Abstract

Since 1972, the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) has provided

free infant formula to low-income families. Today, infant formula purchases through the WIC program account for

roughly half of all infant formula purchased in the United States. Beginning in the late 1980s, WIC agencies, in an

effort to contain rising program costs, secured rebates from formula manufacturers through sole-source contracts

for the infant formula they purchase. During 1980-2002, infant formula did not substantively change but real

wholesale prices nearly doubled. This research examines the impact of providing free formula through the WIC

program and its use of sole-source contracts to control program costs on the wholesale price of infant formula. The

findings show that providing free formula to low-income families is the primary factor in the growth in real wholesale prices of formula and that sole-source contracts not only have reduced the cost of formula to the Government

but also have retarded wholesale price growth.

Impact of the WIC Program

on the Infant Formula Market

Contractor and Cooperator Report No. 51

January 2009

By David Betson, University of Notre Dame, Department of Economics

and Policy Studies

This study was conducted by University of Notre Dame under a cooperative

research contract with USDA’s Economic Research Service (ERS) Food

and Nutrition Assistance Research Program (FANRP): contract number

43-3AEM-3-80107 (ERS project representative: David Smallwood). The views

expressed are those of the authors and not necessarily those of ERS or

USDA.
ii

Table of Contents

Table of Contents ................................................................................................... ii

List of Figures ........................................................................................................ iv

Acknowledgments.................................................................................................. v

Executive Summary .............................................................................................. vi

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

1. Relative Infant Formula Prices – 1981 through 2002......................................8

2. The Structure of the Infant Formula Industry................................................ 11

History of Infant Formula......................................................................... 11

Current Market Structure .........................................................................14

Marketing of Infant Formula....................................................................17

3. The WIC Program ............................................................................................20

WIC Eligibility Criteria...............................................................................21

Size of WIC Program................................................................................. 22

The Sole Source Rebate Program ............................................................ 23

History of the Rebate Program ...............................................................26

4. Modeling the Desired Price of Infant Formula............................................. 32

Assumptions about Competition in Infant Formula Market.................35

Characterizing the Demand for Infant Formula .................................... 36

The Varian Model...................................................................................... 39

Modeling the Rebate Program ................................................................44

Discussion .................................................................................................. 56

Why do Firms Bid on Sole Source Contracts.......................................... 58

5. Empirical Model of Wholesale Price Determination....................................60

Econometric Specification of Empirical Model......................................60

Factors Affecting the Desired Price.........................................................64
iii

Empirical Results....................................................................................... 67

Censored Normal Regression Estimates .................................................69

Estimated Impact of Free Formula and the Rebate Program............... 72

6. Time Pattern of Bids in the Sole Source Rebate Program ........................... 78

Specification of an Empirical Model .......................................................82

Model Estimates and Discussion .............................................................88

Conclusions ........................................................................................................... 97

References............................................................................................................101

Appendix Material

Appendix A: Time Trends in Relative Formula Prices ......................................103

Appendix B: A Model of Nominal Price Adjustment........................................ 115

Appendix C: Data Description and Sources.......................................................119

Appendix D: OLS Estimates of the Wholesale Price Model ............................123

Appendix E: Estimates of the Bidding Model: Dependent Variable Net Price of

Formula to Government..............................................................125
iv

List of Figures

Figure

1 Real Price of a 2 oz Serving of Infant Formula (Milk Concentrate).......9

2 Percentage of Infants Participating in WIC............................................ 22

3 Percentage of WIC Outlays Finance by Rebates (1989 to 2002) .........24

4 Total Dollar amount of Rebates (1989 to 2002).................................... 25

5 Percentage of WIC Infants Covered by a Rebate Contract...................26

6 Share of WIC Market under Sole Source Contracts................................ 31

7 Formula Price Increases with Rising Take Up Rate ...............................42

8 Optimal Choice of the Size of Rebate ......................................................53

9 Growth in Real Prices and Inflation Between Price Changes (Mead

Johnson – Milk Concentrate)................................................................... 63

10 Growth in Real Prices and Inflation Between Price Changes (Ross Labs –

Milk Concentrate)..................................................................................... 63

11 Number of Infants and Breastfeeding Rates .........................................66

12 Number of Non-Breastfeeding Infants...................................................66

13 Rebates as a Percentage of the Wholesale Price....................................80
v

Acknowledgments

This research would not be possible without the generous financial support

(Grant Award 43-3AEM-3-80107) and cooperation of the research staff at the

Economic Research Service of the US Department of Agriculture. In particular, I

would like to thank William Levedahl, David Davis, David Smallwood and Mark

Prell for their comments and suggestions.

The collection of data needed for this project was accomplished with the help

provided by Sandy Clark currently with the Department of Agriculture, Food and

Nutrition Service, Supplemental Foods Program Division (previously with the

Center for Budget and Policy Priorities) and Linda Clarke also with the Food and

Nutrition Service, Supplemental Foods Program Division.

During this project I have been fortunate to have a series of enthusiastic and

helpful research assistants, Clare Brophy, Charles Kennedy, Aaron Rarrick, Chris

Gehring and Nicholas Moeller. In 2004, Robert Goedert wrote his Senior Honors

thesis on this topic under my supervision. The discussions with him and his work

greatly contributed to my progress on this project and I want to acknowledge

and recognize his contributions. However, any errors and omissions that remain

in this paper are my responsibility.
vi

Executive Summary

From 1980 to 2000, the real wholesale price of infant formula almost

doubled even though the formula being marketed remained substantially the

same during this period. The consequences of these events had significant

impacts on the budgets of families with infants as well as the federal

government’s efforts to provide formula to low-income mothers through the

Special Supplemental Nutrition Program for Women, Infants, and Children

(WIC). In 1990 and again in 1991, the Senate committee on Antitrust held

hearings on the rising cost of infant formula. Senator Metzenbaum asked what

he felt all parents were asking, “why is the price of formula so high?” This

research attempts to determine what factors have lead to the escalation of the

wholesale price of formula.

As Senator Metzenbaum noted in the 1990 hearing, the infant formula

market is oligopolistic. During the 1980s and 90s, formula was produced and

marketed by three and, for a limited time, four firms. Existing formula

manufacturers were able to compete for market share on factors other than

price. While a lack of competition may justify high prices, they do not explain

the increase in the real price of formula over this period. As the senator noted,

the real cost of the primary input of formula did not change over the 1980s, nor

were there any significant changes in the number of firms. While manufacturers

did market new formulas for niche markets, the predominant infant formula

remained unchanged during this period. Consequently, changes in the demand

must have taken place to explain the increasing real price of formula. In 1980,

roughly one out of five mothers participated in the WIC program and would

receive their infant formula free of charge. By 2002, roughly one out of two

mothers participated in the WIC program. The expansion of the WIC program
vii

has fundamentally altered the demand for infant formula by both increasing the

demand for formula and making the demand less sensitive to changes in prices.

In the presence of a lack of price competition, manufacturers have been able to

translate these changes in demand for their product into higher prices.

In 1972 the WIC program was implemented and through outreach efforts

participation in the program has steadily grown until 1999 when it reached a

plateau of serving one out of two infants. The steady growth in program

participation compounded with rising formula prices created fiscal pressures on

WIC agencies to contain the costs of the infant formula portion of the WIC

program. The most successful efforts found by state agencies were to secure

rebates from infant formula manufacturers through sole source contracts. The

formula manufacturer offering the lowest net formula price (wholesale price

minus a rebate) would be awarded a contract to be the sole brand for all of the

WIC recipients in the state. The sole source contracting procedure was first used

by several states in 1986 and was later mandated to be used by all states in 1989.

But it was not until 1994 that all states had adopted the sole source contract.

In the Senate hearings, concern was raised that rebate program may

contribute to even higher formula prices as the manufacturers attempt to

recoup the cost of the rebates. In the two-year period of 1989 and 1990, formula

manufactures increased formula prices in percentage terms twice as fast as in

the prior two-year period. Given that this was the time period when the federal

government had mandated the use of sole source contracts by state agencies,

suspicion was raised that families not participating in the WIC program were

subsidizing the rebate program. Although a 1998 GAO report failed to conclude

that there was sufficient evidence to draw any conclusions, suspicion remained

that the rebate program, while successfully reducing the cost of the WIC
viii

program, had an adverse effect on higher income families not being served by

WIC.

To examine the separate impact of providing free formula to low-income

families and the use of the sole source rebate program to contain program costs,

we employ both theoretical and empirical approaches. The theoretical model

assumes the formula manufacturer has a significant degree of market power

that is the result of both barriers to entry to the market and the demand faced

by the firms. We posit that mothers will be sensitive to the price of formula

when deciding the extent to which they will bottle feed their infants. However,

we will assume that mothers decide which brand of formula to use based upon

factors other than price of formula such as advice that they receive from friends,

family and health care professionals.

Finally, the model assumes, in the absence of the WIC program, the demand

for the firm’s product is composed of two types of mothers. One type of

potential infant formula consumer represents low-income mothers whose

demand for formula will be more sensitive to the price than high-income

mothers. When the WIC program is implemented, low-income mothers will be

eligible to participate and receive vouchers redeemable at retail stores for infant

formula. As more low-income mothers participate in the WIC program, the

overall price elasticity of demand for infant formula should fall allowing firms to

charge higher prices for their product. Consequently, in the absence of the

rebate program, the rise in the wholesale price of formula is a reflection of a

steadily declining price sensitivity of demand for formula created by the rise in

participation of the low-income mothers in the WIC program.

With the advent of the sole source rebate program, formula manufacturers

faced a new set of market conditions in which, if they were to continue to sell to
ix

mothers participating in the WIC program, they would have to compete directly

on price for the WIC market. The theoretical model assumes that the existing

firms set their wholesale price and their rebate bid in the sole source auctions to

maximize their expected profits where each firm is assumed to be able to form a

subjective probability of winning the contract that is inversely related to the net

price (wholesale price minus the rebate) they bid. Winning the contract results

in expanding their sales of formula to WIC mothers, however, at a smaller net

average revenue for the sales to WIC mothers. Win or lose the contract, the

firm will hold onto their sales to mothers who pay for their formula (non-WIC

mothers and mothers who are eligible for WIC but have chosen not to

participate in WIC).

The theoretical model predicts that, compared to a situation where the WIC

program exists but it has not implemented a rebate program, the

implementation of a sole source rebate program will induce the firm to lower its

wholesale price. The explanation for this result is the following. The rebate

program creates the opportunity and necessity for the firm to recognize that it is

selling its product to two distinct populations: those mothers who are paying for

the formula and those mothers for whom the government is paying for the

formula. Given, that the sole source contract is given to the firm who bids the

lowest net price, not the greatest rebate, the firm has an incentive to set the

wholesale price at a level that maximizes the profits from the group of mothers

that pay for their formula and offer a rebate that will maximize the expected

profits from WIC mothers. The model shows these decisions are separable. The

demand from those mothers not participating in WIC will be more price

sensitive than the demand the firm would have faced in the absence of the

rebate program (combined demand from WIC and non-WIC mothers).

Consequently, we would expect the wholesale price with the rebate program to
x

be lower than what it would be in the absence of the rebate program. However,

the wholesale price with the rebate program exceeds what it would be if the

WIC program did not exist and all mothers had to pay for their formula.

In bidding for the WIC contract, the firm offers a rebate that reflects a

balance between the marginal change in the expected profits due to an

increased probability of winning the contract and the marginal change in the

expected profits due to lower average profit margin from offering a larger

rebate. From a theoretical perspective, the pricing of formula sold through the

WIC contract follows an inverse elasticity relationship just as did the rule that

governed the setting of the wholesale price of formula. Traditional theory

predicts that a firm with market power will set the price so that the potential

profit margin (price minus marginal production costs) as a percentage of the

price of the good is equal to one over the price elasticity of demand of its

customers. When determining its rebate for the WIC contract, the firm will set

the net price so that the profit margin (price minus rebate and marginal

production costs) as a percentage of the net price (price minus rebate) will equal

one over the elasticity of the probability of winning the contract with respect to

the net price. The elasticity of the probability with respect to the net price bid

by the firm should reflect the competitiveness of the bidding process where

more competitive bidding would be reflected in a higher elasticity and

consequently a lower profit margin.

The theoretical model provides insights about the relationship between the

size of the rebate offered by the firm and other variables of interest. As we have

previously noted, the firm determines the level of rebate to reflect a desired net

formula price (wholesale price minus the rebate) that will be chosen

independent of its wholesale price. Consequently, if the firm increases its
xi

wholesale price, then we would expect to raise its offered rebate by equal

amount.

Smaller states have felt that they had not been able to acquire the same level

of rebates that large states could in their sole source contracts. The theoretical

model suggests that the size of the WIC contract will have no effect on the size

of the rebate offered by the firm. This implication is the result of assuming that

the probability of winning the contract is independent of the size of the

contract. If a larger WIC contract induces more firms to bid and consequently

lowers the probability of the firm’s chances of winning the contract, holding the

net price constant, the firm will be induced to raise its rebate offer.

Our empirical examination of the role the role WIC plays in the infant

formula market utilizes two sets of data. To examine the impact of WIC on

wholesale prices, we analyzed the wholesale prices of Mead Johnson and Ross

Labs for milk-based infant formula in both concentrated and powdered

formulations during the period of 1981 through 2002. The second data set used

in the study is composed of the bids by these two companies from all of the sole

source contract competitions held during the period. We chose to focus upon

Mead Johnson and Ross Labs because their combined sales represents roughly 85

percent of all formula sales. We conclude our analysis with data from 2002, the

year that enhanced formula arrived in the market, to maintain a homogenous

product for comparison.

The empirical examination of the impact of the WIC program on wholesale

formula prices benefits from the existence of four periods differentiated by

stages of the implementation of the WIC program over this twenty-two-year

period. From 1980 to 1987, the sole source rebate program didn’t exist but there

was steady growth in the proportion of infants participating in the WIC
xii

program. From 1987 to 1994, the growth in WIC participation continued with

the gradual implementation of the sole source rebate program. By 1994, all

states had implemented the sole source rebate program but growth in

participation continued. By 1999, participation had reached a plateau and both

aspects of the WIC program found a steady state in terms of their

implementation. To parameterize the extent to which WIC provides free

formula to mothers, we utilized a variable reflecting the percentage of all infants

participating in the WIC program. The rebate program was captured by a timevarying variable reflecting the percentage of WIC infants whose formula was

purchased by a sole source contract. The empirical analysis of the time series of

wholesale prices also controlled for the number of infants, breastfeeding rates,

price of milk, and the composition of other competing formula manufacturers.

As our theoretical model predicted, increasing the proportion of low-income

infants participating in the WIC program in the absence of the rebate program

should allow formula manufacturers to charge higher prices for their product.

The empirical results suggest that, for every percentage point increase in the

participation rate of infants in WIC, the real wholesale price increases by 2.5

percent. The theoretical negative impact of the rebate program on prices was

found in our empirical analysis of wholesale prices. The estimated effect was

that, for a percentage point increase in the number of WIC infants covered by a

sole source contract was associated with a .22 percent point reduction in the real

wholesale infant price. In 2002, the rebate program covered 92 percent of WIC

infants. Consequently, our model predicts that if the sole source rebate had

never been implemented, the real wholesale price would be 20.4 percent higher.

Today, 47.6 percent of all infants participate in the WIC program. To

estimate the impact of the WIC program’s provision of free formula, we would

want to know what would be the wholesale price today if in 1972 we had not
xiii

implemented a WIC program. If there was not a WIC program, it is doubtful

that the government could have implemented a rebate program. Our empirical

estimates suggest that real formula prices have doubled (100-percent increase)

over what they would have been in the absence of the program. If the

government had not implemented the rebate program, the real price of formula

would have been 120 percent higher than in the absence of WIC.

Using the estimates from the empirical model, the predicted real wholesale

price of formula rose by 60.2 percent over the twenty-one-year period. In 1981,

16.8 percent of all infants participated in the WIC program and the rebate

program was not in existence. If the WIC program had not expanded

(participation rate remained at 16.8 percent) and the rebate program had not

been implemented, then the real prices of formula would have increased by 5.3

percent, accounting for all changes in all other factors (number of infants,

breastfeeding rates, price of milk, and competition in the industry).

Consequently, the WIC program accounts for 91 percent of the increase in the

growth of real formula prices during this period.

The second data set examined was the bids by Mead Johnson and Ross Labs

on the 117 sole source contracts during the period studied. The important

implication of the theoretical model was that the firm’s decision to set the

wholesale price and rebate offers in the sole source solicitations were separable.

If the firm chose to raise its wholesale price by $1 it would raise its rebate offers

by $1 in order to keep the net price to the government unchanged. Based upon

the bids made by Mead Johnson and Ross Labs during this period, we found

statistically significant confirmation of the theoretical model’s implications of

the relationship between wholesale prices and rebates.
xiv

While we found that the patterns of rebates offered in initial solicitations

differed from subsequent solicitations of rebates, the rebates proposed by Mead

Johnson did not differ from Ross Labs’ rebates. In addition to controlling for the

real wholesale price, in our analysis, we controlled for the size of the contract,

the number and composition of bidders, and in the case of subsequent

solicitations, the firm who held the current contract.

Small states have been concerned that they have been unable to receive

similar sized rebates that larger states were receiving. While we found

statistical evidence confirming their concern, the elasticity of the rebates offered

by Mead Johnson and Ross is quite inelastic – a ten-percent increase in the size

of the contract produces a less than one-percent increase in the size of the

rebate. We found that states that banded together to request a single

solicitation received rebates that were statistically equivalent to rebates

received by a single similarly sized state.

When examining the rebate bid in subsequent solicitations, we found that

who holds the current contract is an important determinate of the rebates

offered by Mead Johnson and Ross Labs. When firms with a minority market

share (Wyeth and Nestle) held the current contract, Mead Johnson and Ross

Labs aggressively bid for the contract by offering rebates that were 3.3 percent

higher than what they would have bid if one of them had held the current

contract. If one of the firms with a dominant market share held the contract,

then the ‘Big Two’ firm not holding the contract would offer a rebate that was

2.7 percent lower than it would have bid if it had held the contract. This

behavior can be interpreted as either bidding to hold on to a contract you have

or being differential to the other major market player.
xv

Our examination of the impact of the number and composition of bidders

produced mixed results. If only the major market firms bid on a contract, there

is only a statistically insignificant increase in the rebate than if both firms bid

instead of only one of them. While this result is not surprising, the participation

of the minority market share firms created a rather puzzling result. In the initial

solicitations, as more of the minority firms participated, the rebates offered by

Mead Johnson and Ross Labs fell. In subsequent solicitations, if either Wyeth or

Nestle participated, the bids from the ‘Big Two’ fell. But if both Wyeth and

Nestle participated, then the bids of Mead Johnson and Ross Labs were not

statistically different from what would have been bid if neither Wyeth nor

Nestle had bid. The puzzling effect of the smaller market share firms on the bids

of Mead Johnson and Ross Labs remains a result that requires explanation.

1

“We want to know what many American mothers and fathers undoubtedly want

to know. Why are infant formula prices so high?”

Senator Howard Metzenbaum (1990)

Introduction

In 1990 and again in 1991, the Senate Subcommittee on Antitrust,

Monopolies and Business Rights of the Judiciary Committee held hearings

investigating the pricing policy of companies marketing infant formula. The

Senators as well as witnesses expressed concern with the impact of the rising

formula prices was having on the budgets of families with infants. Concern was

expressed over the increased cost of Special Supplemental Nutrition Program for

Women, Infants and Children (hereafter referred to as the WIC program).

Senator Metzenbaum noted that wholesale prices over the 1980s had risen by

more than 150 percent far outstripping the increases in other consumer goods

including food but more importantly in his mind, the prices of inputs such as

milk. Over the same time period, the Senator noted that the price of milk had

only risen by 36 percent.

In the Senator’s mind, the reason for the rising real price of infant formula

was clear – a lack of true competition in this sector of the economy. To

substantiate their views, the critics of the industry noted that two firms, Ross

Labs

1 and Mead Johnson both subsidiaries of pharmaceutical companies, sold

over 85 percent of all infant formula. The remaining share of the market was

sold by Wyeth a subsidiary of American Home Products. This highly

concentrated industry was accused of ‘cozy’ pricing where no one firm

attempted to raise its market share by lowering its price but was characterized

 1 Ross Labs is now called Abbott Nutrition but for this report we used the time appropriate name

of Ross Labs.
2

by one firm taking the lead in raising prices and other firms joining in lock step.

Senator Metzenbaum noted ‘if this isn’t oligopolistic pricing, then this Senator

has never seen it.’

Noncompetitive behavior was also seen by the Senator in the response of the

formula manufactures to cost containment initiatives in the WIC program.

Beginning in 1986, state agencies implemented competitive bidding procedures

for those companies wishing to supply formula to families participating in the

program. During this time, companies offering the largest rebate on formula

would be awarded the contract to supply all of the formula to the state’s

participants. In 1989, the average rebates were roughly $1.50 per can of 13 ounce

of liquid concentrate. In March of 1990, Mead Johnson announced that it would

not bid more than 75¢ per can. In the subsequent state competitions, rebates of

75¢ per can become the standard bid for all firms.

