Disclosure Standards for Vertical Contracts. Anil Arya. The Ohio State University. Brian Mittendorf. The Ohio State University

Transcription

1 Disclosure Stadards for Vertical Cotracts Ail Arya The Ohio State Uiversity Bria Mittedorf The Ohio State Uiversity October 010

2 Disclosure Stadards for Vertical Cotracts Abstract Disclosure stadards promotig trasparecy have expaded i virtually all ecoomic areas. Oe area i which such trasparecy has bee slow to flourish is i the disclosure of vertical (wholesale) cotracts. Casual ituitio suggests such disclosures would be beeficial i protectig cosumers ad retailers alike from discrimiatory supplier practices. I this paper, we formally ivestigate the welfare cosequeces of disclosure of vertical cotracts. I particular, we fid that whe supplier power is cocetrated, disclosure provides a meas through which a powerful supplier ca use its (observed) wholesale prices to coordiate retail behavior of its wholesale customers. From the retail cosumer's perspective, such coordiatio is uwated, ad leads them to favor opacity of cotracts. I cotrast, whe supplier power is dispersed, disclosure of cotracts becomes a coduit through which suppliers compete idirectly via their retail surrogates. Retail cosumers welcome the icreased competitio that accompaies such disclosures. I short, we fid that the efficacy of disclosure stadards for vertical cotracts depeds critically o supplier cocetratio i iput markets.

3 1. Itroductio I the past few decades, the proliferatio of regulatios promotig disclosure has proceeded seemigly uabated. Oe area i which expaded disclosure is particularly apparet is i the realm of retail markets. As recet examples, regulators have compelled hospitals to post pricig for patiets, stipulated "sticker price" ad fuel ecoomy labels for automobile sales, required disclosure of textbook prices to faculty adopters, demaded displays of utritio iformatio from fast-food chais, ad eve sought to madate disclosure of fueral prices, each i the ame of cosumer protectio ad ehaced competitio. Prior to these iitiatives, attempts at establishig retail price disclosure stadards have see varied levels of success i markets such as alcoholic beverages, prescriptio drugs, ad eye exams. While such disclosures have mostly served to hider price discrimiatio ad favoritism, thereby promotig greater competitio, they have also created potetial for greater collusio i some markets (Austi ad Gravelle 008). These dual cosequeces of retail price disclosure have largely echoed the theoretical research otig both societal upsides ad dowsides of ehaced disclosures (e.g., Stigler 1964; Varia 1980; Schultz 005). While the spread of price trasparecy i the retail area has cotiued, the wholesale prices offered to vertical parters have largely bee permitted to remai cofidetial. There are, of course, exceptios. Daish efforts to icrease competitio i the market for the supply of ready-mix cocrete led to efforts to madate disclosure of wholesale pricig cotracts (Albaek et al. 1997). 1 More recetly, strog efforts at both the state ad federal level i the US have pushed for disclosure of medical equipmet ad 1 Subsequet to such disclosure rules, wholesale prices actually icreased, promptig a rescissio of the requiremets. The primary explaatio for this uiteded price icrease is that disclosure served to facilitate collusio amog suppliers i the wholesale market, much like it has bee show to do i some retail markets (Albaek et al. 1997) As will be see shortly, the preset paper will provide a complemetary explaatio for this pheomeo, oe reliat o how disclosures chage a supplier's ability to maage coordiatio amogst retailers.

4 pharmaceutical costs icurred at the wholesale level so as to udercut favored pricig agreemets ad (the perceptio of) secret cocessios. The dichotomy betwee disclosure stadards for retail ad wholesale prices is typically explaied o the grouds that pricig i a wholesale market etails differet cosideratios tha i the retail market, ad these cosideratios may poit to the differetial regulatory treatmet. For oe, supply markets are ofte characterized by limited competitio (or eve moopoly), so the effects of disclosure o competitio i that market are iheretly more muted. Secod, buyers i the supply market are ot ultimate cosumers but istead face competitio of their ow whe sellig i retail markets. I this paper, we seek to model these two key characteristics of supply markets so as to examie the cosequeces of disclosure (ad odisclosure) of vertical pricig cotracts therei. We represet the feature that wholesale buyers ecouter their ow competitio by presumig there are retail providers of a differetiated fial good, each of whom rely o a supplier for a key iput. To capture the feature that supply markets are ofte limited i competitio, we presume each retailer has oly oe supplier upo which it ca rely. With this basic settig as a backdrop, we ivestigate the cosequeces of disclosure (or, coversely, cofidetiality) requiremets o supply chai behavior ad retail competitio. The paper fids that the distict features of supply markets make cofidetiality more attractive to retailers ad eve ed cosumers tha covetioal wisdom would suggest. Relatedly, we demostrate that the extet to which supplier power is cocetrated is a key determiat of the efficacy of madatory disclosure rules. To get a feel for the uderlyig forces at work, cosider the case of two retailers. First, say the retailers are each served by a separate (dedicated) supplier as, for example, whe a Burger Kig frachise competes with a earby McDoalds frachise. I this case, each supplier s motivatio i settig wholesale prices chages depedig o the prevailig disclosure stadards. Whe cotracts are required to be disclosed, the supplier

5 3 recogizes ay price cuts it offers to its wholesale customer will give the customer a twofold advatage i retail competitio: the direct savigs will permit its customer to be aggressive ad, cogizat of this, the retail rival will cosequetly cede market share. Abset disclosure of cotracts, however, the supplier caot use its wholesale price to ifluece the retail competitor, oly its ow customer. As a result, with cofidetiality, wholesale prices are higher. Such higher wholesale prices uder cofidetiality stad to hurt cosumers (due to the esuig icrease i retail prices), ad eve hider idustry profit (due to the detrimetal effect of double margializatio). If, o the other had, both retailers rely o a sigle (commo) supplier, the supplier s icetives are radically differet. This commo supplier case correspods with, for example, two competig electroics retailers who each sell Soy televisios. With both of its customers competig fiercely i the retail realm, the supplier ow seeks a meas through which it ca softe retail competitio ad foster a more cooperative eviromet. Whe cotracts are disclosed, the supplier ca use a high wholesale price for oe customer to sigal a softeed retail stace to aother. The ed result is iflated wholesale prices. I cotrast, cofidetiality prevets the supplier from usig its wholesale prices to udercut retail competitio. I this case, the, cofidetiality poits to lower wholesale prices ad greater welfare. I short, i the dedicated supplier settig, each supplier's itet is to give its customer base (those with whom it shares a de facto alliace) a leg up i competitio. I this case, welfare is ehaced by requirig wholesale prices be disclosed sice such disclosures stregthe competitio betwee its customer base ad the other supplier's customer base (which we deem iter-alliace competitio). I cotrast, i the commo supplier settig, the supplier's itet is to softe competitio betwee its ow customers (deemed itra-alliace competitio). I this case, cofidetiality is welfare ehacig sice disclosures oly weake itra-alliace competitio. These basic cocers impact o iter-alliace ad itra-alliace competitio

