clearly in their favor. They respond

to cheating on this “agreement” with punishments that

take the form of competitive pricing (Green and

Porter; Porter (1983); Koontz et al.). Such punishments are likely expected by other firms in the industry because cheating cannot be tolerated by firms

interested in making the most profit possible year after

year in bargaining with the same set of suppliers.

Implications of Dynamic 

Model of Rivalry 

Retailers’ adherence to fixed-price policies form a key

part of any category management program. We argue

here that they also facilitate tacit cooperation among

their rivals in both their buying and selling activities.

In terms of the prices that are observed in raw product

and retail markets, the prediction of this model is that

retail prices will vary over time, alternating between

regimes of punishment and cooperation among retailers. During cooperative periods, prices are bound

between a competitive level and a monopolistic one

depending upon the extent to which rivals are able to

effectively agree on a common price. When the industry is undergoing punishment, however, margins will

reflect buying prices bound between the competitive

level and somewhat above pure monopsony in the

extreme. On the buying side, firms are assumed to

punish their rivals by periodically paying a relatively

high price when profits in the previous period fall

below some trigger level. However, they cooperate

with their rivals when profits are above the trigger.

Together, these two regimes constitute a pricing strategy, wherein high shipper prices are maintained only

long enough to restore the tacit agreement to set prices

paid to growers.

Example of Discontinuous Behavior 

Typically, evidence of such on-again, off-again behavior

consists of periodic price wars (Slade ,1990; Brander

and Zhang) or, in a more general model of rivalry with

multiple tools, advertising campaigns (Slade 1995;

Gasmi et al.). In the retail produce industry, however,

rival grocers attempt to gain temporary market advantage, and thereby punish rivals, with periodic price promotions. In order to meet the increase in the quantity of

produce demanded during these periods, retailers must

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 9
pay shippers higher prices than would otherwise be the

case. Therefore, we expect to observe falling profits

during periods of aggressive price-promotion activity.

Notice that a fall in profits during periods of relatively

high volume is contrary to predictions of models of

imperfect competition in perishable produce markets

(Sexton and Zhang). These conflicting conclusions are

not inconsistent with each other, however, as suppliers

of “perfectly perishable” commodities are constrained

by the amount of produce they have to sell and have little flexibility to increase or decrease supply during promotional periods. In order to test whether these predictions are consistent with our data on semi-perishable

fruit sales and margins, we construct a statistical model

that allows the extent of cooperation to vary with the

amount of produce sold by retailers and, hence, sold by

fruit suppliers. We describe the way in which we analyze the relevant fruit data next on a heuristic or intuitive level, and leave the formal development to a

technical appendix.

10 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
Empirical Test of Imperfect

Competition in Semi-Perishable

Produce

Empirical Implications of Trigger Model of

Tacit Collusion

Retailer margins are determined by both the prices

they charge consumers and the prices they pay to shippers for their fresh produce. Therefore, in order to

determine how much of the weekly variation in margins is due to the ability to set prices on either the buying or selling sides of the profit equation, and how

much is due to simply market forces, we need to

account for the factors that influence supply and

demand. Further, by allowing both the raw product

supply and retail demand curves to change slope, or

pivot, we can estimate the extent to which variation in

retailer-shipper margins depends upon retailers’ use of

the ability they may have to set prices (Bresnahan). 

To accomplish this, we estimate equations representing: (1) produce supply, (2) retail demand, and (3)

retailer margins. Besides changes in supply and

demand, we also account for changes in retailers’

costs - primarily labor used in stocking shelves and

customer service, energy to heat and light stores, and

business services such as insurance, real estate, and

finance - so include measures of these costs in the

margin equation. According to our conceptual model

of retailer behavior, however, we also need to allow for

the fact that rivals interact in different ways over time,

alternately punishing or cooperating according to their

assessment of rival behavior.

Data Analysis Method 

The usual approach to estimating models of imperfect

competition assumes that sample margins reflect a single set of firm strategies and market conditions.

However, if retailers behave the way we believe they

do, then margins should reflect alternating strategies -

one in which retailers cooperate and the other in which

they punish each other. The problem here is that we

never know when they are cooperating and when they

are punishing. Therefore, our estimation procedure is

designed to estimate the probability of punishment or

cooperation along with parameters that measure the

degree of price-setting ability that may be inferred.

Essentially, margin data are assumed to be produced

by a weighted average of the two types of behavior

that we expect to see in the real world. If this model is

correct, then we should observe regimes in which

retailers’ prices in input and output markets are indistinguishable from those that we would observe in competition, and others in which they are clearly making

cooperative profits. Identifying these regimes requires

a large volume of very detailed pricing, sales volume,

and cost data.

Sample Description 

Unlike prior studies that employ this methodology in

aggregate industry-level data, we estimate the effect of

cooperative pricing on retailer-shipper produce margins using a sample of firm-level price, cost and shipment data. Further, to account for heterogeneity in

regional produce markets, we estimate independent

models for each chain and market in our sample.

Specifically, the sample includes data for retail chains

in Albany, Atlanta, Chicago, Dallas, Los Angeles, and

Miami. For each chain, we have 104 weekly observations over the period January 1998 to December 1999

consisting of price per pound and number of pounds

sold from all stores of a given chain. For some commodities, however—most notably fresh oranges,

grapefruit, and, to a lesser extent grapes—the sample

does not consist of the full 104 weeks because we

excluded weeks of no domestic U.S. shipments. 

For each of our broad category definitions, we select a

specific product as representative of the price dynamics of the entire category in order to control for aggregation errors over products of different quality, local

supply, or local preferences. Specifically, the analysis

concerns Washington Red Delicious apples, California

green seedless grapes, California fresh Navel and

Valencia oranges, and Florida grapefruit. Although our

grape-product definition includes several different

varieties, primarily Thompson seedless and Perlettes,

this aggregation is necessary because there is no distinction between varieties drawn at retail. In the case

of oranges, we combine Navels and Valencias due to

the relatively short shipment season of each and the

need to preserve as many observations as possible for

the estimation of the model parameters. Initial estimates of an aggregate supply function show that the

Navel and Valencia supply functions are similar after

allowing for seasonality, so this variety aggregation is

thought to be reasonable. Further, it is hoped that by

comparing the results across commodities, chains, and

markets, we will be able to provide some degree of

qualitative evidence as to whether the use, or nonuse,

of market power is typical of the produce industry in

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 11
general or is specific to individual commodities,

chains, or markets.

Data Sources and Data Description

All of our empirical results refer only to those companies from which we have sales volume and retail-price

data. The list of participating companies depends, in

turn, on those who are willing to share scanner data to

a partner data-vendor. In this case, the source of all

retail data is FreshLook Marketing of Chicago,

Illinois. These data, commonly used for category management purposes by commodity commissions and

large shippers, includes measures of: (1) weekly movements (quantity, in lbs.) of a given UPC or PLU coded

product by chain and retail market; (2) listed selling

price of the commodity by chain and market; and (3)

number of stores within the chain selling the product.

The exact definition of retail price used in estimation

varies by commodity. 

For apples, the price represents an average over all

non-organic Red Delicious sales each week. Price differences between bagged and bulk apples were

adjusted using the method suggested by Goldman and

Grossman and applied to food demand analysis by

Cox and Wohlgenant. In this way, we define a bulkequivalent apple price for each market-chain-week

observation. Although the retail price for individual

apple varieties and sizes typically change very little

over the sample period, it is necessary to aggregate

this way in order to match our shipping-point price

data, which do not differentiate among apples of the

same variety beyond controlled versus regular storage.

For table grapes, the retail price is defined as the price

reported for the particular green seedless variety sold

in each market by each chain each week. Initial model

estimates attempted to include sales from both Chilean

and other offshore sources and U.S. sources in a complete, year-round model. However, efforts to estimate

the supply response of imported grapes were unsuccessful, so we chose to focus instead on grapes of U.S.

origin and a sample that represents only those weeks

when U.S. grapes are sold. Within the class of “green

seedless grapes,” there are not only several possible

source regions, but many different varieties as well.

Because the retail data do not consistently break out

these varieties, however, we are forced to aggregate

over all that meet this general definition. Fortunately,

these varieties tend to overlap very little and represent

relatively discrete parts of the sample period, so this

retail price should correspond well to our shippingpoint price. Further, all sales are random weight, so no

correction between product forms is required. Fresh

oranges, however, are sold in both bagged and bulk

form, so a similar correction to that made for apples is

also made in this case. 

Although it would be preferable to focus on a particular

variety of oranges, neither Navel nor Valencia oranges

alone represent a marketing window of sufficient length

to allow enough degrees of freedom to estimate the

model. Therefore, we consider an aggregate “fresh

orange” category consisting of both varieties. As in the

grape case, the fact that the seasons for these varieties

overlap very little serves to minimize errors induced by

product aggregation. To further reduce the possibility of

inducing such error into the model, we account for the

different shipping seasons within our econometric procedure through a fixed-variety effects approach.

Therefore, for each product we attempt to ensure that

the calculated retailer-shipper margin represents actual

market results and, as such, does not suffer from any

external source of bias. For similar reasons, we combine

red and white grapefruit prior to estimating the market

structure models for these products. Further, we exclude

those weeks in which domestic shipments were effectively zero—leaving 80 observations for each market.

To explain variation in this margin, we estimate the cost

of buying and marketing fruit using grower prices and

price indices for the retailer cost function that we

describe next.

Labor constitutes the major component of retailers’

costs. Wage data for workers in the retail grocery industry are from the Bureau of Labor Statistics National

Employment, Hours, and Earnings report on a monthly

basis for 1998 and 1999 (U.S. Department of Labor).

This report also provides average weekly earnings for

workers in the advertising, business services, and the

FIRE (finance, insurance, and real estate) sector. These

variables constitute our measures of input prices at the

retail level. All monthly data are converted to weekly

observations using a cubic spline procedure. 

Marketing costs also include transport costs from the

growing region to the destination market. For this, the

USDA-AMS Truck Rate Report provides estimates of

weekly trucking costs between a number of source and

destination points for the sample of fresh produce considered here. Because the Truck Rate Report does not

provide a consistent set of rates for all weeks in which

there were positive shipments, numerous assumptions

were made in developing continuous series for each

12 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
commodity and market. In the case of grapes, weeks

for which rates were not quoted were inferred from

contemporaneous rates for lettuce and tomatoes for the

same terminal market. Adjustments to the vegetable

cost data were made based on the average differential

for weeks in which both commodities were quoted for

a similar source-destination pair. This procedure was

also used for periods in which orange transport data

were not reported.

Estimating the supply curve for fresh produce requires

data on farm input prices, primarily associated with harvest, and prices of alternative uses for each fresh commodity. In each case, the output price is defined as the

shipping-point price paid at the source on a free-onboard (FOB) basis. Any difference between this and the

farm-gate price is due to grading and packing charges

levied on the grower by the shipper. For Washington

apples, the price represents a weekly average over all

sizes and grades of Red Delicious apple as reported by

the Washington Growers’ Clearing House. Because the

proportion of regular-storage and cold-storage apples

that are shipped varies each week, the price is simply a

weighted average of each type. To estimate the extent of

any rotation in the supply curve (i.e., non-parallel shifts

required to identify the market power parameter), this

price is multiplied by the harvesting wage that is relevant to each product. For apples, this is the average

wage of harvest workers in Washington State, which is

obtained from the Washington State Employment

Security Department’s Labor Market Information

report. Similar data for California are used for table

grapes and fresh oranges and for Florida in the fresh

grapefruit model and are obtained from the USDANASS Farm Labor publication.

