Sole-Source Contracts in WIC Infant-Formula Rebate Auctions and their Effect on Manufacturers Markups

Transcription

1 Sole-Source Contracts n WIC Infant-Formula Rebate Auctons and ther Effect on Manufacturers Markups Abstract The WIC program uses an aucton to procure nfant formula. Manufacturers bd on the rght to be an agency s sole suppler of formula by offerng a rebate on formula sold through WIC. Rebates reduce costs, averagng about 90 percent of wholesale prces. However, because rebates are so large, some queston the ndustry s compettveness. Ths paper develops a model for optmal rebates and shows that margnal cost can be estmated from model coeffcents and program characterstcs. Margnal cost estmates suggest large markups, and elastctes consstent wth these markups suggest manufactures prce on the demand curve where demand s nearly unt elastc. Davd E. Davs* October, 2009 *Assstant Professor, Department of Economcs, South Dakota State Unversty Brookngs, SD 57007, PH: , emal:davd.davs@sdstate.edu

2 Introducton Government agences are frequent purchasers of products n unregulated markets. The economc consequences of such nterventons are not well known. Frst-order effects are often obvous as the government uses ts sze to negotate terms more favorable than other purchasers. However, government procurement can have other dstortonary effects. For example, Fona and Duggan (2006) fnd that Medcad purchases of prescrpton drugs are assocated wth hgher drug prces. Ths paper examnes the market for nfant formula, a market n whch the government facltates and nfluences a large proporton of purchases. Over one half of all nfant formula sold n the Unted States s purchased through the Specal Supplemental utrton Program for Women, Infants, and Chldren (WIC). WIC, the thrd-largest Federal food-assstance program, s admnstered by the U.S.D.A. Food utrton Servce n conjuncton wth state and local health departments. It annually supples grants to States to provde supplemental foods, and a varety of servces to low-ncome women; nfants; and chldren up to age fve. Because the cost of provdng nfant formula to WIC nfants (the most costly food tem) was ncreasng durng the 70s and 80s, states became concerned the hgh cost was severely lmtng the number of elgble persons that could be served. To lmt costs, States devsed an aucton format whereby nfant-formula manufacturers could bd on the rght to be a state s sole suppler of WIC nfant formula. In exchange for ths rght, manufacturers pad a rebate on each can of nfant formula sold through the WIC program. Manufacturers provded sealed bds for the sze of the rebate they would pay and the manufacturer supplyng the largest rebate was awarded the exclusve rght to supply formula. 2

3 Rebates have proven very effectve at reducng costs to states, as wnnng rebates have averaged about 90 to 95 percent of manufacturers wholesale prces and have routnely returned over $1.5 bllon to the WIC program on an annual bass. However, the sze of rebates relatve to manufacturers wholesale prces naturally leads to questons about the relatonshp between wholesale prces and margnal costs. It seems ether manufactures sell formula at a substantal level below margnal cost n the WIC market, or that wholesale prces far exceed margnal cost. The latter possblty seems lkely gven the hghly concentrated structure of the formula market. Currently, three manufacturers produce about 99 percent of domestc sales (Olvera and Davs, 2006). Throughout the hstory of the rebate aucton process, rarely have more than 3 manufacturers bd on a gven contract, and n a majorty of cases, only 2 manufacturers bd on a contract. In ths paper, I develop a method to measure markups of prce over margnal cost for frms that prce dscrmnate and sell n separate markets. I adapt and generalze an approach frst developed n Cresp and Sexton (2005) to estmate a manufacturer s probablty of wnnng a rebate aucton whch suggests a method to estmate margnal cost and prce markups. When appled to data on wholesale prces and rebates for nfant formula manufacturers, estmates suggest margnal costs are low relatve to wholesale prces, and that markups are large, and the effect of the WIC rebate system s to dramatcally ncrease prcng power, and therefore markups. Background and lterature The WIC program, establshed n 1972, provdes a varety of servces and supplemental foods for low-ncome women, nfants, and young chldren. The program s admnstered jontly by the U.S. Department of Agrculture (USDA) Food utrton 3