While the Senate hearings provide the most public documentation of the

concern with the lack of competition in the infant formula market, the Federal

Trade Commission (FTC) and nineteen States Attorney Generals sued the

formula manufacturers during the period of 1990 through 1996. After the

Senate hearings in December 1990, the FTC subpoenaed the records of three

major formula firms: Ross Labs, Mead Johnson and Wyeth. Although the FTC

did not charge the firms of engaging in price fixing, in January of 1992 Mead

Johnson entered a consent agreement where they pledged to refrain from pre

bid communications, direct advertisement of their product and to provide the

USDA with 3.1 million pounds of powdered formula for distribution in the US or

in humanitarian efforts abroad.

Simultaneously, states began to bring suits alleging that price fixing and the

marketing strategies of the firms were driving up the cost of WIC program. The
3

Florida States Attorney General based their case on the companies’ marketing

scheme of paying doctors and hospitals to endorse their formula to their

patients. In January 1993, Mead Johnson agreed to pay $4 million and Wyeth $1

million to settle the suit without admitting to any wrongdoing. In other civil

cases, the plaintiffs alleged that the companies conspired to fix prices by forming

the Infant Formula Council in order to share pricing and marketing information

and to limit competition by agreeing to market their product only directly to

doctors and hospitals. This period of civil litigation ended in 1996 with Ross Labs

agreeing to pay seventeen states a total of $32.5 million while not having to

admit to any wrongdoing.

Regardless the cause, the rising real price of formula was having an effect on

the household budgets of young families whose mothers who were returning to

work and relied upon formula as a substitute for breastfeeding. The

government and taxpayers were also feeling the effect of rising formula prices.

The WIC program that provides formula to low-income infants whose mothers

do not exclusively breastfeed was especially feeling the pinch of the rising prices.

While infants represent roughly one quarter of the participants of the program,

the supplements given to them represent over 50 percent of the total costs of

the program. The rapid rise in formula prices during the 1980s forced Congress

with the dilemma of restricting the number of women, infants and children

being served by WIC or raising the budget to pass on the rising costs of the

program to the taxpayers.

The primary question we will focus upon is the question that Senator

Metzenbaum asked – why are formula prices so high? After an examination of

the evidence, we will conclude that real formula prices have increased as the

result of the government’s policy of providing formula to low-income families

through the WIC program. Today, the government pays for over 50 percent of
4

the formula consumed in the United States by families whose demand for

formula in the absence of this program would be the most sensitive to the

formula price. When the government provides formula to these families, the

effect is to increase the total demand for formula and create a total demand for

formula that is less sensitive to price. Consequently allowing firms with market

power to charge a higher price for infant formula.

We will also examine whether the cost containment activities of the

government instituted through a competitive bidding process contributed to

rising wholesale prices as was proposed in the Senate hearings. We will find

there is theoretical reason and some empirical evidence to believe the rebate

program decreased and not increased real wholesale formula prices.

The bidding process of the infant formula firms in the rebate program

represents the second empirical focus of this paper. Using data from over 100

solicitations for competitive bids covering the period from 1986 to 2002, we will

examine the bids made by the two major firms in the infant formula industry,

Mead Johnson and Ross Labs. Based upon our analysis, we find that the two

firm’s bidding behavior is statistically similar. Perhaps unsurprising we find that

bids for initial solicitations for a sole source contract are different than those

from subsequent rounds of bidding. The size of the contract – the number of

infants covered by the contract – induces firms to offer larger rebates and

consequently lower net prices for formula. Finally we find some evidence

although not conclusive that when Mead Johnson and Ross Labs both bid on an

initial contract, the rebates are higher but in subsequent solicitations they don’t

aggressively compete for contracts the other company has won. However, they

tend to bid more aggressively against firms with smaller market shares, Wyeth

and Nestle.
5

The remainder of the paper is organized in the following manner. In the next

section, we document the historical trend in infant formula prices. We begin in

1981 and track the change in the real wholesale price of formula for a twentyone year period. The broad based picture that is formed by this examination is

that real wholesale formula prices have doubled over this period. However most

of the growth in the real price of formula occurred prior to roughly 1996 and

since that time the rate of growth in prices has significantly declined.

The following two sections of the paper provide background information

about the structure of the infant formula industry and the federal government’s

program that provides free formula to low-income mothers. Over the past

twenty-five years, there have never been more than four infant formula

manufactures selling formula under their own brands. The limited number of

competitors in the market is likely the result of the nature of the product. For

many infants, formula is the primary source of nutrition during the first year of

their life. Consequently, both parents and the public have an interest that this

product be both safe and promote healthy infant development. This concern

has led to the regulation of the production of infant formula by the FDA.

Parents wanting what is best for their infant’s development will turn to

sources they can trust will provide advice on which formula to use. While other

parents and relatives may provide this advice, it is reasonable to expect that

many parents will also turn to their health care professionals. Manufacturers of

infant formula seeking to influence the choice of parents turn to medical

detailing of their product to influence health care professionals to recommend

their brands over their competitors. Finally, if their child is digesting their

current brand of formula and their development appears to be normal, parents

would not be likely to change brands even if the cost savings could be achieved.
6

These market conditions suggest that companies associated with

pharmaceutical drug companies would have a comparative advantage over other

manufacturers and would dominate this industry. Additionally, we would

expect mothers to be quite insensitive to the relative prices of different brands

of formula. But given that formula feeding of infants is perceived to be less

desirable for infant development compared to breastfeeding, we would expect

the mothers to sensitive to the real price of formula relative to other goods.

In 1974, the federal government implemented a permanent program to

provide formula free of charge to low-income mothers. This program is known

as the WIC program and is the focus of the third section of paper. The

description of the WIC program begins with a brief historical overview of the

program and a description of the eligibility criterion for participation in the WIC

program. The single most important fact revealed in this section is currently the

federal government pays for more than one half of all formula purchased in the

US. The section concludes with an overview of the government’s efforts to use

its market power to contain the program’s cost of infant formula with the

implementation of a sole source rebate program.

The fourth section of the paper develops a theoretical model of how a firm

with a degree of market power will price its formula in response to the WIC

program’s purchase of formula on behalf of low-income mothers as well as its

offer of a rebate to secure a sole source contract to provide formula to mothers

participating in the WIC program. The primary implication of the model is that

the price of formula set by the firm will be independent of the rebate amount

that the firm would offer to win the sole source contract but the size of the

rebate will depend upon the price of formula.
7

Firms with market power will set the price of formula to reflect the price

elasticity of its customers that will face that price – the less price elastic the

demand for the product, the higher the price will be charged by the firm. As the

WIC program is implemented without a rebate program, low-income, relatively

price sensitive mothers will participate in the WIC program. If we assume the

government’s demand for formula is price inelastic then the price elasticity of

the firm’s overall demand will become more inelastic allowing the firm to set

higher prices. When the government uses its market power as the single largest

purchaser of formula by forcing firms to compete for a sole source contract to

provide formula to WIC mothers, the price elasticity of customers who will face

this ‘full’ price will increase as the government negotiates a different price

through the rebate program. The consequence is that firms will lower the

formula price compared to the situation when the rebate program had not been

implemented.

The next two sections reflect the empirical examination of the framework

developed in the paper. The fifth section reports upon an analysis of real

wholesale prices over the period of 1981 through 2002. This analysis provides

evidence that confirms the predictions of the theoretical model. The sixth

section reports upon a preliminary analysis of the bids offered by Ross Labs and

Mead Johnson for over 100 sole source contract competitions held between 1986

and 2002. The paper concludes with a summary of findings and a discussion of

potential avenues for future research in this area.
8

1. Relative Infant Formula Prices – 1981 through 2002

Stroll down the infant and baby food aisles of any grocery story and one is

confronted a wide assortment of infant formulas. To compare alternative

brands and formulations of infant formula, we have normalized the wholesale

price of any product to the cost of using the product to make a 2 ounce serving

of formula. This normalization will account for changes in the packaging of the

product over time and across brands as well as differences in the formulation of

the product (powder or liquid concentrate).

We have limited our time frame to the period from 1981 through 2002 for

two reasons. The starting point was determined by the availability of data on

wholesale formula prices quoted by the firms. The end point of the analysis was

chosen to represent the emergence of a new enhanced formula being massed

marketed employing DHA/ARA2. Martek Biosciences Corporation’s proprietary

blend of DHA and ARA is used exclusively by United States infant formula

manufactures. These two fatty acids that are found in mother’s milk are

believed to play a key role in an infant’s mental and visual development.

3 These

enhanced formulas sell at a premium compared to the previous formulas.

Consequently to insure that we are examining a fairly homogeneous product, we

decided to conclude our analysis with the advent of these enriched formulas.

A central focus of the 1990 and 1991 Senate hearings was the rising price of

infant formula over the 1980s. While the testimony recognized that rising

formula prices could be a reflection of rising input prices, the details of both the

charts and discussion focused upon the changes of the nominal price of formula.

 2 DHA/ARA refers to the active ingredients in this formula – docosahexaenoic acid (DHA) and

arachidonic acid (ARA).

3 See Chea (2002).
9

However, the real price (price of formula relative to the price of other consumer

goods) is the more relevant comparison. In Figure 1 we have plotted the real

wholesale price of a 2 ounce serving of infant formula based upon liquid

concentrated milk based infant formula from November 1981 through December

2002 (monthly calculations) for the four major formula manufactures during

the time period. The red line represents Ross Labs; the blue is Mead Johnson;

the green (concluding in 1996) is Wyeth; the lower gold line represents Nestle.

The ‘saw tooth’ nature of each trend is the result of setting a nominal price

and then letting inflation of the prices of other goods erode the real price of

formula. The subsequent peak represents the real wholesale price after the firm

has implement a new nominal price.

Figure 1
10

The concerns being expressed in the Senate hearings are reflected in Figure 1.

Over the 1980s, the real price of formula continually rose and the existing three

companies appeared to adjust their prices in lock step. The three formula

manufacturers who are associated with pharmaceutical companies (Ross Labs,

Mead Johnson and Wyeth) have a similar path of real prices over the time

period that all three firms marketed formula. The increases in real prices did not

abate after the Senate hearings but continued in much the same as manner as

they did prior to the hearings. It was not until Wyeth left the market in 1996

that there appears to be slowing in the price inflation of infant formula. It was

not until the late 1990s that the real price of formula appears to have stabilized

at a level that is roughly twice the real price of formula in 1981.

Nestle entered the US market in 1989. Nestle has priced its formula at a

considerable discount compared to the ‘Big Two’ firms, Mead Johnson and Ross

Labs. Nestle has chosen to maintain a constant real price for its product

compared to the other two firms.

The real price of formula (the relative price of formula relative to all other

goods) is not the only relative price that could be analyzed. There exists

alternative formulas that differ in terms of their source of protein (milk versus

soy based) and different formulations (liquid concentrate versus powder) in

addition to the companies that manufacture the formula. In Appendix A, we

document that the relative price of milk relative to soy based formula has not

varied significantly over the time period of interest. Consequently we have

chosen to focus exclusively upon the real price of milk-based formulations

marketed by ‘Big Two’ firms in our analysis.
11

2. The Structure of the Infant Formula Industry

History of Infant Formula4

Before the use of substitutes for breast milk became popular in the 19th

century, mothers who could not, or did not choose to breastfeed their infants

would use a wet nurse. Wet nurses would either come to a family’s home, or

the infant could be sent to live with the wet nurse until it was weaned. Wet

nursing was so popular in the 18th century that governments in Europe created

bureau’s to regulate the practice.

In the 19th century, animal milk became a popular substitute for mother’s

milk, with cow’s milk being the most commonly used. Donkey’s milk, however,

was preferred, as it looked more similar to breast milk.

Infants fed cow’s milk had a higher mortality rate than infants breastfed. In

1838, the German scientist Johann Franz Simon published the first chemical

analysis of breast milk and cow’s milk. His and other studies showed that cow’s

milk was more prone to curding than breast milk, and was harder for infants to

digest. Cow’s milk had a higher protein and a lower carbohydrate content than

breast milk. Physicians began to recommend that water, sugar, and cream be

added to cow’s milk to make it more similar to breast milk.

Around 1860, a German chemist, Justus von Leibig, created the first

commercial product. It was a powder containing wheat flour, cow's milk, malt

flour, and potassium bicarbonate that was added to heated cow’s milk prior to

being served. Marketed as Leibig’s Soluble Infant Food, it soon became popular

in Europe, and was the first commercial baby food to be sold in the United

States at $1 a bottle in 1869.

 4 The historical overview of infant formula and the industry was adapted from Schuman (2003)
12

In the 1870’s, Nestle introduced it’s own infant formula in the US, Nestlé’s

Infant Food. It was mixed only with water, and did not require cow’s milk,

making it the first completely artificial formula in the US. It sold for 50 cents a

bottle.

By the late 19th century, more than 8 different brands of formula were

available in the US. Because of their cost, however, and concerns about their

nutritional value by doctors, most women still breastfed their infants.

From 1890 through 1915, the percentage method developed by Thomas

Morgan Rotch, was the most popular alternative to breastfeeding. It involved

diluting cows milk so that the percentage of Casein, the protein that causes cows

milk to curdle, became equivalent to that of breast milk. Sugar and cream were

then added to make up for the dilution of sugar and protein. This method was

very complicated and labor intensive, however, and fell out of favor by 1920.

The pasteurization of milk in the late 19th century had a nutritional impact on

infants fed with cow’s milk. Because the pasteurization process depletes milk of

vitamins C and D, infants had to be fed orange juice and cod liver oil to make up

for the deficiency.

In the early 20th century, the focus switched from modifying the protein

content of cows milk to trying to make the milk more closely resemble the

carbohydrate and fat content of human milk. In 1912, E. Mead Johnson

introduced a cow’s milk additive called Dextri-Maltrose to supplement the

carbohydrate content of cow’s milk. This additive was sold only through

physicians to mothers.

In 1919, a new formula was introduced called SMA, simulated milk adapted,

which contained a combination of animal and plant fats to more closely
13

resemble breast milk. During the 1920’s, other infant formula manufacturers

introduced their own breast milk imitating formulas to compete with SMA.

In 1924, the Moores and Ross Milk Company introduced a new formula

designed to mimic breast milk. It was named Similac because it was “similar to

lactation.” In the late 1920’s, Mead Johnson introduced Sobee, the first soybased infant formula. In 1941, Nutramigen, the first protein hydrolysate infant

formula was introduced. In 1951, Ross’ Similac became available in concentrate

form. In 1959, Mead Johnson introduced Enfamil, and that same year, Ross

introduced Iron-Fortified Similac.

Despite the advancement in artificial formulas, evaporated milk remained

the most popular choice for non-breastfeeding mothers. In 1883, John B.

Myenberg had developed a process for creating unsweetened evaporated milk.

The evaporation process chemically altered the cow’s milk, making it easier for

babies to digest. By the 1940’s, a combination of unsweetened evaporated milk

and sugar had become the predominant alternative to breastfeeding in the US.

In 1960, an estimated 80% of bottle fed infants received condensed milk

formula instead of a commercial formula because of its affordability and ease of

preparation.

During the 1960’s, commercial formulas began to grow in popularity, and by

the mid 70’s, had almost entirely replaced evaporated milk formula and

breastfeeding. Breastfeeding rates reached an all time low, 25%, in the mid 70’s

because of the ease and affordability of commercial formulas. A major factor in

the growing popularity of infant formula was its usage in hospitals for

newborns. The infant formula manufacturers encouraged this practice by

providing free formula to the hospitals.
14

In 1980, the Infant Formula Act was passed, which set strict standards for the

nutritional content of infant formula, and set manufacturing and testing

standards. Since then, infant formula manufacturers have continued to modify

their formulas to more closely resemble mother’s milk. The manufacturers have

also developed a number of specialty formulas for pre-term infants, and infants

with special dietary needs and medical conditions.

Most of the developments in infant formula since 1980 have been in niche

formulas: special therapeutic formulas designed for infants with particular

medical conditions. After the period considered in this study, in 2002 a major

change was introduced in the standard infant formulas used by WIC. Mead

Johnson, Ross, and Nestle all began to market formulas “enriched” with

DHA/ARA, a nutrient that is reported to help in the child’s brain development.

These enriched formulas sell at a premium to the standard formulas.

Current Market Structure

Today’s infant formula industry is essentially an oligopoly consisting of two

large pharmaceutical companies that price their formula at a premium and

market primarily to healthcare professionals. Bristol-Myers Squibb owns Mead

Johnson, the leading brand, while the number-two brand Ross is a division of

Abbott Laboratories. The industry at times has had two smaller competitors,

Wyeth and Nestle.

5

Since 1980 there have only been two major changes in the US formula

industry, the first being the entrance of Nestle in 1989, and the second being

Wyeth’s switch from marketing formula under its own name to being a

 5 As will be explained later, Wyeth currently does not market formula under its own name but

supplies formula to retail outlet such as Target and Walmart to market under the store’s brand

names.
15

manufacturer of store brand formula (for example, Target) in 1996-1997. In that

time, no other major competitors have attempted to enter the market

6

, and

Mead Johnson and Ross have managed to maintain a firm grip on their

dominant market positions.

Until 1996, Wyeth, also a pharmaceutical company, sold a premium brand

formula in the US, and was a major competitor to Ross Labs and Mead Johnson.

Wyeth was unable to profitably participate in the WIC program decided to

discontinue selling its premium formulas in the US to focus on its international

operations. In 1997, Wyeth reentered the US market, but as a producer of infant

formula for PBM Products, Inc., which markets most of the generic-branded

infant formula in the US and holds about a 1% market share. This generic

formula is usually sold at a discount compared to Mead Johnson and Ross

formulas.

Nestle entered the US market through its purchase of Carnation, and has

been struggling to build market share. Worldwide, Nestle is the leading brand of

infant formula. The unique nature of the US market, however, has kept Nestle’s

marketing and pricing strategies from being effective in the US. Though

considered a premium brand, Nestle formulas are typically also priced at a

discount to Mead Johnson and Ross formulas. Nestle currently has somewhere

between 10% and 15% of the market. The rest of the market is divided fairly

evenly between Mead Johnson and Ross, with Mead Johnson having a slightly

larger market share.

While the ‘Big Two’ formula manufacturers, Ross Labs and Mead Johnson,

have historically held 85 percent of the formula market, their relative

importance has shifted over time. Prior to 1994, Ross Labs brands represented

 6 Mead Johnson introduced a discount brand marketed under the Gerber name in 1989, but

discontinued it in 1997.
16

roughly one half of the market with Mead Johnson holding one third of the

market. By 2000, the relative market shares have been reversed with Mead

Johnson holding more than one half of all formula sales leaving Ross Labs with

one third of the market. The reason for this shift in market shares is not clear.

Executives at Mead Johnson attribute their increased market share to a direct

mailing campaign aimed at expectant and new mothers. The mailing informed

them both about the benefits of breastfeeding and provided samples of the

company’s product. However, this claim does not coincide with the fact that

Ross’s decline in market share appears to have begun two years before the

institution of Mead Johnson’s direct mailings in 1996. Additionally, Ross Labs

has for decades had surveyed mothers about their breastfeeding practices and

also provided mothers with coupons for Ross’s products.

An industry dominated by a small number of manufacturers will create

conditions where firms will be able to price their products above the marginal

cost of producing the good. Firms will set their prices low enough so as to

remain competitive, but high enough so as to not risk causing its competitors to

lower their prices. Because of the small number of competitors in an oligopoly,

firms are either able to collude with each other to agree on mutually beneficial

market prices, or in a non-collusive market, simply anticipate the pricing

strategies of their competitors through experience, and set prices accordingly.

In this way, the firms in an oligopoly manage prices to achieve supernormal

returns.

The fact that the infant formula industry is an oligopoly does not explain

why real prices have increased. Wyeth’s withdrawal from the industry in 1996

could have strengthened the market power of Mead Johnson and Ross, allowing

them to raise prices with greater ease. However, Nestle’s entrance to the

market as a low-price competitor in 1989 and the emergence of generic infant
17

formulas in 1997 (manufactured by Wyeth and marketed by PBM), have

increased competition for Mead Johnson and Ross, creating pressure for lower

formula prices. It is doubtful that story about declining competition in the

industry can explain rising real prices of formula.

Marketing of Infant Formula

One of the most distinguishing features of the infant formula market is the

unique manner in which formula is marketed. Infant formulas especially the

premium brands are very similar to pharmaceutical products in how they are

perceived by consumers. Though this trend is slowly changing in the US,

consumers typically rely on the recommendations of healthcare professionals in

choosing pharmaceutical products. With respect to products they only plan to

use for a limited period of time, most consumers are less concerned with price as

they are with a product’s functionality. Rarely will a consumer switch from

using a pharmaceutical product that is working well to a less expensive product

that may or may not work as well, provided that the consumer will not be using

the product indefinitely.

Similarly, parents often rely on the recommendations of pediatricians or

other healthcare workers in choosing a formula. A recommendation can be

explicit, or tacit as when a hospital provides a newborn a particular brand of

formula. Once parents have made the decision to formula feed their child,

whatever brand they first give the infant will likely be the brand that they use

throughout infancy, provided that their brand is digestible for their infants.