Commodity price and output data are either from the

appropriate commodity organization or from USDAAMS sources. Specifically, shipping-point prices for regular and cold-stored Red Delicious apples are from

internal reports generated by officials at the Washington

Growers’ Clearing House. These reports also provide

monthly shipments for both types of apples to all domestic destinations. For table grapes, similar price data are

from the California Table Grape Commission, while

shipments are from the USDA-AMS Shipment Report.

For purposes of this research, shipments were defined to

include only those from domestic U.S. sources. As mentioned above, periods during which the U.S. market was

supplied from Chilean or other import sources are

excluded from the analysis. This is also true for fresh

oranges and grapefruit as the period of analysis includes

only those weeks in which U.S. fruit was sold through

retail markets. For all fresh citrus, both the shippingpoint price and shipment data are from the USDA-AMS.

Although these shipping-point data include prices for a

range of sizes, the retail data do not, so we construct an

aggregate consisting of a simple average price per week.

Implicitly, therefore, this procedure assumes a uniform

distribution of shipments by size. Finally, all prices are

converted to dollars per pound in order to compare

directly to the retail price data. 

To test the hypothesis that retailers’ ability to set

price falls with the amount of weekly shipments, we

allow a parameter that measures the degree of market power in each model to vary with total weekly

shipments of each commodity. These data were

obtained directly from USDA-AMS officials and

include all shipments either to or within the U.S. on

a weekly basis. Therefore, we include imports to the

U.S., but exclude U.S. exports abroad. 

Although it would have been preferable to allow each

conduct parameter to vary with some indicator of

industry structure such as the level of concentration or

a non-endogenous measure such as any non-strategic

entry barriers, high-frequency data are not available

for any of these variables. Therefore, we are left to

infer any change in the ability to price strategically

from our parameter estimates and observed trends

among retailers in each market. Despite these limitations, however, we are confident that the data

described here provide the most detailed picture of

fresh produce market behavior currently available. 

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 13
Interpretation of the 

Empirical Results

Market Power in Grower and

Retail Markets

As we emphasize in developing our method of analysis, the ability of any approach to separate the use of

market power from changes in supply or demand relies

upon an accurate accounting for all other factors that

may contribute to variation in both grower and retail

prices. However, despite the fact that we do estimate

models of demand and supply for each commodity, the

specific results of these models is not of central interest here, so they are reported in the technical appendix

and fully discussed elsewhere (Richards and Patterson,

2001). This section, therefore, provides an explanation

and interpretation of our empirical results specifically

as they relate to the cooperative price setting behavior

by retailers in commodity and retail produce markets.

In order to preserve the anonymity of individual retail

chains, we present our results in terms of average

indices of pricing or market power for each of the six

regional markets, for each commodity. 

Perhaps more important than these individual index estimates, however, are estimates of the impact of market

volume on retailers’ price setting ability. Rather than

simply describe symptoms of any behavioral problems

that may exist in retail produce markets, these estimates

provide critical insights into their underlying cause.

Specifically, we are able to assess whether or not retailers possess a critical facilitating mechanism through

which they may be able to tacitly cooperate to set

imperfectly competitive prices. In doing so, we interpret

the results commodity by commodity, beginning with

Washington Red Delicious apples. 

Washington Apples

Prior to interpreting the specific results of our statistical

tests on the ability of retailers to set prices, we must

first establish the legitimacy of our overall approach. To

do so, we conduct tests of whether or not the retail-farm

margin data are consistent with a world in which market

rivals go through periods of cooperation with one

another followed by periods of punishment by reversion

to more competitive pricing. Although no statistical tests

can claim to provide entirely conclusive results, we find

strong statistical evidence in support of our view of how

retailers set buying and selling prices for apples.

Specifically, we find that margins appear to follow a

pattern wherein they fall into either of two regimes—

one where they are relatively narrow, where growers or

consumers receive competitive prices, and others in

which they widen significantly, where growers or consumers face noncompetitive prices. This pattern could

arise under a number of different circumstances, but it is

very plausibly explained by our theory of retailer pricing behavior. 

Perhaps stronger support for this theory lies in the

impact of apple sales volume on the index of market

power. According to our hypothesis, observed pricing

power by retailers should fall with sales volume due to

their need to secure sufficient supply to meet higher

quantities demanded under periodic price-promotion

programs. Our statistical evidence is not as strong on

this point, but we do find this effect in a majority of our

retailer/market pairs. Clearly, because there is some

diversity in marketing strategies among major retailers,

there are some that do not follow this generic pricing

strategy. For example, it is well known that one major

retailer follows instead an everyday low price (EDLP)

strategy, irrespective of its rivals’ pricing behavior.

Perhaps for this reason, it is clear that the ability to

price strategically is not uniform across markets. 

Apple Commodity Market

While non-uniform, there does appear to be a relatively consistent pattern of price setting power in both

commodity and retail markets that is, in many cases,

significant both in an economic and in a statistical

sense. Specifically, in Albany we find that retailers, on

average, exercise a significant degree of power in both

their buying and selling activities. Given that the scale

of this index is bound between zero (competitive pricing)8 and one (perfect pricing coordination) on the

buying side and zero and the number of sellers, N, on

the selling side, the degree of buying power is considerably higher than what we would observe in perfect

competition.9

The index of commodity buyer market power varies

from 0.144 in Dallas to 0.765 in Los Angeles (fig. 1).

(The technical appendix reports all the estimated parameters for each region and chain). Interpreted purely as an

14 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

8 Technically, this index approaches 1/N at the lower bound, where

N is the number of retail buyers; this clearly goes to zero as N

becomes large.

9 This range applies to the absolute value, or ignoring negative

signs, for the estimated index. The figures present negative values

for buying-power indices for illustrative purposes only.
index, the degree of buying power exercised by retailers

in the apple market appears to be only moderate, averaging 0.446 over all sample markets. This means that

fully 44 percent of the difference between retail and

shipping-point prices is explained by buying power -

certainly not perfectly cooperative levels of distortion,

but not consistent with perfect competition either. These

results are not statistical anomalies as 80 percent

(32/40) of the index values estimated for individual

markets are “statistically significant.”

Careful readers may also wonder how individual

retailers, or retailers in different markets for that matter, can possibly have different levels of buying

power? Remember that buying and selling prices are

inextricably linked in a retailer’s overall business strategy. To carry out a seasonal or periodic promotion

campaign for a particular produce item, a chain, a

regional office, or a group of stores must arrange to

acquire more than they would otherwise typically buy.

To do so, they must either raise the price that they are

willing to pay, or go to other suppliers that they do not

typically use. Either way, their degree of leverage is

lower than usual.

This observation is also consistent with the distribution

of buying staff within retail chains. If all buying were

centralized, we would expect no difference among

regional markets. However, McLaughlin et al. (1999)

report that 30 percent of buyers are located at corporate headquarters, 45 percent in regional branches, and

25 percent in the field so 70 percent of all acquisitions

originate either in regional or field offices. In summary, though the exercise of buying power in the apple

procurement market is consistent and pervasive, it is

often only moderately imposed. 

Apple Retail Markets

In general, our results lend support to the notion of

buyer collusion; firms will use similar strategies if it is

tacitly recognized that this is in their shared best interests. There is, however, a considerable range in conduct parameters both within and across some of the

other markets. In retail apple markets, or the consumer

side of the market, the pricing index varies from 0.033

to 1.058, again interpreted in absolute value. In this

case, however, the low value (the Chicago market) is

an anomaly as the mean index value is 0.441 (fig. 1).

Excluding this result, it is apparent that retailers exercise a greater degree of power in setting selling as

opposed to buying prices. Without Chicago, over 50

percent of the retail-farm margin is due to imperfect

competition. While there appears to be little effective

cooperation in setting retail prices in Chicago or Los

Angles, the opposite is true in Atlanta. Overall, however, only 2 of 20 parameters are not significantly different from zero, so we can conclude with some

confidence that tacit cooperative pricing behavior is a

least fairly typical among retail supermarket chains.

There appears to be little relationship between market

structure and the ability to set price. Much of the concern surrounding the recent wave of retail mergers

focuses on this connection between structure and conduct - the belief that markets dominated by a few,

large firms provide the participants more incentive and

a greater ability to collude both against consumer and

supplier interests. However, the most competitive output markets are also the ones generally served by

fewer retailers—Chicago (four-firm concentration ratio

(CR4) of 81.6 percent in 1998 according to VNU

Marketing Information Marketscope) and Los Angeles

(CR4 = 76.4 percent). Indeed, the market dominated

by the fewest retailers, Miami (CR4 = 88.2 percent),

appears to be only moderately collusive and, at any

rate, very similar in this respect to other markets

served by more retailers. The results from our empirical model also provide other evidence of the likelihood

that firms will use their ability to price strategically.

Probability of Collusion 

Specifically, our model estimates the proportion of

weeks during which each retailer can be described as

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 15

Figure 1

Washington Red Delicious apple market 

power indices, 1998-99

Source: Economic Research Service, USDA.

Index value

Output market power Buyer market power

Albany

Atlanta

Chicago

Dallas

Los Angeles

Miami

0 0.2 0.4 0.6 0.8 1.0 1.2
either “cooperative” or “punishing.” In the Albany

market, for example, one chain cooperates 65 percent

of the time, whereas another cooperates during 47 percent of the sample weeks. Our expectation is that

chains that are more likely to cooperate are those that

exercise more power over price. However, this relationship appears to be quite loose in the case of apples.

(This effect is more apparent in some of the other

commodities.) Interpreting the probability of cooperation on its own terms, however, leads to a general conclusion that tacitly cooperative behavior in both

commodity and retail markets is common, but far from

perfectly coordinated in each sample period. 

Consumers fare better under a market where firms

engage in periodic price wars, if only to reestablish

cooperation, than in a collusive market where prices,

presumably, never change. This same conclusion

applies to suppliers. In interpreting these results, these

values do not suggest overt or conscious collusion during cooperative periods, but rather the tacit adherence

to a pricing strategy whose intent is to restore order to

what is perceived to be an unfavorable market. 

Impact of Shipment Volumes

By modeling each pricing power index as a function of

weekly shipments, we disaggregate the test for pricing

power into two components: (1) a purely strategic element that captures how firms react to decisions taken

by their rivals, and (2) the impact that shipment levels

have on their ability to use their pricing power in commodity and retail markets. If the second component is

positive, then this suggests that retailers’ bargaining

power is enhanced through the mechanism described

by Sexton and Zhang, namely that large supplies

reduce the relative bargaining power of grower-shippers. If, however, the second part is negative, then this

suggests that retailers have less bargaining power

when market quantities are higher. In this case, the

decline in retailer bargaining power is likely due to

their pre-commitments to higher quantities during promotional periods and meeting retail demands created

through their produce merchandising and category

management programs. 

In buying activities, we find this volume effect to be

negative in 13 of the 20 chain-market pairs for apples

and significantly so in 10 of these. On the other hand,

this parameter is never significantly positive. Although

we would expect the effect of shipments on negotiating

power to vary by chain and market if the source of this

effect is indeed in individual retailing strategies, the evidence support the hypothesis that higher volumes are

associated with a loss of retail buyer power, not a 

gain. In the output market, a similar result obtains.

Specifically, 14 of the 20 chain-market volume relationship are negative on the retail side, and 10 of these are

statistically significant, while only 2 are significantly

greater than zero. This result suggests that when a

retailer commits to a large volume and buys produce

accordingly, he or she loses pricing power on both the

buying and selling side of the market. 

Summary of Apple Market Results

Retailers do exercise power over price in both buying

and selling activities apples. To the extent that this

behavior causes the retail-shipping point margin to be

wider than it would otherwise be, both consumers and

producers incur losses as a result. Whether or not this is

a general result, however, requires a similar analysis be

performed with data from other commodity markets. 