4 Servce (FS) and authorzed state agences. Fundng s provded through FS to state agences wth annual congressonal appropratons. Each state s cash grant ncludes a food grant and a utrton Servces and Admnstraton (SA) grant. Because avalable funds are lmted, state agences have enacted a varety of measures to control costs attemptng to ensure the effcent use of funds and the full partcpaton for all elgble ndvduals. Food benefts are typcally dstrbuted through retal outlets. Partcpants receve food vouchers that can be redeemed at authorzed retal stores, nsolatng them from prce consderatons when purchasng supplemental foods. Federal mandates dctate allowable quanttes of supplemental foods, whch are noted on food vouchers. State regulatons also frequently mpose further restrctons on the types of foods (brands, package szes etc) that can be purchased, n the nterest of controllng costs (Davs and Lebtag, 2005). Based on redeemed vouchers, states remburse retal outlets for the tems sold to WIC partcpants. Infant formula s a food tem avalable to partcpatng nfants less than one year old. Because of the large number of nfants n the US who partcpate n WIC, WIC purchases of nfant formula account for over 50 percent of the product s sales (GAO, 1998). 1 Durng the 1980s nfant formula prces ncreased more than the rate of nflaton and the rsng cost of nfant formula lmted the ablty of state agences to serve all elgble ndvduals leadng them to nvestgate ways to lmt nfant-formula costs. Whle most agences dstrbute formula through retalers, a few agences use other methods of dstrbuton. Vermont currently uses a home-delvery system and Msssspp uses a drect-dstrbuton system, and some countes n Oho and Maryland have used drect- 1 In 2005, 49.5 of all US nfants partcpated n the WIC program. 4

5 dstrbuton methods n past years (Harvey et. al., 1988). These states were successful n provdng nfant formula at reduced costs by usng a varety of methods that gave preference to one brand of nfant formula. In partcular Msssspp used a system of warehouses across the state to dstrbute nfant formula. The state purchased nfant formula n bulk and startng n 1984 used a compettve bddng process to select the manufacturer that would sell formula to the state at the lowest cost (Harvey et. al, 1988). Usng the experences of these states as examples, WIC offcals n Tennessee developed a system whereby a sngle manufacturer was awarded the exclusve rght to provde nfant formula n that state n exchange for a rebate on each unt sold through the program n that state. Dstrbuton remaned through approved retal vendors. Manufacturers offered ther rebates for consderaton va sealed bds and the contract was awarded to the manufacturer who offered to provde the hghest rebate per unt sold. The success of ths system led other states to adopt smlar systems, although some developed systems that dd not use compettve bddng. Contracts that provde exclusve sellng rghts and that solct sealed rebate bds have become known as compettve sole-source contracts. Wyomng and Florda developed a system whereby the states negotate wth manufactures for contracts to provde rebates for ther products sold n the state. These so-called open-market contracts dd not provde manufacturers the exclusve rght to sell n a state, and dd not usually use sealed bds when askng manufactures for ther rebate offer. The method that would provde the greatest cost savngs was n doubt durng the early years of adopton. 2 In Aprl, 1988 Florda requested bds under both an openmarket system and a compettve sole-source system. Because the compettve system 2 For example, n Texas n 1998 Ross Laboratores contended that open market contracts would provde equal or greater cost savngs over sole-source compettve contracts. 5

6 resulted n a hgher rebate, the state adopted the compettve system. A few other states adopted the Florda method of requestng rebate bds under both systems, attracted by the opportunty for hard data suggestng whch method provded the greatest cost savngs. Ths usually led to the adopton of a sole-source compettve bddng system. In October 1988, federal law requred all WIC agences to explore mplementng cost-contanment methods for procurng nfant formula and to begn mplementng costcontanment practces f they proved to lower costs. In 1989, federal law requred all state agences to adopt a compettve bddng process or another process that provded equal or greater savngs. The law defned compettve bddng as a procurement process n whch the State WIC agency selects the sngle source offerng the lowest prce for the nfant formula, as determned by the submsson of sealed bds (Olvera et. al., 2004). State agences rebate systems have been very successful reducng the cost of procurng nfant formula. Fgure 1 shows wnnng rebates, wholesale prces, and net prces (wholesale prce mnus rebate) for wnnng contracts from md 1998 to 2006 (13- ounce can of mlk-based lqud concentrate). Clearly, net prces are low compared to wholesale prces. Ths s also reflected n total rebates returned to states n fgure 2. Currently, rebates annually return over $1.5 bllon to state agences. Development of the WIC rebate systems has been a boon to WIC agences as procurement costs have been reduced allowng more elgble WIC partcpants to be served. However, the sze of the rebates has led to speculaton, and some research, about the source for such large rebates. It seems that ether manufactures set wholesale prces much greater than margnal costs, or that they sell nfant formula at a prce below cost n the WIC market. Sellng below cost may be proft maxmzng f manufactures are able to 6