7

Parents are typically unwilling to risk changing to a less expensive infant

 7 Occasionally, a child’s body chemistry will cause it to react negatively to a particular brand of

formula, in which case parents will switch brands.
18

formula if their child has responded positively to whatever formula it was first

given.

Thus the key for infant formula manufacturers is to be the first formula a

mother gives her infant. To the extent mothers are influenced by their physician

or the hospital where the child is born, gaining favor of these two groups is

important to the marketing of formula. Ross, Mead Johnson and Wyeth (when

they were marketing their own formula) rely upon medical detailing of their

products to doctors and hospitals to promote their products. Pursuing this

strategy for these firms was cost effective because they could piggyback upon

their parent pharmaceutical companies marketing efforts. This has allowed

Mead Johnson and Ross to keep such a dominant hold on their market shares

over the years, while keeping Nestle from getting a strong foothold in the US.

Nestle, on the other hand, is an international food and beverage

manufacturer, without any ties to a pharmaceutical company. It has attempted

to gain market share in the US by beating its competitors’ prices, and marketing

its formula as it would any other nutritional product. So far, Nestle has been

unsuccessful, and Mead Johnson and Ross have been able hold onto their market

shares.

8

The costs of medical detailing could be prohibitively high for a nonpharmaceutical company. This may have served as a deterrent for any smaller

firms considering entering the US market. Adding to the high cost of marketing

is the expense of meeting the nutritional standards and performing the testing

of formula required by the FDA. These costs present a formidable barrier to

 8 It should also be noted that in 1989, the year Nestle entered the US market, Mead Johnson

entered into an agreement with Gerber to produce formula under the Gerber name. The Gerber

formula was apparently set up as a direct competitor to Nestle: it was priced at a discount to

other Mead Johnson formulas, and like Nestle formulas, it was marketed directly to consumers.

After several years it became obvious that Nestle and Gerber were failing to gain market share,

and that pharmaceutical marketing and premium pricing really did work best in the US market. Thus, Mead Johnson discontinued the Gerber brand formula in 1997.
19

entry, sufficient to discourage the emergence of any small or regional

competitors.

Marketing of infant formula has been problematic for the industry. Direct

marketing to mothers has been criticized for promoting mothers to abandon

breastfeeding in favor of the bottle. During the 1970s, Nestle was singled out

for its aggressive marketing of formula in the third world. In the US, the

Academy of Pediatricians has actively campaigned against direct advertising to

mothers. Yet the original FTC complaint singled out the absence of direct

advertising as evidence of the noncompetitive behavior within the industry.

The marketing of formula to doctors has not been without controversy. In

1998, Mead Johnson brought suit against Ross Labs for their claim that Similac

was the ‘first choice of doctors.’ In 2001, a federal judge ordered Mead Johnson

to stop distributing inaccurate and misleading information about generic

formula brands (PBM manufactured by Wyeth) to doctors.
20

3. The WIC Program

After a slow beginning as a pilot program in 1972, WIC became a permanent

program in fiscal year 1974. The number of women, infants, and young infants

served per month increased from 205 thousand in FY1974, to 3.6 million in

FY1988, to 7.2 million in FY2000. WIC provides three types of benefits:

supplemental food, usually in the form of vouchers or checks that can be

exchanged for specific foods from participating retail grocers; nutrition

education; and referrals to health care and other social services.

The federal government gives grants to states and Indian tribes to provide

the supplemental food, nutrition education, and health and social service

referrals, and to administer the program. State grant allocations are based on

the amount the state received in the previous year and the estimated number of

eligible persons for that state. States then fund local agencies that provide the

services to participants. Since WIC is not an entitlement program, allocated

amounts of funding may not be sufficient to serve all the eligible persons who

wish to participate. If local agencies do not receive enough funds to serve all

eligible applicants, they establish a prioritized waiting list. Federal regulations

specify a seven-point priority system (7CFR 246.7(e)4) in which priority is based

on the type of nutritional risk and the eligibility category. The last year a state

had to implement a priority waiting list was 1999. States that have experienced

shortages of funds to serve all eligible applicants usually have obtained

supplemental funding from the federal government.
21

WIC Eligibility Criteria

To receive WIC benefits, an applicant and their child must be categorically

eligible, residentially eligible, income eligible, and nutritionally at risk. The WIC

program is intended to provide supplemental nutritious foods to all pregnant,

post-partum women, breastfeeding women, infants (birth to age one) and

children less than 5 years old. The primary demographic group for this study is

infants whose mothers will receive vouchers for infant formula if they have

ceased or reduced breastfeeding.

To be income eligible, an applicant’s family income must be less than 185

percent of the U.S. poverty income guidelines. Those who are enrolled in the

federal Medicaid, Food Stamp, or Temporary Assistance for Needy Families

(TANF) programs are adjunctively eligible for WIC even if their income exceeds

185 percent of poverty. States also may use enrollment in other means-tested

programs, such as the National School Lunch Program or the Supplemental

Security Income (SSI) program, to qualify an applicant as automatically income

eligible for WIC.

To be certified as nutritionally at risk, an applicant must meet at least one of

the many approved nutritional risk criteria. These risk criteria fall under five

broad categories: anthropometric risk (e.g., underweight, obesity); biochemical

risk (e.g., low hematocrit); medical risk (e.g., diabetes mellitus); dietary risk

(e.g., inappropriate dietary patterns); and predisposing factors (e.g.,

homelessness).

Once the infant has been certified to receive benefits from WIC, States may

choose to allow the participant to receive benefits without further eligilbility

until their first birthday, provided the quality and accessibility of health care

services are not diminished.
22

Size of WIC Program

Since 1974 when the WIC program was implemented, the percentage of

infants who participated in the program has increased until roughly 1998 when

one out of two infants participated in the WIC program (see Figure 2). Since

1998, the percentage of infants participating in the WIC program has decline but

is still 47 percent of all infants. Even if WIC mothers breastfed their infants at

the same rate as mothers not participating in WIC, the government today would

be paying for roughly one half of all infant formula purchased on market. But as

many surveys have documented, the breastfeeding rate for WIC mothers is

lower than for non-WIC mothers and hence it is reasonable to claim that the

government pays for more than one half of all formula purchased in the US.

Figure 2
23

The Sole Source Rebate Program

Beginning in 1986, states experimented with cost containment. Since states

were the single largest purchaser of formula, they believed they should be able

to acquire a discount or rebate based upon the volume of purchases made

through the WIC program. The methods the states chose to obtain these

rebates varied. The sole source competitive bid contract is the prevalent

approach adopted by states. This type of cost containment effort requires

companies to submit a rebate offer on a per can basis. The company who offers

the state the lowest net price of formula (wholesale price minus rebate) is

awarded the right to supply of the formula to WIC mothers within the State.

The States reserve the right to authorize infant formula from other

manufacturers.

The cost savings are then used to fund expanded coverage of all WIC eligible

individuals, infants, children, pregnant and post-partum women. We should

note that the difference between the net price of formula (wholesale price

minus the rebate) and the net cost of a can of formula is the retail store markup.

In this study we have not examined how the WIC program’s provision of free

formula and its rebate program has affected this potentially important

component – the retail markup -- of the full cost of formula to the government.

The rebate program has become a significant source of funds for the WIC

program (see Figure 3). When the rebate program first began on a national

basis, the rebates represented 13 percent of WIC outlays. As the rebate program

matured, this percentage roughly doubled to 25 percent.
24

Figure 3

The aggregate dollar amount of rebates grew from $.3 billion in 1989 to $1.5

billion dollars in 2002. These nominal amounts would tend to overstate the

growth of the program in real terms. Figure 4 depicts both the trend in the

aggregate rebate amounts from 1989 to 2002 in nominal and real terms

(constant $2002 dollars). While the trend in nominal terms shows consistent

growth, in real terms the aggregate amount of rebates appear to have reached a

plateau in 1998 and has remained stable over the remaining period.

Another factor determining the aggregate rebate is the number of WIC

infants receiving benefits. To normalize for changes in the infant caseload, we

assumed that each infant enrolled in WIC received the same amount of formula

and consequently we multiplied the real aggregate rebate amount by the ratio

of the infant caseload in 2002 to the infant caseload in the respective year. This
25

normalized trend is presented in Figure 4. The growth in WIC infant recipients

began to decline around 1996, consequently prior to this time the growth in the

rebate program was overestimated but does not alter our impression that the

growth in the aggregate dollar amount of rebates has come to an end.

Even though all states were mandated to institute competitive sole source

contracts in 1988, it is not until late 1993 that all states had complied with public

law. Figure 5 presents the percentage of WIC infants who were covered by a

sole source rebate contract and reside in a state that provide vouchers

redeemable at retail outlets. Mississippi and Vermont operate direct distribution

systems that dispense formula to WIC participants and are not included in these

totals.

Figure 4
26

Figure 5

Stagnation in the rebate program has become a source of concern for WIC

officials. Over are the days of easy infusion of funds to maintain or expand the

program’s reach to low-income families. We turn to a short history of the rebate

program. From this history, it is clear that formula manufactures have been and

most likely will continue to be resistant to the sole source rebate program.

History of the Rebate Program

In 1985, Tennessee, Oregon and South Carolina in an effort to reduce the cost

of their WIC programs announced they would implement a competitive bidding

procedure that would award to a single company the right to be the primary

supplier of infant formula to the WIC program in their respective states. The

reaction of the infant formula manufactures was swift and sure. Formula
27

manufacturers were opposed to this plan and saw no reason to depart from the

current procurement methods that they believed well served the WIC clientele

over the years.

Apart for the obvious reason this method of cost containment would erode

their profits, the companies argued the strategy was ill conceived. The reasons

they put forward were

• The plan was anticompetitive;

• The plan undermined the right of mothers to choose which formula to

feed their infants;

• The plan would undermine the relationship between mothers and

their doctors; and

• The plan would not guarantee cost savings.

They threatened the state and federal governments with legal action but in the

end they found their best strategy was not to cooperate. In 1986, Tennessee

opened the seal bids to find that no one had bid on the state’s contract. Only

later when Tennessee reopened the auction did Wyeth break rank and submit

bids to both Tennessee and Oregon’s competitive sole source solicitations.

During this period, the ‘Big Two’ – Mead Johnson and Ross Labs – proposed

an alternative cost containment strategy to the states. They would provide

rebates that would equal the difference between the future and current

wholesale price of formula if the states would continue to provide vouchers for

the infant formula chosen by the mother with their doctor’s advice. While this

proposal would limit increases in the cost of formula resulting from rising future

wholesale prices, compared to the sole-source contract this proposal did little to

reduce the overall cost of the program that the states sought.

In 1987, the states of the Florida, Wyoming and Michigan sought rebates in

what was called the Open Market strategy. In this type of contract, the WIC
28

clientele would continue to choose the brand of formula and the states would

receive the rebate proposed by the company for the number of cans purchased

by WIC mothers. When these ‘competitions’ were held, the states received

considerably less in rebates than the states who had held sole source auctions.

In their competitive sole source solicitations, Tennessee and Oregon had

received bids of 40¢ and 60¢ per can respectively from Wyeth while the states

that held the Open Market bids received on average of 20¢ per can.

Interestingly, while Wyeth was a consistent bidder in the sole source auctions

they rarely would participate in an Open Market bid. This pattern may reflect

the low market share of Wyeth’s hope that it could increase its market share if

the ‘Big Two’ continued not to bid in the sole source auctions.

In 1988, Texas became a battleground. The ‘Big Two’ wanted the state to

adopt the Open Market approach. The state officials rejected their suggestion,

pointing to the low savings of this approach compared to the sole source

approach. When the bids were opened, Mead Johnson broke down and offered

the winning bid of 92.5¢ per can almost five times the size of the rebates they

have offered in previous Open Market solicitations. The size of the Texas

market was too large for Mead Johnson not to bid. Yet Ross continued to

boycott the sole source solicitation.

On the heels of Texas, Florida decided to rebid their contract and adopted a

hybrid approach asking for both a rebate under the Open Market approach but

also a rebate if the contract was made as a sole source contract. The state would

pick the approach and company that provided the greater cost savings to the

state. Now all three companies proposed rebates with Mead Johnson offering a

rebate of 87.7¢ per can for both types of contracts and Ross Labs offering $1.05

per can rebates under the sole source arrangement and 63¢ per can under the

Open Market approach. Wyeth’s bid of $1.085 was the winning bid under the
29

sole source but did not provide a rebate under the Open Market approach.

Immediately after winning the contract, Wyeth increased its wholesale price

making the effective rebate equal to $1.01 per can, less than what had been

offered by Ross Labs. Based upon this experience in Florida and other states,

future contracts would contain a clause stating that if the company increased its

wholesale price during the contract then the rebate would increase by the same

amount.

After the Texas battle, Ross Labs began submitting bids to competitive sole

source auctions. In what could be one last attempt to convince states that an

Open Market approach could provide significant savings to states while

maintaining choice for WIC clientele, Ross Labs and Mead Johnson began to

offer larger rebates to Open Market solicitations. The rebates offered by both

companies were consistently 93¢ per can during 1989 considerably higher than

the offers made in the previous year. Their efforts were paying off. By the end

of 1989, 25 states had signed Open Market contracts with the ‘Big Two’ although

Wyeth stubbornly chose not to participate in the Open Market approach. Of the

twenty Open Market agreements signed in 1989, Wyeth participated in only two

– Kentucky and Washington. In both cases, offering 10¢ and 20¢ less per can

than the ‘Big Two’.

In the same year, 1989, the federal government implemented two important

pieces of legislation affecting the rebate program. The FY 1989 appropriation

act required that all states to engage in some form of cost containment. The

WIC reauthorization legislation enacted in November of 1989 required that

when states’ current contracts with formula manufactures ended, the new cost

containment activities must be a competitive sole source solicitation unless they

could show at least as large of savings from their desired approach. What the
30

companies had won at the state level was now being lost at the hands of the

federal government.

In late 1989, Ross Labs submitted a 75¢ offer to Hawaii’s Open Market

request. In March of the next year, Connecticut opened the seal bids for a

competitive sole source contract. Ross Labs submitted a 75¢ bid. In both cases,

Ross’s bids were significant lower than either Mead Johnson or Wyeth. Six days

after the opening of the Connecticut bids, Mead Johnson sent a open letter to

four states holding competitive bids in the coming months that they would be

submitting a bid of 75¢. True to their word, they did. Only in the Texas

solicitation did Mead Johnson bid $1.25 to retain their existing contract.

It was this series of events that provoked the Senate Hearings in 1990 and

1991 but also precipitated the FTC investigation of Mead Johnson. While Mead

Johnson did not initiate what many felt was bid rigging, they were held

accountable for the open letter. The consequence was for the federal

government to legislate against the practice of announcing bids prior to the

opening of a seal bid WIC auction.

By 1991, the ‘Big Two’ appeared to have come to terms with the presence of

the sole source solicitation of rebates. While initially ceding the WIC contracts

to Wyeth, the ‘Big Two’ began to participate in the states solicitation for

competitive bids. Figure 6 presents Mead Johnson and Ross’s share of the WIC

market during the period of 1986 through 2002. While Ross Labs was initially

much more successful than Mead Johnson in securing sole source contracts,

there was a dramatic reversal of fate in 1995. The reversal also coincides with

the departure of Wyeth from the market and the seemingly acceptance of the

sole source contracts by the remaining firms.
31

Figure 6
32

4. Modeling the Desired Price of Infant Formula

In this section, we first examine a model that describes how a firm with a

degree of market power will price its infant formula when the government

purchases formula on behalf of a subset of mothers who use formula to feed

their infants. We will assume that the government pays the same price for

formula that any mother who purchases formula for their infant. The primary

implication of the model is when the government provides formula vouchers to

mothers who would have been the most sensitive to the price of formula,

formula manufacturers will raise their formula prices in response to the

increased demand (the government purchases more formula than the mothers

would have if they had to pay for the product) and the reduction in the overall

price sensitivity of demand. This framework used to explain the impact of

providing free formula on formula prices in the absence of sole source contracts

has become to be known as the Varian model that appeared in an online

supplement to his undergraduate microeconomic textbook.

9

The Varian model will then be modified to explain how firms would respond

to the government’s attempt to lower the cost of their formula purchases

through competitive bidding for a sole source contract to provide formula to the

mothers served by the program – the rebate program.

10 We will demonstrate

that if the government awards the sole s0urce contract to the firm offering the

lowest net price (the difference between the current formula price and the

 9 See Salant (2003) for an analysis of the WIC program attributed to Hal Varian.

10 We will not explain to impact of an open market rebate program used by states during the late

1980s and early 1990s to contain costs of the WIC program.
33

rebate offered by the firm) then the firm’s formula pricing decision will be

completely separable from its decision of how much to bid on the sole source

contract. Prior to when the competitive bidding process is implemented (in the

Varian model), the firm bases its formula price on the aggregate price elasticity

reflecting both the price elasticity of mothers who pay for their formula and the

price inelastic demand of the government who is paying for the formula

acquired by mothers participating in the WIC program. Once the competitive

bid process is implemented, the firm’s market is effectively divided into two

segments – one segment where mothers purchase formula using their own

monies and the other segment representing the WIC program. Firms will set the

price of their formula to reflect the price elasticity of their customers who will

be paying that price for their purchases. They will set the net price (price minus

rebate) by offering a rebate that will maximize their expected profits from

bidding on the contract. The competitive bidding process can then be expected

to depress formula prices as the firm now prices its product to reflect the price

elasticity of its self-paying customers not the combined price elasticity of both

market segments.

A word of caution should be offered. The reader may be tempted to

interpret the previous explanation as a story based upon traditional market

segmentation theory that serves to explain how a firm with market power can

increase its profits by differentiating its price across segments of its market. The

sole source competitive bidding process while effectively allowing the firm to

segment its market will not lead to increased profits. In fact the purpose of the

rebate program created by the government will lead to lower profits for formula

manufactures and lower cost for the WIC program.
34

Traditional market segmentation theory suggests the firm would set prices to

the various market segments inversely related to their price elasticities. In the

current context, this implies that the government would be charged a higher not

a lower price than what is being charged to the self-paying mothers. The sole

purpose of the rebate program is for the government to use its market power to

secure a lower price. The model suggests that the firm will set its effective price

(net price) to the government to reflect the probability of winning the sole

source contract and not on the government’s price elasticity of demand. Since

the price elasticity of self-paying mothers will be higher than the aggregate

market price elasticity (self-paying mothers and government demand), the price

that they will face should be lower than they would have faced had the sole

source competitive bidding process had not been implemented.

The two-part development of the theoretical framework serves to distinguish

two distinct aspects of the WIC program – the distribution of free formula to

low income mothers and the partial financing of the program through price

reductions resulting from the government exercising its market power.

Drawing these distinctions are important because as we have suggested in this

introduction, the provision of free formula to mothers whose demand is quite

sensitive to the price is expected to increase the price of formula while the sole

source competitive bidding process is expected to have the oppose effect on

prices.

We will be focusing upon how the WIC program and its rebate program

affect the wholesale price of infant formula and hence the price, P, we will be

modeling is the wholesale price. But clearly, mothers can’t purchase formula at

wholesale prices but at retail prices. We will assume that retail stores adopt a
35

constant mark up to the wholesale price that is not affected by the WIC program

or the rebate program.

11

Assumption about Competition in Infant Formula Market

To develop a tractable model, we will adopt some simplifying assumptions

about the nature of competition existing in the infant formula market. As we

have previously observed, infant formula is supplied by a limited number of

firms who have been predominately subsidiaries of pharmaceutical drug

companies. The sole exception is Nestle – the worldwide leading producer of

infant formula. It is our contention these facts reflect barriers to entry into the

infant formula market created by the FDA’s regulation of manufacturing of

infant formula. While drug companies may face lower marginal cost of

regulation because of their existing relationship with the FDA, a more significant

competitive advantage may be found in the manner by which formula is

indirectly marketed to mothers through hospitals and physicians. Formula

manufacturers who are subsidiaries of drug companies should experience a

competitive cost advantage in marketing their products to hospitals and

physicians over other firms.

While the number of infant formula manufacturers is limited, we would still

expect the existing firms to compete between themselves for customers. In this

preliminary version of the model, we will abstract from potential competition

between firms providing formula by assuming that the demand for each firm’s

formula is unaffected by the price of other firms producing formula.

Consequently, as the real price of formula (the nominal price of formula relative

to the price of all other non-formula consumption) increases mothers buy less

 11 For an empirical examination of the rebate program on retail mark ups of formula, see

Oliveria, Prell, Frazao, and Smallwood (2001).
36

formula from the firm and do not increase their consumption of formula

produced by other firms but increase their use of non-formula means to feed

their infants.

Characterizing the Demand for Infant Formula

The impact of WIC program on the firm will be characterized by its effect on

the demand for infant formula. Following Varian (Salant, 2003), we will assume

there are two types of mothers, WIC eligible low-income mothers and higher

income mothers who are not eligible for WIC. We will assume the number of

mothers in each group may differ but remain constant during the time period

being considered by the firm.