California Fresh Grapes

Due to the fact that the California grape season lasts

only about 7 months, we estimate the statistical model

using only 67 of the 104 weeks in our sample data set.

Perhaps due to this, or the fact that some chains exhibited very little price variation at retail over the entire

sample period, the model does not appear to fit the

data as well as in the apple case. However, statistical

tests still indicate that the trigger-price model is preferred to a static or single-regime alternative, so our

approach is still preferred to the generally accepted

alternative approach. On a market-by-market basis,

however, the grape results are less plausible than in the

apple case.

Grape Commodity Market 

For grapes, 3 of the buying power indices and 2 of the

output market power estimates are significantly less

than zero. These estimates fall outside of the range

permitted by the theory and imply that margins actually fall (either retail prices are lower or grower prices

are higher) due to the strategic behavior of rival retail

chains. This is not a plausible result. With this caveat

in mind, however, most other markets and chains provide estimates that are plausible, and somewhat consistent with the apple results. In particular, the input

market (buying) conduct parameter is statistically

greater than zero in 10 of the 20 sample chain / market

pairs and averages 0.040 over the entire sample (fig.

2). Miami retailers appear to exercise the most signifi16 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
cant buyer power. However, in each case, the degree of

power is considerably less than in the apple case and,

in most instances, could be argued to be not significantly different from zero in an economic sense. Even

in the Miami market, the conduct parameter ranges

from 0.080 to 0.292, which is only slightly off the

competitive standard. These results, therefore, suggest

that retailers do not exercise a significant degree of

buying power in purchasing seedless green grapes,

insofar as pricing behavior is concerned. 

Grape Retail Market 

Among retail grape markets, the estimated average

index ranges from a low of 0.045 in Chicago to 1.781

in Albany, and averages 0.569 over the entire sample

(fig. 2), suggesting that most of the difference between

retailer and shipper prices is due to retail pricing activity in Albany. The estimate for the Albany market is

suggestive of cooperative behavior, which is observed

much of the time. Chains within the Atlanta and

Miami markets tend to be relatively consistent in their

ability to set price, whereas Los Angeles presents

somewhat of an enigma. Although two chains in this

market can be described as relatively cooperative in

their behavior, the other two are very nearly competitive. This result is instructive, as it argues against

painting all retailers with the same brush with respect

to their pricing and other strategic activities. Except

for one retailer, the Dallas market appears to be fairly

competitive in both buying and selling fresh grapes. 

Impact of Shipment Volumes

Because grapes are more perishable than the rest of

our semi-storable fruits, we expect higher shipment

levels to lead to higher degrees of bargaining power

for retailers relative to suppliers. This would imply a

significant positive parameter in the conduct parameter

functions. In fact, of the 11 parameters that are statistically different from zero on the input side, 7 of these

are positive. Although this evidence is not conclusive,

it is suggestive that this volume effect is more prevalent than with apples. Further, of the significantly negative parameters, none are large in an economic sense. 

In the output market, we hypothesize that higher levels

of output are largely due to unobservable, nonprice promotion efforts such as newspapers or other store-level

ads. For a given level of supply, consumers are more

sensitive to price in these instances and retailers must

refrain from charging a higher price. Again, this suggests a negative value for the impact of sales volumes

on pricing power. From the chain-by-chain results, this

occurs 9 times out of 20 and 5 of these relationship are

statistically significant. Therefore, these results provide

only weak support for this hypothesis. 

California Fresh Oranges

For fresh oranges, we initially sought to focus only on

Navel oranges in order to minimize the degree of

product aggregation error that is inevitably induced in

models of this type. However, the freeze of December

1998 and the seasonality of orange production meant

that this focus would leave very few observations over

our relatively short, 2 year time frame. Therefore, we

estimate the fresh orange market power model and

each of its components (supply and demand curves)

with a fresh orange composite product, consisting of

Navel oranges during the first part of each year and

Valencia oranges for the remainder. We account for

fundamental differences in these products by allowing

for seasonal variation in all model components. 

Including only the weeks in which fresh oranges are

shipped from U.S. sources, figure 3 shows the results

from using 87 weekly observations over the 1998-99

calendar years. Again, statistical tests of the triggerprice model suggest that it is preferred to the “static”

alternative for each chain in every market. Thus, each

chain experiences periods in which prices at both retail

and the shipper level are set such that the retail-shipping point margin is at relatively cooperative levels,

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 17

Figure 2

California fresh table grape market 

power indices, 1998-99

Source: Economic Research Service, USDA.

Index value

Output market power Buyer market power

0

Albany

Atlanta

Chicago

Dallas

Los Angeles

Miami

0.5 1.0 1.5 2.0
and other periods in which margins are set more competitively.

Orange Commodity and Retail Markets 

Retailers in the fresh orange market appear more likely

to cooperate in consumer (output) rather than in input

(buyer) markets. Whereas only 8 of 20 chains appear

to use considerable leverage in setting prices for raw

oranges from shippers, 15 chains set significantly noncompetitive retail prices - significant, that is, in a statistical sense. With respect to the retail market, the

average pricing index is 0.231 and ranges from 0.032

in Chicago to 0.750 in Atlanta (fig.3). The deviation

from purely competitive pricing appears to be significant in an economic sense, as well. On the input side,

the extent of deviation from competitive pricing

appears to be far greater than in the grape case, and

similar to apples. The commodity pricing index is

0.310 for oranges, suggesting that retailer-shipper margins are roughly 30 percent wider than they would otherwise be (fig. 3). (This average is somewhat skewed

by the Dallas market result, where retailers appear to

possess very little ability to set price.)

It is tempting to look toward Sunkist and a few other

large independent packing houses as effective countervailing forces in this market. Whereas growers of the

previous two commodities (apples and grapes) tend to

either sell alone, go through an independent packing

shed, or form some sort of marketing alliance, fresh

orange growers are more likely to belong to an organized cooperative or to supply a large, independent

packing house. Therefore, with more effective supply

coordination by growers, it is more difficult for retailers to exert any buying power. 

Impact of Sales Volume 

Retailers that fail to secure sufficient quantities of

fruit prior to a promotion will more likely scurry to

meet demand at the last minute, thereby paying higher

prices. In the output, or retail market, however, a negative relationship between sales volume and market

power may also arise as promotional periods could be

viewed by rivals as violations of the tacit market-sharing agreement, providing just cause for a round of

punishing loss-leadership or price wars. As with table

grapes, however, the orange results are mixed on this

point. Only 8 of 20 chains experience a reduction in

buyer power as a result of higher quantities going to

market, while only 2 of 20 undergo the same effect in

the output market. 

Again, it is tempting to posit explanations from the

trading institutions particular to this industry. Namely,

the more control over supply growers and shippers

have, the less likely the use of buying power as decision over the quantity shipped is more the shipper’s

than the retailer’s. Furthermore, there is very little support for the theory that retailers’ bargaining power

rises with the total amount marketed of each fruit.

Florida Fresh Grapefruit 

As with fresh oranges, grapefruit data represent a

potentially heterogeneous product as different seasonal

arrangements fill store shelves throughout the year.

Moreover, grapefruit shipment data consist of both red

and white varieties, each from a different growing

region and slightly different growing season. Once

again, in order to construct a reasonably continuous

data set of grapefruit shipments, we define fresh

grapefruits as an aggregate of both reds and whites.

However, we exclude months of zero domestic shipments from the model. This avoids potential complications related to world grapefruit shipments handled by

Florida shippers. In general, June, July, and August are

the only months in which domestic shipments fall to

zero and retailers must rely on imported product.

Because consumers are able to source imported grapefruit over these months, however, we include all

months in the retail model and account for any seasonal differences in demand accordingly. 

18 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

Figure 3

California fresh orange market power 

indices, 1998-99

Source: Economic Research Service, USDA.

Index value

Output market power Buyer market power

0

Albany

Atlanta

Chicago

Dallas

Los Angeles

Miami

0.2 0.4 0.6 0.8
Grapefruit Commodity and Retail Markets 

Our analysis supports the assertion that retailers use

periods of price promotion to reinforce cooperation

around commonly agreed prices in two ways. First, as

with other commodities, a two-regime model that

describes retailers as behaving according to a triggerprice strategy does a far better job of explaining the

data than a model without this feature. When there are

few buyers (retailers) that sell the bulk of fresh grapefruit to consumers, (and buy from shippers), our

results are highly suggestive of collusive behavior on

the part of retailers. Second, strong statistical results

suggest that periods of punishment occur roughly onequarter of the time for most chains—approximately

the amount of time between promotional periods.

Intermittent promotions, in turn, are the mechanisms

through which retailers punish, given common retailing practices that we observe for fresh produce. Our

empirical analysis of the grapefruit data again indicates how close observed prices are to the “competitive ideal” in both input and output markets. Buyer

power clearly exists in the majority of our sample markets (fig. 4). In fact, 12 out of 20 chain-market pairs

exhibit statistically significant deviations from competitive pricing and, of these, nearly all are economically

significant. Indeed, the mean pricing index on the buying side ranges from 0.330 in Los Angeles to 1.020 in

Chicago, suggesting that grapefruit growers are not

being paid full value for their produce. In terms of

shipping-point prices, this latter result implies that

prices are (almost) fully collusive in Chicago. 

Although the emergence of national, centralized buying

offices for the major chains may lead to an expectation

that buying power is likely to be exercised upstream, the

data make a stronger case for pricing power downstream. In fact, all but two of the selling indices are positive and statistically significant, indicating some degree

of price setting in retail markets. Although the degree of

deviation from competitive pricing appears to be quite

small in Los Angeles and Miami, prices in the Dallas

and Atlanta markets appear to be highly noncompetitive. Whether this is due to tacit cooperative collusion,

however, is another question.

Impact of Sales Volume 

Again, our hypothesis on sales volume is supported if

it is found that buyer power falls in proportion to the

amount of grapefruit sold in any given week. In 13 of

20 cases, this is so. In fact, deviations from this pattern

- in terms of significantly positive effects of volume on

buying power—occur in only three chain-market pairs

and even then the estimated parameter is very small.

The evidence is less strong on the output-market side

as only 11 chain-market pairs exhibit significantly

negative effects of volume on output market power,

but again the positive parameters are uniformly very

close to zero. Therefore, these results seem to bear

witness that retailers’ promoting of produce from time

to time represents periods in which they exert less control over price in return for punishing rivals into subsequent cooperative behaviors. 

Summary of Market Power Results 

With respect to individual commodities, we find consistent and pervasive evidence of tacitly cooperative

behavior and, hence, the exercise of buyer power for

Washington Red Delicious apples. Although we cannot

reject cooperative behavior among buyers of California

green seedless grapes, their ability to suppress grower

price does not appear to be significant in economic

terms. Fresh oranges represent an intermediate case,

with some retail chains demonstrating cooperative

pricing practices in shipping-point markets and others

not. For fresh grapefruit, the bulk of the evidence lies

in support of buyer power, but there is no clear pattern

among the sample markets. 

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 19

Figure 4

Florida fresh grapefruit market power 

indices, 1998-99

Source: Economic Research Service, USDA.

Index value

Output market power Buyer market power

0

Albany

Atlanta

Chicago

Dallas

Los Angeles

Miami

0.2 0.4 0.6 0.8 1.0 1.2
In retail markets, we also find reasonably consistent

evidence of imperfectly competitive pricing for apples,

grapes, and grapefruit, although the extent of the deviation from perfect competition appears to be less for

fresh oranges than for the other commodities. In the

case of grapefruit, however, the pattern of imperfect

pricing is both consistent and significant in terms of

the extent of deviation from competitive pricing levels.