7 subsdze the loss wth ncreased profts from non-wic customers. For example, f WIC produces a spllover effect whereby the brand of nfant formula holdng the WIC contract s gven preference by non-wic customers, then there may be an ncentve for manufacturers to secure the WIC contract even f that means sellng to WIC customers at a loss. The General Accountng Offce (GAO, now the General Accountablty Offce) n 1998 dentfed two potental sources for a spllover effect. Doctors may gve preference to the WIC brand of nfant formula when recommendng a brand of nfant formula to new mothers. Or, WIC contracts may gve the WIC brand greater shelf-space on grocery-store shelves ncreasng sales to non-wic customers (GAO, 1998). Whle the GAO s 1998 report recognzed the possblty of a spllover effect, t dscounted the possblty of the effect beng large enough to entce manufactures to sell to WIC below cost. Olvera, et. al, (2004) note that snce the mplementaton of state rebate programs, the retal prce of nfant formula has rsen faster than the rate of nflaton. 3 They suggest that WIC and ts rebate program may affect retal prces to non-wic customers n two ways. WIC may remove many of the prce senstve, low-ncome customers from the market, leavng only less prce senstve hgh-ncome customers payng for nfant formula out of ther own pockets. Wth few prce-senstve customers actually payng for nfant formula, manufactures may have the ablty to charge hgher prces. Alternatvely, they suggest a spllover effect from sole-source contracts may ncrease demand for the contract brand from non-wic customers, leadng to hgher retal prces. An event study analyss and a multple regresson analyss suggested that beng the contract brand of nfant formula ncreased that brand s prce and that the larger the 3 The 1998 GAO report also notes that nfant formula prces ncreased at a real rate of about 9 percent annually after sole-source contracts were mandated, compared to about 3 percent n other tme perods. 7

8 sze of the WIC market relatve to the non-wic market the hgher the prce of the contract and non-contract brands of nfant formula. Betson (2007) develops a theoretcal model of manufacturer behavor, gven the presence of the WIC program and sole-source contracts. Betson s prmary concluson s that the effect of the WIC program wll be to decrease prces to non-wic consumers, rather than to ncrease them. A substantal weakness of the Betson model s the lack of attenton to the possblty of a spllover effect. Huang and Perloff (2007) show the mportance of spllover effects for nfant formula markets. They use a multnomal logt model to estmate market shares of dfferent brands of nfant formula when they hold and do not hold the WIC contract. They fnd that after a brand gans the WIC contract, ther share of the market ncreases substantally mmedately. However, they fnd that the brand s share grows even more, gradually over tme. Market shares of wnnng frms grow from less than 20 percent to over 70 percent n a perod of tme less than two years. The authors also fnd a smlar, but opposte, reacton n the brand that loses the WIC contract. A theoretcal model of rebate bds and wholesale prces Infant formula manufacturers (potentally) derve proft from two dstnct markets: the WIC market (Q W ) and the non-wic (Q ) market. I assume the number of unts sold n the WIC market s exogenous and perfectly prce nsenstve. 4 The WIC market ncludes persons partcpatng n the WIC program. Once a person no longer qualfes for the WIC program, or does not partcpate n the WIC program, they become part of the non-wic market f they contnue to purchase nfant formula. 4 WIC nfants are determned by program elgblty standards, and total amount of formula a famly can purchase for an nfant s set by Federal mandate. 8

9 WIC contracts are between WIC state agences, or allances f multple states negotate contracts jontly, and nfant-formula manufacturers. Hereafter, I wll refer to nfant-formula manufacturers as frms and state agences/allances as agences. Frms bddng decsons are based on potental contracts wth agences whch have mplcatons for sales n the WIC and non-wic market. Defne the demand for formula from non-wic customers n market as Q = Q (P m,. P M ), where P m P M represent frm-specfc prces for the m=1 to M frms sellng to customers n market. Market ncludes customers n the geographc area correspondng to agency ; that s, states or groups of states f states are alled n contract negotatons. Huang and Perloff (2007) suggest that a WIC contract produces a spllover effect for a frm and ths shelf-space effect seems exogenous to the frm s decson. Consderng Huang and Perloff s evdence, a frm should expect some share of the non-wic market f they wn the WIC contract and a smaller share f they do not wn the contract, therefore demand for frm m s wrtten swq f awarded the contract Qm, =, (1) slq f not awarded the contract where s w > s l are market shares when awarded or not awarded the WIC contract. Lettng ρ m, equal the probablty of frm m wnnng the contract n market, the non-wic demand can be wrtten as Q = ρ s Q + (1 ρ ) s Q + ζ 2 m, m, w m, l l m, ( ) ( ) = ( s + θ ρ ) Q + ζ, 3 whereζ s a mean-zero stochastc element, and Ө =(s w -s l ). Let (Q W + η) represent (uncertan) formula demand from WIC customers n the market area represented by 9