For simplicity, we will assume that each type of mother’s demand for the

firm’s formula depends upon the real price of formula, P, which we will assume

will be the price charged to all purchasers of formula. The subscript ‘W’ will be

used to denote the WIC eligible mothers and ‘NW’ to denote the high-income

mothers who are not eligible for WIC. Each group of mothers’ aggregate

demand for infant formula can be expressed as QW(P) and QNW(P) respectively.

To simplify the model, we assume that the aggregate demand from both groups

reflect a constant price elasticity that differs between the two groups. Given

WIC eligible mothers are low income and consequently compared to the higher

income mothers are likely to be more sensitive to changes in the price of

formula. In particular, we will assume the price elasticity of WIC mothers is

larger than mothers not eligible for WIC

 

!

"W > "NW

where η denotes the price elasticity of demand.
37

If all WIC eligible mothers participate in the program, the aggregate amount

of formula that would be provided by the WIC program would be equal to B

(equal to QW(P=0)) which is assumed to exceed QW(P). To reflect the fact that

not all WIC eligible mothers will participate in the program, let τ denote the

percentage of low-income mothers enrolled and participating in the WIC

program. This rate will be denoted as the ‘take up’ rate of the program. We will

assume that enrolling in WIC does not affect the mother’s choice of formula in

the absence of a sole source contract and she is free to choose her preferred

brand of formula. Consequently the firm’s demand given the price P is

QT(P) = QNW(P) +(1- τ) QW(P) + τ B (1)

In the initial version of the model, we will assume that τ doesn’t depend upon

the price paid by mothers. However, the assumption that the ‘take up’ rate of

the WIC program is unaffected by the price of formula is dubious. The firm’s

total sales volume could rise by increasing the formula price as long as the

increase of sales to WIC eligible mothers exceeded the loss in sales to non-WIC

mothers. The firm could raise their volume of formula sold if at the current

price

 

!

" (B #QW !P")

QT

$

P

"

%"

%P

&

'

(

)

*

+ > , !##-".NW +-.W

(2)

where

 

!

" =

QNW + !"# $#QW

QT

= the proportion of total volume sales made to selfpaying mothers, and
38

 

!

" =

QW

QNW + !"# $#QW

= the proportion of volume sales to self-paying

mothers who were eligible for WIC.

While the ‘take up’ rate may be determined by the formula price, it is also

influenced by the outreach efforts of the WIC agencies to inform mothers about

the WIC program and its benefits as well as by the decisions of individual

mothers who may or may not view the program as beneficial to their family. To

the extent to which the ‘take up’ rate is determined by actions outside the firm’s

control, the more faith we can place in the assumption that the ‘take up’ rate is

exogenous to the firm.

Given the assumption that the ‘take rate’ is independent of the formula price,

the price elasticity of demand for the firm’s product equals

 

!

"T = #[!"$%#"NW +%"W ] = #"SP(3)

where the subscript SP denotes the group of self-paying mothers and T denotes

the total or overall sales to all customers – self-paying mothers and the WIC

participating mothers paid by the government. As ‘take up’ in the WIC program

increases (τ), the price elasticity of demand for formula will fall for two reasons:

the portion of paying customers (ρ) will decrease and the proportion of paying

customers who are low-income and more price sensitive (ω) will also decline.

Mathematically, the change in the price elasticity with respect to τ is equal to

 

!

"#T

"$

= #P

"%

"$

+ %(#NW &#W )

"'

"$

> ! . (4)
39

The Varian Model

In the absence of the rebate program, the firm will be assumed to price its

product so as to maximize its profits

P QT(P) – C(QT(P)) (5)

where C(Q) denotes the total cost of producing Q units of formula. The first

order conditions for maximizing the firm’s profits is

 

!

QT +P"QT

"P

#

$

%

&

'

()

"C

"Q

*

"QT

"P

= !

or

 

!

MR(Q!P") =P #+

#

"T

#

$

%

&

'

( =P #+

#

)"SP

#

$

%

&

'

( =

*C

*Q

= MC . (6)

The first order condition implies the firm would set the formula price so that the

marginal revenue is equal to the marginal cost of producing the last unit of

formula. To simplify the discussion, we will assume the marginal cost (MC) is

independent of the scale of operation of the firm.

The primary conclusion of the Varian analysis is that the WIC program

(provision of free formula to low-income mothers) would result in an increase in

the price of formula. If the WIC program didn’t exist then all mothers would

have to pay for the formula (ρ=1.0) and the ‘take up’ rate would be zero.

Consequently the price elasticity of demand for formula (ηo) would equal

 

!

"o =

QNW

QNW + QW

"NW +

QW

QNW + QW

"W (7)
40

that would be greater (in absolute) value than the price elasticity of demand if

the WIC program is implemented with a take up rate of τ

 

!

"o > "T = #"SP . (8)

Note this is a restatement of equation (4) where we showed that price elasticity

of demand and the ‘take up’ rate for the WIC Program were positively related.

Consequently as the WIC program expands, the demand for formula will

increase (see equation (1)) and the price elasticity of demand will decline in

absolute value (equation (8)).

Let Po denote the formula price in the absence of the WIC program. This

price must satisfy equation (6) when ρ equals 1.0 and τ is equal to zero

 

!

Po !+

!

"o

#

$

%

&

'

( = MC . (9)

As the WIC program is implemented and expands, the firm faces a less elastic

demand for its product because of two factors – less of its product is paid for by

mothers who will be responsive to the price and the government is paying for

formula who would have been the most sensitive to the price. The consequence

of the lower price elasticity of demand is the bracketed term on the left hand

side of equation (9) becomes smaller – the marginal revenue at Po declines. For

the firm again to maximize its profits (satisfy equation (6)) it will raise its price.

This presentation may be a little confusing because typically the presentation

of firm behavior is told in terms of the quantity supplied not the price it charges

customers. Since the quantity of formula produced and sold will be negatively

related to the price the firm can charge, the relationship between the marginal

revenue and the price will be opposite of the relationship between the marginal

revenue and output of the firm. As the firm raises its formula price, the quantity
41

demanded will fall and consequently the marginal revenue for the firm will rise.

Hence if we have a change of variable – quantity output to price – the graph of

the relationship between the price and marginal revenue would be upward

sloping holding all of the other parameters of the model constant. The marginal

cost as a function of the formula price will be a constant because as price

increases, output will fall but by assumption this will not affect the marginal

cost of producing formula. If the marginal cost of producing formula rose with

output then as a function of the price of the good, the marginal cost relationship

would be decline with increases in the price. The relationships between marginal

revenue, marginal cost and the formula price are depicted in Figure 7 for two

different ‘take up’ rates of the WIC program. If the ‘take up’ rate of the WIC

program is τ1 the firm would maximize its profits by adopting the price P1. If the

‘take up’ rate rose to τ2, the marginal revenue at every price would fall reflecting

the decline in the price elasticity of demand and consequently the firm would

raise its price to P2 to once again maximize its profits (satisfy equation (6)).
42

Figure 7: Formula Price Increases with Rising Take Up Rate (τ)

While the ‘take up’ rate of the WIC program will become the primary factor

that emerges from the empirical work, the model proposes three other avenues

by which changes in other factors could affect the price of formula – the

aggregate quantity purchased by non-WIC eligible mothers (QNW); the

aggregate quantity purchased by WIC mothers but with their own money under

the assumption that no WIC eligible participated in the program (QW); and the

amount purchased by the government for WIC mothers if all WIC eligible

mothers participated in the program (B). While the first quantities are

envisioned to be determined by the price of formula, other factors such as

income, breastfeeding rates and population trends will also play an important

role.

If breastfeeding rates among high-income mothers declined, we would

expect a shift in the demand for formula from this group of mothers. When

QNW increases holding everything else constant, the marginal revenue at any

P

MC

P1 P2

MR(τ1) MR(τ2) $

0
43

given price will be affected in two opposing directions. As QNW increases the

proportion of self-paying mothers (ρ) would increase resulting in an increase in

the marginal revenue and providing an incentive for the firm to lower prices.

However when QNW increases, the proportion of self-paying mothers who are

WIC eligible (ω) declines resulting a decline in the average price sensitivity of

those mothers who pay for formula (ηSP). This latter effect results in a decline in

the marginal revenue (holding the price constant) leading to an increase in the

price of formula. The net impact on formula prices is ambiguous.

Changes in the quantity of formula purchased by the WIC eligible population

are a little more difficult to characterize because in most scenarios a change in

QW will also be reflected with a change in B. For example, an increase in the

number of mothers eligible for WIC should increase both Qw and B. In general, B

will be a constant multiple of QW (B =λQW where λ > 1.0), consequently a

change in QW (holding τ -- the ‘take up’ rate -- constant) will produce a decline in

the price of formula while the change in B will cause the price to rise. When QW

increases, both ρ and ω will increased due to a more price elastic demand for the

firm’s product. With the upward shift in the marginal revenue, the firm will

lower its price to sell more formula. If B also rises then the overall price

elasticity (ηT) will decline because the proportion of sales to non-governmental

customers will decline. This will result in a decline in the firm’s marginal revenue

inducing them to raise prices. When both QW and B change in the same

direction, their impact on formula prices is ambiguous.

Finally if QNW, QW and B change by the same proportionate factor (α), the

firm’s desired price is predicted by the model to remain unchanged. Changes in

aggregate quantities will leave the parameters (ρ and ω) unchanged and
44

consequently the total price elasticity (ηT) remains unchanged. This conclusion

of the model underscores how the Varian model relies upon relative price

elasticities as opposed to a scale effect to explain the impact of WIC on the price

of formula.

Modeling the Rebate Program

In 1989, the federal government required all WIC agencies to implement a

competitive bidding process for a sole source contract. In these procurement

auctions, manufacturers submitted a proposed rebate. The firm who offerred

the lowest net price (wholesale price minus rebate) was awarded the contract to

provide all of the formula for the WIC mothers in the jurisdiction of the WIC

agency. By 1993, all WIC agencies had implemented the rebate program. The

question that we will now turn is how will the firm bid on a sole source contract

and how will this cost containment procedure affect the wholesale price of

formula.

The modeling strategy has been to assume the price charged by the firm’s

competitors had no impact on the firm’s demand. This assumption is reasonable

if mothers primarily rely upon non-price related information to decide which

brand of formula to purchase. Given that mothers may be reluctant to change

brands solely in response to prices, competition on the basis of price for selfpaying customers may not be high. However, when the government places the

formula consumed by WIC mothers for competitive bids based upon price, the

firm’s behavior may become more competitive. Consequently to talk about one

firm in isolation from the other firms may create some confusion for the reader.
45

Let us assume there are only two firms (X and Y). We will also assume that

the government has already implemented a program to provide formula free to

low-income mothers but pays the same price for formula as non-WIC mothers

pay for their formula. For all practical purposes, this describes the WIC program

prior to the institution of the rebate program. We will assume that the infant

formula market can be divided into four distinct types of sales: Firm X’s sales to

WIC mothers; Firm Y’s sales to WIC mothers; Firm X’s to mothers who pay for

their formula; and Firm Y’s sales to mothers who pay for their formula.

With the rebate program, the government submits for a competitive bid the

total purchases of formula intended for all WIC mothers. If the firm loses the

competitive bid, it will be assumed that they will be able to maintain the sales

they had made to the self-paying mothers prior but will lose the sales they had

made to WIC mothers. For the firm who wins the contract, their total sales will

increase because they now will be providing formula to all of the WIC mothers

as well as the sales to the self-paying mothers who had purchased their brand

prior to the institution of the rebate program.

It has been suggested that the winner of a sole source contract wins more

than the sales to the WIC mothers who would have bought a different brand if

they had the choice. Some observers have proposed a ‘shelf space effect’ on

sales of the winning brand. Because the WIC program represents a majority of

volume sales in a state, winning the sole source contract will most likely result in

an increase in the shelf space retailers will provide to the winning brand. If selfpaying mothers use the increased shelf space as an implicit endorsement of the

winning brand and begin purchasing the winning brand then it is possible that

the winning firm could win more by capturing other firms’ sales from the selfpaying mothers. While this effect is possible, in this version of the model we

ignore this additional benefit to the firm of winning the sole source contract.
46

With the rebate program, winning the sole source contract means not only

the firm will ‘keep’ the WIC eligible mothers on WIC who would have bought

their formula in the absence of WIC but also the other WIC mothers who would

have bought other brands. Hence if the firm wins the contract, their total sales

will be

QC = (1+σ) τ B (10)

where σ represents the purchases of WIC mothers who would have bought

other brands expressed as a percentage of the firm’s WIC sales in the absence of

the rebate program. Note the firm’s share of the WIC market in the absence of

the sole source rebate program is 1/(1+σ).

We will assume that the firm is risk neutral and chooses the formula price

and rebate amount prior to knowing whether or not they have ‘won’ the

contract. In particular they will choose the price (P) and the per unit rebate (R)

to maximize their expected profits. The winning firm will be the firm that offers

the lowest net price (NP=P-R) and consequently the firm’s probability of

winning the contract will increases as the net price falls. Let π(NP) denoted the

probability of winning the contract and consequently the expected profits would

be equal to

 

!

(! " # ) PQLose "C"QLose [ #] + #[PQWin "C"QWin# "RQC ]

 

!

PQLose "C(QLose ) + # $QC(11)

where

 

!

"QC = (P #R)QC # (C (QWin) #C(QLose )) = (P #R #MC )QC

 

!

" =P #R #MC =NP #MC
47

 

!

QLose = QNW + (! " # )QW

 

!

QWin = QLose + QC

and

 

!

#"=

$#

$NP

< ! .

The term, ΓQC, represents the firm’s gain in profits if it wins the competitive bid

– the net price (P-R) times the quantity of sales to WIC (QC) reflects the total

net revenues while the difference C(QWin))-C(QLose)) represents the total cost of

supplying the formula for the sole source contract. Given our assumption of

constant marginal costs of production, the change in total costs equals MC QC.

The first order conditions for the firm’s profit maximizing choice of price and

rebate are

 

!

QLose +P"QLose

"P

+ #QC =

"C!QLose "

"Q

"QLose

"P

$ #%&QC(12)

 

!

"$#%QC = $QC

(13)

The left hand side of equation (12) represents the impact of a marginal change in

the price of formula on expected revenues of the firm. As the firm raises its

price the firm’s revenues from selling formula to the self-paying mothers will

change by the amount

 

!

QLose +P"QLose

"P .

As the firm changes the price then the total revenues from sales made through

the sole source contract will also change by the amount of the quantity

purchased through the contract, QC. Consequently the firm’s expected revenues

from the sole source contract will increase by πQC.
48

The right hand side of equation (12) represents the cost to the firm of

changing the price of formula. The first term represents effect of a marginal

change in price on the production cost of the firm. The second term of the right

hand side reflects the impact of a change in price on the probability of winning

the contract. If the firm raises the price holding the amount of the rebate

constant then the probability of winning falls by -π’ and consequently the firm’s

expected loss of profits is – π’ ΓQC .

Equation (13) represents the condition for the profit maximizing choice of a

rebate amount. The benefit to the firm of a larger rebate is the increased

probability of winning the contract and the profits associated with winning.

Consequently the expected profits from a marginally larger rebate is – π’ Γ.

However increasing the rebate amount lowers profits if the firm wins the sole

source contract. This loss in profits represents the expected cost of a higher

rebate (πQC) – the right hand side of equation (13). Note that given our

assumption of constant marginal production costs, the first order constraint for

the rebate is independent of the scale of operation of firm and the size of the

sole source contract. Consequently equation (13) can be rewritten as

!

"$#% = $

(13’)

For the firm to maximize its expected profit from selling formula it will select

values for P and R in a manner that two conditions expressed in equations (12)

and (13) are both met. Given that the net price reflects the average revenue

from the sales from winning the contract and determines the probability of

winning the sole source contract, the marginal impact of a change in the price of

formula on the expected profits from the sole source contract will equal and

opposite in sign to the impact of a marginal change in the size of the rebate.

Consequently if the firm is to maximize its profits it will set a value of R given P
49

so that it meets the condition expressed in equation (13) and consequently the

condition expressed in equation (12) can be simplified to

 

!

QLose +P"QLose

"P

= MC "QLose

"P

or

 

!

P !+

!

"SP

#

$

%

&

'

( = MC

(12’)

Examining equation (12’), the rebate amount (R) is absent. Consequently, the

choice of the formula price is independent of the rebate the firm chooses to bid.

Specifically, the firm will price its formula to reflect the price elasticity of the

customers who will be facing the ‘full’ formula price – the self paying mothers

who are not participating in the WIC program. The government will be paying a

different price, the net price, which can always be determined independent of

the price through an adjustment of the rebate amount.

In the absence of the rebate program when the government paid the

identical price that self-paying mothers paid, the price elasticity of its paying

customers (government and self-paying mothers) would be lower than just the

price sensitivity of its self-paying mothers. Consequently, we would expect the

firm to set a lower price compared to what it would charge in the absence of the

rebate program.

While it simplifies our thinking about the impact of the rebate program if the

choice of the formula price is independent of the choice of rebate amount, it is

the result of the simplifying assumptions we have made. Earlier in this section,

we discussed the potential ‘shelf space’ effect on the demand of self-paying

mothers. To the extent this effect is present, we would expect winning the
50

contract would reduce the price elasticity of the demand for formula of the selfpaying mothers. Consequently, the firm’s decision to set the price P will be

influenced by the probability of winning and hence the rebate amount.

Even in the absence of the ‘shelf space’ effect on demand of self-paying

mothers, the assumption of constant marginal costs is also important to this

result. If the marginal production cost (MC) was a function of the scale of

operation then equation (12’) would equal

 

!

P !+

!

"SP

#

$

%

&

'

( = "!) *#MCLose + *MCWin

(12”)

where MCLose and MCWin reflect the marginal cost at the scale of operation losing

and winning the contract respectively. Given the probability of winning the

contract depends upon the net price, the firm’s decision of formula price will be

determined simultaneously with the rebate amount (equation (13)).

The choice of criterion for winning the sole source contract plays an

important role in creating the separability between the decision of price and

rebate. As we noted in the previous section of the paper, the first competitive

bids were based upon which firm would offer the largest rebate even though the

net price of formula from the winning firm could be higher than the losing firm.

If π is a function of the rebate amount, R, and not the net price, the

corresponding condition to equation 12’ equals

 

!

P ! +

!

"SP

+

#

"SP

QC

QLose

$

%

&

'

(

) = MC (12’’’)

Consequently the rebate amount appears in this condition and the firm will have

to simultaneously determine the formula price and the rebate amount.
51

Each of these three alternative scenarios not only make the discussion of the

model less transparent but undermine the primary insight – the implementation

of a sole source contract system of bidding will lower the formula price not raise

it. Under each of these three scenarios, the definite conclusion of the model

becomes ambiguous and we can’t determine a priori the impact of the rebate

program on wholesale prices. Since the criterion for winning the sole source

contract is the net price and not the size of the rebate, the third situation is not

troublesome. The assumption of constant marginal costs is also not too

troubling as long as firms do not bump into capacity constraints. This leaves the

‘shelf space’ effect as a potential source of concern for this modeling effort.

Let us now turn to the factors determining the size of the rebate. The firm

will offer a rebate (participate in the competitive bid) only if it can make a profit

on sales to the WIC participating mothers. Given our assumption of constant

marginal costs of producing formula, the firm will offer a bid as long as the net

price exceeds the marginal costs of producing a unit of formula

 

!

P "R "MC > !.

If the firm can make a profit from winning the WIC contract then the profit

maximizing rebate offer must satisfy

 

!

"$#% = $

(13’)

where the left hand side represents the marginal benefit to the firm of a higher

rebate offer while the right hand side reflects its marginal cost. The firm will

offer a rebate as long as the marginal benefit exceeds the marginal cost when

the firm’s rebate is zero,

 

!

"$#(P)(P "MC ) > $(P) (14)
52

If the condition expressed in equation (14) is met, the firm will compete for the

sole source contract. The amount it bids will be determined by the marginal cost

and benefits expressed in equation (13’). The marginal cost of the rebate (π) will

rise with larger rebate amounts because our assumption that larger net prices

offered by the firm will lower its probability of winning the contract,

 

!

"#

"R

= $#%> !

(15)

The marginal benefit (-π’ Γ) can’t be expected to have a monotonic relationship

with rebate amount,

 

!

"(#%$&)

"R

= %$$& # %$

"&

"R

= %$$& + %$

(16)

While we have assumed π’ to be negative for all net prices (rebate amounts), we

have not made any assumptions pertaining to the second derivative of the

probability of winning with respect to the net price (π”). At low level of rebates,

we would expect the probability of winning to be rising at a increasing rate (π”

> 0). Consequently the marginal benefit of larger rebate amounts should

initially be rising as long as

 

!

#""[P $R $MC ] > $#". (17)

As the rebate continues to increase diminishing returns to set in and the rate of

increase in the probability of winning the contract should decline. The marginal

benefit should continue to decline until the rebate is equal to P-MC when the

marginal benefit to further increases in the rebate are zero. Figure 8 reflects the

marginal benefit and marginal cost at different rebate offers where R* reflects

the profit maximizing level of rebate.
53

Figure 8 – Marginal Benefit and Cost of Alternative Rebate Offers

When the firm sets the wholesale price, equation (12’) indicates that the

mark up of the price over the marginal cost (P-MC) relative to the price will be

equal to the inverse of the price elasticity of demand of the self-paying

customers. This suggests that the firm will be operating in the elastic portion of

the demand of their self-paying mothers. A similar inverse elasticity rule is

implicit in the firm’s decision of setting its rebate or net price of formula to the

government. Equation (13’) can be written as

 

!