For each of these commodities, however, there is considerable variation in price setting ability both among

retailers and markets. Therefore, it is difficult to make

a sweeping generalization as to the nature and extent

of cooperative behavior in the fresh produce industry

as a whole. 

Further, in the case of apples we find that retailer price

setting ability tends to decline both in buying and selling when market volume is higher. This we attribute to

retail strategies that commit sellers to higher volumes

during promotional periods, requiring them to either

obtain favorable prices from suppliers or price more

aggressively in commodity markets at the time of the

promotion. This result is not consistent across commodities, however, as we find that the opposite effect -

of retailer bargaining power rising with market volumes - more likely to occur in the grape market. Our

hypothesis on volume is strongly supported in fresh

grapefruit. On the buying side, buyer bargaining power

consistently falls with the amount of produce sold.

Thus retailers may embrace periods of power over

price as they promote fresh produce as a means of

enforcing market discipline, thus tacitly enforcing

cooperation in the amount of fruit bought from growers and, ultimately, sold to consumers.

20 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
Conclusions and Implications

This study represents a comprehensive analysis of

pricing behavior in the fresh orange, table grape, fresh

apple, and fresh grapefruit markets. For specific varieties of each commodity, we investigate issues including the locus of price determination, the symmetry of

price transmission, the degree of retail price fixity, and

the apparent control over price by fruit retailers in both

output and input markets. Our data for this analysis

consist of 2 years (1998 and 1999) of weekly retailscanner price and sales data from six major metropolitan markets in various regions throughout the country.

Within each market, most major retail chains are represented in the data. At the shipper level, our data consist of shipping-point prices and volumes obtained

from either the USDA, or individual commodity commissions. These data are supplemented with data from

a variety of other sources to account for transportation

costs, marketing costs, and variations in factors that

are critical to the demand or supply of each commodity. At each stage of our analysis, we apply econometric modeling techniques to these data that are widely

accepted and acknowledged as appropriate for the particular purpose. While we are confident in the accuracy of our findings, they are, of course, conditional on

the market conditions that prevailed during our particular period of study.

In order to gain an understanding of the behavior of

prices in each market, we first determine where prices

are determined within the marketing channel of each

commodity. The results are consistent across all commodities—shipping-point prices cause retail prices, so

we can conclude that prices are formed at the shipper

level for all of the fresh fruits considered here. We also

investigate the symmetry with which price changes at

the shipping point are transmitted to retail price

changes. For all commodities, we find that retail prices

respond more rapidly to shipping-point price increases

than decreases, although this result was less significant

for apples than for the other commodities. This result

is commonly interpreted as evidence, albeit indirect, of

retailers’ ability to extract some surplus from shippers

when prices are volatile. 

Retail prices not only adjust after and more slowly

than shipping point prices, but we find that they are

virtually fixed on statistical grounds. To maintain fixed

prices in the face of volatile buying prices, a key feature of category management, a produce retailer must

have some ability to control retail prices. Indeed, Slade

(1999) shows that the extent of price fixity is likely to

rise with strategic pricing behavior and shows that this

is the case with store-level retail data. However,

despite the fact that retail price fixity can cause losses

at the grower level (Sexton et al.) due to imperfect

transmission of price signals, it may also benefit the

consumer due to greater price stability. Moreover,

there are many explanations for fixed prices (menu

costs, constant production costs, consumer search

costs) that are entirely consistent with competitive

behavior. Therefore, we require more conclusive evidence of imperfectly competitive pricing than this preliminary analysis provides. To that end, we develop a

model of price determination at retail and wholesale

that not only allows for a wide variety of retail and

input-market pricing strategies, but also for explainable variations in supply and demand. 

Specifically, our explanation for fresh fruit pricing is

based on the logic of a “trigger-price” that has been

shown to underpin cooperative agreements among

19th century railway companies, airlines in the 1990s,

and present-day potato and beef processors. If tacit

cooperative agreements exist among fresh fruit retailers who engage in day-to-day interaction in commodity and retail markets, then there must be some

mechanism by which they are able to sustain the

agreement among themselves to hold prices at a certain level. In the trigger-price model, this mechanism

consists of a commonly understood price threshold. If

an individual retailer believes that a rival is pricing

below that threshold (above, in the input market) punishment ensues with a round of competitive pricing,

often price discount meant to restore some market

share lost to the cheating firm. 

To determine whether this model is a good explanation

for how prices are actually formed, we estimate a

model that allows for separate regimes of cooperation

and punishment and see if this does a better job of

explaining the data than a simple, single-regime

model. Applying this model to each of our commodities, we find evidence that these regimes do indeed

exist and that pricing behavior within the cooperative

regime may result in lower prices for growers and

higher prices for consumers. However, these results

vary considerably by commodity, market, and retail

chain. For apples, we find evidence of both buyer and

seller power that is both statistically and economically

significant in virtually all market / chain pairs. For

fresh grapes, we find a consistent pattern of output

market power. Input market power is often statistically

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 21
significant, but inconsequential in magnitude. Given

the importance of grape imports, it is tempting to suggest that import competition causes this result, but we

consider only the U.S. production season, in which

imports play a minor role. 

Retail orange prices also appear to reflect a considerable

degree of price setting ability, but as in the grape case,

the use of buyer power is less consistent and of a lower

magnitude in most markets. For grapefruit, we find an

irregular pattern of buying power—statistically and economically significant in approximately 60 percent of the

market-chain pairs, but insignificant in the remainder of

cases. On the other hand, grapefruit sellers consistently

exercise a moderate level of market power in retail markets. For all commodities, periods of collusion occur

roughly two-thirds of the time, so any benefit consumers or shippers may receive from periodic price

wars is likely to be short-lived and unpredictable.

We also find some evidence that the degree of pricing

power—whether in input our output markets—falls

with the amount of volume in the system. This finding

is in stark contrast to previous research showing that

buyers of more perishable produce commodities (i.e.,

lettuce) tend to secure a greater share of the growerretailer margin in years of relatively large supply, but

tend to offer growers more competitive prices when

supplies are tight (Sexton and Zhang). We believe that

our result is due to the fact that retailers use periodic

promotions of semi-perishable commodities as a facilitating mechanism for their cooperative behavior. By

publishing prices that demonstrate their willingness

and ability to reduce profits of other sellers, retailers

are able to establish effective trigger levels in the

absence of a formal mechanism of explicit collusion.

During these periodic promotions, retailers “cheat” on

the collusive arrangement and tend to price relatively

competitively, only to return to the collusive pricing

level once discipline is restored in the market. 

This conclusion is supported by our estimates in several ways. First, finding that punishment regimes occur

anywhere between one-third to one-fifth of the time is

consistent with the frequency of price promotions in

retailers’ produce departments. Second, the fact that

our statistical results show varying degrees of pricing

power being exercised by different chains also supports this conclusion—some choose to behave as punishers while others tend to follow. Third, this result is

also consistent with some retailers adopting an entirely

different pricing strategy—instead of using the market

power engendered by the collusive behavior to extract

rents through the price mechanism, they choose

instead to price competitively and then extract any

rents through some other form of rent-shifting mechanism. However, a more complete study of this issue

would compare estimates of retailer behavior, such as

we do here, to measures of retail concentration using a

longer time series data set that contains significant

temporal and geographic variation in concentration. 

22 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
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26 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA
Technical Appendix

Appendix 1. Econometric Model of Tacit Collusion 

Formally, assume a firm maximizes the present value of its expected future profits

given an infinite series of input price strategies with the t element given by: wit.=

sit (x0,x1,...,xt-1), so the objective function becomes:

for a set of rival strategies s-i, a discount factor ∃t , and input prices wt

. Further,

assume that the observed price is the realization of a random market price variable

subject to a multiplicative disturbance: where Ρ are i.i.d with continuous density ƒ and distribution function F. Under perfect information, rivals’ actions

are known with certainty and a collusive equilibrium can be supported if a punishment strategy is individually rational for all firms.1 Individual rationality requires

that the value of the firm under a collusive strategy be greater than the value of a

single-period defection, followed by industry reversion to Bertrand prices:

where wi is the price a firm pays in “normal” or collusive periods, and zi is the

price in reversionary or Bertrand periods. Because information is assumed to be

imperfect, however, the firm chooses between wi and zi based upon the only signal

that can be observed – the market price. Consequently, a discontinuous pricing

strategy results depending upon the relationship between market prices observed in

the previous period and a trigger price :

Stanford shows that such discontinuous strategies are necessary to support subgame perfect collusive equilibria except in the trivial case where continuous reactions specify replication of the Nash component game outcome.2 However, within

the class of discontinuous strategies, Porter (1985) argues that there are many

possible equilibrium price and punishment-period length pairs, so it remains to

describe the optimal strategy.

Defining the single-period profit during cooperative periods as πi (wi

) and that in

reversionary periods as πi (zi

) , the value of the firm initially in a cooperative

period is given by the weighted average of the present value of profits from operating in each period:

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 27

V ( ) = max E[ (1) 1 1 si

1

1 1

t=0

s 1 s β π ( , )] s ∞

∑ −

w w t t xit

i

=ψ ( ), ∑

V ( ) > ( + ) (2) 1

i

w π β i t i

i w Vz * (

w

w

w w w

z w w

it

it tit t-

= >

<

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

, ,

, . (3) 1

1

1 This is the Folk Theorem of Fudenberg and Maskin, the primary implication of which is that there

is potentially many equilibria in a repeated game with discounting.

2 Nevertheless, Slade (1987, 1990) develops a model wherein price wars are an equilibrium outcome

of continuous dynamic reaction function strategies.

i i i i ii t i t

T

i

T V w w w w V w w w z Vi wi ( ) ( ) ( ) ( ) )[ ( ) ( )], = Pr Pr( (4) π β ψ ψ βπ β + < +≥ ∑ + =

−

1

1
for reversionary periods of length T. Recognizing that

can be rewritten as:

which simply states that the expected present value of firm i is equal to the present

value of setting prices at the Bertrand level forever, plus the discounted value of

profit earned during collusive periods. 

Maximizing the value of the firm, therefore, requires the following first order

condition to hold:

which states that the incremental benefit from cheating on an existing collusive

arrangement (πi

(wi)) must equal the expected marginal loss that is incurred if rivals

interpret this increase in input prices correctly and adopt a punishment strategy

(Green and Porter). Because this condition defines a subgame perfect strategy, every

firm in the industry will indeed be expected to follow it and, therefore, never

completely defect from the cooperate / punish cartel. In a repeated-game context,

however, firms often have both the ability and incentive to renegotiate new equilibrium in order to avoid the punishment phase. Farrell and Maskin are among authors

who show that renegotiation reduces the likelihood of observing an effective triggerprice equilibrium, but this ability again depends on the structure of the industry and

the nature of rival interactions. Clearly, however, determining whether or not the data

are consistent with this conceptual pricing model requires an empirical approach that

is able to identify both the exercise of market power during collusive regimes, and

the endogenous switch to periods where firms price competitively.

A general model of processor profit maximization under imperfect competition

forms the basis for estimating an econometric model of shipper- and retail-level

produce price determination. However, given the relationships between buyers and

sellers, and among buyers themselves described above the usual approach to

modeling Bertrand rivalry must be extended to allow the dynamic Nash behavior

described above. Namely, this model must account for the possibility that observed

behavior, and the estimated market power parameters, vary both over time and

discontinuously by behavioral regime. At the core of the model presented by Green

and Porter lies a familiar conduct mechanism similar to that developed by

Appelbaum; Bresnahan; or Lau. Our extension to this approach involves estimating endogenous switch points within the sample period that delineate competitive from cooperative periods.