10 agency. (η s a zero mean stochastc element). Expected formula demand for frm m from agency (market ), can be wrtten as: E[ Q ] = E[ Q ] + E[ Q ] = ( s + θ ρ ) Q + ρ Q. (4) W W m, m, m, l m, m, Expected proft for frm m s: ( ) E[ Π ] = P ( s + θ ρ ) Q + ( P R ) ρ Q c ( s + θ ρ ) Q + ρ Q, (5) W W m, m, l m, m, m, m, m, l m, m, where R m, s frm m s rebate bd and c m, s a the constant margnal cost of producng, transportng, and sellng a unt of nfant formula n market. It may seem napproprate to model margnal cost as beng constant. It s arguable that there may be economes of scale and that sellng n the WIC market allows the frm to lower per unt costs by operatng at a hgher scale. However, the assumpton here s that margnal costs are nvarant only n market. I assume that frms have two choce varables, P and R, but that they make optmzng decsons n two steps. Evdence suggests that frm s choose P before they choose R. Wholesale prces change nfrequently (Olvera and Davs), whle rebate auctons occur n varous markets qute frequently and at tmes that do not generally concde wth wholesale prce changes, suggestng the rebate bds are formulated at dfferent tmes than prces. So, frm m chooses prce n market : E Π dq dq = ( + ) + ( + ) + ( + ) = 0 (6) W Pm, sl m, sl m, Q m, Q cm, s P ρ θ ρ θ ρ l ρ m, θ m, dpm, dpm, Solvng equaton (6) provdes the optmal prce to charge n market 1 W dq ρ Q m, =, m + dpm, sl + θ ρ m, P c Q m, ( ), ( 7) 10

11 where dq Q dp Q = + dp P P dp o, m o m, m, o, m, s the total dervatve of non-wic demand wth respect to frm m s prce. It s the change n non-wic demand n market from a change n frm m s prce, recognzng that competng frms may react to m s prce change. In short, t recognzes olgopolstc reactons n lght of the concentrated ndustry structure. Infant formula manufactures contend they do not prce dscrmnate geographcally and charge a sngle prce n all markets. Lackng any gudance for how a sngle prce mght be determned, I assume the sngle natonal prce s determned by averagng over all markets. Lettng Q I I I ρ θ Pm,, θ, Q, m ρ m = = = I I P I I I I I W Pm, Q Q W c m P m =, Q =, Q =, c = I I I I equaton 7 becomes, 1 W ρm Q ( ). ( 7 ) * Q P m = cm Q + a P m sl θρ + m An nterestng comparatve statc examnes the effect of a change n the WIC market on the wholesale prce of nfant formula. m Q P ρ m W = > 0 (7b) Q P m sl + ρ m θ Equaton 7b shows that a proft maxmzng frm wth market power wll ncrease prce as the sze of the average WIC market ncreases. 11

12 Equaton 7a can be rearranged to gve the markup of prce over margnal cost n a Lerner ndex as, where ε ( sl θρ m) Q ( sl+ θρ m) W Pm cm 1 ρ m Q + + =, (8) P ε m m Q Q P m Q P m Q P o d P o P m = P = +, s m Q P m Q m o P o Q d P m P o m the total prce elastcty of demand faced by manufacturer m. The porton of equaton 8 n the square brackets s the effect of the WIC program on prce-cost markups. It s clearly greater than 1 whch suggests that the effect of the WIC program s to ncrease prce-cost markups for nfant formula sold n the non-wic market. Denote the optmal prce for frm m, determned from equaton 7a, as P. Because * P s predetermned, the frm s decson to fnd the optmal rebate s to smply choose R m, by maxmzng ( ) * * W W W m, m l θ ρ m, m m, ρ m, m, l θ ρ m, ρ m, E[ Π ] = P ( s + ) Q + ( P R ) Q c ( s + ) Q + Q. (5 a) * The frst-order condton s ρ ρ * W W W ( Pm Rm, ) Q ρ m, Q cm, ( Q θ Q ) Π m, m, m, = = 0. (9) R R m, R m, Solvng equaton 9 gves the optmal rebate n market, * * ρ Q m, Rm, = Rm, = P m cm, 1 + θ, (10) W ωm, Q 12