NP "MC

NP

=

!

#C

(13”)

where ηC is the elasticity of the probability of winning the sole source contract

with respect to the net price offered by the firm

 

!

"C = #

NP

$

$%.

Given the left hand side of equation (13”) must be less than one, the firm will

offer a net price to the government that is in the elastic proportion of the

Rebate

MC=π

MB =-π’ Γ

R*

$

P-MC
54

probability of winning the contract. The function determining the probability of

winning the sole source contract, π, plays the same role in guiding the firm

where to set its net price for the WIC contract that the demand function plays in

its decision to set its wholesale price.

Assuming the firm has chosen the profit maximizing wholesale price and

rebate to bid (NP*=P*-R*), the choices must meet the first order conditions

(equations (12’) and (13’)) but at the optimal choices, the second order condition

with respect to the choice of rebate must also be met

 

!

#""(NP *)[NP *$MC] + !#"(NP *) < "

(18)

This condition will be met if the firm’s marginal benefit exceeds the marginal

cost of the rebate amount when the rebate amount is zero and the probability of

winning the sole source contract declines with increases in the net price.

Let us assume that the firm has chosen the profit maximizing price and

rebate (P* and R*). If the firm adopts a higher real wholesale price for formula

due to changes in other factors then the marginal benefit (-π’Γ) of the rebate

offer increases at initial profit maximizing choices,

 

!

"!#%$&"

"P

= #%$$& # %$> #

(19)

while lowering the marginal cost of the rebate,

 

!

"(#)

"P

= #$< !. (20)

Consequently, the firm will increase its rebate offer in response to an increase in

the price of formula. But we can be more specific with regards to the magnitude

of the change in rebate offer with respect to a change in the price. Since the

pricing decision is separable from the choice of rebate, an increase in the
55

wholesale price will be met with an equal increase in the rebate amount to keep

the net price constant.

In the model we have specified, the size of the contract (QC) does not affect

the size of the rebate. This result is a consequence of our assumption of

constant marginal production costs that renders the first order constraint

guiding the firm’s choice of rebate (equation (13’)) independent of the size of the

contract. However, a slight modification of the model will allow for the size of

the contract to have an effect on the rebate.

We will assume that the probability of winning depends not only upon the

net price offered by the firm but the size of the contract and the number of

firms bidding on the contract,

 

!

" NP !Qc ( !N)

We will further assume that a larger contract as well as more number of firms

bidding on a contract will reduce the firm’s probability of winning at every net

price,

 

!

"#

"Qc

< ! and "#

"N

< !.

These assumptions appear reasonable since a larger contract may produce more

‘competitive’ bids from all companies and more firms bidding should also

increase the competitiveness of the bids.

Consequently, increases in either the size of the contract or the number of

firms bidding will lower the marginal cost of the rebate. If this effect was the

only consequence of a more competitive bidding process, the firm would be

induced to raise its own rebate offer. However, the impact of either of these

variables on the marginal benefit of the rebate (-π’Γ) is ambiguous. The
56

increased competition in the bidding for the sole source contract will most likely

also reduce the marginal benefit of the profit-maximizing rebate given the less

competitive environment. But as long as the marginal benefit falls by a smaller

amount than the reduction in marginal cost,

 

!

"#

"QC

< $

"#%

"QC

& < ! or 

"#

"N

< $

"#%

"N

& < !

the firm will increase its rebate offer.

Discussion

During the 1992 Senate Hearings, the rebate program was held responsible

for the significant increases in the wholesale price of infant formula. It was

believed that companies were attempting to recoup the lost profits due to the

rebate program by raising the wholesale price. This model questions that logic

and suggests that profit maximization would lead to the opposite conclusion –

the rebate program would induce the firm to lower its wholesale price. In the

absence of the rebate program, the firm will price its formula to reflect

combined price elasticity of non-WIC mothers and the assumed inelastic demand

of WIC mothers. But with the rebate program, the firm has the opportunity to

charge different formula prices to both self-paying mothers and the government

who is purchasing the formula on behalf of WIC mothers. The firm sets a

wholesale price that maximizes its profits of selling formula to non-WIC mothers

ignoring the size of the rebate and offers a rebate that maximizes its expected

profits of selling formula to the WIC population that effectively sets the price to

WIC mothers at the wholesale price minus the rebate.
57

While there are similarities of the current model to a story of market

segmentation, the analogy is not complete. Let us assume that the firm could

segment its clientele into two markets and for simplicity we will denote them as

the WIC and non-WIC markets. The theory of market segmentation suggests

that the firm would want to charge different prices to both markets based upon

the price elasticity present in the separate markets – charging higher prices in

the market with the more price inelastic demand. Compared to the situation

where the firm could not segment the market, individuals that are more

sensitive to the price would face lower prices when the market was segmented

and consequently benefit from segmentation.

As we have argued, in the absence of the WIC program, WIC mothers will be

more price sensitive than non-WIC mothers. But the WIC program ‘transforms’

these mothers into perfectly inelastic consumers. In the absence of the rebate

program, the WIC program lowers the market price elasticity of the demand for

formula that allows the firm to raise the price of formula to both non-WIC

mothers and the government who is purchasing the formula for the WIC

mothers. With the rebate program, the firm can effectively charge different

prices to non-WIC and WIC mothers. Market segmentation theory would

predict that when the market are segmented the price to non-WIC mothers will

fall since the price elasticity of their demand is greater than the total market

when the WIC program is instituted. We should also note that the price the firm

would charge to non-WIC mothers with the rebate program would be higher

than the price they would charge these mothers in the absence of the WIC

program. The reason being that if WIC mothers did have to pay for their

formula then they would be more price elastic than the non-WIC mothers and

hence in the absence of the WIC program, the price elasticity of the total market

demand would be more price elastic than of the non-WIC mothers.
58

While there is a great deal of similarity between the present model and the

market segmentation story for non-WIC mothers, the analogy breaks down for

WIC mothers. In the absence of the rebate program, firms can’t distinguish

between types of customers but the rebate program creates a mechanism that

allows them to do so. When the market is segmented in the rebate program, the

price of elasticity of the WIC mothers is no longer relevant. If it were then the

net price to WIC mothers should rise not fall. What is missing is the reality that

when rebate program is implemented, the government can also exercise its

market power by demanding a lower price for the formula it is purchasing. The

market segmentation model assumes that the presence of market power only on

the seller’s side of the market.

Why do Firms Bid on Sole Source Contracts?

For infant formula manufacturers, the rebate program has eroded the

profitability of the market. Prior to the implementation of the sole source

contracts, firms were enjoying rising profits as real formula prices steadily rose

even though the cost of their inputs didn’t. The government was a passive

‘customer’ who paid for the decisions being made by WIC mothers. The rebate

program spelled an end to this relationship as government demanded and was

able to acquire discounts for their purchases.

As we retold in the previous section of the paper, the manufacturers were

not happy with this arrangement and actively attempted to undermine the

rebate program. Faced with the sole source contract, what could the firms do?

Their only option was to refuse to bid on the contracts. This was exactly what

they attempted to do. But this option would only work if the demand from WIC

mothers would have gone unmet. If the firms could enter into a binding
59

cooperative agreement not to bid then the government could have been forced

into abandoning its rebate program. But in the absence of such agreement, each

firm had an short-term incentive of greater profits by submitting a bid. We

believe that Wyeth was just such actor in the story. Here was a company who

held a relatively small market share and was being offered an opportunity to

greatly expand their volume of sales if they bid on these contracts. Once Wyeth

began bidding and winning contracts, it was only a matter of time before the

others would begin to participate. In many respects, this situation mirrors the

prisoner’s dilemma problem. While it is in the interests of all infant formula

manufacturers not to bid, each firm has incentive to do so as long as the others

don’t.

The model developed in this section also sheds light on the ‘Big Two’s’ offer

of the Open Market rebate alternative to the sole source contract as well as

Wyeth’s reluctance to endorse this alternative approach. By allowing WIC

mothers to continue to determine which brand they would utilize, the

manufacturers would continue to face a rather price inelastic demand for their

product and consequently they would able to maintain their real prices for

formula. While they would have to surrender some of their profits to the

government, they were betting that the level of profits they would enjoy under

the Open Market approach would be higher than they would receive from the

sole source contract when they truly would have to compete for sales for WIC

mothers. Wyeth on the other hand realized that they stood to potentially gain a

larger market share from the sole source contracts than to continue with the

current situation where WIC mothers choose their brand of formula.
60

5. Empirical Model of Real Wholesale Price Determination

Econometric Specification

In Appendix B, we specify a statistical model of how the firm would decide to

adjust its nominal price as the price as the price of other goods changed. The

proposed adjustment process suggests that any point in time, the firm has

previously set a nominal price that it now can change or allow to remain in

effect. To determine whether the firm will change its nominal price, the firm

examines whether the current nominal price adjusted for changes in the price of

other goods (P

C ) is sufficiently below (λ) the firm’s desired real price (P*). If it is

not then the firm does not change its nominal price. If it is then the firm

changes its nominal price to reflect the firm’s current desired price plus a ‘mark

up’ (μ). This relationship is summarized in equation (21),

 

!

ln!Pt

*

" + μ if ln!Pt

c " " ln!Pt*

" # $

ln!Pt " =

ln!Pt

c " if ln!Ptc " > ln!Pt*

" # $

. (21)

The theoretical model developed in the previous section explains how the

firm would determine its desired price in the presence of the WIC program

providing formula free of charge to low-income mothers and a cost containment

effort patterned after a competitive sole source rebate program. We

hypothesized that the desired price would be affected by market conditions such

as the number of infants who would be formula fed and the number of

competitors in the market as well as the cost factors such as the price of inputs
61

(milk). Let us represent all of these factors with the vector X and assume that

the firm’s desired price would be a linear combination of these factors

 

!

ln!Pt

*

" =" + $#Xt + %t . (22)

If we assume that ε is independently and normally distributed with mean zero

and standard deviation σ and Δ represents the set of all t where a nominal price

change occurred, the log likelihood function would equal

 

!

ln f ln!Pt " " !# + μ" " %$Xt

&

'

(

)

*

+

,

-

.

/

0

1

2

t 34

5 + ln F ln!Pt

C " " !# " 6" " %$Xt

&

'

(

)

*

+

,

-

.

/

0

1

2

t 74

5

(23)

where f() and F() are the standard normal density and cumulative functions

respectively.

Given values for μ and λ, equation (23) represents the likelihood function for

the censored normal regression model, a generalization of the Tobit model.

Unfortunately, all three parameters can’t be identified by the available data. In

Appendix B, we show that the sum of μ and λ will equal the desired growth in

the real price plus the anticipated inflation. Consequently at the time of a

contemplated price change, λ will be a linear function of μ and can’t be

estimated separately by the model. In practical terms this implies that any

combination of μ and λ that yields the same sum will produce the same set of

estimates of the model.

It was hoped that at a minimum, we could estimate α and the sum of the

other two parameters, (μ+λ). Unfortunately, when we tried to estimate this
62

specification, the model could not be identified. Hence to estimate our model,

additional information about (μ+λ) or α is needed.

The data on price changes by the firms was examined to glean a reasonable

guess about the sum of real price growth and anticipated inflation. By

comparing the real price established at the time of subsequent prices changes,

we approximated the desired growth in real prices and the amount of inflation

experienced.

Given we know the prices of both Mead Johnson and Ross Labs have been

similar, it is not too unsurprising that these calculations suggest the average of

(μ+λ) is similar across both firms and product formulations. The average sum

for Mead Johnson was 5.2% for milk based liquid concentrate and 5.1% for milk

based powder. For Ross Labs, the averages were 5.4% for both formulations.

Given these calculations, one estimation approach is to adjust the formula

prices when the firm changes prices by subtracting .051 for Mead Johnson milk

based liquid concentrate brands; .052 for Mead Johnson milk based powder; and

.054 for all of Ross Labs brands. This is equivalent to constraining λ to be zero

and assuming μ to have the above values (recall the any combination of the

parameters producing the same sum will yield the same model estimates).

One would expect the sum of μ and λ to vary over the time. Figures 9 and 10

display the calculated sum of (μ+λ) (marked by the Total line with triangles),

growth in real prices (line with circle) and experienced inflation between price

changes (line with no symbols). The first figure is for Mead Johnson’s milk

based liquid concentrate while the second is for Ross Labs. The data for the two

companies’ powder formulations are similar and not presented.
63

Figure 9

Figure 10
64

Over the period of our study, increases in the nominal prices (the sum of

(μ+λ)) have been created equally by increases in growth in real prices and

inflation. The patterns between the two companies is similar until 2000 when

Ross Labs appears to be engaging in a policy to raise the real price of its product

compared to the modest increases implemented by Mead Johnson.

The second approach to estimation is to allow the variation in the sum of

(μ+λ) to be reflected in the estimation by adjusting the price by the estimated

sum (μ+λ) at the time of the price change instead of a constant adjustment done

in the first approach.

Factors Affecting the Desired Price

Based upon the theoretical model, we hypothesize that increases in the size

of the WIC program should have induce firms to increase the wholesale price of

their formula in response the increasing price elasticity of demand for their

product as well as increased sales. The variable we have chosen to capture the

size of the WIC program is the percentage of infants who are WIC (onWIC). As

we documented in that chapter, outreach of state agencies has over the time

period of our analysis increased the percentage of infants participating in WIC

from about 20 to 50 percent.

The model also suggests that the rebate program would lead to lower real

wholesale prices for formula. To account for the time lag in the states adopting

these cost containment we constructed a variable, Rebate, that represents the

percentage of all WIC infants covered by a sole source contract in the state they

resided.
65

Over the time period covered by this study (1981 through 2002), the

potential size of the infant formula market has undergone some significant

changes due to changes in fertility and breastfeeding rates. Figure 11 presents

the time trends in both the number of infants and breastfeeding rates during

this period.

Since 1981, the total number of infants (aged from birth to 1 year old) has

ranged from 3.6 million to slightly over 4.1 million. The 1980s witnessed a

steady increase of roughly 10 percent in the number of infants in the United

States. Since 1991, the number of infants initially fell and then recovered after

1996 to the point where in 2003 there are slightly over 4 million infants.

Breastfeeding rates have fluctuated over this period. During the 1980s as the

number of infants rose, breastfeeding rates decline from 29 percent to 21

percent – roughly a 27 percent decline12. Since 1990, the breastfeeding rate of

mothers has increased from the low of roughly 21 percent to the average rate of

breastfeeding of 38 percent.

Consequently, the size of potential market for the formula companies has

been altered by these two trends. Shown in Figure 12, the number of infants

who would have been potentially fed with formula rose over the 1980s but since

1990, the number of infants fed with formula has steadily decline.

We chose to capture these trends by allowing for separate effects for the

number of infants and changes in breastfeeding rates over time by including the

log of the number of infants (expressed in millions) denoted by the variable

LnInfants and by the log of percentage of the infants not breastfeeding (100 –

breastfeeding rate) denoted by the variable LnFFRate. 

 12 The breastfeeding rates used in this study reflect the average rates over the first year of the

child’s life. See Appendix C for the description of how this breastfeeding rate was constructed.
66

Figure 11

Number of Infants and Breastfeeding Rates: 1980 to 2002

Figure 12

Estimated Number of Infants Using Formula
67

Increases in the cost of inputs should have a positive effect on prices. The

only input price that we could obtain was for the primary component of

formula, milk or soy. In a previous section we documented that over the period

of this study, the real price of both milk and soybeans have been declining. Since

we will be focusing solely on milk-based products, we constructed a variable

reflecting the log of the real price of milk, LnRPMilk.

While the ‘Big Two’ firms – Mead Johnson and Ross Labs – have continuously

marketed formula over this time period, they have faced competition from

different firms. Wyeth marketed formula under their name but ceased in 1996.

Nestle with its acquisition of Carnation began marketing its Good Start brands in

1990. To capture the changed nature of the competition for the Mead Johnson

and Ross Labs, we constructed two dummy variables reflecting these different

time periods. Comp4 is a dummy variable equal to one for the time period

when there were four firms marketing (1990 through 1996) and zero otherwise.

NestleOnly is a dummy variable equal to one for the time period when Nestle

was the only competition (after 1996) and zero otherwise. The coefficients on

these variables would reflect the differential effect of these competitive

situation compared to the level of competition when only Wyeth was the sole

competitor. Given that Nestle has been adopted a different marketing strategy

compared to the other three firms based upon price, we would expect that both

of these variables would have a negative effect on the real wholesale price.

Empirical Results

We have chosen to focus solely upon the determination of the real price of

milk based infant formula (both liquid concentrate and powder formulations)
68

marketed by Mead Johnson and Ross Labs. We have limited our attention to the

milk based products primarily because they represent the vast majority of WIC

purchases. As we have noted previously, the data covers the period from

November 1981 through December 2002.

For each of the four types of milk-based formula (liquid concentrate and

powder formulation for both Mead Johnson and Ross Labs), there were 254

monthly observations. After completing separate analysis of each formula type,

we conclude that we could statistically combine the data into one analysis

sample of 1,016 observations

13

. We did account for differences between with

four different types of formula with series of dummy variables.

In our analysis, we controlled for the following variables that varied by

month:

OnWIC Percentage of infants participating in WIC (0 to 100)

WICRebate Percentage of WIC infants covered by a rebate Contract (0

to 100)

LnInfants Log of the number of infants (in millions)

LnFFRate Log of the proportion of infants NOT breastfed (0 to 1)

LnRPMilk Log of the real price of wholesale milk

Comp4 Four (Mead Johnson, Ross, Wyeth and Nestle) Firms are

marketing formula

NestleOnly Three firms ((Mead Johnson, Ross and Nestle) are

marketing formula

Omitted Category: Three Firms (Mead Johnson, Ross and

Wyeth) are marketing formula

RossMC Ross Labs’ liquid concentrate

MJPowder Mead Johnson’s powder formulation

RossPowder Ross Lab’s powder formulation

Omitted Category: Mead Johnson’s liquid concentration

 13 Although we will treat the observations as independent, the 1,016 observations represent 4

observations per time period (two companies and two product types) and 254 time periods. The

observations are most likely correlated both at a point in time and across time. To account for

these correlations is beyond the scope of this project.
69

Censored Normal Regression Results

We employed two approaches to solve the problem of under identification of

the model. One approach was to assume a constant value for the sum of the

adjustment factors (μ+λ) that reflected the anticipated growth in real prices and

inflation for each of the two types of formula produced by the two firms. The

second approach was to allow the sum to vary over time by using the

percentage change in nominal price computed at a subsequent price change as

the estimate of (μ+λ). The maximum likelihood estimates of the desired real

wholesale price model based upon these two approaches are found on the next

page. For comparison purposes, we report OLS estimates of the wholesale price

model in Appendix D. If the censored normal model is correct then we would

expect the OLS estimates of coefficients to be attenuated and the standard

errors to be understated. Both of these expectations were present when the

OLS is compared to the maximum likelihood.

Comparing the results from the two approaches, there are only minor

differences between the magnitudes of the estimates and estimates of the

standard errors. Consequently for the remainder of the paper, we will focus

upon the first approach of a constant value for (μ+λ).
70

Censored Normal Regression

Approach One: Constant Value for (μ+λ)

------------------------------------------------------------------------------

ALnPrice | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

OnWIC | .0253026 .0009166 27.61 0.000 .023504 .0271013

WICRebate | -.0022243 .0002594 -8.58 0.000 -.0027333 -.0017154

LnInfants | .8326889 .0777006 10.72 0.000 .6802152 .9851627

LnFFRate | -.0814404 .0545312 -1.49 0.136 -.1884484 .0255676

LnRPMilk | .0200853 .0190793 1.05 0.293 -.0173544 .057525

Comp4 | -.0181004 .0088623 -2.04 0.041 -.0354911 -.0007097

NestleOnly | -.0399155 .0135846 -2.94 0.003 -.0665728 -.0132581

RossMC | .0072932 .0043994 1.66 0.098 -.00134 .0159263

MJPowder | -.0387837 .0043568 -8.90 0.000 -.0473332 -.0302342

RossPowder | -.0211428 .0044166 -4.79 0.000 -.0298096 -.012476

_cons | .8809812 .1351697 6.52 0.000 .6157345 1.146228

-------------+----------------------------------------------------------------

/sigma | .0225118 .0014785 .0196104 .0254131

------------------------------------------------------------------------------

Censored Normal Regression

Approach Two: Time Varying Value for (μ+λ)

------------------------------------------------------------------------------

CALnPrice | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

OnWIC | .0251905 .0008892 28.33 0.000 .0234457 .0269353

WICRebate | -.0021955 .0002516 -8.73 0.000 -.0026892 -.0017018

LnInfants | .8389881 .0756771 11.09 0.000 .690485 .9874912

LnFFRate | -.0808874 .0532011 -1.52 0.129 -.1852852 .0235104

LnRPMilk | .021432 .0185491 1.16 0.248 -.0149675 .0578314

Comp4 | -.0183913 .0085675 -2.15 0.032 -.0352035 -.001579

NestleOnly | -.0389689 .0132262 -2.95 0.003 -.064923 -.0130148

RossMC | .0086673 .0042939 2.02 0.044 .0002413 .0170934

MJPowder | -.0383046 .0042653 -8.98 0.000 -.0466745 -.0299348

RossPowder | -.0198801 .0043084 -4.61 0.000 -.0283346 -.0114256

_cons | .8706964 .1313244 6.63 0.000 .6129952 1.128398

-------------+----------------------------------------------------------------

/sigma | .0215048 .0014006 .0187565 .0242532

------------------------------------------------------------------------------
71

The estimated effect of the expansion of the WIC program conforms to our

theoretical predictions that providing more infants with free formula would lead

to increases in the wholesale price. For every percentage point increase in the

take up rate, the wholesale price is estimated to rise by 2.5 percent. The sole

source rebate program is estimated to have depressed wholesale prices. Today,

the rebate program covers roughly 92 percent of WIC infants consequently the

estimates indicate it has resulted in 20.4% lower real wholesale prices for infant

formula.