Estimating a model with discontinuous regimes of market power requires the

ability to identify two sets of conduct parameters where the switching behavior

between the two is determined endogenously. Due to this endogeneity, the

switching points between regimes are unidentifiable, or latent quantities.

Consequently, this study uses an empirical approach that is able to identify both

the degree of market power exercised in each regime and switching points between

regimes. To do so, we use a finite mixture estimation (FME) model (Titterington,

Smith, and Makov) and estimate it using an expectation / maximization (EM) algorithm (Dempster, Laird, and Rubin). The logic behind this approach is straightfor28 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

i i i i

T

i i i i

T i V ( ) ( )[ ( ( ) ( ))[( ) ( / )] , ww wz = )F] + ( (6) π β ββ π π ββ ∂ ∂ ′ 1 0 −+ − − − = fF s

Pr( ) ( / ( )), ψw w Fw ww i i < = (4)

V w w z

F

z

i i

i i ii

T

i i ( ) ( ) ()

( )

( ) = , −

−+ −

+ −

π π

β ββ

π

1 1 β (5)
ward and well understood in the literature. Further, in order to separate the exercise of market power from the impact of changing supply and demand on produce

margins, we develop a model of price determination within each regime of punishment or collusion.

Assume that the produce-retailing industry consists of N firms, all selling a

product that is differentiated on the basis of a quality reputation, a market location,

or by providing associated retail services to its customers. Further assume that

these retailers convert produce at the farm level to saleable goods using the same,

fixed proportions technology, herein assumed to be one-for-one without loss of

generality. This assumption means that raw inputs are separable from other, nonfarm inputs. To simplify notation, assume the production technology can be

written as: xij = λijqij where xij is the amount of produce of type j purchased by

retailer i, qij is the amount of j sold by the ith retailer, and 8ij is a constant of

proportionality, assumed here to be 1.

To allow for grower reputations for quality, or simply for the value of relationshipbuying among retail agents, the model is cast in a differentiated-product framework where an individual seller’s price is allowed to differ from an industry-wide

average price. Assuming retailer i receives a price pij (Xj

(Wj,z2),z1) where z1 is a

vector of demand-shifting exogenous variables, z2 is a vector of supply-shifting

exogenous variables and W is the industry-wide grower price. Assume each retailer

pays its suppliers a price wij for xi pounds of produce of type j and 

that the cost of selling produce can be described by a cost function that is separable between buying and selling activities, so that the retailers’ profit maximization problem is:

maxwi[πi

] = maxwi [(pi – wi)xi(W) – C(xi(W), v]∀j∈J. (7)

Interpreting xj

(Wj, z2) as the supply curve facing each retailer for each commodity,

and pj

(Xj, z1) as the inverse retail demand curve - again specific to each seller - and

C(xi

(wi),v) as total cost, a representative retailer’s first order condition becomes:

for each commodity, suppressing the j subscript. Because our data is specific to

each retailer, we write firm-level margin equations in terms of supply- and

demand-curve slopes and conjectures of both input and output market reactions for

each commodity j as:

mi = [pi – wi

] = ci + xi(W)(ηiθi)-1–xi(W)(∈iΦi), (9)

where ci is the marginal cost of marketing for firm i, 0i is the slope of the supply

curve facing each firm, 2i is firm i’s conjecture of how the input market price

changes for a one unit change in the price it pays, ,i is the slope of each firm’s

perceived inverse retail demand function, and Ni is the firm-specific conjectural

variation in output quantities. Equation (9) is simply a statement of the condition

for optimal input employment by a firm with oligopsony and oligopoly power --

that the marginal value product for each input is set equal to its marginal outlay.

Whereas the conduct parameter, or conjecture, is typically interpreted as parameterizing the degree of market power, in this application it is more general in that it

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 29

∂π

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

i

i

i i

i

i

i i

i

i

i

i i

i

w i

p w

p

W

W

w

xW xW p

X

X

x

x

W

W

w

C

x

x

W

W

w

= ( - ) - - = 0 (8) () () +

( ) X xj j ij

i

= ∀ ∑
describes the extent to which conduct is bounded away from perfect competition

given that the industry is in a stage of non-cooperative behavior.3 In order to identify this parameter, however, it is necessary to impose additional restrictions on the

slope of the supply curve, 0 and the demand curve, ,. 

Typically, this is accomplished by simultaneously estimating input supply and

output demand functions wherein their slopes are allowed to vary over time, or to

rotate independent of price changes caused by the exercise of market power

(Bresnahan). Therefore, input supply is estimated as a function of the grower price,

an interaction term between price and another explanatory variable, and a set of

other exogenous variables. A similar specification is used for the demand curve.

Following Lau or Schroeter and Azzam, the supply curve is specified as a linear

function of farm-level own-commodity prices and a set of exogenous factors such

as input prices, weather-events, or prices of alternative crops:

whereas the inverse-demand curve is a function of industry quantity demanded and

such demand-shifters as income, alternative commodity prices and seasonal

dummy variables:

With weekly data, this model is estimated assuming fixed weekly effects as supply

clearly differs due to seasonal factors. Moreover, we estimate both supply and

demand models using two-stage least squares due to assumed endogeneity of

grower prices and market demand, respectively. The results obtained by applying

these two models to the apple, grape, grapefruit and orange data are found in

tables 1 and 2 (apples), tables 4 and 5 (grapes), tables 7 and 8 (oranges) and tables

10 and 11 (grapefruit). For further interpretation of the results shown there, the

interested reader is referred to Richards and Patterson (2001). Once the values of 0

and , are substituted into (9), an expression for retail produce marketing costs must

be included prior to estimating the entire system. 

From the class of flexible functional forms, Diewert’s Generalized Leontief (GL)

provides several favorable characteristics for the cost function: it is inherently

homogeneous in prices without normalization, it is affine in output without further

restriction, and it imposes convexity in output, while concavity in prices,

symmetry, and monotonicity can be maintained and tested. For a single output (q)

and m input prices (vi), the GL cost function becomes:

30 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

Xwz w z z o k ii

i j

(, ) ( / ) , 2

1 =+ + + 2 22 ∑ −

≠

αη α μ (10)

pXz X z z o k ii

i k

(, ) ( / ) . 1 1 13 = +∈ + + ∑

≠

α αμ (11)

c x x v v x v ij

j

i j ii

i i

(,) ) , / v = ∑ ∑γ γμ ( (12) + + ∑ 12 2

1

3 There is considerable debate on the interpretation of these parameters in the literature. Appelbaum

maintains that if 2 = 1 and N = 1, then a retailer behaves as if it is a monopsonist in the input market and a monopolist in the output market, respectively, while if 2 = 0 and N = 0, it behaves as if

both the input and output markets are perfectly competitive. However, in a homogeneous product

oligopsony with N firms it can be shown that 2 is bound by 1/N (which implies that 2 goes to zero as

N becomes large) and 1 if the market price is regarded as an average over all firms’ individual prices.

On the other hand, N is instead bound by [0, N] under these same assumptions. We thank Rich

Sexton for these insights.
where :1 is a random error term, and the set of input prices include indices of fuel

and electricity prices, business services, and a measure of wages for workers in

food retailing. With this specification, derivation of the associated marginal cost

function is straightforward. While this model allows the elasticity of supply to vary

over time, it is also common to assume that the conduct parameter may also vary

with various aspects of the economic environment (Schroeter and Azzam, for

example). This is particularly important in our case in order to test the hypothesis

that retailer market power falls in the level of fresh produce shipments.

In a more general sense, there may be other factors that influence the exercise of

market power. Therefore, define K as a vector of economic factors that are likely to

influence the degree of market power. In particular, if reliable data on concentration levels, barriers to entry or other structural indicators were available on a more

frequent basis, then we could directly test the hypothesis that certain structural

features may contribute to a retailer’s ability to use market power. Limiting the

model to the existing data, however, each market power parameter can be written

as a linear function of quantity:

Although it is common practice to estimate equations (9) - (12) simultaneously,

this study estimates raw product supply, retail demand and the fresh produce

margin equations sequentially due to the added complexity of the multiple-regime

finite mixture model.4 The logic underlying this model and its value in estimating

multiple market-power regimes are outlined in the following section. 

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 31

θδ δδ μ

φτ τ μ

( ) ()

) () .

X X ,

X x

=+ + o

= +

1 4

1 5

 (13)

(

4 Sequential estimation produces parameter estimates that are consistent, but inefficient relative to

those found with a full-information estimator such as FIML or 3SLS.
Appendix 2. Finite Mixture Estimation of Switching Regressions Model 

Essentially, the FME approach maintains that observations of the dependent variable, retail-shipper margins in the current case, are not drawn from one distribution, but rather two distinct distributions described by unique sets of parameters. In

general, Titterington, Smith, and Makov define f(mi

) as a finite mixture distribution

of margins over k distinct regimes if:

f

i

(mi) = ρif

1i

(m)+...+ρkf

ki(mi

) (14)

where the mixing weights are defined as and the indvidual densities must, of course, meet the restrictions that: f

i

(> 0,∫ f

j

(mi )dm = 1

Thus, the density for margins is a probabilistically weighted average of each of the

component densities (f

j

), each with its own mixing weight. Assuming commodity

margins are normally distributed, and simplifying the mixture distribution to represent only two regimes, the density can be written as:

f

i

(mi ⎜Ω) = ρ(mi ⎜μ1,σ) + (1 – ρ)ψ(mi ⎜μ2,σ), (15)

where Ρ is the normal density function, and μi = Zαi for regime i and a vector of

explanatory variables, Z. Wolfe describes a modified likelihood ratio test that is

typically used to test the null hypothesis of a two-regime model against a more

restrictive single-regime alternative. Wolfe’s test is an approximation to likelihood

ratio test based on a modified Chi-square distribution with test statistic:

S = (2 / N)(n – 1– d – (C1 / 2)) log L, (16)

where L is the value of the likelihood ratio under the null hypothesis of no

mixture, N is the sample size, C1 is the number of components in the mixture (two

in our case), and d is the dimension of the underlying normal distribution. The test

statistic is Chi-square distributed under the null hypothesis with 2d (C1 - 1)

degrees of freedom. In terms of the produce buying market structure example, the

two regimes are defined by differences in each element of their respective parameter vectors, but most importantly, by differences in the conjectural elasticity of

input supply. Modifying equation (9) to be consistent with the switching-regression logic, the margin model becomes:

for each commodity j. However, estimating (15) is not straightforward because the

separation points between the two regimes are unobservable. 

Unlike Porter (1983), who has data indicating, albeit imperfectly, periods of collusion among nineteenth century railways belonging to the Joint Executive

Committee, no such data exists for this study. Therefore, the estimation technique

must be able to infer an optimal mixing weight from the data that defines two

distinct regimes that are relatively homogeneous within each, but significantly

different between.1 One such latent variable method is the expectation / maximiza32 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

ρ ρ j j

j

> == 0 1 12 , , ,, , ∑ j k K

m

c withprob

c ( ) x withprob i t

i,t

i t i,t i i,t

,

,

.

.( = + −

⎡

⎣

⎢ ⎤

⎦ − ⎥

 

 , (17) ρηθ ρ 1 1

1 In this respect, FME is very similar to latent class and cluster analysis.
tion algorithm (EM) (Dempster, Laird, and Rubin). The EM algorithm, also known

as the “missing data approach” has become increasingly popular in recent years to

estimate a wide variety of latent variable models such as dynamic structural latent

variable models or Kalman filters. Dempster, Laird, and Rubin explain the intricacies of this approach, but its fundamental logic is easy to understand. 

