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PAGE 1 1 ESSAYS IN INDUSTRIAL ORGANIZATION By BUR N NEL A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 PAGE 2 2 2007 Burin nel PAGE 3 3 To my parents PAGE 4 4 ACKNOWLEDGMENTS I would like to thank my chair David Sappingt on for his incredible patience and wonderful guidance through out my graduate studies. In additi on to his help with my research, he has been a wonderful role model. Jonathan Hamilton was very supportive of me and my research. Sarah Hamersma has been an amazing unofficial mentor. I am incredibly grateful to Steven Slutsky, without whom I could not have finished my di ssertation. His personal a nd professional support at every stage of my graduate career was invaluable. I thank all my friends, here and in Turk ey, whose support was crucial during this adventure. I especially thank Kevi n Christensen for helping me at every stage of my life. He was always there for me when I needed support. Alper ngr provided me with much needed motivation and entertainment during the fina l stages of my graduate studies. I could never have succeeded without the support of my family. I would like to thank my aunt, Rengin Kan k, who encouraged me to start this a dventure. She was always there for me when I needed her. My cousin, Ebru Noyun helped me put everything in perspective. Finally, I would like to thank my parents, Hseyin and Nilgn nel. Their unconditional love and support guided me all my life. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF FIGURES................................................................................................................ .........7 ABSTRACT....................................................................................................................... ..............9 CHAPTER 1 INTRODUCTION..................................................................................................................11 2 INTERNATIONAL STRATEGIC ALLIANCES..................................................................13 Introduction................................................................................................................... ..........13 Model.......................................................................................................................... ............16 International Strategic Alliances.............................................................................................19 Free Trade Alliances........................................................................................................20 Conditionally Restri cted Alliances..................................................................................23 Restricted Alliances.........................................................................................................27 Conclusions and Extensions...................................................................................................28 3 INTERNATIONAL R&D ALLIANCES...............................................................................31 Introduction................................................................................................................... ..........31 Model.......................................................................................................................... ............33 International R&D Alliances..................................................................................................36 Free Trade Alliances........................................................................................................37 Restricted Trade Alliances..............................................................................................43 Extensions..................................................................................................................... ..........45 Conclusions.................................................................................................................... .........47 4 PRIVATELY NEGOTIATED INPUT PRICES....................................................................49 Introduction................................................................................................................... ..........49 The Benchmark Setting with No Retail Price Regulation......................................................52 Setting with Retail Price Regulation.......................................................................................56 Setting with Multiple Potential Entrants.................................................................................59 Alternative Cost Structures.................................................................................................... .61 Product Heterogeneity.......................................................................................................... ..63 Extensions and Conclusions...................................................................................................65 APPENDIX A APPENDIX FOR CHAPTER 2..............................................................................................67 PAGE 6 6 B APPENDIX FOR CHAPTER 3..............................................................................................91 Proofs......................................................................................................................... .............91 Simulation Results............................................................................................................. ...102 Cournot Model...............................................................................................................102 