13 whereω m, ρ m, = > R m, 0 s the margnal change n the probablty of wnnng an aucton, from a change n the rebate bd. 5 Estmatng margnal cost Rearrangng equaton 10, margnal cost n market equals W * * ρ Q m, cm, = Pm Rm,. (11) W ωm, Q + θq Assumng that frms choose prces and rebates optmally, then the margnal cost of provdng nfant formula to market can be calculated from equaton 11. * P and * R are observable. Q and Q W represent the total WIC and non-wic demand n market. Whle not drectly observable, approxmatons for them are avalable. It seems reasonable to assume that a non-breastfeedng nfant n the WIC market consumes, on average, the same amount of formula as a non-breastfeedng nfant n the non-wic market. Let a equal the average amount of nfant formula consumed by nfants. Let q, w represent a W sngle formula consumng nfant n the WIC market, then Q = aq, w for w=1 to W WIC nfants n market. 6 * Let, n( ) q P represent a sngle non-wic nfant for whom W w * P s less than ther parent s reservaton prce, then Q = aq, n for n = 1 to nonbreastfeedng nfants not n the WIC market. Focusng momentarly on the term n the second set of brackets n equaton 11, n 5 See Cresp and Sexton, 2005 for an applcaton of ths method to cattle procurement. 6 ote that f a w s the amount of formula consumed by nfant w, then Σa w q,w =aσq,w where the summaton s over the w nfants n market. 13

14 W W W a q q Q w=1, w w=1, w W W W + θq a q + θ q q + θ q w=1, w n=1, n w=1, w n=1, n = =, (11a) Q + + under ths formulaton, WIC and non-wic demand can be approxmated by the number of (non-breastfeedng) WIC and non-wic nfants n each market. Fnally, equaton 11 requres parametersθ, ρ m,, and ω m,. I rely on Huang and Perloff who estmate market shares for nfant formula manufactures when they hold a WIC contract compared to when they do not hold a contract to provde an estmate ofθ. The fnal parameters needed to calculate margnal cost n equaton 11 are the probablty, and margnal probablty of supplyng the wnnng WIC rebate. I detal a method to estmate these parameters below. Estmatng the probablty of wnnng a contract Frms are awarded WIC contracts by offerng to sell nfant formula to a WIC agency at a lower net prce, wholesale prce mnus rebate, than other manufacturers. Manufacturers bds are a functon of ther probablty of wnnng. I assume manufacturers assess ther probablty of wnnng from ther own bd relatve to ther wholesale prce, the expected bds and wholesale prces of rvals, and any nformatonal advantages from prevously holdng an agency s contract. To begn, I estmate a lnear regresson where rebate serves as the dependent varable, and wholesale prce, the number of brths n a market, and WIC nfants n a market are ndependent varables. I also nclude annual dummy varables and a dummy varable that takes a value of one when a manufacture held the WIC agency s prevous contract. So for each manufacturer m, I estmate a regresson of the form, 14

15 Rm = a 0 + δ t + β P P m + β b Brths + β W WICInfants + PCH M + ε. (12) I assume each manufacturer forms expectatons for other manufactures bds as the predcted value from these regressons. Let ϑ ( P, R ) = α P + γ R + ξ ndcate the cost of nfant formula to WIC m m m m m m m m agency, f they award the contract to manufacturer m, where α, γ are parameters to be estmated andξ m s a well-behaved error term arsng from manufacturers nablty to fully observe costs. WIC chooses the manufacturer wth the lowest cost, ϑ ( P, R ) < ϑ ( P, R ). However, manufactures cannot observe rvals bds before the m m m o o o aucton and so estmate the cost to WIC from rvals as ϑ ˆ o = α opo + γ oro + ξ o where R ˆ o s the rval s expected bd. Let Y represent a random varable ndcatng that the WIC agency chooses manufacturer m when ϑ m < ϑ o for all o m. Each manufacturer s probablty of beng chosen s, ρ m, = Pr ob( Y = m), where m m ˆ ρm, = F α Pm + γ Rm, + α Po + γ Ro, + ξo (13) o m o m I assume ξo s normally dstrbuted and estmate equaton 13 wth a probt regresson. o m To estmate margnal cost, I need the probablty that an agency would choose a partcular manufacturer, ρ m, and the margnal effect, ω m,, of that manufacturer s rebate bd on the probablty of beng chosen. I can estmate these from the parameters n equaton 13. Data 15