The estimation method begins in the expectation step, and then iterates between

expectation and maximization. Initial estimates of the aggregate mixing weights,

or the proportion of observations falling into each regime, are combined with

initial model parameters to update the segment weights by calculating the posterior

probability of segment membership of each observation. Specifically, these

updated weights, si

, are defined as:

Calculating these weights constitutes the expectation step. Next, the updated

weights are used to form diagonal matrices S1 and S2, where:

Each observation is then assigned to a regime depending upon its dominant posterior probability. For example, if observation i has a posterior probability of

belonging to segment 1 of 0.60 and a probability of belonging to segment 2 of

0.40, then it is assigned to segment 1 and the sample is:

thus delineated for all observations. In the maximization step, new regime-specific

response parameters are obtained by weighted least squares:

New aggregate regime shares are found by averaging the weights calculated in

(18) over all observations. With these updated aggregate shares, the posterior probability of each observation belonging to each regime is once again found using

Bayes’ rule (18). These weights are, in turn, used to find new weighted least

squares estimates through (20). This process iterates between expectation and

maximization until the log-likelihood function changes by less than some prespecified convergence level. Once the model converges, the resulting parameter estimates possess the asymptotic properties of maximum likelihood estimates. These

parameters permit tests of a departure from perfectly competitive input pricing if

retailers behave according to a very realistic and theoretically consistent model of

strategic behavior over time.

Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 33

s ff

s ff

i ii

i ii

1 1

2 2

18

1

=

= −

ρ

ρ

( /) ()

( )( / ).

 

s1 11 12 1

2 21 22 2

= 19

=

diag s s s

s diag s s s

k

k

[ ()

[ .

, , , 

, ,,

K

K

α [ ]

σ αα

j j jj

j j j jjj j

j ij

i

n

SZ ZSm

n m Z Sm Z

n s

= ′ ′

= −′ −

= ∑

−

Z

1

2 ( / )( ) ( ) (20) 1
Appendix 3. Parameter Estimates

34 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

Appendix table 3-1—Washington Red Delicious apples: Supply function 2SLS estimates

Variable Coefficient t-ratio

pg /w1 7.438* 4.810

W2 -0.094* -3.022

W3 -1.046* -7.352

W4 -7.402* -6.011

Px -69.977* -6.657

ppo -4.338* -17.340

T 0.184* 16.880

Jan. -10.269* -16.090

Feb. -7.877* -9.799

Mar. -7.229* -9.594

Apr. -7.111* -9.670

May -6.706* -7.774

June -8.492* -9.738

July -12.098* -13.760

Aug. -12.994* -14.870

Sep. -12.364* -15.340

Oct. -5.680* -9.405

Nov. -4.874* -8.370

Constant 256.170* 15.090

R2 0.746

DW 2.287

BP 8.971

The variables are defined as follows: pg = grower price, px = export price, ppo = processing price (apple juice), w1 = harvesting labor wage rate, w2 = price

index of agricultural chemicals, w3 = energy price index, w4 = interest rate index, t = linear time. A single asterisk indicates significance at a five percent level.
Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 35 Appendix table 3-2—Market-level Red Delicious retail demand functions: 2SLS estimates Market 1 Market 2 Market 3 Market 4 Market 5 Market 6 Variable Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio

pr -0.073* -1.985 -0.147* -13.570 -0.951* -5.621 -0.162* -8.373 -0.687* -6.704 -0.358* -9.932

z1 0.131 1.433 0.229* 4.127 1.314* 3.968 0.137 1.783 0.850* 2.879 0.430* 2.951

z2 0.005 0.711 0.001 0.342 0.042 1.532 0.007 1.529 0.023 0.774 -0.007 -0.786z3 0.017 0.877 0.031* 4.091 0.062 1.076 -0.013 -1.640 -0.017 -0.323 0.106* 4.785z4 -2.086 -0.994 0.222 0.724 -2.242 -0.499 1.038 0.909 12.607 0.974 -5.036* -2.912

t 0.001 0.862 0.000 -0.942 0.001 0.488 0.000 -1.426 -0.002 -1.167 0.002* 2.726Chain 2 -0.005 -0.812 0.033* 24.960 -0.035* -3.237 0.031* 12.300 0.097* 6.444 0.138* 39.82Chain 3 N.A. N.A. 0.009* 5.241 -0.035* -2.179 -0.034* -12.160 0.054* 3.775 0.003 0.484Chain 4 N.A. N.A. N.A. N.A. N.A. N.A. -0.039* -8.626 0.102* 7.249 N.A. N.A.Chain 5 N.A. N.A. N.A. N.A. N.A. N.A. -0.081* -13.090 N.A. N.A. N.A. N.A.

Constant 0.703 0.993 -0.226 -0.889 1.057 0.457 -0.203 -0.553 -2.324 -0.942 2.009* 2.751R2 0.207 0.774 0.387 0.734 0.35 0.872

DW 2.108 1.363 1.379 1.345 1.619 1.557

BP 17.433 11.901 6.086 16.396 9.647 20.089The variables are defined as follows: pr = retail price, z1 = retail price of bananas, z2 = retail price of table grapes, z3 = retail price of fresh oranges, z4 = personal disposable income per capita, t = linear time

trend. Note: Jan. - Nov. dummy variable estimates are suppressed for presentation purposes. All Durbin-Watson tests fall in the inconclusive range. Critical chi-square values for the BP test at 5% and 15, 16,17, and 18 df are 24.996, 26.296, 27.687, and 28.869, respectively. Therefore, we fail to reject the null hypothesis of no heteroscedasticity in each case. A single asterisk indicates significance at a five percentlevel.
36 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

Appendix table 3-3—Summary of apple market power parameter estimates

Chain *0 *1 Total 2 θ0 θ1 Total N Weight Wolfe

Albany: 1 1.008* -0.007* 0.656* 0.091 -0.001 0.057* 0.653*

(22.184) (-6.585) (24.295) (1.429) (-0.615) (2.246) (11.407) 55.607

Albany: 2 1.064* -0.011* 0.508* 1.813* -0.011* 1.279* 0.469*

(2.901) (-2.416) (2.461) (9.005) (-3.001) (10.018) (5.728) 61.841

Atlanta: 1 0.453* 0.001 0.519* 0.376 0.012 0.973* 0.734*

(2.845) (0.683) (5.217) (0.707) (1.573) (5.166) (12.086) 50.243

Atlanta: 2 0.219* -0.004* 0.033 0.983* -0.006* 0.676* 0.412*

(3.244) (-4.710) (0.963) (25.864) (-12.097) (37.484) (6.004) 80.032

Atlanta: 3 1.943 -0.056* 0.776* 6.609* -0.084* 1.524* 0.794*

(1.903) (-3.242) (2.174) (5.979) (-4.885) (7.336) (14.803) 128.429

Chicago: 1 0.599* 0.002* 0.685* -0.385* 0.007* 0.033* 0.727*

(9.104) (2.097) (19.270) (-23.411) (23.752) (5.510) (13.508) 57.846

Chicago: 2 0.402* -0.002 0.325* 0.099 -0.001 0.061 0.668*

(3.633) (-1.053) (5.193) (1.029) (-0.521) (1.032) (8.469) 65.927

Chicago: 3 1.135* -0.019* 0.239* 0.035* -0.001* 0.006* 0.839*

(28.278) (-38.577) (11.422) (7.783) (-12.360) (4.407) (22.287) 123.958

Dallas: 1 0.573* -0.006 0.277* 0.207 0.001 0.210* 0.338*

(2.266) (-1.652) (2.544) (1.689) (0.041) (5.169) (5.011) 85.944

Dallas: 2 0.036 0.001 0.059* 0.116* -0.001* 0.096* 0.754*

(1.161) (1.197) (4.041) (19.097) (-4.709) (40.822) (16.063) 66.418

Dallas: 3 -0.156 0.003 0.016 0.831* -0.001 0.806* 0.624*

(-0.798) (0.944) (0.213) (6.139) (-0.253) (12.617) (9.449) 62.43

Dallas: 4 0.432 -0.003 0.243 0.357* -0.002 0.251* 0.396*

1.152 (-0.776) (1.237) (2.316) (-1.082) (2.714) (5.001) 48.584

Dallas: 5 0.236 -0.002 0.125 0.611 0.002 0.714 0.641*

(0.099) (-0.069) (0.094) (0.521) (0.119) (1.528) (5.996) 53.879

Los Angeles: 1 0.5358* -0.001 0.468* -0.014 0.001* 0.052* 0.234*

(4.181) (-0.759) (6.391) (-0.337) (2.019) (3.918) (4.120) 111.133

Los Angeles: 2 4.685* -0.065* 1.562* 0.461* -0.006* 0.157* 0.809*

(8.542) (-8.323) (6.718) (8.373) (-6.084) (18.957) (16.329) 136.696

Los Angeles: 3 0.614* -0.007* 0.265* 0.145* -0.002* 0.039* 0.131*

(6.807) (-5.501) (5.502) (5.790) (-5.466) (5.984) (21.175) 132.817

Los Angeles: 4 -0.832 0.014 0.764* 0.09 -0.001 0.033* 0.659*

(-1.934) (0.221) (3.977) (1.122) (-0.741) (2.847) (10.129) 67.2

Miami: 1 0.215 0.003 0.382 0.256 0.010 0.761* 0.487*

(0.348) (0.394) (1.243) (0.424) (1.313) (2.458) (6.394) 58.692

Miami: 2 0.644* -0.010* 0.162 0.425* -0.003* 0.269* 0.569*

(2.723) (-2.768) (1.426) (9.371) (-5.328) (11.085) (7.256) 37.359

Miami: 3 0.409 0.001 0.427* 0.294* -0.002 0.171* 0.591*

(1.394) (0.087) (3.497) (3.436) (-1.802) (3.820) (8.191) 59.843

The market power parameters are defined by the linear specifications: θ = δ0 + δ1Χ, on the buying side, and φ = τ0Χ in the output market for the collusive

regime only. For Wolfe's test, the critical chi-square value at 5% and twelve degrees of freedom is 21.026. The values in parentheses are t-rations; a single

asterisk indicates significance at a 5% level. In this table, the “weight” parameter is interpreted as the percentage of observations observed in a punishment

phase.
Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 37

Appendix table 3-4—California green seedless grapes: Supply function 2SLS estimates

Variable Coefficient t-ratio

qs, t-1 0.596 1.400

pg /w1 -0.672* -5.169

w2 -0.227* -3.178

w3 -7.433* -2.783

px -0.006* -2.518

ppo1 -0.005 -1.069

ppo2 9.839* 8.834

t -0.078 -1.495

May 19.563* 3.522

June 19.030* 3.349

July -11.156* -2.032

Aug. 19.064* 3.637

Sep. 7.178 1.401

Oct. 2.036 0.412

Nov. 3.969 0.825

Constant -1351.103* -8.938

R2 0.717

DW-h 0.622

BP 11.116

The variables are defined as follows: pg = grower price, px = export price, ppo1 = processing price (raisins), ppo2 = processing price (wine), w1 = harvesting

labor wage rate, w2 = price index of agricultural chemicals, w3 = energy price index, w4 = interest rate index, t = linear time trend. A single asterisk indicates

significance at a 5% level. The critical value of the BP test with 16 degrees of freedom at a 5% level is 26.696. The DW-h statistic is asymptotically normal.
38 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA Appendix table 3-5—Market-level green seedless grape retail demand functions: 2SLS estimates Market 1 Market 2 Market 3 Market 4 Market 5 Market 6 Variable Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio

pr

z1 -0.163* -9.885 -0.011* -4.196 -0.131* -3.732 -0.083* -8.673 -0.211* -8.592 -0.031* -3.062

z2 0.551* 2.333 -0.026 -0.808 -1.549* -3.36 -0.025 -0.204 0.779 1.935 -0.163 -1.343

z3 0.024 0.383 -0.007 -1.39 0.256 1.554 -0.039 -1.387 -0.494* -4.798 -0.123* -5.675z4 -9.644* -2.229 -0.522* -3.745 -20.871* -4.276 -6.332* -4.092 -61.329* -5.224 -2.046 -1.622

t 0.004* 2.293 0.003* 3.771 0.011* 4.016 0.002* 4.676 0.009* 5.043 0.009* 2.017Chain 2 0.005 0.259 0.037* 29.31 -0.141* -4.491 -0.072* -9.743 0.097* 4.031 0.034* 7.196Chain 3 N.A. N.A. -0.005* -3.199 0.085* 2.005 -0.089* -10.501 0.015 0.609 -0.008* -9.249Chain 4 N.A. N.A. N.A. N.A. N.A. N.A. -0.091* -5.701 0.182* 6.984 N.A. N.A.Chain 5 N.A. N.A. N.A. N.A. N.A. N.A. -0.136* -5.981 N.A. N.A. N.A. N.A.