Bertrand Model..............................................................................................................103 C APPENDIX FOR CHAPTER 4............................................................................................112 BIOGRAPHICAL SKETCH.......................................................................................................141 PAGE 7 7 LIST OF FIGURES Figure page B1 The market prices under different scenarios with Cournot competition when = 15, = 2, and b = 2. ..............................................................................................................104 B2 The total profits firms would secure under different scen arios with Cournot competition when = 15, = 2, and b = 2. ....................................................................105 B3 The success probabilities each firm woul d choose under different scenarios with Cournot competition when = 15, = 2, and b = 2. .....................................................106 B4 The success probabilities each firm woul d choose under different scenarios with Cournot competition when = 30, = 2, and b = 2. .....................................................107 B5 The market price under different sc enarios with Cournot competition when = 15, = 2, and b = 2. .................................................................................................................108 B6 The total profits firms would secure under different scenarios with Bertrand competition when = 15, = 2, and b = 2. ....................................................................109 B7 The success probabilities each firm woul d choose under different scenarios Bertrand competition when = 15, = 2, and b = 2. ....................................................................110 B8 The success probabilities each firm woul d choose under different scenarios Bertrand competition when = 30, = 2, and b = 2. ....................................................................111 C1 The difference between the profit entrant B secures when an input price is negotiated successfully and its corresponding profit ab sent such successful negotiation as a function of Bw whenAw is less than the entrants upstream unit cost, E uc.....................132 C2 The difference between the profit the incu mbent secures when it negotiates an input price with the entrant B successfully and its corresponding profit absent such successful negotiation as a function of Bw whenAw is less than the entrants upstream unit cost, E uc.....................................................................................................133 C3 The difference between the profit entrant B secures when an input price is negotiated successfully and its corresponding profit ab sent such successful negotiation as a function of Bw whenAw is higher than the en trants upstream unit cost, E uc.................134 C4 The difference between the profit the incu mbent secures when it negotiates an input price with the entrant B successfully and its corresponding profit absent such successful negotiation as a function of Bw whenAw is higher than the entrants upstream unit cost, E uc.....................................................................................................135 PAGE 8 8C5 The difference between the profit entrant A secures when an input price is negotiated successfully and its corresponding profit ab sent such successful negotiation as a function of Aw.................................................................................................................136 C6 The difference between the incumbent secure s when it negotiates an input price with the entrant A successfully and its corres ponding profit absent such successful negotiation as a function of Aw.......................................................................................137 PAGE 9 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ESSAYS IN INDUSTRIAL ORGANIZATION By Burin nel August 2007 Chair: David Sappington Major: Economics This study consists of three essays which anal yze the market outcome when the firms that are competing in the retail market have an opportunity to share resources like production, distribution or R&D facilities. The first essay examines the welfare effects of international strategic alliances when firms produce differentiated products. A foreign firm that forms an internationa l strategic alliance to enter a market does not have to pay fixed costs to establish a new network in the foreign country. This cost saving increases total welfare. However, firms can use internal compensation arrangements to coordinate market prices, th ereby reducing consumer surplus. The overall welfare effects of international st rategic alliances are shown to va ry with the prevailing market structure, the regulations imposed on the foreig n firm, and the form of internal compensation employed by alliance members. The second essay analyzes research and development (R&D) incentives in an international strategic alliance when firms can invest in co streducing R&D. An alliance may both induce nonoptimal levels of investment and promote intern al transfer payments that increase the market price of retail products above competitive levels. Trade restrictions imposed on the foreign firm reduce the R&D incentives of the foreign firm comp ared to the prealliance setting. Regulation 9 PAGE 10 10 of transfer payments alone generally will not induce optimal investment levels and competitive retail prices. The last essay examines settings where inpu t prices are negotiated by industry suppliers, rather than dictated by regulators. It shows that