6 4 are simultaeously preset ad balaced i the more geeral case of retailers. The more eve the bifurcatio i the supply market (i.e., each supplier s retail reach is comparable), the more disclosed cotracts are used as a tool to give a supplier s customers a edge i retail competitio. But, as the retail reliace o oe supplier icreases (i effect, the higher the Hirfidahl idex of the supply market), the more disclosed cotracts are used to softe retail competitio via higher wholesale prices. As a cosequece, cofidetiality becomes more desirable, both from a cosumer ad a overall welfare perspective, the greater the cocetratio of power i the supply market. We detail two key variats to the aalysis both to erich the coclusios ad to examie their robustess. First, we edogeize the costs that form the basis for the supplier s chose pricig. More specifically, we cosider how each disclosure regime iflueces the supplier s choice of cost-cuttig ivestmet, i.e., its preferred tradeoff betwee fixed ad variable costs. I this case, if supplier power is cocetrated, the disclosure of cotracts provides the domiat supplier with a useful strategic tool. I particular, with a commo supplier, price disclosure permits the supplier to softe competitio ad extract a greater share of the esuig idustry profits, thus ecouragig it to make greater cost cuttig ivestmets. The more importat such ivestmets are i developig supply chai efficiecy, the more attractive disclosure becomes. I cotrast to covetioal wisdom, the, it is the supplier who is the impetus for disclosure; cofidetiality, whe it arises, is drive by retailers ad cosumers. O the other had, whe retailers rely o separate suppliers, the supplier actually has greater icetives to ivest i cost cuttig whe cofidetiality is i place: disclosure creates a prisoers' dilemma of sorts amog the suppliers which, i tur, dampes icetives to ivest. Despite this added cosideratio, with dedicated suppliers, the shrikage of wholesale prices uder disclosure is the pressig cosideratio i diviig the welfare ehacig disclosure stadard. Secod, we examie how more complex cotractual arragemets i the supply

7 5 chai alter the coclusio. I particular, we revisit the aalysis uder two-part tariff cotracts. The typical view is that two-part tariff cotracts lead to a fully coordiated supply chai ad thereby preclude ay strategic wholesale pricig cosideratios. However, i the presece of retail competitio ad cofidetiality of cotracts, this is ot ecessarily the case. That is, eve with two-part tariffs, a sole supplier fids it hard to commit to a variable charge above its margial cost to softe competitio whe the terms are ot disclosed (istead, it has icetives for uilateral deviatio to provide cocessios to a customer). Similarly, without disclosure, dedicated suppliers fid it hard to commit to a variable charge below margial cost to give their customer a edge. Thus, the variable charges uder two part tariffs have similar properties as those uder stadard liear wholesale prices: with high (low) cocetratio of supplier power, variable charges are greater (lower) uder disclosure of cotract terms. As such, though cotract terms are of course differet, the basic coclusios i the mai setup persist i the case of two-part tariffs. This research is related to both the supply chai (vertical) ad competitive (horizotal) iformatio sharig literatures. I terms of supply chai iformatio sharig, the literature focuses primarily o a retailer s (supplier s) decisio to share stochastic private iformatio with its supplier (retailer) (e.g., Li 00; Li ad Zhag 008). This research cocludes that eve whe a retailer seeks to share iformatio with its supplier, it does so oly if the supplier ca credibly guard such iformatio from the retailer s competitors. I cotrast, the preset paper fids that strict cofidetiality betwee supply chai parters is ot ecessarily preferred (either by the parters or by society as a whole) whe the iformatio shared is ot exogeous ad stochastic but rather arises edogeously as a result of cotractual terms. Relatedly, the vast literature o horizotal iformatio sharig explores competitors desires to share iformatio with each other (e.g., Gal-Or 1985; Li 1985). Oe clear coclusio of this literature is that uder Courot competitio, each retail

8 6 competitor opts to publicly disclose (withhold) its cost (demad) iformatio due to competitive ramificatios. I the preset aalysis, where the iformatio disclosed is ecessarily cost-related (it is the retailer s prevailig wholesale price), a stark differece arises. Whe the cost iformatio is ot stochastic but rather strategically set, the retailers' strog desire to disclose iformatio is perturbed. I fact, whe retail firms rely o a commo supplier, the retailers (ad society as a whole) prefer to maitai cofidetiality of cost terms. I cotrast, whe the wholesale market is bifurcated equally amog suppliers, the reverse icetives arise. Thus, the edogeous ad strategic ature of wholesale prices makes them distict from other costs whe it comes to disclosure policies. As a result, our results suggest that the ature of the retail market ad the wholesale market joitly determie the efficacy of full disclosure regulatio. I this vei, the curret paper also builds o the literature o observability of supply chai cotract terms ad secret price cocessios (e.g., O'Brie ad Shaffer 199; McAfee ad Schwartz 1994; Rey ad Verge 004). While this literature is ostesibly aimed at examiig meas for supplier commitmet i the absece of observable cotracts, it also idetifies the equilibrium outcomes uder a commo supplier ad cotract odisclosure. Our aalysis exteds this literature alog two dimesios, by comparig welfare implicatios of disclosure ad odisclosure regimes ad the critical tie-i to supplier cocetratio. I this sese, the preset aalysis seeks to fid what characteristics of supply markets would udge regulators towards (or away from) madatory disclosure regulatio. The paper proceeds as follows. Sectio presets the basic model. Sectio 3 presets the results: 3.1 idetifies the equilibrium outcomes uder each disclosure regime; 3. cotrasts the disclosure regimes; 3.3 cosiders the effect of edogeous As auditors are apt to poit out, aother potetial differece is that cotractual terms are by their very ature more easily audited/cofirmed. Iformatio about stochastic costs or forecasts thereof, o the other had, are more easily maaged. The cosequeces of such earigs maagemet i this realm is ivestigated i Bagoli ad Watts (009).