Constant 3.145* 2.14 0.455* 3.868 11.334* 4.569 2.19* 4.467 11.979* 5.257 1.116* 2.12R2 0.456 0.871 0.462 0.499 0.433 0.598

DW 1.873 1.904 1.963 1.704 2.354 1.773

BP 7.773 2.835 4.699 2.951 5.911 2.891The variables are defined as follows: pr = retail price, z1 = retail price of bananas, z2 = retail price of apples, z3 = retail price of fresh oranges, z4 = personal disposable income per capita, t = linear time trend.

Note: June - Dec. dummy variable estimates are suppressed for presentation purposes. All Durbin-Watson tests fall in the inconclusive range. Critical chi-square values for the BP test at 5% and 15, 16, 17, and18 df are 24.996, 26.296, 27.687, and 28.869, respectively. Therefore, we fail to reject the null hypothesis of no heteroscedasticity in each case.
Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 39

Appendix table 3-6—California green seedless grapes: Market power estimate summary

Chain *0 *1 Total 2 θ0 θ1 Total N Weight Wolfe

Albany: 1 -0.005* 1.476* 0.003* 1.573* 0.002 1.574* 0.787*

(-4.280) (-5.308) (3.227) (3.872) (0.011) (4.402) (12.862) 106.036

Albany: 2 0.001 -0.032 -0.001 2.435* -7.764* 1.987* 0.686*

(0.504) (-1.158) (-0.255) (10.829) (-9.020) (8.765) (9.737) 86.561

Atlanta: 1 -0.003* 6.929* 0.001 1.229* -2.481* 1.091* 0.800

(-3.448) (2.033) (0.015) (6.365) (-3.054) (6.018) (15.901) 143.975

Atlanta: 2 -4.165* 9.126* -0.277* -3.532* 8.395* 0.441 0.582*

(-11.995) (12.503) (-3.680) (-8.168) (12.114) (1.929) (8.764) 74.656

Atlanta: 3 0.059 4.999 0.076* 0.03 3.906 0.155 0.513*

(1.889) (0.702) (3.368) (0.049) (0.739) (0.304) (5.944) 47.359

Chicago: 1 0.002 -0.113 0.002 -0.048 0.248* 0.471* 0.465*

(1.896) (-0.806) (1.953) (-4.515) (4.454) (4.448) (7.238) 178.797

Chicago: 2 -0.033* 0.001* 0.007 -1.386* 0.021* -0.356* 0.324*

(-2.587) (3.134) (1.366) (-3.088) (2.177) (-3.045) (3.887) 104.317

Chicago: 3 -0.092* 0.002* -0.015* -0.014 0.001 0.020* 0.525

(-6.859) (6.899) (-3.310) (-0.455) (1.250) (2.109) (0.084) 38.547

Dallas: 1 0.222* -0.004* 0.027* 0.463* -0.007* 0.127* 0.664*

(23.520) (-31.409) (4.946) (7.503) (-7.623) (6.822) (10.066) 46.931

Dallas: 2 -0.010 0.001 0.019* -0.787* 0.009 -0.321 0.775*

(-0.760) (1.873) (2.661) (-2.517) (1.781) (-3.687) (11.083) 93.375

Dallas: 3 -0.149* 0.001 -0.097* 0.612 -0.009 0.193* 0.675*

(-3.547) (1.659) (-5.339) (-0.009) (-1.728) (2.025) (8.994) 45.523

Dallas: 4 -0.082* 0.001* 0.058* -1.019* 0.016* 0.055 0.403*

(-2.760) (3.165) (4.172) (-2.600) (2.716) (0.437) (5.222) 81.278

Dallas: 5 0.589 -0.001 0.017 1.026 -0.003 0.866* 0.748*

(1.116) (-0.944) (1.272) (1.496) (-0.248) (2.948) (10.688) 72.512

Los Angeles: 1 0.118 -0.003* -0.023 1.964* -0.021* 0.911* 0.733*

(1.557) (-2.331) (-0.897) (3.662) (-2.721) (4.324) (10.253) 63.011

Los Angeles: 2 -0.028 -0.001 0.028 0.017 0.001 0.019 0.608*

(-0.525) (-0.362) (0.341) (0.127) (0.157) (0.289) (6.727) 49.381

Los Angeles: 3 -0.089 0.001 -0.018 0.116* 0.019 1.094* 0.613*

(-0.969) (0.965) (-0.719) (2.561) (1.107) (2.947) (8.801) 139.519

Los Angeles: 4 0.273* -0.003 0.121* 0.432* -0.007 0.084 0.600*

(2.775) (-1.881) (3.649) (1.967) (-1.523) (1.451) (6.397) 51.094

Miami: 1 0.661* -0.006* 0.292* 0.789* -0.008 0.393* 0.650*

(3.027) (-2.743) (3.104) (2.786) (-1.717) (5.184) (8.423) 84.335

Miami: 2 0.092* -0.001* 0.042* 0.213* -0.001* 0.145* 0.780*

(20.951) (-14.027) (18.331) (25.167) (-8.877) (48.187) (13.763) 126.31

Miami: 3 0.005 0.002* 0.080* -2.724* 0.337* 0.416* 0.552*

(0.134) (2.787) (4.334) (-5.925) (6.124) (3.952) (5.893) 55.34

The market power parameters are defined by the linear specifications: θ = δ0 + δ1Χ, on the buying side, and φ = τ0Χ in the output market for the collusive

regime only. The critical chi-square value at 5% and twelve degrees of freedom is 21.026. For all other variables, a single asterisk indicates significance at 

a 5% level. In this table, the "weight" parameter is interpreted as the probability an observation is in a punishment phase.
40 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

Appendix table 3-7—California fresh oranges: Supply function 2SLS estimates

Variable Coefficient t-ratio

qs, t-1 0.278* 20.14

pg w1 5.461* 19.450

w2 -1.698* -7.472

w3 -17.694* -5.489

px -0.785* -8.957

Mar. -171.54 -13.550

Apr. -322.660* -19.530

May -361.510* -23.350

June -531.130* -36.210

July -196.740* -12.380

Aug. -303.720* -21.870

Sep. -582.540* -33.980

Oct. -472.440* -28.310

Nov. -306.000* -18.03

Constant 3322.800* 8.126

R2 0.792

DW-h 1.456

BP 3.745

The variables are defined as follows: pg = grower price, px = export price, w1 = harvesting labor wage rate, w2 = price index of agricultural chemicals,

w3 = energy price index. A single asterisk indicates significance at a 5% level. The critical value of the BP test with 15 degrees of freedom is 24.996. 

The DW-h statistic is asymptotically normal.
Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 41 Appendix table 3-8—Market-level fresh orange retail demand functions: 2SLS estimates Market 1 Market 2 Market 3 Market 4 Market 5 Market 6 Variable Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio

pr /z1 -330.56* -7.54 -6.979 -1.293 -347.450* -3.739 -53.606* -3.708 -413.460* -6.861 -91.942* -4.099

z2 677.140* 3.262 167.020* 2.225 -655.960 -1.015 286.290* 2.768 -988.280* -2.387 432.280* 2.060

z3 7.337 0.146 11.712 1.640 494.620* 3.172 52.179* 4.270 -151.380* -2.034 36.382 1.504z4 3.281 0.619 1.052* 3.782 7.251 0.856 2.547* 2.185 1.529 1.116 7.006* 3.604t -1.299 -0.670 -0.692* -3.878 -4.431 -0.999 -0.928* -2.995 -4.426* -1.970 -3.135* -4.422Chain 2 66.350* 3.440 66.457* 33.110 -267.790* -6.803 -34.042* -7.362 123.480* 6.495 82.068* 11.010Chain 3 N.A. N.A. 6.229* 2.598 61.424 1.493 -66.220* -14.600 68.638* 3.762 -39.689* -3.425Chain 4 N.A. N.A. N.A. N.A. N.A. N.A. -17.656* -2.561 90.817* 4.567 N.A. N.A.Chain 5 N.A. N.A. N.A. N.A. N.A. N.A. -42.025* -3.952 N.A. N.A. N.A. N.A.

Constant -1.255 -0.698 -0.917* -4.170 -3.463 -0.791 -0.835* -2.344 -1.545 -0.603 -3.000* -3.801K 15 16 16 18 17 16R2 0.647 0.872 0.429 0.711 0.589 0.779

DW 1.435 1.638 1.489 1.809 1.841 1.705

BP 2.592 4.738 4.826 7.805 6.112 9.213The variables are defined as follows: pr = retail price, z1 = retail price of bananas, z2 = retail price of apples, z3 = retail price of table grapes, z4 = personal disposable income per capita, t = linear time trend.

Note: Mar. - Nov. dummy variable estimates are suppressed for presentation purposes. All Durbin-Watson tests fall in the inconclusive range. Critical chi-square values for the BP test at 5% and 15, 16, 17,and 18 df are 24.996, 26.296, 27.687, and 28.869, respectively. Therefore, we fail to reject the null hypothesis of no heteroscedasticity in each case.
42 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA

Appendix table 3-9—Summary of orange market power parameter estimate

Chain *0 *1 Total 2 θ0 θ1 Total N Weight Wolfe

Albany: 1 0.499* -0.003* 0.308* -0.168* 0.002* 0.057* 0.588*

(2.892) (2.722) (2.658) (-2.950) (2.226) (3.219) (8.252) 71.577

Albany: 2 0.618* -0.002 0.428* 0.221 0.001 0.255* 0.755*

(2.191) (-1.195) (2.159) (1.507) (0.241) (6.802) (14.357) 84.525

Atlanta: 1 1.770* -0.001* 0.994* -1.535 0.005 1.832* 0.632*

(2.608) (-3.564) (2.086) (-0.699) (1.856) (3.101) (9.162) 95.816

Atlanta: 2 -0.572 0.001* 0.119 -0.132 0.004 0.118* 0.666*

(-1.086) (2.703) (0.310) (-0.755) (1.282) (2.713) (8.449) 66.293

Atlanta: 3 -0.112 0.001 -0.043 0.241 0.001 0.299* 0.801*

(-0.851) (1.369) (-0.479) (0.750) (0.195) (2.321) (16.504) 188.045

Chicago: 1 0.618 -0.001 0.508 0.099 -0.001 0.027 0.469*

(0.933) (-0.312) (1.446) (0.964) (-0.669) (0.972) (7.548) 145.224

Chicago: 2 0.122 -0.001* 0.038 0.065 -0.006 0.023 0.572*

(1.609) (-3.161) (0.698) (0.513) (-0.376) (0.805) (7.492) 52.299

Chicago: 3 1.759* -0.001* 0.813* -0.025 0.001* 0.045* 0.619*

(9.098) (-10.421) (7.182) (-1.137) (3.542) (8.482) (8.197) 53.485

Dallas: 1 0.755* -0.001* 0.372* 0.136* 0.001 0.183* 0.572*

(3.479) (-5.005) (2.313) (2.571) (0.784) (7.083) (9.183) 79.301

Dallas: 2 0.243 -0.001 0.161 0.123 -0.003* -0.068* 0.611*

(1.638) (-1.197) (1.686) (1.681) (-2.494) (-1.972) (9.616) 78.429

Dallas: 3 0.192* -0.002 0.177* 0.267* -0.001 0.143* 0.727*

(1.638) (-1.197) (1.686) (1.681) (-2.494) (-1.972) (9.616) 82.927

Dallas: 4 -1.210* 0.001* -0.5818 -0.479* 0.001* 0.111* 0.564*

(-5.814) (6.196) (-4.154) (-3.297) (4.521) (3.527) (8.817) 74.411

Dallas: 5 -0.387* 0.002* -0.242* -0.073 -0.001 -0.117* 0.495*

(-3.336) (2.239) (-3.701) (-0.476) (-0.322) (-2.201) (6.260) 55.976

Los Angeles: 1 -0.267 0.002 0.021 0.176* 0.001 0.045* 0.625*

(-0.735) (1.021) (0.132) (2.489) (0.723) (2.513) (9.787) 86.806

Los Angeles: 2 -0.164 0.001* 0.068 0.036* -0.001 0.027* 0.650*

(-1.501) (2.885) (0.823) (3.043) (-0.733) (15.686) (12.144) 128.209

Los Angeles: 3 -0.233 0.004* 0.030 -0.022 0.005 0.012* 0.525*

(-1.560) (4.351) (0.303) (-1.145) (1.840) (3.553) (8.713) 118.739

Los Angeles: 4 2.627* -0.002* 1.164* 0.233* -0.018 0.120* 0.593*

(4.832) (-5.570) (3.530) (2.883) (-1.476) (3.076) (8.740) 69.683

Miami: 1 0.371 -0.002* 0.495* 1.296* -0.007* 0.862* 0.686*

(1.677) (-2.105) (2.896) (8.933) (-3.447) (17.761) (10.749) 49.831

Miami: 2 0.249 -0.001* 0.130 0.014 0.001 0.024 0.614*

(1.951) (-3.154) (1.393) (0.513) (0.478) (1.802) (7.804) 48.282

Miami: 3 0.537* -0.002* 0.384* 0.129 0.003 0.147 0.387*

(3.278) (-2.530) (3.535) (0.604) (0.109) (1.509) (5.551) 101.594

The market power parameters are defined by the linear specifications: θ = δ0 + δ1Χ, on the buying side, and φ = τ0Χ in the output market for the collusive

regime only. The critical chi-square value at 5% and twelve degrees of freedom is 21.026. For all other variables, a single asterisk indicates significance at a

5% level. In this table, the "weight" parameter is interpreted as the probability of an observation being in a punishment phase.
Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 43

Appendix table 3-10—Fresh grapefruit: Supply function 2SLS estimates

Variable Coefficient t-ratio

pg / w1 7.259* 4.52

w2 -209.610* -13.92

w3 -71.895* -11.45

w4 40.136* 4.869

px -1.800* -13.67

ppo -14.856* -5.826

t 0.002* 2.064

Jan. -71.172* -4.853

Feb. -120.520* -7.774

Mar. 3.085 0.2332

Apr. -161.400* -12.41

May -401.240* -34.63

Sep. -506.300* -28.22

Oct. -183.830* -14.52

Nov. -174.390* -17.21

Constant 11.612* 13.62

R2 0.888

DW 1.479

BP 0.721

The variables are defined as follows: pg = grower price, px = export price, w1 = harvesting labor wage rate, w2 = price index of agricultural chemicals,

w3 = energy price index. A single asterisk indicates significance at a 5% level. The critical value of the BP test with 18 degrees of freedom is 28.869. 
44 ● Competition in Fresh Produce Markets/CCR-1 Economic Research Service/USDA Appendix table 3-11—Market-level fresh grapefruit retail demand functions: 2SLS estimates Market 1 Market 2 Market 3 Market 4 Market 5 Market 6 Variable Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio

pr z1 -0.073* -1.985 -0.147* -13.570 -0.951* -5.621 -0.162* -8.373 -0.687* -6.704 -0.358* -9.932

z1 0.131 1.433 0.229* 4.127 1.314* 3.968 0.137 1.783 0.850* 2.879 0.430* 2.951

z2 0.005 0.711 0.001 0.342 0.042 1.532 0.007 1.529 0.023 0.774 -0.007 -0.786z3 0.017 0.877 0.031* 4.091 0.062 1.076 -0.013 -1.64 -0.017 -0.323 0.106* 4.785z4 -2.086 -0.994 0.222 0.724 -2.242 -0.499 1.038 0.909 12.607 0.974 -5.036* -2.912

t 0.001 0.862 0.000 -0.942 0.001 0.488 0.000 -1.426 -0.002 -1.167 0.002* 2.726Chain 2 -0.005 -0.812 0.033* 24.960 -0.035* -3.237 0.031* 12.300 0.097* 6.444 0.138* 39.82Chain 3 N.A. N.A. 0.009* 5.241 -0.035* -2.179 -0.034* -12.160 0.054* 3.775 0.003 0.484Chain 4 N.A. N.A. N.A. N.A. N.A. N.A. -0.039* -8.626 0.102* 7.249 N.A. N.A.Chain 5 N.A. N.A. N.A. N.A. N.A. N.A. -0.081* -13.090 N.A. N.A. N.A. N.A.

Constant 0.703 0.993 -0.226 -0.889 1.057 0.457 -0.203 -0.553 -2.324 -0.942 2.009* 2.751K 15 16 16 18 17 16R2 0.637 0.812 0.696 0.755 0.424 0.943

DW 1.883 2.152 2.112 1.276 1.377 1.988

BP 2.24 4.652 3.073 5.544 6.172 16.022The variables are defined as follows: pr = retail price, z1 = retail price of bananas, z2 = retail price of apples, z3 = retail price of table grapes, z4 = personal disposable income per capita, t = linear time trend.

Note: Mar. - Nov. dummy variable estimates are suppressed for presentation purposes. All Durbin-Watson tests fall in the inconclusive range. Critical chi-square values for the BP test at 5% and 15, 16, 17,and 18 df are 24.996, 26.296, 27.687, and 28.869, respectively. Therefore, we fail to reject the null hypothesis of no heteroscedasticity in each case.
Economic Research Service/USDA Competition in Fresh Produce Markets/CCR-1 ● 45

Appendix table 3-12—Summary of grapefruit market power parameter estimate

Chain *0 *1 Total 2 θ0 θ1 Total N Weight Wolfe

Albany: 1 -0.516 -0.004 -0.244 0.462* -0.005* 0.1808* 0.601*

(-0.194) (-1.405) (-1.155) (4.497) (-2.696) (10.667) (6.709) 43.429

Albany: 2 -0.437 -0.012* -1.085* 2.632* -0.003* 1.011* 0.371*

(-0.812) (-4.094) (-2.583) (9.003) (-6.115) (23.011) (5.561) 45.453

Atlanta: 1 0.475* -0.003* 0.318* 0.662* 0.002* 1.675* 0.206*

(34.218) (-25.697) (36.781) (10.503) (20.757) (113.800) (3.986) 78.636

Atlanta: 2 2.073* -0.005* 1.811* -0.074* 0.001* 0.413* 0.208*

(58.582) (-11.754) (34.895) (-2.159) (14.578) (386.911) (4.039) 97.563

Atlanta: 3 15.473* -0.029* 0.03 0.779* -0.008* 0.350* 0.219*

(14.414) (-28.686) (0.046) (73.345) (-40.526) (180.077) (4.137) 86.616

Chicago: 1 2.969* -0.025* 1.644* -0.039 0.001 0.0568* 0.376*

(5.584) (-4.654) (4.376) (-0.347) (0.866) (2.255) (5.335) 43.546

Chicago: 2 1.611* -0.011* 0.981* -0.406* 0.001* -0.065* 0.261*

(28.936) (-8.472) (12.356) (-2.596) (2.624) (-2.263) (4.563) 95.931

Chicago: 3 1.920* -0.028* 0.435* 0.427* -0.001* 0.055* 0.276*

(43.275) (-74.792) (16.045) (100.828) (-99.085) (35.526) (4.781) 73.533

Dallas: 1 0.984* 0.001 1.056* -0.564* 0.002* 0.532* 0.266*

(4.565) (0.509) (6.905) (-3.278) (5.774) (7.329) (4.511) 52.767

Dallas: 2 0.249* 0.004 0.272* 0.206* 0.004* 0.454* 0.214*

(2.575) (0.410) (6.749) (20.020) (18.392) (80.829) (4.185) 114.884

Dallas: 3 0.161 0.014* 0.934* -2.984* 0.006* 0.550* 0.214*

(1.041) (6.279) (19.493) (-18.919) (17.895) (13.530) (4.192) 116.826

Dallas: 4 0.008* -0.001* -0.047* 0.042* -0.001* 0.003* 0.213*

(3.311) (-74.880) (-25.733) (82.154) (-99.189) (18.952) (4.181) 117.36

Dallas: 5 -0.186* 0.008* -0.143* 2.125* -0.001* 1.596* 0.329*

(-10.011) (6.587) (-11.516) (28.259) (-7.401) (132.702) (5.121) 89.842

Los Angeles: 1 -0.181 0.007 0.194 -0.269 0.001 0.549* 0.215*

(-0.266) (0.949) (0.486) (-0.527) (1.924) (2.947) (4.203) 151.681

Los Angeles: 21 0.072 0.003 0.089 0.091 -0.001 0.026 0.203*

(0.104) (0.056) (0.182) (0.845) (-0.616) (1.821) (3.918) 62.949

Los Angeles: 3 0.563* -0.008* 0.137* 0.302* -0.003* 0.133* 0.243*

(120.957) (-251.958) (41.229) (272.496) (-181.513) (697.101) (4.536) 131.107

Los Angeles: 4 2.078* -0.021* 0.919* 0.152* -0.001* 0.093* 0.263*

(18.277) (-19.419) (15.005) (33.404) (-12.851) (79.614) (4.654) 75.827

Miami: 1 3.643* -0.034* 1.722* 0.119* -0.001* 0.091* 0.226*

(135.500) (-122.942) (136.781) (100.459) (-23.048) (185.329) (4.302) 103.327

Miami: 2 -1.087* 0.009* -0.572* 0.254* -0.002* 0.089* 0.212*

(-98.347) (76.822) (-114.884) (265.745) (-239.673) (251.729) (4.129) 101.726

Miami: 3 1.429* -0.010* 0.842* 0.149* -0.001* 0.096* 0.224*

(7.656) (-6.091) (8.935) (18.841) (-6.395) (42.319) (4.054) 59.679

The market power parameters are defined by the linear specifications: θ = δ0 + δ1Χ, on the buying side, and φ = τ0Χ in the output market for the collusive

regime only. The critical chi-square value at 5% and twelve degrees of freedom is 21.026. For all other variables, a single asterisk indicates significance at 

a 5% level. In this table, the "weight" parameter is interpreted as giving the probability of an observation being in a punishment phase.