We anticipated that both the number of infants and rate that infants are not

breastfed would have a positive effect on prices by increasing the size of market

for all manufacturers. While the number of infants has the predicted sign, the

estimated coefficient of the formula feeding rate (LNFFRate) is negative. This

negative coefficient implies that if the number of infants remains the same and

the breastfeeding rate decreases (increases) then wholesale price will decrease

(increase). This result remains somewhat of a mystery but when estimated a

slightly different specification where a single variable (LNFFInfants =

LNInfants+LNFFRate) reflecting the number of infants estimated to be using

formula, the estimated positive relationship reflects our prior expectations.

Our control for the price of production inputs (LNRPMilk) has the expected

effect. Increases in the price of milk are associated with a increases in the price

of formula although the statistical significance of the estimate is not high.

The effect of competition from other firms was expected to depress the price

of formula prices of the ‘Big Two’ – Mead Johnson and Ross Labs. The estimated

coefficients confirm our expectations. When both Wyeth and Nestle

represented the competition to the ‘Big Two’, wholesales were on average 1.8

percent lower. After Wyeth exited from the market, the competitive pricing
72

practices of Nestle had even a larger impact on the ‘Big Two’ depressing real

wholesale prices by 4 percent.

Brand and formulation of the type of formula have an effect on the price of

formula. Ross Lab’s liquid concentrate after controlling for other factors is .7

percent more expensive compared to Mead Johnson’s liquid concentrate over

this time period. Powder from both firms is less expensive than Mead Johnson’s

liquid concentrate. Mead Johnson’s powder is 3.8 percent lower while Ross Lab’s

powder is 2 percent lower than Mead Johnson’s concentrated formulation.

Estimated Impact of Free Formula and the Rebate Program

One of the central goals of this research project has been to determine the

extent to which the provision of free formula to low-income families and the

sole source rebate program have affected the wholesale price of infant formula.

We have specified a theoretical model that predicts that providing infant

formula to low-income mothers whose demand would be extremely price elastic

would reduce the overall price elasticity of the demand for infant formula

allowing firms with market power to raise the real price of formula.

In the absence of a sole source rebate program, the government acts as a

passive buyer of formula even though they are accounting for roughly half of all

formula sales. With the implementation of the sole source rebate program, the

government is exercising its power in the market. With the rebate program, the

firms must compete for the WIC market. Under the assumption of risk

neutrality, the profit maximizing firm will set the wholesale price to reflect the

willingness of self-paying mothers to pay for formula that presumably will be

less than if the market was the combined purchases of all mothers.
73

Consequently we would expect the wholesale price to be less than it would be in

the absence of the rebate program.

These predicted effects of WIC and the rebate program were found in our

analysis of the time series (1981 through 2002) of milk-based infant formula of

the largest two manufactures of infant formula – Mead Johnson and Ross Labs –

that account for roughly 85 percent of all sales of formula. The coefficient on

the percentage of all infants participating in WIC (OnWIC) of .0253 implies that

for every percentage point increase in the participation rate of infants in WIC,

the real wholesale price would increase by 2.5 percent. The coefficient on the

percentage of WIC infants covered by a rebate contract (WICRebate) was a

negative .00222 implying that as more states implemented a rebate program the

real wholesale price would be lower than previously. That is not to imply that

companies actually lowered their prices but increased their wholesale prices by a

lesser amount than they would have had if the sole source rebate program was

not in effect. Today, state rebate program covers 92 percent of WIC infants (it is

not 100 percent in our data because we didn’t have rebate information for two

states, Mississippi and Vermont, and Indian tribal agencies). This implies that if

the sole source rebate program had never been implemented, real wholesale

prices would be 20.4 percent higher than are today.

Today, 47.6 percent of all infants participate in the WIC program. To

estimate the impact of the WIC program’s provision of free formula, we would

want to know what would be wholesale price today if in 1972 we had not

implemented a WIC program. Of course if there was not a WIC program, it is

doubtful if the government could have implemented a rebate program.

Consequently, the total effect of the current WIC program on real wholesale

prices is .0253(-47.6) - .00222(-92) or real formula prices have doubled (100

percent increase) over what they would have been in the absence of the
74

program. If the government had not implemented the rebate program, real

price would have been 20 percent higher still or 120 percent higher than in the

absence of WIC.

The consequences of WIC on formula prices for non-WIC mothers can’t be

understated. Doubling of the price of formula for those mothers who must pay

from their own pockets can be a financial burden that can be avoided only if one

chooses methods other than formula to feed their infants. The ideal alternative

would be breastfeeding and perhaps the most significant promotion of

breastfeeding that WIC has had on non-WIC mothers is through its effect on

formula prices. While it is not a focus of this project, an interesting project

would be to examine the differences in breastfeeding rates between WIC and

non-WIC mothers over time. If rising formula prices are affecting breastfeeding

rates then we should expect to see breastfeeding rates to increase faster for nonWIC mothers than for WIC mothers.

The potential costs of WIC mothers using infant formula instead of

breastfeeding must be balanced against the financial benefits derived from

participating in the WIC program. However from the perspective of the WIC

mothers, the rebate program is inconsequential. Since infants have high priority

in WIC funding, rising formula prices are unlikely to limit their access to the

program. However, other WIC eligible families who might not be served if

overall funding is limited would be affected by the absence of the rebate

program. But if Congress continues its pledge to fully fund WIC then taxpayers

will bear the burden of the higher prices. In the absence of the rebate program,

taxpayers and non-WIC mothers would be paying $2.20 for formula that in the

absence of the program would cost only $1.00. If the real costs of formula

manufacturing have remained constant then producing formula has been

extremely more profitable with the implementation of the WIC program.
75

The rebate program based upon sole source competitive bidding was aimed

at reducing the cost to the taxpayers at the expense of the formula companies.

Our estimates suggest that with the rebate program the real price of formula

would be $2.00 for what would have cost $1.00 in the absence of the program –

saving non-WIC mothers 20¢ but even more for taxpayers. Historically, the

rebates have been on average 85% of the wholesale price. This implies that the

net price to the taxpayer would be 30¢ implying a much lower profit margin on

formula sold to the WIC program.

Compared to the world without WIC, the current WIC program creates a

situation where the firms can increase their profit margins on volume sold to

non-WIC mothers but at the expense of lower profit margins for formula sold to

WIC. Overall profits of the firms will depend upon the volumes of formula sold

to the two groups. As the firm raises the prices to the non-WIC mothers, the

volume of sales can be expected to fall but we would not expect them to raise

prices so that total profits to this group would be less than under the old price of

$1.00. But the profits would not be as great as in the absence of the rebate

program – they would fall by 20 percent. Profits with the rebate program

should still exceed the profits the firm would make on the non-WIC mothers if

there hadn’t been a WIC program providing free formula. The comparison of

profits with and without the WIC program for sales to WIC mothers is less clear.

When the rebate program is implemented, the profit margin per unit should fall

but it should expect to continue to make a profit otherwise the firm would not

offer a rebate or bid. Consequently, the firm’s profits from sales to WIC mothers

will be less with the rebate program unless increased volume of sales to the WIC

is substantially higher.

This argument about the impact of the rebate program on profits compared

to the situation without a WIC program (also no rebate program) may explain
76

the exit of Wyeth from the infant formula market. Given its relative low

volume of sales, it found that its total profitability under the WIC rebate

program was less than it was when there was no WIC program. It could

effectively capture the old days of the absence of the WIC program by stop

marketing its own brand, stop participating in the WIC program, and become in

essence a low price brand sold directly to retail outlets for their marketing to

non-WIC mothers.

The above comparisons examine the total impact of the WIC program on

wholesale prices but we can also examine the contribution of the WIC program

to the growth in the prices over the two decade period. Instead of calculating

the percentage change based upon actual prices, we examined the predicted

desired real prices derived from the censored normal regression model. Over the

twenty year period, the predicted real wholesale price of formula rose by 60.2%.

In 1981, 16.8 percent of all infants participated in the WIC program and the

rebate program was not in existence. If the WIC program had not expanded

(participation rate remained at 16.8) and the rebate program had not been

implemented then the real prices of formula would have increased by 5.3 percent

accounting for all changes in all other factors (number of infants, breastfeeding

rates, price of milk, and competition in the industry). Consequently the WIC

program accounts for 91 percent of the increase in the growth of real formula

prices during this period.

While we are convinced by the evidence that the expansion of the WIC

program’s provision of free formula is largely responsible for the dramatic

increases in the price of infant formula, some additional analysis could provide

even more convincing evidence. If we could obtain data covering a time period

starting prior the implementation of WIC (for example starting in the late

1960s), we could have some direct evidence on the pattern of prices without the
77

WIC program. Unfortunately, we were unable to obtain the wholesale price

data from the companies.
78

6. Time Pattern of Bids in the Rebate Program 

 For the time period of this study (1986 through 2002), 117 competitive sole

source solicitations were held. In only three of these competitions, Mead

Johnson and Ross Labs both chose not to offer a bid. Two of these bids were

early in the rebate program where Wyeth was the only bidder. In fourteen

other competitions, one of the ‘Big Two’ chose not to bid – in nine occasions

Ross Labs was the sole representative of the ‘Big Two’ to bid. In the remaining

100 contracts, both Mead Johnson and Ross Labs submitted bids.

When Mead Johnson or Ross Labs were the sole representatives of the ‘Big

Two’, they were very successful in obtaining the contract against Wyeth or

Nestle. When Mead Johnson submitted a rebate bid and Ross Labs didn’t, Mead

Johnson won each of the five contracts. Ross Lab’s success wasn’t perfect but

they did win eight of the nine contracts where they chose to submit a bid and

Mead Johnson didn’t. When both of the ‘Big Two’ submitted rebates bids, Mead

Johnson was successful in winning 44 percent of the contracts and Ross Labs in

35 percent of the time.

Given the dominance of Mead Johnson and Ross Labs both in the overall

market and in securing sole source contracts, we decided to focus our analysis on

the bidding practices of the these two companies. Consequently, our analysis

will be limited to the 105 bids of Mead Johnson and 109 bids of Ross Labs

submitted to competitive bids prior to 2003 when the enriched formulas

containing DHA/ARA began to enter the market in significant quantities.

The winner of a competitive bid is determined by which company that offers

the lowest net price for the various formulations and bases stipulated in the call
79

for bids provided by the state. For example, the state proposes to pay for W

cans of milk based concentrated formula; X cans of milk based powder; Y cans of

soy base concentrate; and Z cans of soy base powder. The companies are

required to provide rebates for each base and formulation of infant formula.

Then using the firm’s wholesale price, the net price of each type of formula is

computed. Finally a weighted net price is calculated based upon the relative

amounts of formula called for in the bid announcement. The winner of the bid

process is the company offering the lowest weighted net price.

This procedure does allow for companies to offer lower rebates on the types

of formula that are not highly weighted (utilized) by the state. Unfortunately,

we were not able to acquire the bids on all of the various types of formula

requested by the state but had access to only the rebates and net prices offered

on milk based concentrate. Consequently the analysis will be limited to this type

of infant formula. While in the early years of the rebate program milk based

concentrate was the dominant formula requested by states, over time milk

based powder has become the most requested type of formula. We will not able

to estimate how the trend from concentrate to powder formulation has affected

the rebates offered by manufactures.

While the net price is the most relevant perspective to examine the

effectiveness of the rebate program on containing costs, the size of the rebate

has also historically been of interest. To account for changes in the wholesale

price over time, we computed the rebate amount offered by the firms expressed

as a percentage of the wholesale price. Figure 13 presents the offered rebates of

Mead Johnson and Ross Labs over the time period of our study.
80

Figure 13

Examining the bids by the ‘Big Two’, there appears to be three distinct

periods. The period covering 1988 through 1991 represents the initial rebate

solicitations from states. During this time period there was the infamous series

of bids where first Ross Labs and then Mead Johnson tried to establish a baseline

rebate of 75¢ per can that accounts for rebates bids in the 40 percent range.

Over the time period, the average rebate as a percentage of the wholesale price

was 65% for Mead Johnson and 69% for Ross Labs. Yet there was significant

variation in the bids – the standard deviation for both companies’ bids was 15

percentage points. When both companies bid on a contract, the difference

between their bids was substantial. The average difference during this period

was 12 percentage points.
81

The second time period runs from 1992 through 1997 when the solicitations

were primarily for subsequent contracts. The average rebate was 84 percent of

the wholesale price while the variability of offers for each company substantially

fell – the standard deviation of the bids of Mead Johnson and Ross Labs was 7

percentage points. When both companies bid the average difference between

their bids fell to 3 percentage points. This period could be characterized as when

the companies were finally accepting the reality of the rebate program and

began to finally adjust. The bidding was competitive and the result was

welcomed by the states as the size of the rebates steadily grew over the period.

The final time period running from 1998 through 2002 can be characterized

as when rebate program had matured. During this period, the average rebates

of both companies averaged 91 percent of the wholesale price. The variability of

the submitted rebate bids remained at the same level as in the previous period (7

percentage points). The one distinctive feature of this period was the increase in

the average difference between the two companies – increasing from 3 to 8

percentage points.

Two hypotheses emerge from this examination of the data. First as one

might expect, the initial solicitation for rebates for a geographic area differs

from the subsequent bids. Second, the firms did in fact take a good deal of time

to adapt the sole source auctions. It was not ‘overnight’ and the transition

period may have lasted five years (1992 through 1997).

Prior to moving to a discussion of our empirical model, a few comments are

required on the geographic area covered in the rebate contract. In most

instances, the geographic area being bid in a competitive contract is a state. Of

the 114 contracts where either Mead Johnson or Ross Labs submitted a bid, 94

bids were for a single state. However, groups of states have formed to
82

collectively solicit rebate bids. In the remaining 20 requests for bids, the number

of states included in the contracted ranged from 2 to 10 states. In the following

empirical analysis, all variables used in the analysis were constructed to reflect

the characteristics of the geographic area covered by the contract whether it

was a single state or a group of states.

Specification of an Empirical Model 

This section provides the details of the empirical model that we will employ

to examine the bidding behavior of the two major firms in the infant formula

industry, Mead Johnson and Ross Labs. We chose to focus upon the bidding

behavior of these two firms because since 1996 they have held WIC sole source

contracts that cover 85 percent of all WIC infants – a percentage that mirrors

the estimates of their combined market shares of all infant formula sales. After

an early attempt to resist the states’ efforts to employ competitive sole source

bids, beginning in 1991 the ‘Big Two’ adopted bidding strategies that has steadily

increased the share of WIC infants using their brands. A second reason for

focusing upon these two firms is that the major participant and winner of

numerous contracts during the early years of bidding, Wyeth, no longer markets

formula under its own name and consequently doesn’t participate in the

competitive bids. Its replacement, Nestle, participated in a limited number of

bids during the time period ending in 2002. Consequently it was felt that there

was insufficient data to produce an explicit comparison to the strategies of the

‘Big Two’ firms.

Our theoretical model suggests that three factors can influence the rebate

offers made in a competitive contract: the wholesale price of formula, the size of

the contract, and subjective probability of winning the contract. In this section,
83

we will discuss the variables we have constructed to reflect these theoretical

constructs.

Dependent Variable: Rebate for a Can of Milk Based Concentrate

While the bids are judged upon the basis of which firm’s bid offers the state

the lowest net price (wholesale price minus the rebate amount), the theoretical

model focused upon the factors that determined the rebate the firm would

choose to bid in order to maximize their expected profits. While the model

viewed the decision making process as simultaneously determining both the

wholesale price and the rebate, we believe that a more realistic perspective is to

assume that the firm sets its wholesale price based upon expectations about its

potential success in winning the sole source contracts and then determines its

bidding strategy based upon the previously sent wholesale price. If this

perspective is correct then an empirical modeling of the rebate offer should

mirror the estimates of an empirical modeling of the net price submitted by the

firm.

In this report, we will provide estimates of an empirical model where the

dependent variable is the log of the real (in $2002 dollars) rebate (lnRebate)

that the firm submitted to a competitive sole source bid held from 1986 through

December of 2002. In Appendix E, we report estimates of the empirical model

explaining the net prices offered by the two companies.

Independent Variable: Wholesale Price of a Can of Milk Based Concentrate

Based upon our theoretical model, we would predict that if the wholesale

price rises then the firm would increase its rebate offer by an identical amount
84

resulting no change in the net price of formula to the government. Based upon

the date when the bids for a contract were due, we computed the log of the real

(constant dollar) value of the firm’s current wholesale price. Given concerns

with the possible endogenity of the wholesale price, we chose to employ an

instrument for the wholesale price. We constructed this instrument from the

fitted values from a regression based upon the model we estimated in the

previous section of the paper. Separate regressions for Mead Johnson and Ross

Labs were estimated using the same monthly data (1981 through 2002)

employed in the previous analysis but where the dependent variable was the log

of the real wholesale price of a can of milk based concentrate. The variables

controlled for in the OLS regression were the percentage of infants participating

in the WIC program (OnWIC), the log of the number of infants in the US

(LnInfants), the log of the rate that infants are fed with formula (LnFFRate),

the log of the real price of milk (lnRPMilk), a dummy variable indicating

whether four firms marketed formula (Comp4), and a dummy variable

indicating whether Nestle was the only competitor to the ‘Big Two’

(NestleOnly). The variable indicating the proportion of WIC infants covered

by a competitive sole source contract (WICRebate) was not included in this

regression. The predicted variables from this regression (fitlnRWP) were then

matched to the data based upon the date when the bids for the contract were

due.

As we have already noted, the theoretical model predicts that a dollar change

in the wholesale price should be reflected with a dollar increase in the rebate bid

by the firm. Since the empirical model seeks to explain changes in the log of the

rebates with changes in the log of prices, the coefficient on the price variable

reflects the elasticity of the rebate with respect to the wholesale price.

Consequently the theoretical model predicts the coefficient on the price variable
85

will equal P/R. For example, if the rebate as a proportion of the wholesale price

was .75 then we would expect the coefficient to be 1.33.

Independent Variable: Size of the Contract

WIC agencies have speculated that the rebate they receive from the formula

manufactures is determined by the size of their state or the contract group they

have joined. Small states feel that they are at a disadvantage relative to larger

states in their efforts to contain the cost of their programs through the rebate

program. The constant marginal cost assumptions of theoretical model led us to

conclude that the size of contract should not have an effect on the firm’s bid.

However, if the size of the contract increases the competitive bidding for the

contract and reduces the probability the firm would win the sole source contract

then we would expect the larger contract to be associated with higher bids by

the firm. We experimented with several different measures to proxy for the

size of the contract but chose to employ a rather simple variable – the log of the

ratio of the average of the number of infants in the geographic area covered by

the contract relative to the number of infants participating nationally in WIC

over the six months prior to the time when the bids were due. This variable is

denoted as lnCSize whose coefficient is hypothesized to be positive.

Independent Variable: Probability of Winning a Contract

While it is impossible to obtain direct measures reflecting the firm’s chances

of winning a contract, the number and composition of the firms submitting bids

might serve as an indirect indication of the chances of any firm winning. We are
86

hypothesizing that as the number of firms submitting bids increases, the

probability of any firm winning should fall. A lower probability of winning the

contract, should induce the firm to bid a higher rebate. We included three

dummy variables in our analysis to reflect the number and composition of the

bidders. The dummy variable, CB_BigTwo is set equal to one if the other

member of the ‘Big Two’ also bids on the current contract and consequently the

omitted category is when only one of the dominant firms bids. Holding the

number of bidders from the firms representing a minority share of the market

(Wyeth and Nestle), we would expect having both dominant firms bidding

would increase the size of the rebate.

The number of minor market share firms, Wyeth and Nestle, participating in

the solicitation should affect the bidding of the dominant firms. Again we

would be believe that if these firms bid, their presence would reduce the

probability of the dominant firms winning the bidding and consequently induce

the dominant firms to raise their rebate offers. We created two dummy

variables to capture the number of these minor market share firms participating

in the current solicitation. CB_Minor1 equals one if there was only one minor

market share firm participating and CB_Minor2 equals one if both participated.