9 7 supplier costs; ad 3.4 cosiders the cosequece of two-part tariff cotractig. Sectio 4 cocludes the paper.. Model We study a basic formulatio of supply chai iteractios with a focus o the cosequeces of varyig the degree of trasparecy of cotractual terms. I particular, retail firms are (Courot) rivals i a dowstream (fial good) market. The (iverse) demad fuctio for the fial good for firm i is p i = a q i γ, i, j = 1,...,; i j, q j j i where p i deotes the market price for firm i's good, ad q i ad q j deote the quatities supplied by firms i ad j, respectively. The parameter γ, 0 < γ 1, represets the degree of substitutio amog the competig products with the extreme values of 0 ad 1 correspodig to the cases of idepedet goods ad perfect substitutes, respectively. The retail firms rely o key iputs supplied by oe of two idepedet upstream suppliers, deoted suppliers A ad B. I particular, retailers 1,...,m each rely o the iput provided by supplier A i creatig their fial product. I tur, retailers m+1,..., rely o supplier B's iput. For example, suppliers A ad B may be frachisors such as McDoalds ad Burger Kig, where retailers 1,...,m are frachises of supplier A ad the retailers m+1,..., are frachises of supplier B. Without loss of geerality, say supplier A has more customers, i.e., m - m, or m /. For each retailer, oe uit of the fial product requires oe uit of the iput. For each supplier, the uit cost of makig the iput is c, 0 c < a. The supplier sets a (wholesale) uit price w i for iput procured by its retail customer, firm i, ad each retail firm respods by procurig the umber of uits it desires. 3 While each firm is, of course, aware of its ow procuremet terms (i.e., firm i kows w i ), whether or ot it is aware of its rivals' procuremet terms depeds o the 3 The iput buyers' coversio ad sellig costs are readily icorporated ito the aalysis. I particular, followig Sigh ad Vives (1984), the itercept a ca be viewed as beig et of dowstream costs.

10 8 trasparecy of the reportig system i place. We cosider the outcomes uder two distict disclosure stadards: (i) full disclosure wherei (w 1,...,w ) is disclosed to all firms prior to competitio; ad (ii) a cofidetial regime wherei the retail firms are ot made aware of the procuremet terms of their retail rivals. I evaluatig the efficacy of each disclosure stadard regime, we employ the stadard welfare measure that reflects a weighted sum of firm profits ad cosumer surplus (e.g., Baro 1988; Baro ad Myerso 198): W = Π A + Π B + i =1 Π i +βcs, where Π A ad Π B reflect the profits of suppliers A ad B, respectively, Π i, i = 1,...,, reflects the profit of retailer i, ad CS reflects cosumer surplus. I the welfare expressio β 1, reflectig that stadard setters may be equally cocered with all ecoomy participats or may place more (or all) emphasis o cosumers' fates (Shapiro 1986; Baro 1988). I the aalysis that follows, we idetify the uique (Perfect Bayesia) Nash equilibrium that satisfies the stadard assumptio of passive beliefs (e.g., Hart ad Tirole 1990; O'Brie ad Shaffer 199; McAfee ad Schwartz 1994; Rey ad Tirole 006). Passive beliefs preset a atural restrictio o potetial equilibria by requirig that whe a firm does ot directly observe its rivals' pricig, its beliefs about the cotract offered to a rival are ot iflueced by off-equilibrium cotract offers to itself. The sequece of evets is summarized i Figure 1. Disclosure stadards are established. Suppliers A ad B set wholesale prices w 1,...,w m ad w m+1,...,w, respectively. Cotract terms are revealed i accordace with the disclosure stadard. The retail firms simultaeously choose quatities, q 1,...,q. Retail purchases are made, ad firms realize profits. FIGURE 1. Timelie.

11 9 3. Results 3.1. Equilibrium To set the stage for evaluatio of disclosure stadards for supply chais, we first derive the equilibrium outcomes uder each disclosure regime Full Disclosure of Cotracts With full disclosure, each retailer kows both its ow wholesale price ad those of its competitors prior to egagig i retail competitio. This advace warig of its competitors' positios, of course, refies a firm's behavior i the retail market. Though we will provide a complete characterizatio of the equilibrium outcome for ay m ad i due course, it will prove coveiet to rely o the case of = to demostrate the key forces i the aalysis. With =, the effect of m is quite clear: for m = 1, each retailer relies o a differet supplier (i.e., dedicated suppliers), whereas for m =, each retailer relies o the same supplier (i.e., a sole supplier). The case of dedicated suppliers implied by m = 1 reflects a circumstace where the competig retailers rely o distict iputs to produce related outputs. For example, the dedicated supplier case could reflect competig fast-food frachises each of whom has a differet fraschisor; or, it could reflect the sales ad distributio of differet cell phoe pla providers (retailers) who each have exclusive distributio arragemets with differet cell phoe maufacturers. I cotrast, the case of m = represets the circumstace where both competig retailers rely o the same supplier for their retail product. For example, differet retail outlets each rely o Apple for the supply of ipod products. Such a sole supplier arragemet is perhaps the most commoly studied supply chai wherei all retailers are captives of a moopoly supplier. We ext derive the outcomes i each of these cases. First, cosider the case of dedicated suppliers (m = 1). Workig backwards i the game, give disclosed supplier terms ad its cojecture of retailer j's output, q j, retailer i