the input buyer may agree to pay a high price for an input because the high price serves to reduce the intensity of retail price competition with the input seller. Full explo itation of retail customers can result. However, retail price regulation, competition among buyers, and product heterogeneity all can limit the extraction of consumer surplus. It also identifies conditions under wh ich input price negotiati ons will fail to produce a mutually agreeable input price. PAGE 11 11 CHAPTER 1 INTRODUCTION This study analyzes the market outcome when the firms that are competing in the retail market have an opportunity to sh are resources like produc tion, distribution or R&D facilities. It looks at if and how the welfare le vels of different parties change in different scenarios. Using different market structures, it shows the condi tions under which firms can use terms of their mutual agreements to manipulate the market out come in the downstream retail competition. One chapter analyzes strategic alliances in which the firms share their distribution networks. Another chapter looks at research and development (R &D) alliances, in which the firms share the outcome of their R&D with their al liance partner. The last chapter, which is a joint work with D. Sappington, looks at the market outcome when the entrant buys the upstream product from the incumbent. The first essay looks at the welfare effects of strategic alliances when firms share their distribution networks. It shows that firms agree on a high per unit transfer price in exchange for using the distribution facilities to coordinate market prices to secure monopoly profits. In addition firms use a lump sum payment to share the additional surplus created by the alliance. The second essay analyzes the welf are effects of R&D alliances, in which firms share the results of their R&D efforts to reduce thei r costs. It shows that these e ffects depend on the nature of the retail market competition as well as the nature of the R&D process. If the cost reduction is deterministic, quantity competition leads to unde r investment compared to the first best investment where as the effects of price compe tition on total investment is not certain and it depends on the relative magnitude of demand elastic ity compared to the cost of R&D. If firms are producing differentiated products, say for example like the competition characterized by Hotelling, then firms can secure monopoly profits as well as investing at the efficient level. In PAGE 12 12 addition this essay provides simulation result s which shows that the results obtained by deterministic cost reduction do not extend to cases of probabilistic R&D. In the case of uncertain process innovation, price competition may lead to under investment and depending on the demand parameters and the cost of R&D, firms may not find it beneficial to form an alliance. There are three main contributions of this work to the existing literature. First, in addition to analyzing firms in a single country, it looks at collaboration among international firms. The results in a single country do not necessarily extend to internati onal firms, since many countries impose trade restrictions on foreign firms. Trad e restrictions change the nature of the retail competition, leading to a different outcome in the bargaining stage. It shows that the nature of the trade restriction, whether it is a tariff or quot a is very important in determining the market outcome. Second, it derives policy implications that may help to find the appropriate antitrust treatment. The appropriate policy will vary with the trade restrictions, the nature of the retail market competition, and the nature of the R&D pr ocess. Finally it prov ides results that are empirically testable for future work. PAGE 13 13 CHAPTER 2 INTERNATIONAL STRATEGIC ALLIANCES Introduction Strategic alliances are cooperative organizati onal structures formed by separate firms. Firms form strategic alliances for many purposes including joint research and development, production, final assembly, marke ting, or distribution. In a st rategic alliance, firms share operational and financial responsibil ities even though they remain sepa rate identities. A strategic alliance is not considered to be a separate busine ss entity. The last two decades have witnessed a significant growth in both domestic and international strategic al liances (ISAs). The number of alliances has grown more than sixfold betw een 1989 and 1999. ISAs accounted for 68% of all alliances between 199099 (Kang and Sakai, 2000). While ISAs are very common, the economics literature has mostly focused on joint ventures. An ISA differs from a joint venture because a joint venture typically constitutes a separate business entit y, which can make its own decisions. In contrast, when firms form a strategic alliance, each firm retains its inde pendence. Even though firms combine resources on different matters in an ISA, each firm continues to act independently, pursuing its own interest. Thus, even when firms form an alliance, they may still compete against each other. This difference suggests that st rategic alliances a nd joint ventures may have di fferent welfare effects. This essay examines the welfare effects of IS As. ISAs can reduce welfare when the parties design internal compensation schemes to increase their joint profit, to change the degree of the effective competition, and to exploit consumers. In contrast, ISAs can increase consumer surplus by increasing product differentiation in the market. ISAs also can improve welfare by limiting the duplication of fixed costs. PAGE 14 14 The overall welfare