The omitted category was when neither Wyeth nor Nestle participated. It was

our expectation that both of these variables would have a positive impact on the

size of the rebate with CB_Minor2 having a greater positive effect on rebates

than CB_Minor1.

Other Factors

Contracts covering larger proportions of WIC infants can be the result of

large states or several states banding together for the purpose of a single

competition. While the formation of a group may lead to larger rebates for the
87

states, the companies may incur higher costs in dealing with numerous state

agencies compared to a single state with comparable numbers of infants.

Consequently, the firms may value the large contracts from groups compared to

contracts from single states and bid a smaller rebate even holding the size of the

contract constant. We included a dummy variable, Group, to indicate whether

the contract up for bid was from a group of two or more states. The omitted

category represents when the contract is solicited by a single state. The

hypothesis coefficient on this variable is negative.

During the time period of the analysis, contracts have been both initially

awarded and then reopened for new bids. We hypothesized that the initial

solicitation of a sole source contract would differ from later solicitations when a

‘benchmark’ would have been established by the previously winning rebate as

well as the knowledge of what the other firms bid. While we didn’t have a

specific hypothesis how the bids would differ, we decided to estimate separate

models for initial and subsequent solicitations.

For the subsequent contracts, we wanted to examine whether firms tend to

bid aggressively with firms who currently hold the contract by offering larger

rebates or tend to bid in a way to let the current holder of the contract to keep

the contract. Our initial hypothesis was that the ‘Big Two’ firms would tend to

try to outbid competitors who were less dominant in the market (from the ‘Big

Two’s’ perspective this would be Wyeth and Nestle) and be differential to a

fellow member of the ‘Big Two.’ We constructed two dummy variables to

reflect who currently holds the contract. One dummy variable, CC_Minor was

constructed to equal one if either Wyeth or Nestle currently holds the contract.

The second dummy variable, CC_BigTwo was set to one if the other firm in the

‘Big Two’ currently holds the contract.
88

It is reasonable to expect the firms would require time to adjust to bidding

for the sole source contracts. As our short history of the rebate indicated, the

‘Big Two’ firms actively tried to undermine the sole source competitive

contracts. Most notable was the period when Mead Johnson tried to signal to

other firms their intention of setting a baseline rebate of 75¢ per can. After

some empirical testing, we determined that Mead Johnson and Ross Labs

bidding behavior during this period was significant different than other periods.

For that reason, we have eliminated the bids for Mead Johnson and Ross Labs

from 15 competitions during the period running from February 1990 through

April 1991.

After eliminating these solicitations, the remaining solicitations were

effectively divided into two time periods. The first time period (from 1986 to

1990) was composed of initial solicitations while the second was composed of

subsequent solicitations. Given we had already decided to estimate the model

separately for the initial and subsequent solicitations, we decided to construct

separate proxies for the adjustment process as the time that had passed from the

beginning of the respective time periods. For the initial solicitations, Time0

was constructed as the number of years (months divided by 12) that had passed

from the first solicitation in 1986 to the current bid. For subsequent

solicitations, Time1 was constructed to reflect the number of years that had

passed since April 1991 – the end of the 75¢ rebate era.

Model Estimates and Discussion 

 We began our analysis of the bidding data by testing whether there was a

statistically significant difference of the model specification for bids of Mead

Johnson and Ross Labs. For the initial and subsequent solicitations, we
89

separately estimated the empirical specification on Mead Johnson and Ross Labs

bids and tested the null hypothesis of equality of the coefficients across firms.

The statistical tests based upon the data for the initial solicitations indicated that

there was no statistical difference (the p value .582). However, for the

subsequent solicitations we found that the sole exception of the effect of the

size of the contract, there also was not a significant difference between the bids

of the two firms. Consequently we will report estimates based upon the

combined data from both manufactures while including a dummy variable,

Ross, that will equal one if the bid is for Ross Labs and zero otherwise. When

analyzing the data for subsequent solicitations, we will include an additional

variable that is an interaction between the firm and the size of the contract

(Ross*lnCS). The coefficient on this variable will reflect the difference between

how Ross Labs and Mead Johnson react to different contract sizes.

Our cursory examination of the bid data suggested that the first bids on a

state’s (or group) contract might differ from subsequent bids. To test that

hypothesis, we analyzed separately the bid data by whether the data was a first

bid or a subsequent bid. We tested the null hypothesis that the variables

common across the two specifications were equal for the two samples. We were

able to reject this hypothesis at the 1% level and consequently we will report

estimates of the bidding models estimated separately for the initial solicitation

of a contract and subsequent bids. Estimates of the bidding model where the log

of the real value of the rebate amount.
90

OLS Model Estimates of Rebate Amount: Initial Solicitations

Source | SS df MS Number of obs = 47

-------------+------------------------------ F( 7, 39) = 7.35

Model | .848139092 7 .121162727 Prob > F = 0.0000

Residual | .643146638 39 .016490939 R-squared = 0.5687

-------------+------------------------------ Adj R-squared = 0.4913

Total | 1.49128573 46 .032419255 Root MSE = .12842

------------------------------------------------------------------------------

lnRebate | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

fitlnRWP | 1.293455 .2090545 6.19 0.000 .8706023 1.716308

lnCSize | .0783273 .0229918 3.41 0.002 .031822 .1248325

CB_BigTwo | .0508939 .0563347 0.90 0.372 -.0630538 .1648416

CB_Minor1 | -.1226476 .0818704 -1.50 0.142 -.2882461 .042951

CB_Minor2 | -.2769715 .1187182 -2.33 0.025 -.5171016 -.0368414

Group | .0372369 .0758257 0.49 0.626 -.1161351 .1906089

Ross | .0388875 .0382133 1.02 0.315 -.0384063 .1161813

_cons | -.5294064 .1814657 -2.92 0.006 -.8964555 -.1623573

------------------------------------------------------------------------------

OLS Model Estimates of Rebate Amount: Subsequent Solicitations

Source | SS df MS Number of obs = 138

-------------+------------------------------ F( 11, 126) = 35.48

Model | 2.41378667 11 .219435152 Prob > F = 0.0000

Residual | .779260774 126 .006184609 R-squared = 0.7560

-------------+------------------------------ Adj R-squared = 0.7346

Total | 3.19304745 137 .023306916 Root MSE = .07864

------------------------------------------------------------------------------

lnRebate | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

fitlnRWP | 1.095137 .2060902 5.31 0.000 .6872905 1.502983

lnCSize | .023043 .0113405 2.03 0.044 .0006005 .0454855

Ross*lnCS | -.029655 .0150482 -1.97 0.051 -.0594348 .0001249

CB_BigTwo | .0054869 .0341322 0.16 0.873 -.0620598 .0730336

CB_Minor1 | -.0314488 .0167184 -1.88 0.062 -.0645341 .0016365

CB_Minor2 | .0175777 .0267609 0.66 0.512 -.0353813 .0705366

Group | -.0035263 .0166099 -0.21 0.832 -.0363968 .0293442

CC_minor | .0325019 .0180698 1.80 0.074 -.0032577 .0682614

CC_bigtwo | -.026714 .015551 -1.72 0.088 -.0574889 .004061

Time1 | .0184442 .003924 4.70 0.000 .0106786 .0262097

Ross | .0410169 .0189025 2.17 0.032 .0036093 .0784244

_cons | -.3713409 .2085925 -1.78 0.077 -.7841393 .0414576

------------------------------------------------------------------------------
91

First Solicitations of Contracts

Estimates of the size of the rebate offered by a firm to an initial contract

solicitation suggest that the wholesale price is positively related to the size of

the rebate. As we have noted, the theoretical model predicts that every dollar

increase in the price of formula would be met with a dollar increase in the rebate

amount and consequently there would not be a change in the net price. In terms

of elasticities, the theoretical model predicts the elasticity of the rebate should

be equal to the ratio of the wholesale price to rebate (P/R). During this period

of time, the average ratio of rebate to wholesale price was .76 implying the

theoretical model would predict the coefficient on the price variable in the

rebate equation to be 1.32. We can’t reject the null hypothesis that the

coefficient on fitlnRWP is equal to 1.32 (p value equals .900).

The size of the contract has a statistically significant effect on the size of the

rebate offered by the firms. Contracts covering a larger portion of the WIC

population estimated to lead to larger rebates but the relationship is quite

inelastic. For a ten percent in the size of the contract, the rebate is expected to

increase by .7 percent.

We hypothesized that as other firms bid on any given contract, the firm

might be led to believe that their chances of winning were lower and

consequently offer higher rebates. If both of the dominant firms bid on the

solicitation, the average rebate is 5 percent higher than if only one of the ‘Big

Two’ offered a rebate. While the estimated effect is in the hypothesis direction,

the effect is not significantly different from zero. When at least one minor

market share firm bids, the expected rebate of the ‘Big Two’ declines by an

estimated 12 percent. If both Wyeth and Nestle bid then the expected rebates of

Ross Labs and Mead Johnson decline by 28 percent compared to the situation
92

when both would had not bid. The estimated effect of participation of Wyeth or

Nestle wasn’t consistent with our prior expectation.

When a group of states solicit a bid on a contract, the firms are estimated to

provide higher rebate amounts and lower net prices compared to when a single

state had solicited the bid. The estimated effect is exactly opposite to the

direction we hypothesized, however, the estimated effect isn’t significantly

different from zero (p value equals .626). The final control variable included

was a dummy variable indicating whether the data was for Ross or Mead

Johnson. While the coefficient suggests that holding all other factors constant,

Ross Labs offered rebates that were on average 4 percent higher than Mead

Johnson, this relationship is not significantly different than zero (p value .315).

Subsequent Bids of a Contract

After the initial award of a sole source contract in a state, firms should have

more information of what is necessary to win the contract and could adjust their

bidding strategy accordingly. The lower unexplained variance of the rebates

offered by Mead Johnson and Ross Labs strongly suggests this to be the case.

The estimates of the impact of wholesale prices reflect a less elastic response

to the changes in wholesale prices than compared what was found in the initial

solicitations. One factor leading to the less elastic response of the rebates to

changes in wholesale prices is the increase in the ratio of rebates relative to

wholesale price that occurs as the subsequent bids are solicited. The average

ratio of rebates to wholesale price rose from .76 to .86 during this period. If the

theoretical model is correct then the coefficient on the log of real wholesale

prices should decline from 1.32 to 1.16. The estimated coefficient of 1.095 is not

significantly different from 1.16 (p value equals .754).
93

In subsequent solicitations, the impact of the size of the contract plays a less

important role than it did in the initial bids. The effect of contract size on the

rebate for Mead Johnson’s bids suggests that large states continue to benefit

from being large although the effect is considerably smaller (1/3 of the effect in

initial solicitations). However, Ross Labs bids are not affected by the size of the

contract (p value for the effect of contract size on Ross Labs’ bids is .537). When

states band together for a solicitation, the bids made by Ross Labs and Mead

Johnson are not significantly negatively affected as being estimated by the

coefficient on the variable Group.

The impact of having both members of the ‘Big Two’ bidding on a contract

continues to the have the hypothesized sign but the estimated coefficient is

statistically insignificant. The participation of Wyeth and Nestle in the

solicitations results in smaller rebate offers of the dominant firms if only one of

the minority market share firms participate. But if they both participate then

rebate offers from the ‘Big Two’ are statistically identical to the offers they

would have made if neither Wyeth nor Nestle had submitted bids. While the

estimates of the impact of the number of firms competing are still puzzling they

are less puzzling than the estimates from the initial solicitations. With the sole

exception of having only one of the minority market share firms participating,

the evidence suggests that the number and composition of firms participating in

a solicitation has no effect on the size of rebate offered by the ‘Big Two.’

In subsequent bids for an existing contract, we tested whether or not firms

bid more aggressive when other firms hold the existing contract as opposed to

when they hold the contract. We constructed two dummy variables to capture

this effect – CC_Minor is set to one when either Wyeth or Nestle holds the

existing contract and CC_BigTwo is set one when the other member of the ‘Big

Two’ holds the existing contract. The omitted category and consequently the
94

comparison group is when the firm making the bid holds the contract. For

example, let us assume that the firm making the bid is Mead Johnson then the

coefficient on CC_Minor tells us the difference between the bid when either

Wyeth or Nestle holds the existing contract and when Mead Johnson holds the

existing contract. The coefficient on CC_BigTwo reflects the difference in the

bid when Ross Labs holds the existing contract and when Mead Johnson holds

the contract. A positive coefficient on either variable in the rebate specification

indicates that Mead Johnson bids aggressively against these competitors

compared to when they hold the contract. A negative coefficient implies a

differential stance toward these competitors.

The estimated coefficients on CC_Minor and CC_BigTwo are statistically

significant at 10% level of confidence and tell an interesting story. Compared to

when the firm bidding holds the existing contract, a member of the ‘Big Two’

will be bid more aggressively against Wyeth or Nestle than when they hold the

contract. They will offer a rebate that is 3.3 percent higher than what they

would have offered if they had the contract. But the firm is deferential to the

other member of the ‘Big Two’ holds the contract. They will bid a rebate that is

2.7 percent lower when the other member of the ‘Big Two’ holds the contract.

An equally valid interpretation of this coefficient is that when a member of the

‘Big Two’ holds a contract (CC_BigTwo = 0) they will bid aggressively to hold

onto the contract compared to the situation when the other ‘Big Two’ firm holds

the contract. However, they will bid less aggressively compared to the situation

when either Wyeth or Nestle holds the current contract.

While there was not a significant time trend in the initial bids, we found a

significant growth in rebates associated with the elapsed time since the end of

the 75¢ rebate debacle that we placed in April of 1991. Over the time period, the

real rebates holding all other factors constant grew at annual rate of 1.84
95

percent. If we don’t control for all of the other variables contained in the model,

the average growth rate of the real rebates is 3.62 percent. This implies that one

half of the growth in the rebates can be attributed to changes in other factors

mostly increases in the real wholesale prices.

The final variable included in the model is the dummy variable indicating

whether the bid was from Mead Johnson or Ross Labs. The estimated

coefficient indicates that holding everything else constant Ross Labs offered

rebates were 4.1 percent higher than Mead Johnson. But this is somewhat

misleading because holding everything else constant doesn’t account for the

differences between Ross Labs and Mead Johnson’s reactions to different

contract sizes. For median size contracts during this period (covering 2.1 percent

of all WIC infants) there is no statistically significant difference between Mead

Johnson and Ross bids even though the point estimate of the difference would

be 1.9 percent. For the largest contract during this period (covering 14.9 percent

of WIC infants), Ross is estimated to underbid Mead Johnson by 3.9 percent but

this point estimate is not statistically significant different from zero. For smaller

than median contracts, Ross is statistical significantly estimated to over bid

Mead Johnson. For example, if the contract covers 1.6 percent of all WIC infants

the point estimate of the difference between Ross Labs and Mead Johnson is 2.7

percent whose p value equals .070.

Appendix E contains the estimates of bidding functions when the

independent variable is the net price. The model estimates for the net price are

opposite in sign from the estimates based upon the rebate amount discussed

above. The only exception is the hypothesized coefficient on the real wholesale

price should be zero instead of P/R when the rebate is employed as the

dependent variable. We find that the coefficient on wholesale prices is not

statistically different from zero as hypothesized in the theoretical model. A final
96

observation is that the overall fit of the model employing the net price is less

and consequently the mean squared error is higher resulting lower significance

of the estimated coefficients. However, using the net the price instead of the

rebate amount doesn’t substantially alters any conclusion about the statistical

significance of estimated relationships.
97

Conclusions

In this study, we have examined the relationship between two features of

the WIC program – the provision of free infant formula to low income mothers

and the sole source contracting procedure implemented to contain the

program’s cost – with the setting of wholesale prices in the industry and the

amount of rebates secured by sole source rebate program. We first examined

the impact of both features of the WIC program on wholesale prices. Based

upon our analysis of the data from 1981 to 2002, we arrived at the following

conclusions. The increasing participation of infants in the WIC program has

resulted in a less price sensitive demand for formula and consequently formula

manufactures have able to increase the real wholesale price. The effort to

contain the formula costs of the WIC program through the implementation of a

contracting process where firms had to competitively bid for the exclusive right

to supply formula to WIC infants within a geographic area (sole source

contracts) has resulted in lower wholesale prices not higher wholesale prices as

was expected by policymakers in the early 1990s. The impact of the rebate

should be welcomed news not only by taxpayers but also by those eligible for

WIC whose participation is made possible by the savings in formula cost from

the rebates but also by parents who pay for formula out of their own pocket.

The second part of the paper focused upon the bidding behavior of Mead

Johnson and Ross Labs from the start of the sole source competitive contracts in

1986 through 2002 – a period when the type of formulas were similar in content

but potentially significantly different from the enriched (DHA/ARA) formulas

not being marketed by manufactures. Some tentative conclusions do emerge

from the data. First, the bidding behavior of Mead Johnson and Ross during this

period does not significantly differ. Secondly, we found confirmation of an
98

important finding of theoretical model that the firm’s wholesale pricing decision

wouldn’t affect the net price (wholesale price minus rebate) of formula to the

government. Thirdly, we found evidence to support the hypothesis that bids to

an initial solicitation do differ (initial solicitations led to lower rebate amounts)

from those bids made to subsequent solicitations. Perhaps this result reflects

the fact the theoretical model is a static representation of the bidding process.

But in subsequent bids the model does not account for the dynamic nature of

the bidding process where the firm has already acquired some WIC contracts. In

future versions of the modeling effort, accounting for the dynamic and

sequential nature of the bidding process should be a priority.

The size of the contract – the number of infants covered by a contract – has

been shown to affect the rebates and consequently net prices faced by the

government. A larger contract will result in larger rebates and lower net prices.

While the empirical findings conformed quite well with the predictions of the

theoretical model, the impact of having more firms bid on the solicitation

remains a puzzle. In the initial solicitations when more of the minority market

share firms bid on a contract, the rebate offers of Ross Labs and Mead Johnson

fell. In subsequent solicitations, a similar result was found if only one firm

joined in the bidding but if a second minority firm bid the rebate offer was not

significantly different from when none of the minority firms bid. These findings

remain a puzzle to explain.

Our examination of the bids from subsequent solicitations provided some

evidence of Mead Johnson and Ross Labs defending the contracts they hold but

not going after contracts by the other. They were more likely to pursue new

contracts by bidding more aggressively against the firms with smaller market

shares – Wyeth and Nestle.
99

Currently there is concern that the aggregate level of rebates has peaked and

with the advent of the enriched formulas the aggregate level of real savings in

the WIC program may begin to decline. Given we have not examined any of the

more recent solicitations that have begun to included the enriched formulas or

solicitations when this new formulation had begun to become the predominate

choice of mothers, what follows should be viewed as speculation based upon

what we have learned from this study.

Assuming the cost of producing the enriched formula is higher than the

formula it is replacing, it is difficult to believe that the net price to WIC of the

enriched formula will ever be less than or let alone equal to the net prices WIC

was paying for non-enhanced formula in 2002. If the net price of formula to the

WIC program is going to be higher, the question is going to be how much

higher? In the near future, it is plausible that mothers paying for their formula

out of their own pockets may become more insensitive to the price allowing

formula manufacturers greater profit margins as well as higher real wholesale

prices on the enriched formula. To the extent this is true, one could envision a

scenario where in efforts to continue their WIC contracts, the firms would offer

higher rebates. Depending upon the extent of the cost increases caused by the

use of DHA/ARA in formula, it is quite possible that over time the ratio of

rebates to wholesale prices would move back to levels close to the level we are

experiencing today.

 The optimism in our prediction is based upon history and a belief in the effect

that competition for WIC contracts will have on rebate offered by firms. During

the 1990 and 1991 Senate hearings, a similar concern was raised about a

potential decline in the aggregate savings in the rebate program. Yet over time,

the rebate as a percentage of the wholesale price rose steadily over the next five

year until it stabilized to a level roughly where we were in 2002. Competition
100

often takes time but in the end it will lead to larger rebates even though there is

a limited number of firms in this market. Unless the firms have entered into an

implicit agreement undermine the rebate program, the cost savings should be

restored to the WIC program.

We will conclude with a suggestion for future research that has not been

mentioned prior to this point in the paper but it is probably so obvious that it

does not need mentioning. Central to the framework that has been developed

to understand how the WIC program affects the price of formula is how mothers

decide upon the extent to which they will rely upon formula to feed their infants

and how they make their decisions of which brand of formula to purchase. Of

particular interest is how the price of formula enters the decision to how to feed

their infants (breastfeeding or formula) and if they choose to utilize formula the

decision of which brand to use.
101

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103

Appendix A

Time Trends in Relative Formula Prices

In this appendix, we will examine the time trends of the relative prices of

alternative infant formula all normalized to reflect the cost of a two-ounce

serving of formula. Beside the company producing the formula, formula can

differ by its source of protein (milk versus soy based) and formulation (liquid

concentrate versus powder). The purpose of this appendix to examine the

question whether the price (cost) of alternative formula differ more over time

than does the cost of formula relative to the price of other consumption goods.