12 10 chooses its output i the retail realm, q i, to solve: Max q i [a q i γ q j ]q i w i q i. (1) The first-order coditio of (1) yields firm i's reactio fuctio q i (w i, q j ) = [a w i γ q j ] /. Give observability of wholesale prices, each firm chooses quatities kowig the other's wholesale price. Thus, usig the two reactio fuctios take together with the equilibrium coditios q 1 = q 1 ad q = q yields the retail equilibrium as a fuctio of the disclosed wholesale prices (the superscript "d" idicates disclosure): q i d (w 1, w ) = [a w i ] γ[a w j ] 4 γ. () The quatities q 1 d (w1, w ) ad q d (w1, w ) i () serve as the iduced demad fuctio for supplier A ad B, respectively. Thus, supplier A chooses w 1 ad supplier B chooses w to maximize their respective profits as oted i (3): Max w 1 [w 1 c]q 1 d (w 1,w ) ad Max w [w c]q d (w 1,w ). (3) Joitly solvig the first-order coditios associated with (3) reveals w i d, the suppliers' equilibrium wholesale prices. Substitutig these prices i () yields the equilibrium quatities deoted q i d qi d (w1 d,w d ). Give the equilibrium characterizatio, firm profits, cosumer surplus, ad total welfare are readily obtaied. I particular, retailer i's profit is Π i d = [a q i d γq j d w i d ]q i d, supplier profits are Π d A = [w d d 1 c]q 1 ad Π d B = [w d c]q d, ad cosumer surplus is CS d = 1 [ (q 1 d ) + γq d 1 q d + (q d ) ]. Take together, these yield total welfare of W d = Π A d + Π B d + Π 1 d + Π d + βcs d. These outcomes are detailed i Lemma 1(i). Now, cosider how the outcome is differet uder a commo supplier (m = ). I

13 11 this case, the retail subgame is as before, but the wholesale price determiatio is differet. Istead of two suppliers simultaeously settig the wholesale price of their respective customers, oe supplier sets the wholesale price for both customers. I particular, supplier A chooses wholesale prices to solve: Max w 1,w [w 1 c]q 1 d (w1,w ) +[w c]q d (w1,w ). (4) The first-order coditios of (4) reveal the supplier's chose wholesale prices: w i d = c +[a c] /. As before, whe substituted ito qi d (w1, w ), equilibrium retail quatities obtai; substitutig these ito the firm profits, cosumer surplus, ad total welfare formulae, i tur, yields equilibrium profit ad welfare expressios. Lemma 1(ii) summarizes the results of this exercise. (All proofs are provided i the Appedix.) Lemma 1. I the = case, uder full disclosure, the equilibrium outcome is: (i) with dedicated suppliers (m = 1): d (a) w 1 = d [a c][ γ ] w = c + d ; q 4 γ 1 = d [a c] q = [4 γ ][ + γ ] ; d (b) Π 1 = d [a c] Π = [4 γ ][ + γ ] ; Π A d = ΠB d = [a c] [ γ ] [4 γ ] [ + γ ] ; (c) CS d = 4[a c] [1+ γ ] [4 γ ] [ + γ ] ad Wd = 4[a c] [6 + β(1 + γ ) γ ] [4 γ ] [ + γ ]. (ii) with a commo supplier (m = ): (a) w 1 d = w d = c + a c ; q 1 d = q d = a c [ + γ ] ; d (b) Π 1 = d a c Π = d [a c] ; Π [ + γ ] A = [ + γ ] ; Π B d = 0 ; (c) CS d = [a c] [1+ γ ] 4[ + γ ] ad W d = [a c] [6 +β(1 + γ ) + γ ] 4[ + γ ].

14 1 From the Lemma, a key differece i wholesale pricig betwee the dedicated ad commo supplier cases is worth otig. For ay γ > 0, the wholesale price is higher uder a commo supplier tha uder dedicated suppliers. The reaso for this is that with dedicated relatioships, each supplier has icetives to drive dow its wholesale price to put its customer i a positio of competitive advatage i retail competitio. I effect, with m = 1, there is a de facto alliace betwee a supplier ad its retailer, ad each supplier's focus is o obtaiig a edge i iter-alliace competitio. I cotrast, uder a commo supplier (m = ), iter-alliace competitio is moot sice both retailers form a alliace with supplier A. I this case, the supplier's focus is squarely o softeig itra-alliace competitio. I particular, the supplier's aim is to iduce retail providers to raise retail prices, ad the supplier does so by raisig the wholesale price it charges the buyers. 4 The above ituitio is bore out by formally examiig the supplier's tradeoff betwee profit margis ad purchase quatities whe settig its prices i (3) ad (4). I the dedicated supplier case of (3), a icrease i w 1 etails two effects: a icrease i the d profit margi, (w 1 c), ad a decrease i quatities sold to retailer 1, q 1 (w1, w ). O the other had, with a commo supplier i (4), a icrease i w 1 etails three effects: a icrease i the profit margi, (w 1 c), a decrease i quatities sold to retailer 1, d d q 1 (w1, w ), ad a icrease i quatities sold to retailer, q (w1, w ). This last effect provides a added icetive for the commo supplier to boost wholesale prices. A atural cosequece of icreased retail competitio with dedicated suppliers is that cosumer surplus is higher i the m = 1 case. However, this greater cosumer surplus does ot come at the expese of idustry profit. Recall, the icreased iteralliace competitio comes i the form of reduced wholesale prices ad, thus, a reductio i the double-margializatio problem that typically plagues such supply chais. I other 4 Such a strategic role of observed wholesale prices i raisig retail prices has bee oted elsewhere (e.g., Sappigto ad Uel 005).

15 13 words, welfare is higher uder a dedicated supplier for all β. These basic forces stregtheig iter-alliace competitio (the oly issue i the m = 1 case) vs. softeig itra-alliace competitio (the oly issue i the m = case) are both simultaeously preset ad balaced i the more geeral setup of retailers. The balacig depeds critically o each supplier's market share. I particular, as supplier A's market share icreases (m icreases), its sphere of ifluece expads ad, as a result, its focus is less o icreasig the share of the retail market for its wholesale customers ad more o icreasig wholesale prices so as to extract more of its customers' already sizable retail profits. I other words, with icreasig m, supplier A's focus shifts more towards softeig itra-alliace competitio resultig i higher wholesale prices ad lower retail quatities. Formally, i Lemma, which details the equilibrium outcome uder full disclosure for all (m,), w d A is icreasig ad q d A is decreasig i m. I cotrast, with icreasig m, supplier B's wholesale market share decreases (-m decreases). With its sphere of ifluece shrikig, supplier B's focus o givig its wholesale customers a edge i competitio becomes eve sharper. Thus, i Lemma, w d B is decreasig ad q d B is icreasig i m. Lemma. Uder full disclosure, the equilibrium outcome is: (a) w d [a c][ γ ][4 + γ ( + m )] i (m,) = c γ[ ] γ [4( 1) 3m( m)] w A d, if i = 1,...,m; w d [a c][ γ ][4 + γ ( m )] i (m,) = c γ[ ] γ [4( 1) 3m( m)] w B d, if i = m+1,...,; d [a c][4 + γ ( + m )][ + γ ( m 1)] q i (m,) = γ [ ] γ [4( 1) 3m( m)] [ ] + γ ( 1) [ ] q A d [a c][4 + γ ( m )][ + γ (m 1)] q i (m,) = [ γ [ ] γ [4( 1) 3m( m)] ] + γ ( 1) [ ] q B d, if i = 1,...,m; d, if i = m+1,...,.