effects of an ISA depend on at least three factors. First, the existing market structure and the degree of product diffe rentiation are important determinants of the overall welfare effects of an ISA. Even t hough ISAs may increase market price, they may increase total welfare compared to the prealliance situation by increasing product differentiation and hence consumer surplus. Second, the form of internal compensation among alliance members matters. Depending on the transfer paymen t scheme they adopt, firms may be able to reduce the intensity of retail price competition. Third, the regulatory structure is important. The type and the extent of restrict ions on the foreign firm can a ffect the final welfare level by changing the ability of the foreign firm to compete. Even though ISAs have received considerable attention in the management and business strategy literatures, ISAs have not received considerable attenti on in the economics literature. A few authors have analyzed differe nt aspects of ISAs. Chen (2003) examines the welfare effects of ISAs with bilateral supply and distribution agreements for homogenous products. He shows that if firms can commit to specific output le vels, firms can ensure monopoly output levels. Even if firms cannot credibly commit to output leve ls, ISAs can result in higher market price. Chen concludes that the welfar e effects of ISAs are ambiguous. Chen and Ross (2000) examine the anticompetitive effects of strategic allian ces that involve shari ng of production capacity. They show that the incumbent can use a strategi c alliance to prevent a new entrant from building a new plant that would result in lower market prices. Morasch (2000a) examines the in centives of oligopolistic firms to form domestic strategic alliances, and analyzes the effect of e ndogenous alliance formation on product market competition. Using a linear Cournot model, he sh ows if there are fewer than five firms in a market, one alliance will be formed and output will decline. Morasch also shows that in markets PAGE 15 15 with more than five firms, an alliance will in crease competition (when an equilibrium exists). Morasch (2000b) analyzes strategi c alliances as a substitute for strategic trade policy. He shows that permitting alliances and using a strategic trad e policy yield exactly the same outcome if the good is not consumed domestically and all firms in that country form a single alliance. He shows that the share of domestic consumption, the nature of product market competition, the existing market structure, and the feasibility of international alliances play an important role in determine the performance of strategic alliances relative to the strategic trade policies. Eerola and Mttnen (2004) examine the benefits of a strategic alliance to jointly invest in the production capacity when production capacity is limited; when new capacity becomes available sequentially. They show that even though strategic al liances may limit market entry, strategic alliances do not have to be anticompetitive. This essay extends the existing literature in at least five ways. First, this essay considers the product differentiation that IS As can introduce and the corres ponding increase in consumer surplus. Most of the existi ng literature considers homoge nous products. Second, this essay demonstrates how trade policies infl uence the welfare effects of ISAs.1 Third, this essay shows that in most ISA cases both tariff and quota rest rictions on the foreign firm lead to the same outcome. Fourth, this essay deri ves policy implications that may help to inform the appropriate antitrust treatment of ISAs, and demonstrates how appropriate polic y will vary with the existing trade restriction policy and the prev ailing market structure. Finall y, this essay demonstrates that both domestic and foreign firms have incentive s to lobby for relaxing trade restrictions on alliances. Relaxed restrictions increase the firms power to act like a jo int monopolist. 1 Morasch (2000b) considers strategic trade policies, but does not examine trade restrictions imposed on foreign firms. PAGE 16 16 Model First consider a simple model of ISAs. Suppos e there are two countries with one firm in each country. These firms produce differentiate d products. The products are characterized by their position in the product spac e, which is a line segment of length 1. Each firms product is located at one end of the product space.2 Each firm produces its product with constant marginal cost, c. Each firm has an established distributio n network in its own country. This network allows the firm to transport its goods from its production facilities to its showroom, where the consumers purchase the goods. This showroom may be a car gallery, a designated space in a supermarket chain or, a depart ment store, for example. If a firm decides to expand to a new market it has two alternatives. It can export its products directly by setting up a new network in the foreign country. Alternatively, it can choose to form an alliance with the in cumbent in the foreign market to use the existing network of the incumbent. This kind of alliance is common in automotive, film distribution, and pharmaceutical industries as well as some tec hnology, food and cell phone firms. For simplicity, the incumbent firm does not bear any additional co st if the foreign firm uses its network. If the firms choose to form an alliance, initially they bargain for a payment schedule. The payment schedule is assumed to be determined via Nash bargaining. If firms agree on a paymen t schedule, they form an alliance. If firms cannot reach an agreement, the