16 The prmary data n ths study are a tme-seres, cross-secton of frms wnnng and losng rebate bds for all contract auctons from 1986 through Cross-sectons are state WIC agences, or allances of multple state agences. Typcally, agences offer contracts for terms of about 3 years, and so over the duraton of the data, agences have a tme-seres of multple contracts. Agences ntated rebate systems n dfferent years, and contracts can be extended so the number of contracts per agency vares. The data were compled from a varety of sources ncludng bddng records kept by the FS and the Center for utrton Polcy Promoton. Data were collected as avalable for both mlkand soy-based formula n both powder and 13-ounce cans of lqud concentrate forms. Bds for soy-based formula are only sporadcally avalable, and bds for powder-based are avalable for only the years snce However, a nearly complete data set of bds for 13-ounce cans of mlk-based lqud concentrate are avalable from 1986 to 2007 documentng wnnng and losng bds for each contract auctoned by WIC agences. Whle agences determne wnnng based on a weghted average net prce, where the weghts are the antcpated proportons of powder and lqud concentrate n mlk and soy forms, Olvera and Davs show that lqud-concentrate and powder bds are hghly correlated suggestng that bds for ether type should be a good proxy for the other, and for the weghted average bd. So, gven the dearth of data on powder bds, the analyss n ths report uses bds for mlk-based lqud concentrate. The data also nclude the natonal wholesale prces for a truckload sze shpment of nfant formula; the prce agences use when evaluatng whch rebate bd wll provde the lowest net prce (wholesale prce mnus rebate). Rebates and wholesale prces are adjusted to constant 2007 dollars usng the consumer prce ndex. 16

17 The number of partcpatng WIC nfants comes from the Food and utrton Servce of USDA (FS). The FS s the federal agency that manages and coordnates the ndvdual state agences. They regularly montor state caseloads and other program characterstcs, ncludng the number of partcpatng WIC nfants. on-wic nfants are estmated by takng the number of brths n a state and subtractng the number of partcpatng WIC nfants. Brths for are from the atonal Centers for Dsease Control. Census estmates of brths are used for Counts of WIC and non-wic nfants are adjusted wth breastfeedng rates as estmated by the Ross Mothers Survey. Table 1 presents the means and standard devatons for rebates and wholesale prces n constant 2007 dollars. It s nterestng to note that wholesale prces are qute smlar for the two domnant frms, Mead Johnson and Ross, and for the two secondary frms Wyeth and Carnaton. It s also nterestng that frms dd not bd for every contract avalable. The number of avalable auctons s gven by the number of wholesale prce observatons, whle the number of bds offered s gven by the number of rebate observatons. Future research wll examne the determnants of bd submsson. Probt results and markup estmates Table 2 shows the results from estmatng equaton 12 for each manufacturer wth OLS regressons. An aucton s ncluded n each sample condtonal on a postve rebate bd to reflex that manufacturers expectatons are based on postve bds only. The predcted values from these regressons are ndependent varables n the probt regressons that follow. 17

18 Table 3 shows the results from probt regressons for each manufacturer. Mead Johnson and Ross bd n nearly every aucton, but Wyeth and Carnaton bd n only a subset of auctons. In only a very few auctons do Wyeth and Carnaton both bd n the same aucton. To facltate estmaton of Mead Johnson and Ross probabltes, I create varables Thrd Bdder Rebate and Thrd Bdder Wholesale Prce. If Wyeth bds n an aucton wth Mead Johnson and Ross, then Wyeth s the thrd bdder. If Carnaton bds n an aucton wth Mead Johnson and Ross, then Carnaton s the thrd bdder. If both frms bd, then the thrd bdder s the average of Wyeth and Carnaton. Ft statstcs at the bottom of the table suggest the model fts the data reasonably well. A manufacturer s own rebate and wholesale prce are the most consstently sgnfcant predctors of the probablty of wnnng an aucton. As expected, the hgher manufacturer s own rebate the greater the probablty of wnnng, holdng wholesale prce constant. Conversely, hgher wholesale prce decreases the probablty of wnnng. Beng the prevous contract holder seems mportant for Mead Johnson and Ross. Ths reflects that all else constant, Mead Johnson and Ross are lkely to be awarded a contract f they also held the prevous contract, lkely because changng supplers s costly. Changng supplers s costly because vendors and WIC partcpants must be notfed of the change n the brand acceptable to WIC. Agences are also lkely senstve to nfant partcpants, whose mothers do not want to change brand of nfant formula once feedng has begun wth another brand. Table 4 shows the margnal effects wth standard errors for each manufacturer s rebate. The estmates suggest that a $0.10 ncrease n rebate ncreases the probablty of 18