16 14 d (b) Π i (m,) d =[qa ] d, if i = 1,...,m; Π i (m,) d =[qb ], if i = m+1,...,; Π d A (m,) = m[w d A c]q d A ; Π d B (m, ) = [ m][w d B c]q d B. (c) CS d (m, ) = [1 / ][m(q d A ) + ( m)(q d B ) + m(m 1)γ (q d A ) + ( m)( m 1)γ (q d B ) + m( m)γq d A q d B ]; ad W d (m, ) = m[q d A ] + [ m][q d B ] + m[w d A c]q d A + [ m][w d B c]q d B + β[1 / ][m(q d A ) + ( m)(q d B ) + m(m 1)γ (q d A ) + ( m)( m 1)γ (q d B ) + m( m)γq d A q d B ]. Overall, the equilibrium outcome uder full disclosure of cotracts reflects two competig supplier desires: (i) higher wholesale prices help support softer retail competitio amog the supplier's ow customers; ad (ii) lower wholesale prices give the supplier's customers a edge i competitio over their rivals ad leads to stiffer retail competitio. The relative size of each supplier's customer base determies the weight each places o (i) ad (ii). We ext cosider how odisclosure of cotractual terms chages this balacig act ad affects the equilibrium outcomes Cofidetial Cotracts Without disclosure of cotracts, each retailer kows oly its ow wholesale price ad relies o its cojectures of others' wholesale prices whe egagig i retail competitio. Agai, to help highlight the uderlyig forces, cosider the case of = with dedicated suppliers (m=1). Workig backwards i the game, firm i's reactio fuctio i the retail realm is obtaied by solvig (1), q i (w i, q j ) = [a w i γ q j ] / as before. With wholesale prices uobservable this, rather tha (), ow serves as the iduced demad fuctio from the suppliers' perspective. Notice, the iduced demad fuctio, deoted q i φ (wi, q j ), reflects passive beliefs i that the supplier's price quote to ay retailer does ot alter the recipiet's cojectures about offers to its rivals (the superscript "φ " idicates o disclosure):

17 15 q j φ q i (wi, q j ) = a w i γ. (5) Give the iduced demad fuctio i (5), supplier A (B) chooses w 1 (w ) to maximize its profit as oted i (6): Max w 1 Max w [w 1 c]q 1 φ (w1, q ) ad [w c]q φ (w, q 1 ). (6) Joitly solvig the reactio fuctios i (5), the first-order coditios associated φ with (6), ad the equilibrium coditios q 1 = q 1 ad q φ = q reveals the equilibrium wholesale prices w i d ad quatities q i φ uder cofidetiality with m = 1. Lemma 3(i) presets these values, ad also the correspodig equilibrium values for retailer profits (Π i φ ), supplier profits (Π A φ ad ΠB φ ), cosumer surplus (CS φ ), ad total welfare (W φ ). The equilibrium outcome proceeds similarly uder a commo supplier, except that supplier A joitly determies both wholesale prices. I particular, supplier A chooses wholesale prices to solve: Max w 1,w [w 1 c]q 1 φ (w1, q ) + [w c]q φ (w, q 1 ). (7) Joitly solvig the reactio fuctios i (5), the first-order coditios associated φ with (7), ad the equilibrium coditios q 1 = q 1 ad q φ = q reveals the equilibrium wholesale prices ad quatities uder cofidetiality with m =. Iterestigly, ad i cotrast to the full disclosure case, the equilibrium outcome uder cofidetiality is the same for both m = 1 ad m =. Ituitively, with o disclosure of cotractual terms, the supplier is uable to use the wholesale price it charges to oe retailer to ifluece the behavior of other retailers. As a result, the supplier's pricig to oe retailer does ot deped o the ature of its relatioship with others. The equilibrium outcome uder cofidetiality is summarized i Lemma 3.

18 16 Lemma 3. I the = case, uder cofidetiality, the equilibrium outcome is: (i) with dedicated suppliers (m = 1): φ (a) w 1 = φ [a c] w = c + φ ; q 4 + γ 1 = φ a c q = 4 + γ ; φ (b) Π 1 = φ a c Π = φ ; Π 4 + γ A = φ [a c] ΠB = [4 + γ ] ; (c) CS φ = [a c] [1 + γ ] [4 + γ ] ad W φ = [a c] [6 + β(1+ γ )] [4 + γ ]. (ii) with a commo supplier (m = ): φ (a) w 1 = φ [a c] w = c + φ ; q 4 + γ 1 = φ a c q = 4 + γ ; φ (b) Π 1 = φ a c Π = φ 4[a c] ; Π 4 + γ A = [4 + γ ] ; Π B φ = 0 ; (c) CS φ = [a c] [1 + γ ] [4 + γ ] ad W φ = [a c] [6 + β(1+ γ )] [4 + γ ]. I effect, uder cofidetiality, the suppliers are uable to ifluece either itraalliace or iter-alliace competitio. This is because the ability to so ifluece rests critically o a supplier adjustig a retailer's price terms with the expectatio that ot oly the retailer but also its rivals will respod to such chages. The cofidetiality of cotracts blocks the spillover to rivals. As a cosequece, the wholesale price uder cofidetiality lies betwee the low wholesale price with m = 1 uder full disclosure ad the high wholesale price with m = uder full disclosure. To see the above formally, cosider the iduced demad fuctios i () ad (5). The supplier is disciplied i its price settig by the retailer's demad reactio, ad the effectiveess of this disciplie is tied to whether wholesale prices are disclosed or kept cofidetial. From (), uder full disclosure, the demad sesitivity is:

19 17 q i d (w 1,w ) w i = for m = 1; ad 4 γ [q 1 d (w 1, w ) + q d (w 1,w )] w i = 1 + γ for m =. (8) Similarly, from (5), uder cofidetiality, the demad sesitivity is: q φ i (w i, q j ) w i = 1 for m = 1; ad [q 1 φ (w1, q ) + q φ (w, q 1 )] w i = 1 for m =. (9) The rakig of the sesitivity expressios follows immediately from (8) ad (9): q i d (w 1,w ) w i < q i φ (w i, q j ) = [q φ φ 1 (w1, q ) + q (w, q 1 )] < [q 1 d (w 1,w ) + q d (w 1, w )]. (10) w i w i w i The followig coclusios follow. First, the equality i (10) implies the disciplie o supplier pricig uder cofidetiality is uaffected by whether the supplier provides to oe retailer or to both retailers; this is i lie with the equilibrium outcome i Lemma 3 beig uaffected by m. Secod, the iitial iequality i (10) implies the disciplie o the dedicated supplier's pricig is weaker i the cofidetial regime; thus, the wholesale price i the o disclosure regime is higher tha the disclosed price for m = 1. Third, the last iequality i (10) implies the disciplie o the commo supplier's pricig is more striget i the cofidetial regime; thus, the cofidetial wholesale price is lower tha the disclosed price for m =. The basic equilibrium forces from the case of two retailers persist i the case of retailers. Ad, i cotrast to the full disclosure regime, uder cofidetiality each supplier-retailer relatioship is idepedet of the customer base of each supplier, ad oly the total umber of retailers matters. The followig lemma summarizes the outcomes uder cofidetiality.

20 18 Lemma 4. Uder cofidetiality, the equilibrium outcome is: φ [a c] (a) w i (m, ) = c +, for i = 1,...,; 4 + γ[ 1] q i φ (m, ) = a c, if i = 1,...,; 4 + γ[ 1] d a c (b) Π i (m,) =, for i = 1,...,; 4 + γ [ 1] φ m[a c] Π A(m,) = [4 + γ ( 1)] ; Π B φ [ m][a c] (m, ) = [4 + γ ( 1)] ; (c) CS φ (m, ) = [a c] [1 + γ ( 1)] [4 + γ ( 1)] ; ad W φ (m,) = [a c] [6 + β(1 + γ ( 1))] [4 + γ ( 1)]. Give the characterizatio of the equilibrium outcomes uder each disclosure regime, we ext coduct a welfare compariso to determie the relative efficacy of each. 3.. Compariso of Disclosure Regimes I comparig the equilibria amog the two regimes, we garer ituitio by begiig with the familiar case of =. Recall, with dedicated suppliers (m = 1), each supplier views the full disclosure regime as a ivitatio to cut its wholesale price i a attempt to drive away its customer's rivals. Sice both suppliers have this icetive, it leads to a "race to the bottom" i price settig. This prisoers' dilemma i wholesale pricig alleviates iheret iefficiecies i the supply chai (due to double margializatio) ad creates a circumstace where, despite o competitio i the supply market (each is a moopolist), the suppliers compete idirectly through their retail surrogates. The decreased double margializatio problem ad icreased retail competitio stad to beefit the idustry ad cosumers alike.

21 19 I cotrast, with cofidetiality of pricig terms, the supplier is o loger able to use price cuts to ifluece competitio i the retail market. The ed result is higher wholesale prices ad, thus, higher retail prices. I this case, cofidetiality serves oly to magify supply chai iefficiecies ad udercut retail competitio. With a commo supplier (m = ), a etirely differet picture arises. Uder full disclosure, the sole supplier has icetives to raise its wholesale price to softe retail competitio ad thereby promote more cooperatio amog its parters. Besides softeig competitio i the retail market, the, the higher wholesale prices exacerbate efficiecy losses due to double margializatio ad ca udercut cosumer surplus. I cotrast, cofidetiality agai disables the supplier's idirect ifluece o oe retailer via the prices charged to aother. As a result, it prescribes a lower wholesale price. The cosequece is that with a commo supplier, cofidetiality is a boo to both cosumers ad the idustry. These ituitive results are bore out formally i Propositio 1 which cotrasts total welfare to determie the preferred regime. Propositio 1. I the = case, the preferred regime is: (i) full disclosure with dedicated suppliers (m = 1) ad (ii) cofidetiality with a commo supplier (m = ). The mai take away from Propositio 1 is that the ature of supply market cocetratio is a key factor i determiig the desirability of full disclosure. Though the expressios become a bit more cumbersome i the case of retailers, the essece of the result persists. I particular, with retailers, the larger m, the larger the cocetratio i the supply market. I a sese, m roughly proxies for the Hirfidahl idex (or similarly, the cocetratio ratio) i the supply market. 5 The greater m, the more promiet 5 Of course, this is ot a precise coectio, because the Hirfidahl idex depeds o the quatities chose i equilibrium. Thus, the Hirfidahl idex would vary based o the disclosure regime itself rather tha just the m/ cocetratio ratio.

22 0 supplier A, ad the more cocered supplier A is with softeig competitio amog its customers ad the less it is cocered about its customers' ability to compete agaist other retailers. Accordigly, as m icreases, the promiet supplier views full disclosure of vertical cotracts as a ivitatio to icrease its wholesale prices ad softe itraalliace competitio. Cosistet with this otio, the higher m, the more attractive is cofidetiality from a welfare perspective. This argumet is cofirmed formally i Propositio. Propositio. There exists a m *, m * <, such that cofidetiality (full disclosure) is the preferred regime if ad oly if m m * (m < m * ). Further, For γ 1, m* =, For 1 < γ < 1, < m* < + 1 For γ = 1, m * = + 1 [4 + 3] [4 + 3] ad is icreasig i γ, ad Ituitively, for m =, there is effectively a commo supplier for the etire retail market ad, thus, the oly force preset is that wholesale prices are icreased uder full disclosure to softe competitio. For lower m values, a supplier weighs the beefits of softeed competitio amog its customers from a higher wholesale price with the cost of retail market share lost to the customers of the other supplier. Recall, this latter feature etails a prisoers' dilemma i that the two suppliers are each tempted to cut costs which creates the potetial for such cost cuts to spiral dowward i a race to the bottom. As such, the greater the retail competitio, the more promiet is this race to the bottom. Importatly, from a efficiecy stadpoit, this "bottom" is still too high due to doublemargializatio. I fact, m *, the m-value below which full disclosure is welfare ehacig due to its ability to create itese competitio-by-proxy amog the suppliers is icreasig i γ, reflectig that the greater retail competitio, the easier it is for these