foreign firm enters the market on its own, and the firms compete in prices. If the market is not profitable enough to cover the fixed costs, firm 2 does not enter the market and firm 1 con tinues to be a monopoly in its own country. The profits the firms secure under such independent op eration determine the threat level for the Nash bargaining. The alliance relationship can be mutu al (if each firm enters the foreign market via 2 The degree of differentiation is exogenous in this model. Product choices will be discussed later as an extension to this simple framework. PAGE 17 17 alliance) or it can be unilateral (if one of the pa rties does not enter the othe r market). If the firms operate in the same market, they compete in pr ices. Each firm charges a single price in the market, i.e., it does not engage in any form of price discrimination. Each firm chooses its price independently, as antitrust regulations typically forbid coor dinated pricing by the firms involved in a collaborative agreement. So, even though the firms choose the terms of their agreement cooperatively, they subsequently choose retail prices independently and simultaneously. There is a continuum of consumers in each c ountry, distributed uniform ly on the [0, 1] line segment.3 Each consumer is indexed by a location parameter x [0, 1], which represents his ideal product variety. If a consumers preferred good is not available, he incurs an additional disutility of consuming a different product. This disutility is equal to the distance between the consumers location and the location of the differentiated good on the product space, multiplied by disutility parameter d, which is the same for all consumers. The full price the consumer pays is equal to the sum of the price the firm char ges and the disutility the consumer incurs from consuming a product other than his most preferre d product. Each consumer will buy one unit of the good if this full price is less than his reservation price, r. This reservation price is the same for all consumers in both countries. Three different regulatory cases will be considered: (i) no tr ade restrictions are imposed; (ii) trade restrictions are imposed on foreign firms, but firms enga ged in an ISA are exempt from these restrictions; (iii) trade restrictions are im posed on foreign firms, regardless of whether they are a party to an ISA. These thr ee regulatory structures will be referr ed to as free trade, restricted trade and restricted alliances, respectively. 3 For simplicity, the number of consumers is assumed to be the same in each country. PAGE 18 18 Initially, each firm is a monopoly in its own count ry. Each firm acts to maximize its profit. The analysis in this essay fo cuses on the case where all consumers purchase a unit of the product in question, i.e. the whole market is covered. This will be the case, for example, if the reservation price of the consumer s is sufficiently high relative to the disutility parameter and the marginal cost of the product.4 In this case a profitmaximizing monopolist will set its price so that the most distant consumer is indifferent between consuming the product and not consuming the product. Lemma 2.1 identifies: (i) the profit maximizing price for the monopolist,mp; (ii) the corresponding profit level,m ; and (iii) the net consumer surplus under monopoly, mCS where the superscript m denotes monopoly.5 Lemma 2.1 In the monopoly setting, 2 ; ; d CS and c d r d r pm m m Consumer surplus is independent of the rese rvation price in the monopoly setting because the monopolist has the power to extract all the ad ditional utility consumers derive from having a high reservation price. Any increase in r will call forth an identical increase in the market price and the monopolists profit. Also note that cons umer surplus is increasing with the disutility parameter d This is because a higher disutility parameter limits the ability of the firm to exploit its monopoly power. When the consumers are highl y sensitive to differe ntiation, th e monopolist has to lower the price to ensure all consumers are willing to buy the produc t. Consequently, the higher is the disutility parameter, the lower is the profitmaximizing price, and thus the higher is the consumer surplus. 4 For rc 2d, a profit maximizing monopolist serves the whole market. 5 The (net) consumer surplus is the sum (for all consumer s) of the difference between the consumers reservation price and the full price a consumer pays for the product, including disutility costs, over the [0, 1] line segment. PAGE 19 19 International Strategic Alliances The remainder of the chapter focuse s on analyzing unilateral alliances.6,7 This focus simplifies the calculations and pr ovides a basic understanding of incentives of the firms in an alliance structure. If firms form an ISA, they play a twostage ga me. In the first stage, firms bargain over a payment scheme. The payment scheme is determined via Nash bargaining in the first stage. Firms bargain over a lumpsum amount T to use firm 1s network a nd a perunit transfer price, TP, which firm 2 will pay firm 1 for each good it se lls in the market. Note that a lumpsum transfer payment will not change the intensity of the price competition in the market because firm 2 will view the transfer payment as a fixe d cost which would not affect the firms price decision. A lumpsum transfer payment also will not change firm 1s behavior because it is a one time, constant payment. On the other hand, a perunit transfer price will change the firms reaction functions. Firm 2 will treat TP as an additional marginal cost, which will induce firm 2 to favor a higher retail price. Because firm 1 va lues the perunit transfer price it receives from firm 2, firm 1 will have reduced incentives to lower its retail price, since doing so will reduce firm 2s sales and thus its transfer payments from firm 2. In the second stage firms engage in price competition. They chose retail prices simultaneously and independently. Backward induc tion will be used to find the market outcome, and the equilibrium payment scheme. 