19 wnnng, by.0887,.0924,.0697,.167 for Mead Johnson, Ross, Wyeth, and Carnaton respectvely. Table 5 shows the results from estmatng margnal cost accordng to equaton 11. Equaton (11a) shows that counts of non-breastfeedng nfants and the dfference n market share wth and wthout a WIC contract are needed to estmate margnal cost. I use the estmate of the dfference n market share estmated n Perloff and Huang. Ther analyss suggests that wthn the length of a typcal contract (that s to say, n a perod of tme less than 3 years) market shares of the non-contract brands fall to less than 20%, whle market shares of contract brands ncreased to over 70%. Gven ths evdence, I use.55 as a measure of θ n equaton 11. WIC nfant counts and on WIC nfants are readly avalable, as noted above, and there rato s multpled tmes P m R m, ρ ϖ m, m, s used to calculate margnal costs n accordance wth equaton 11. I estmate margnal cost for each observaton ncluded n each manufacturer s sample, and estmate a standard error for each observaton usng the delta method. Margnal costs appear small when compared to wholesale prces and rebates. Estmates for Mead Johnson, Ross, and Carnaton are all below 30 cents per 13-ounce can of lqud concentrate (n constant 2007 dollars). In contrast, average wholesale prces for a 13- ounce can were $3.29 for Mead Johnson, $3.27 for Ross, $2.91 for Wyeth, and $2.92 for Carnaton. Implcatons of the WIC rebate program for non-wic purchases Equaton 8, reproduced below, suggests the effect of the WIC program on prcecost margns. 19

20 ( sl θρ m) Q ( sl+ θρ m) W Pm cm 1 ρ m Q + + =, (8) P ε m m Q Because I have estmated margnal costs and have data on prces, I can calculate the left hand sde of equaton 8. The markup of prce over margnal cost s.9200 (Mead Johnson),.9258 (Ross),.8251 (Wyeth), and.9342 (Carnaton). I also have estmates for the parameters n the square brackets n equaton 8. Let s l =.2, Ө=.55 based on Huang and Perloff. Table 4 gves estmates ofρ for Mead Johnson, Ross, Wyeth, and Carnaton. m Dvde the numerator and denomnator by 1/Q w and let the rato of Q /Q W = Wth these estmates, the value of the terms n the square brackets equals for Mead Johnson, for Ross, for Wyeth, and for Carnaton. Solvng 8, the total elastctes of demand are (Mead Johnson), (Ross), (Wyeth), and (Carnaton). It s nterestng to consder the effect of the WIC rebate program on prce settng. The markup wthout the WIC program would be equaton 8 wthout the value of the term n square brackets, or 1/(1.75) = , 1/1.67=.5975, 1/1.77=.5663, 1/1.60=.6233, for Mead Johnson, Ross, Wyeth, and Carnaton. The effect of the WIC rebate program s ncrease markups by =34.92, =32.83, =25.88, =31.09 percent for Mead Johnson, Ross, Wyeth, and Carnaton. Alternatvely, I can solve for the elastcty of demand that gves the observed markups. These effectve elastctes are 1.09, 1.08, 1.21, and Assumng that a monopolst wll not set prce on a porton of the demand curve wth an elastcty of demand less than 1, snce rasng prce when demand s nelastc wll always ncrease profts, we see that the effect of the WIC rebate program s to allow manufacturers to set prce at the pont on the demand 20

21 curve provdng nearly the hghest possble proft. The ntuton for these results s that the beneft from ownng the sole-source contract s very large. Once the frm has the solesource contract the exogenous ncrease n market share from the spllover effect, and the sales to WIC customers, effectvely solates demand from prce ncreases. Consumers buy the product based on non-prce factors, lke promnence on the shelf and doctors recommendatons. It seems clear that n such crcumstances frms would have much greater ablty to ncrease prce. Concluson The WIC program has developed a creatve way to lmt the cost of procurng nfant formula for partcpatng nfants by offerng manufacturng frms the exclusve rght to sell to WIC customers n exchange for a per unt rebate. Whle savng the government over $1.5 bllon annually, WIC rebates have consderable mplcatons for non-wic purchasers of nfant formula. The results of ths study suggest that nfant formula manufacturers possess consderable market power allowng them to set wholesale prces n excess of margnal cost. I estmate margnal costs below 30 cents per 13-ounce can of mlk-based lqud-concentrate nfant formula for each of the manufacturers currently sellng nfant formula. Wholesale prces average over $2.50 for all manufacturers and over $3.00 per can for the two domnant frms (Mead Johnson and Ross). Gven the estmate for margnal cost, I am able to estmate prce cost margns and to examne the effect of the WIC rebate program on margns. I fnd that WIC contract holders are effectvely solated from prce competton whch allows them to prce as f demand were nearly unt elastc. In contrast, wthout the WIC program, frms would prce accordng to ther demand elastctes, whch I fnd range from to The result 21

22 s that frms can set prces about 26 to 35 percent hgher than they could wthout the effect of the WIC program. 22

23 Table 1. Varable Means Mean Observatons Mead Johnson Rebate Mead Johnson Wholesale Prce Ross Rebate Ross Wholesale Prce Wyeth Rebate Wyeth Wholesale Prce Carnaton Rebate Carnaton Wholesale Prce Brths WIC Infants