23 1 competitive pressures to bubble over i the supply market. Yet, eve for γ = 1, m * <, reflectig that such competitio-by-proxy effect is sure to be overwhelmed oce a supplier has sufficiet market cocetratio. Notice the m * -cutoff characterizatio i Propositio applies for ay weighig of cosumer ad firm prefereces (i.e., all β values). Of course, the precise value of m * does deped o β. Further, from Propositio, the value of m * ca be expressed succictly i closed form for the extreme values of γ. For itermediate values of γ, the value of m * is more complex ad is affected by, γ, ad β. To see its derivatio ad the ature of comparative statics, cosider a example with = 4 ad β = 1. A compariso of welfare with γ = 3/4 for various values of m is preseted i Pael A of Figure. The preferred regime depedig o m ad γ is preseted i Pael B. m a c a c 65 W Φ.8.6 Cofidetial m.45 W d. Disclosure m.45 3 m Γ PANEL A. Welfare as m Chages. PANEL B. Preferred Regime as γ ad m Chage. FIGURE. Example. 3.3 Edogeous Supplier Costs The wholesale price set by a supplier is impacted by its uderlyig productio costs ad the disclosure stadards i place. I order to hoe i exclusively o the latter, the aalysis thus far presumes that supplier costs (deoted by c) are the same irrespective

24 of the disclosure regime i place. As a added beefit, such presumptio of determiistic supplier costs permits a stark cotrast to existig work o disclosure of ucertai costs. I particular, the focus is o disclosure of strategic costs (retailer's wholesale price) rather tha stochastic costs. I this sectio, we exted the theme of idetifyig strategic repercussios of disclosure stadards to edogeize supplier costs. That is, istead of presumig that the uit cost of each supplier is c, cosider the outcome if c ca be affected by supplier ivestmets. I particular, say supplier i's cost is c i = c δ, where δ reflects supplier cost-cuttig efforts, ad the fixed cost (ivestmet) icurred to eact such cost reductios is kδ /. 6 Also, for simplicity, we examie the = case. With ivestmets, the cosequeces of full disclosure (or cofidetiality) for wholesale prices ad productio decisios are as before, except the prevailig disclosure stadard also iflueces the suppliers' ivestmet icetives. 7 Deote the equilibrium ivestmet level of the participatig suppliers as a fuctio of m by δ d (m) uder full disclosure ad by δ φ (m) uder cofidetiality. The followig lemma idetifies the equilibrium ivestmet levels i each regime ad for each supply market structure. Lemma 5. The equilibrium supplier ivestmet levels are: (i) with dedicated suppliers (m = 1): δ d (1) = 4[a c ][8 γ ] [4 γ ] [4 + γ ][ + γ ]k 4[8 γ ] ; ad δ φ 16[a c ] (1) = [4 γ ][4 + γ ] k To obtai otrivial solutios, we presume k is sufficietly large that each supplier prefers a iterior level of cost reductio. The ecessary ad sufficiet coditio for this to be the case throughout this sectio is k 1/[+γ]. 7 Cosistet with this lie of iquiry, Che ad Sappigto (010) demostrate that the structure of vertical chaels ca ifluece the degree to which a supplier egages i cost-cuttig iovatio. I a complemetary way, the preset paper demostrates that the disclosure eviromet too ca ifluece such iovatio.

25 3 (ii) with a commo supplier (m = ): δ d () = a c [ + γ ]k 1 ; ad δ φ 8[a c ] () = [4 + γ ] k 8. With dedicated suppliers, recall that disclosure prompted a prisoers' dilemma of wholesale price cuts from the suppliers' perspectives. Thus, cofidetiality creates a eviromet where, all else equal, suppliers stad to icrease their share of the idustry profits. As a result, cofidetiality comes with the added beefit of promptig additioal supplier ivestmet, i.e., δ φ (1) > δ d (1). From Propositio 1, with equal costs across regimes, full disclosure esures greater welfare due to the retailer cost savigs from lower wholesale prices. The cosideratio of edogeous supplier costs poits to a opposite welfare effect i that full disclosure leads to cost icreases due to lower supplier ivestmet. Give the symmetry of ivestmet amog the two suppliers, oe ca readily idetify the et effect of these two by replacig c with c δ d (1) i the profit expressios ad adjustig welfare by k[δ d (1)] / i Lemma 1(i), ad replacig c with c δ φ (1) ad adjustig welfare by k[δ φ (1)] / i Lemma 3(i). The, comparig welfare across regimes reveals that full disclosure is agai the preferred regime for all k ad β. I effect, with dedicated suppliers, the direct reductio i wholesale prices iduced by disclosure is of first-order importace whereas the idirect icrease due to dimiished ivestmet icetives is a secod-order effect. The key forces are differet uder a commo supplier. I this case, disclosure provides the supplier a opportuity to ecourage retail cooperatio ad, thereby, boost its ow profit. This added profit, i tur, promotes ivestmet icetives relative to those uder cofidetiality, i.e., δ d () > δ φ (). Agai, this provides a offsettig force to the welfare effect oted i Propositio 1 where supplier costs were exogeous. I particular, a welfare compariso ca be obtaied by replacig c with c δ d () i the profit expressios ad adjustig welfare by k[δ d ()] / i Lemma 1(ii), ad replacig c with