To the extent that the relative price of alternative types of formulas do not vary,

it provides a justification to focus upon only type of formula.

Milk versus Soy

While the majority of infants are fed with milk-based infant formula,

companies market alternative formulas such as soy-based, low iron, or more

recently the ‘enhanced’ formulations containing DHA/ARA. During the time

period of interest of this study, the only alternative formulation with sufficient

market share is the soy-based formula. The decision to use a soy-based

alternative formula is most likely reflective of the inability of the infant to

tolerate a milk-based formula. This decision could also reflect the food

predilections or nutritional concerns of the parents. However, for other parents

the decision of which formula base to use could be determined by the relative

price of the soy versus milk based products.
104

Figures A.1 (for Mead Johnson) and A.2 (for Ross Labs) depict the relative

price of soy based formula relative milk based formula. In each figure, the line

with the ‘X’ denotes the relative price for powder formulation while the line with

without a mark reflects the concentrated formulation. Since the late 1980s, the

price of soy-based formula has been higher than the price of milk based formula.

For both brands, there has been upward trend in the relative price of soy-based

formula.

The trend of the relative price of soy-based formula could be reflecting the

rising cost of the soybeans relative to the price of milk. To examine this

potential explanation, we computed the relative price of a bushel of soybeans to

the wholesale price of Grade A milk during the period of 1981 through 2002. The

data was acquired from the National Agricultural Statistics Service Web site. As

Figure A.3 shows the relative price of soybeans to milk has displayed

considerable variability over this twenty-two year period, however, the data

reflects a downward trend in the relative price of soybeans (linear time trend

shown in figure). Figure A.4 documents separately the real price of milk (solid

line) and soybeans (line marked with ‘X’) over the time period. As shown in the

figure, the real price of both inputs has been falling. Consequently the rising

relative price of soy-based formula could be the result of smaller scales of

operation coupled with an increasing consumer base that is relatively insensitive

to the relative price of soy to milk.
105

Figure A.1

Figure A.2
106

Figure A.3

Figure A.4
107

Liquid Concentrate versus Powdered Formulations

Both milk and soy formulas are provided to consumers in three formulations:

ready to use, liquid concentration, and powdered form. While this study does

not examine the ready to use formulation, this formulation clearly provides the

greatest convenience of use for the parents. The other two formulations do

require mixing of the formula with water. Figures A.5 (Mead Johnson) and A.6

(Ross Labs) display the relative price of the powder versus liquid concentrated

formulations for the two major companies’ milk and soy based (line marked with

‘X’) formulas.

For milk-based products, both Ross and Mead Johnson have historically

priced their powder formulations roughly four percent lower than their liquid

concentrated formulations. Since the relative costs of producing and

distributing formula in these two forms is not known, the lower cost of powder

may reflect either lower costs to the producer or ‘compensation’ to the

consumer to use the more inconvenient formula.

For soy-based formula, the relative price of powder to liquid concentrate

display clear trends that are opposite for the two companies. Mead Johnson

over this time period has steadily increased of the price of formula in powder

form relative to liquid concentrate. Ross Labs on the other hand has done

exactly the opposite. Today, Ross Labs offers a larger discount on their soy

powder than they do on the milk-based products. Mead Johnson provides no

discount for the purchase of powder soy-based formula compared to the mid

1980s when the discount was roughly 14 percent.
108

Figure A.5

Figure A.6
109

Mead Johnson versus Ross Labs

The final comparison between the two brands provides the clearest and

cleanest comparisons between potentially homogeneous products given the

regulation of the production of formula by the FDA. The next four figures

display the relative price of the Ross Labs product relative to Mead Johnson’s

price. Figure A.7 is for milk-based liquid concentrate while Figure A.8 is for milkbased powder formulation. Figures A.9 and A.10 present the corresponding data

for the soy-based formulas.

These figures reveal more information than which company’s price is higher

at any point time. Spikes or peaks in the data indicate which company initiated

a price increase and the amount of time before the other company responds.

For example, in August of 1982, Ross Labs implemented a price change in its

products to which Mead Johnson did not respond until September of 1983. In

February of 1985, Ross Labs implemented a price change and one month latter

Mead Johnson responded. Nine times during this time period, both companies

implemented price changes in the same month. The simultaneously

implemented price changes are marked with an ‘X’.
110

Figure A.7

Figure A.8
111

Figure A.9

Figure A.10
112

At any point in time, the relative price of any product across the two

companies will not fully reflect the relative cost to the consumer. Since mothers

will be reluctant to switch formula as the price changes, the cost relative cost of

the two brands will depend upon the time path of price changes. We have

constructed an index of the relative cost of using one brand over the other by

first computing the average price of each brand over a twelve month period.

For example, for May of 1995 we computed the average price of both brands

over the period of May of 1995 through April of 1996. From these two averages,

we computed the average cost of using Ross products relative to Mead Johnson

products for an infant who would have born in May of 1995 and used formula

throughout their first year of life. To reflect the fact that in any given month,

there are infants born in June of 1994 through May of 1995, we then computed

of average of the relative costs from each of cohort born in these months. We

will denote this as our index of relative costs of formula to mothers in any given

month. These calculations are presented in Figures A.11 (milk-based products)

and A.12 (soy-based products) where the line marked with ‘X’ reflects the values

for powder formulation and the unmarked is for liquid concentrates.

For milk based liquid concentrate brands, the two companies have on

average priced their products so that the cost formula was almost identical

between the brands. Only during the period around 1990 and since 2000, has

Ross Labs undertaken price changes to make their liquid concentrate more

expensive than Mead Johnson. The pattern of relative costs of powdered milk

formula follows the same pattern as liquid concentrate until 1996 when Ross

Labs begin to undertake a series of price changes to make powder product more

expensive than Mead Johnson.
113

Figure A.11

Figure A.12
114

The relative cost of soy products of Ross Labs versus Mead Johnson display

similar time trends as milk based products. During the period around 1990, Ross

Labs’ products were more expensive than Mead Johnson. At the peak in 1991,

they were roughly 5 percent more expensive. However during the period from

1994 through 2001, Mead Johnson’s soy products were more expensive.

However starting in 2000, Ross Labs undertook a strategy of raising its soy

based product prices. By 2004, Ross’s soy based powder formula was roughly

the same price as Mead Johnson but it had increased its price of liquid

concentrate to be 10 percent more expensive than Mead Johnson.

Summary

When examining the set of all relative prices of infant formula, the single

clearest difference over this time period has been seen the price of formula

relative to the price of all other goods – the real price of formula. While the

price of milk and soy based formula have changed over time as well as the

relative price of formulation preparation (liquid concentrate versus powder), the

variations in these dimensions have been small compared to the increase in the

real price of formula for both companies, Mead Johnson and Ross Labs. This

result justifies our approach to focus upon the determination of the real prices

of milk-based formula.
115

Appendix B

A Model of Nominal Price Adjustment

To either establish or to maintain a real or relative price for infant formula,

manufactures would have to be constantly change the price of their product in

response to variation in the prices of other goods (not necessarily inputs to the

production of formula). For example, if the price of all other goods rose by 10

percent and the manufacturer maintained the nominal price of formula then not

only would have formula become relatively cheaper for consumers of formula

but the real value of the firm’s revenues have fallen. Consequently even if we

ignore the increase in the cost of manufacturing the formula, the real value of

profits would have fallen. In response, we would expect the firm to adjust its

price (nominal) to maintain the real value of its price.

It has been proposed that it is costly for the firm to continuously change its

price. If there is a fixed cost to the firm of adjusting its price, the firm faces a

tradeoff between the frequency of adjusting their nominal price and the gap

between the current price and their desired price at any given time. While other

researchers have examined this problem in a broader context, we will only

consider a more simple context where the firm anticipates a given rate of

inflation in the prices of other goods (continuous rate of inflation is assumed to

be i ) and it has chosen to continue charging its current nominal price for a time

period of length T. If the fixed costs of changing its price is F dollars per unit of

output then for the firm to break even it would chose to set a nominal price

above its desired price so over the time period it ‘breaks even.’ If δ is the

percentage growth rate in the real desired price for formula, the firm would
116

initially set the nominal price to be μ percent above the desired price at time 0

so that

 

!

Po

*

eμ"it"Po

*

e

#t

[ ]

!

T

$ dt "F = !

where Po

* is the desired real price at time 0. Solving the above relationship for μ

yields

 

!

eμ=

iT

!"e"tT

F

Po

*

T

+

e

#T

" !

#T

$

%

&

'

(

).

The above expression can be simplified using the approximation

 

!

ex" !

x

# ex "

consequently

 

!

μ "

iT

!

+ ln F

Po

*

T

+ e

#T ! $

%

&

'

(

) =

iT

!

+

#T

!

+ ln Fe*#T !

Po

*

T

+ "

$

%

&

'

(

)

or

 

!

μ "

iT

!

+

#T

!

+D F "Po

*

( ###T ).

where D is an amount (D>0) that will be positively related to the fixed costs

relative to the desired price but negatively related to the growth in desired real

prices and length of time between price changes.

While we have motivated this price adjustment process were the firm adjusts

its price once every T time periods, it can also be interpreted as the firm

establishing a threshold so that when the firm’s established real price (nominal

price deflated by the amount of inflation since the last price rise) falls below this

threshold, the firm changes it price. We will express this threshold as being λ
117

percent below the desired price at time T. In terms of the above model, the

threshold would equal

 

!

Threshold =P!

*

e

"T #$

where

 

!

" =

iT

!

+

#T

!

$D .

Once the real price at any time falls below this threshold amount then the firm

will increase its nominal price and consequently the real price to be equal to μ

percent above the desired price at that time. Note the percentage increase in

the nominal price will equal

 

!

μ + " = iT + #T

the anticipated inflation over the next time period plus the growth in desired

prices but does not reflect the fixed costs of the price adjustment.

Over the period the firm maintains its nominal price, the observed real price

for the product will be in the interval

 

!

Pt " Po

*

eμ!Po

*

e

#T $%

[ ] &t " ["!T ]

where μ > λ. Given this pricing strategy, the firm will anticipate that for more

than T/2, the real price it charges its consumers will exceed the desired price and

the remaining time, the firm’s price will be less than its desired price.

The model of price of adjustment we are proposing can be summarized with

the following equation defining the real value of the price of formula at time t:

 

!

ln!Pt

*

" + μ if ln!Pt

c " " ln!Pt*

" # $

ln!Pt " =

ln!Pt

c " if ln!Ptc " > ln!Pt*

" # $
118

where Pc

t is the real price of formula at time t based upon the previous nominal

price and Pt is the observed real price of formula at time t.

While the parameters, μ and λ, have been characterized to be constants, they

are a function of the firm’s expected rate of general inflation, the firm’s own

desired growth in real prices, and the fixed costs of changing prices. Clearly as

time progresses, the firm’s expectations about inflation and desired growth in

the real price of its product will evolve and consequently also will the

parameters μ and λ. However, we will assume the firm formulates a pricing

strategy (sets μ and λ) for the next T time period based upon the firm’s actual

experience since the last price change and maintains that strategy until the next

price change. This does not imply that firm will change its price every T time

periods. For example, consider the situation where the actual rate of inflation

exceeds (is less than) the firm’s expected rate. In this scenario, the firm will

change its price sooner (later) than the anticipated time of T. If conditions

change and the firm’s desired price deviates from its expected desired price

formulated at the last price change, the firm will be assumed to change its

timing of its next price change. For example if after the previous price change

the firm’s desired real price exceeds (is less than) what the firm expected its

desired price to be at that time then the firm will be more likely to change its

price sooner (later) than time T. Not because the firm has altered the value for

λ but because the probability that current real price is less than firm’s current

actual desired price minus λ has increased (decreased).
119

Appendix C

Description of Variables

Size of Infant Population

The population estimates of infants in the US were obtained from the annual

report, “Resident Population of States (by single year to 85+ and sex)” published

by the Population Distribution Branch and Population Estimates Branch of the

U.S. Bureau of the Census. This report contains intercensal estimates of the US

population, on July 1, by single year of age in each state. These reports can be

obtained on the Census Bureau’s web site. The population aged 0 to 1 was

chosen to define the US infant population. The data from the Census Bureau

reflected the population size in each July. A linear extrapolation was used to

estimate the population in months August through June.

Breastfeeding and Formula Feeding Rates

The breastfeeding rates for US infants, when in the hospital and at six months

after birth, from 1980 through 2000 were obtained from the Ross Mothers

Survey. Ross acquires data for the Mothers Survey by sending questionnaires to

all new mothers in the US. To estimate the percentage of infants formula fed in

the hospital and at six months, the one minus the breastfeeding rates at those

dates were computed. Next, the average annual formula feeding rate was

estimated by finding the area under the curve as shown in the firgure below, and

dividing that area by twelve. It was assumed that formula-feeding rates

increased less rapidly in the first six months after birth, and more rapidly in the

following six months. This is why the curve appears to have a logarithmically
120

curved shape.

14 In the figure below, A% is the formula feeding rate in the

hospital and B% is the formula feeding rate at six months. The area of the

yellow figure calculated at 2.75*(B%-A%) represents approximately 92% the

area of the triangle with the hypothesis going from A% at 0 months to B% at 6

months. Similarly, the area of the green figure, calculated at 3.3*(1-B%)

represents approximately 110% of the area of the triangle with the hypotenuse

connecting B% at 6 months with 100% at 12 months. Thus the total area under

the curve is equal to 6*A% + 6* B% + 2.75*(B%-A%) + 3.3*(1-B%), and the

average annual formula feeding rate is that area divided by 12.

The average formula feeding rate for each year was assumed to be equal to

the July rate for each year. A linear extrapolation was then performed to

calculate the rates for August through June of each year. The formula feeding

rates for 2001 and 2002 were estimated by projecting out the trend line of the

 14 Note that it was not necessary to make this assumption, and would have been more correct to

simply measure the area under two straight lines, from A% to B%, and from B% to C% (C%

being measured at 12 months, and just below 100% to account for the small percentage of

mothers who continue breastfeeding after one year). Both methods of calculating the average

annual formula feeding rate produce similar results; therefore it is irrelevant which method is

used.
121

1980 through 2000 rates two additional years, and estimating the points on that

line.

Percentage of infants on WIC

The population of infants on WIC in each state and in the US as a whole was

obtained from the Center on Budget and Policy Concerns. For October 1988

through August 2003, monthly counts were available. For 1980 through 1982,

only the infant count at September was available, and for 1983 through 1988,

only the yearly average was available. Thus, linear extrapolation was used to

estimate the monthly population of infants on WIC from September 1980

through October 1988. For each month the total number of infants on WIC was

divided by the total infant population in the US to obtain the percentage of

infants on WIC.

Percentage of WIC Infants Covered By Rebate Program

A history of all bids for sole source contracts, specifying the net price of the

bids and the winning bidder from 1986 through May of 2003, was obtained from

the Center on Budget and Policy Concerns. From this was constructed a chart

detailing which manufacturers held sole-source contracts in each state from

1986 through 2003. Using the population of infants on WIC for each state, the

total number of infants in states for which a manufacturer held a sole source

contract was calculated from 1986 through 2002. The number of infants on WIC

in sole-source states was divided by the total number of infants on WIC to

obtain a monthly percentage of WIC infants in sole-source states.

It was necessary to create this variable because the rebate program was

phased in slowly over the years, and thus had different levels of impact at

different points in time. This variable will allow the model to take this into
122

account. It should be noted that this variable is still not at 100% because several

states have yet to adopt the rebate program.

Real Wholesale Price of Milk and Soy

The plant pay prices of milk, that is the wholesale price that a

manufacturer would pay to farmers for Grade A milk, from 1980 through 2002

was obtained directly from the National Agricultural Statistics Service. The per

bushel price of soybeans was taken from the same source. These prices were

then inflated by the CPI to reflect December 2002 prices.
123

Appendix D

OLS Estimates of the Wholesale Price Model

For sake of comparison, the following are the estimates of the OLS

regression of the log of the real price of a 2 ounce serving of formula (LnPrice)

on the control variables reflecting factors believed to determine the desired real

wholesale price of formula.

OLS Regression Results

Source | SS df MS Number of obs = 1016

-------------+------------------------------ F( 10, 1005) = 6298.15

Model | 40.3370579 10 4.03370579 Prob > F = 0.0000

Residual | .643661383 1005 .000640459 R-squared = 0.9843

-------------+------------------------------ Adj R-squared = 0.9841

Total | 40.9807193 1015 .040375093 Root MSE = .02531

------------------------------------------------------------------------------

LnPrice | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

OnWIC | .0216609 .0004375 49.51 0.000 .0208024 .0225194

WICRebate | -.0017042 .0001343 -12.69 0.000 -.0019679 -.0014406

LnInfants | .7722456 .0392468 19.68 0.000 .6952305 .8492607

LnFFRate | -.0670394 .025707 -2.61 0.009 -.1174849 -.0165938

LnRPMilk | -.02491 .010168 -2.45 0.014 -.0448629 -.0049571

Comp4 | .0016767 .0052075 0.32 0.748 -.008542 .0118955

NestleOnly | -.0141302 .0069799 -2.02 0.043 -.027827 -.0004334

RossMC | .00701 .0022457 3.12 0.002 .0026033 .0114167

MJPowder | -.0395161 .0022457 -17.60 0.000 -.0439229 -.0351094

RossPowder | -.019613 .0022457 -8.73 0.000 -.0240197 -.0152063

_cons | 1.24529 .0689986 18.05 0.000 1.109893 1.380688

------------------------------------------------------------------------------

Comparing the estimates from the Censored Normal Regression to the OLS,

we see that as we would expect the estimates of the coefficients from the OLS
124

analysis are attenuated toward zero compared to the maximum likelihood

estimates. Not only are the magnitudes of the estimated effects of the variables

larger, they now have the predicted sign with the sole exception of LnFFRate.

The estimate of the effect of the real price of milk (LnRPMilk) is positive while

the effect of having four firms (Comp4) is negative. Accounting for the

censoring of the errors, lowered the estimated significance levels of the

estimated coefficients, however all of the estimated coefficients remain

significant at the 5% level with the exception of the estimated effect of

LnFFRate, LnRPMilk and RossMC.
125

Appendix E

Estimates of the Bidding Model: Dependent Variable Net Price

In this appendix, we report the estimates of the bidding model for initial and

subsequent solicitations.

OLS Model Estimates of Net Price Amount: Initial Solicitation

Source | SS df MS Number of obs = 47

-------------+------------------------------ F( 7, 39) = 1.79

Model | 1.88315638 7 .26902234 Prob > F = 0.1176

Residual | 5.8704948 39 .150525508 R-squared = 0.2429

-------------+------------------------------ Adj R-squared = 0.1070

Total | 7.75365117 46 .168557634 Root MSE = .38798

------------------------------------------------------------------------------

lnRNP | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

fitlnRWP | .405566 .6315997 0.64 0.525 -.871965 1.683097

lnCSize | -.1843887 .0694632 -2.65 0.011 -.3248912 -.0438862

CB_BigTwo | -.2352362 .1701995 -1.38 0.175 -.5794973 .1090248

CB_Minor1 | .2424209 .2473485 0.98 0.333 -.2578887 .7427305

CB_Minor2 | .6024603 .3586737 1.68 0.101 -.1230256 1.327946

Group | -.1743526 .2290862 -0.76 0.451 -.6377232 .2890181

Ross | -.0672358 .1154509 -0.58 0.564 -.3007573 .1662857

_cons | -.843958 .5482479 -1.54 0.132 -1.952894 .264978

------------------------------------------------------------------------------

OLS Model Estimates of Net Price: Subsequent Solicitations

Source | SS df MS Number of obs = 138

-------------+------------------------------ F( 11, 126) = 12.27

Model | 29.1898766 11 2.65362514 Prob > F = 0.0000

Residual | 27.2460678 126 .216238633 R-squared = 0.5172

-------------+------------------------------ Adj R-squared = 0.4751

Total | 56.4359443 137 .4119412 Root MSE = .46501

------------------------------------------------------------------------------

lnRNP | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

fitlnRWP | .6954429 1.218619 0.57 0.569 -1.716167 3.107053

lnCSize | -.1980596 .0670567 -2.95 0.004 -.3307628 -.0653563

Ross*lnCS | .20259 .0889803 2.28 0.024 .0265007 .3786793

CB_BigTwo | .1172324 .2018252 0.58 0.562 -.2821737 .5166385

CB_Minor1 | .1332769 .0988568 1.35 0.180 -.0623577 .3289116

CB_Minor2 | .025122 .158238 0.16 0.874 -.2880264 .3382704

Group | .047163 .098215 0.48 0.632 -.1472015 .2415276

CC_Minor | -.180134 .1068472 -1.69 0.094 -.3915815 .0313134

CC_BigTwo | .1137804 .0919535 1.24 0.218 -.0681929 .2957536

Time | -.1317434 .0232028 -5.68 0.000 -.1776611 -.0858257

Ross | -.2804791 .1117712 -2.51 0.013 -.501671 -.0592871

_cons | -1.100936 1.233415 -0.89 0.374 -3.541828 1.339956

------------------------------------------------------------------------------