24 Table 2. Rebate OLS Regressons Mead Johnson Ross Wyeth estle Wholesale Prce *** *** *** *** (0.1636) (0.1901) (0.7076) (0.2319) Brths (0.0069) (0.0081) (0.0127) (0.0221) WIC Infants (0.0151) (0.0177) (0.0351) (0.0561) Prevous Contract Holder * *** (0.0584) (0.0619) (0.1181) (0.1181) Constant *** *** ** (0.6355) (0.7377) (1.7248) (0.6447) Adjusted R Annualy dummy varable ncluded, std. errors n parentheses. *** p<0.01, ** p<0.05, * p<0.1 24

25 Table 3. Wnnng Proablty Probt Regressons Manufacturer Varables Mead Johnson Ross Wyeth Carnaton MJ Rebate 2.397*** *** * (0.528) (0.636) (2.442) (1.368) MJ Wholesale Prce * (1.897) (2.098) (5.987) (5.415) Ross Rebate *** * (0.57) (0.573) (1.797) (1.993) Ross Wholesale Prce * -6.58* 8.412* (1.83) (2.018) (3.553) (5.020) Wyeth Rebate 3.185*** (0.810) Wyeth Wholesale Prce (4.264) Carnaton Rebate 4.172*** (1.473) Carnaton Wholesale Prce * (2.166) Thrd Bdder Rebate (0.491) (0.534) Thrd Bdder Wholesale Prce (0.757) (0.789) Prevous Contract 0.523** 0.531** (0.260) (0.252) (0.549) Constant (1.621) (1.543) (7.883) Observatons Percent Correctly Predcted 72.61% 75.00% 87.18% 73.81% Predcted Wnnng Probablty Actual Wnnng Percent Psuedo R Log lklhood Standard errors n parentheses *** p<0.01, ** p<0.05, * p<0.1 25

26 Table 4. Rebate Margnal Effects Manufacturer Margnal Effect Mead Johnson 0.887*** (.184) Ross 0.924*** (.174) Wyeth 0.697*** (.189) Carnaton 1.607*** (.559) Standard errors n parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 5. Estmated Margnal Costs Per 13 oz. can of mlk-based lqucd concentrate Mead Johnson Ross Wyeth Carnaton Margnal Cost Margnal Cost Standard Error

27 Fgure 1. Rebates, net prces, and wholesale prces of mlk-based lqud concentrate, by State $4.0 $3.5 $3.0 Dollars per 13-ounce can $2.5 $2.0 $1.5 $1.0 $0.5 $0.0 Y 7/1/98 PA 10/1/98 T 7/1/99 SD, E 10/1/99 IL 2/1/00 WSCA 10/1/01 TX, M, IA 10/1/02 CA 8/1/03 T 7/1/04 D 7/1/05 et Prce Rebate 27

28 Fgure 2. Rebates Blled (ml $): Domestc, Retal Delvery Actual Rebates Blled (ml $) 28

29 References Betson, Davd, (2007) Impact of the WIC Program on the Infant Formula Market Fnal Report for Grant Award 43-3AEM , mmeo. Cresp, John M., and Rchard J. Sexton, (2005) A Multnomal Logt Framework to Estmate Bd Shadng n Procurement Auctons: Applcaton to Cattle Sales n the Texas Panhandle, Revew of Industral Organzaton, 27: Davs, Davd E. and Ephram S. Lebtag, (2005) Interstate Varaton n WIC Food Package Costs: The Role of Food Prces, Caseload Composton, and Cost-Contanment Practces, Food Assstance and utrton Research Report o. 41 (FARR-41), USDA Economc Research Servce. Greene, W. H. (2000) Econometrc Analyss, 4th edn. Upper Saddle Rver, J: Prentce Hall. Harvey, Stephan., Robert Greensten, and Scott Baranck. (1988) Savng to Serve More: Ways to Reduce WIC Infant Formula Costs. Center on Budget and Polcy Prortes Huang, Ru and Jeffrey M. Perloff, (2007), WIC Contract Spllover Effects Unversty of Berkeley Workng Paper Olvera, Vctor, Mark Prell, Davd Smallwood, and Elzabeth Frazao, (2004) WIC and the Retal Prce of Infant Formula, Food Assstance and utrton Research Report o. 39, USDA Economc Research Servce. Olvera, Vctor and Davd E. Davs, (2005) Recent Trends and Economc Issues n the WIC Infant Formula Rebate Program, Economc Research Report o. 22, USDA Economc Research Servce. U.S. General Accountng Offce, (1998), Resource, Communty and Economc Development, Food Assstance: Informaton on WIC Sole-Source Rebates and Infant Formula Prces. GAO/RCED , May 1998, 29