26 4 c δ φ () ad adjustig welfare by k[δ φ ()] / i Lemma 3(ii). Comparig welfare across regimes reveals that cofidetiality is the preferred regime for sufficietly large k. However, for small values of k, the iduced ivestmet effect becomes more proouced, ad ca be proouced eough that full disclosure ca become the preferred regime whe edogeous costs are cosidered. Propositio 3 details these results. Propositio 3. With edogeous ivestmets: (i) Supplier costs are lower uder cofidetiality for m = 1 (i.e., δ φ (1) > δ d (1)) ad lower uder full disclosure for m = (i.e., δ d () > δ φ () ); (ii) For m = 1, the preferred regime is full disclosure. For m =, the preferred regime is cofidetiality (full disclosure) if ad oly if k k (k < k ) Two-Part Tariffs Although liear (wholesale) prices are prevalet i practice ad routiely udergird ivestigatios of supply chai efficiecies, may have oted that at times richer two-part tariff cotracts ca provide a aveue to achieve vertical efficiecy. Give this observatio, we ext revisit the aalysis uder two part tariff cotracts. That is, for each customer a supplier stipulates a take-it-or-leave-it cotract offer of (F i,w i ), where F i represets i the fixed fee to be paid to the supplier ad w i represets the uit wholesale price. I a world with oe retailer ad oe supplier, it is well kow that such a cotract permits the moopoly outcome (full supply chai coordiatio) to be achieved. However, with multiple retailers, this is ot as clear cut. To see this most simply, cosider the case of =. The followig lemma presets the equilibrium pricig uder two-part tariff cotracts for each regime ad uder each market structure.

27 5 Lemma 6. The equilibrium two-part tariff terms are: (i) with dedicated suppliers (m = 1): d d [a c]γ w 1 = w = c 4 + γ [ γ ] ; ad F d 1 = d [a c] F = 4 + γ[ γ ] φ w 1 = φ φ w = c ; ad F1 = φ a c F = + γ (ii) with a commo supplier (m = ): d w 1 = d [a c]γ w = c + [1+ γ ] ; ad F d 1 = d F = φ w 1 = φ φ w = c ; ad F1 = φ a c F = + γ.. a c [1+ γ ] Notice the parallel to results i the sigle-tariff (liear pricig) case studied earlier. First, uder full disclosure, the wholesale prices is lower for m = 1 relative to m =. With m = 1, promotig iter-alliace competitio is i the forefrot while, with m =, softeig itra-alliace competitio is key. Secod, uder cofidetiality, the solutio is uaffected by m. That is, give the iability to ifluece rival behavior, the supplier treats each retailer i a idepedet fashio. Third, the cofidetial wholesale price is itermediate to the low disclosed wholesale price uder m = 1 ad the high disclosed wholesale price uder m =. To refie the ituitio uderlyig the lemma ad to idetify the welfare cosequeces, cosider first the outcome uder dedicated suppliers. With two suppliers seekig to extract retail market share via their surrogates, the optimal variable charge i the case of full disclosure etails below margial cost pricig. I other words, to promote its customer i the retail market, the supplier is willig to udercut its uit prices so much that it loses margially o each uit sold, kowig it ca extract retail profit via the fixed fee. The ed result is agai a prisoers' dilemma i pricig. I cotrast, with cofidetial ; ;

28 6 cotracts, a supplier is uable to ifluece retail competitio. I this case, it treats each retailer i a idepedet fashio, ad sets margial cost pricig to maximize the profits of that particular relatioship (kowig its pricig will ot chage rival behavior). As a cosequece, cofidetiality leads to familiar Courot outcomes. Note, the, that with two part tariffs the same essetial tesios arise: disclosure promotes lower uit prices ad thereby ca promote greater social welfare. As far as the commo supplier outcome, agai the ituitio from before carries forward to the two-part tariff case. A sole supplier who relies o disclosed cotract terms ca use a uit charge above margial cost to help reduce competitive pressures i the retail market ad ca the use the fixed fee to extract the larger surplus. I fact, i this case, the sole supplier fully exploits its power to achieve moopoly outcomes. Uder cofidetiality, the supplier caot use the uit charge to oe party to ifluece the behavior of aother ad, thus, relies istead o margial cost pricig, leadig to Courot outcomes. Thus, with a commo supplier, cofidetiality is the regime with o double margializatio problems ad, thereby, greater welfare. This ituitio is cofirmed formally i Propositio 4, a result aki to Propositio 1. Propositio 4. With two-part tariffs, i the = case, the preferred regime is: (i) full disclosure with dedicated suppliers (m = 1) ad (ii) cofidetiality with a commo supplier (m = ). I short, ot oly does cosideratio of two-part tariffs ot derail the uderlyig coclusios herei, it poits to a uifyig theme i that the ature of the supply market (ot the ature of cotracts) is the key feature i diviig the efficacy of disclosure stadards for vertical cotracts.

29 7 4. Coclusio I this paper, we examie the oft-discussed ad at times cotetious issue of disclosure of vertical cotracts. While covetioal wisdom suggests that suppliers keep cotracts uder wraps as a meas to exploit retailers ad cosumers, we fid that the uderlyig forces may be more subtle. I particular, whe retailers rely o a commo supplier for iputs, full disclosure of cotracts provides the supplier a meas through which to softe retail competitio amog the firms. I this case, the, disclosure actually harms cosumers. I cotrast, for retailers who rely o differet suppliers for iputs, disclosure of cotracts creates a eviromet wherei a supplier wats to cut its wholesale price to its retailer to give that retailer a edge i dowstream competitio. As a cosequece, disclosure beefits cosumers ad ehaces welfare. With these dual roles of disclosure i play, the ature of the supply market (ad cocetratio therei) becomes a critical determiat of the efficacy of disclosure. While we iitially ivestigate this questio i a stadard formulatio of supply chai iteractios, we also ivestigate the cosequeces of edogeous supplier costs ad two-part tariff cotracts. I each case, the basic results are show to be robust to the variatios; yet, each variatio itroduces subtle additioal cosideratios. I particular, supplier ivestmet icetives push i a directio that mute welfare differeces betwee the regimes. Ad, two-part tariff arragemets prescribe both below ad above margial cost trasfers with disclosure depedig o supplier cocetratio, while margial cost pricig is the orm uder cofidetiality. With the focus herei exclusively o the ature of vertical ad horizotal relatioships, future work could also layer i capital market cosideratios to the aalysis. For example, while capital markets typically view disclosure i a positive light, it may be iterestig to examie how capital markets would perceive disclosure whe edogeous strategic cosequeces of wholesale prices ad ivestmets studied here are