6 The qualitative results do not change if the firms form a mutual alliance. 7 Without loss of generality, I will focus on firm 1, the domestic producer in country 1 for the remainder of this chapter. PAGE 20 20 Free Trade Alliances Assume first that country 1 does not impose any trade restrictions on the foreign firm. To analyze the welfare effects of an alliance, first consider the se tting where the firms do not form an alliance. If the firms do not form an alliance, each firm secures its free trade profit level. When firm 2 exports its product on its own, it must first establish its own distribution network to be able to make its product available to consum ers. To establish a new network in country 1, firm 2 has to incur a fixed cost, F Lemma 2.2 identifies the equilibrium prices and profits in the free trade setting. Lemma 2.2. In the direct exporting benchmark, d c p p pe e e 2 1; 21de ; F de 22; and ] ] [ 4 [ 4 1 d d c r CSe Lemma 2.2 reveals that the market price is lower and consumer surplus is higher under duopoly with free trade than under monopoly. The increased competition under duopoly increases consumer surplus both by reducing the market price and increasing product variety in the market. Competition allows consumers who were incurring high disutility under monopoly to secure higher surplus by consuming firm 2s product. Now assume that the firms decide to form an alliance. Firms first bargain over a transfer payment schedule including a lumpsum and a perunit transfer price. After negotiating the transfer payment schedule at the fi rst stage, firms compete in pri ces in the second stage. Each firm chooses its price to maximize its prof it given the lumpsum transfer payment, ftaT, and the perunit transfer price, fta pT, that the firms agreed to in first stage. fta fta p ftaT x T x c p ] 1 [ ] [1 1 (21) PAGE 21 21 fta fta p ftaT x T c p ] 1 ][ [2 2. (22) In this setting firm 1 derives profit fta 1 from two different sources: ( i ) revenue from selling its own product; and ( ii ) revenue from collecting the transf er payment from firm 2. The transfer payment ensures firm 1 secures revenue fta pT for every unit firm 2 sells and a lump sum payment ftaT. Lemma 2.3 identifies the prices that the firms will charge in the second stage given the outcome of the first stage. Lemma 2.3. fta p fta fta ftaT d c p p p 2 1; fta fta p ftaT T d 21; and fta ftaT d 22. Lemma 2.3 reveals that the firms in an alliance charge the same price in equilibrium even though they effectively have different costs. One might expect the domestic firm would employ its cost advantage to lower its price and thereby capture more of the market. However, in this case, a price reduction by firm 1 reduces firm 2s sales and thus the magnitude of firm 2s transfer payment, which directly reduces firm 1s profits. Given these profits firms could secure in th e second stage, firms use Nash bargaining to decide on the transfer payments in the first stag e. Lemma 4 identifies the perunit transfer price fta pT and the lumpsum transfer price ftaT for free trade alliances. Lemma 2.4. If the firms form a free trade alliance, c d r Tfta p 2 3 ; and 2 2 / 3 2 c d r F Tfta PAGE 22 22 Lemma 2.4 reveals that the firms will char ge the highest perunit transfer price,fta pT, possible while ensuring that all of the market is se rved. This way, firms can increase the price to the joint monopoly level and secure joint monopoly profits. Note that fta pTactually transfers all the profit to the domestic firm. Firms use ftaT to share these profits. The lumpsum transfer payment has two parts: ( i) a transfer from firm 1 to firm 2; and ( ii) a transfer from firm 2 to firm 1. Firm 2 pays 2 F to firm 1 for the use of its network and avoiding the fixed costs, and firm 1 pays 2 2 / 3 c d r to firm 2 to share the additional prof its earned by the free trade alliance. Proposition 2.1. If firms form a free trade alliance, they will use transfer payments to reach the joint monopoly outcome, where firms maxi mize their joint profit. Even though a free trade alliance increases the tota l welfare compared to the free trade benchmark because of the savings in the fixed cost, it lowers domestic welf are if the fixed cost is sufficiently low. Firms use the terms of the alliance to increase the market price to th e joint monopoly level. Consumers are even worse off than if they f aced a monopoly supplier. Firms secure the joint monopoly profit by using the peruni t transfer price and share th ese profits by using the lumpsum transfer payment. By agreeing on a high perunit transfer price, firms essentially agree to intentionally increase their perceived marginal cost s. This gives firms the ability to increase the market price. In this case even though there are two firms in the market and there is free trade, there is effectively no price competition and firms are able to increase the market price to the joint monopoly level. Consumers are harmed by th e lack of price compe tition. Part of the reduction in consumer welfare is transferred to the foreign firm, lowering the domestic welfare. If the fixed cost is not high enough, the transfer payment from firm 2 will not be high enough to offset this significant reduction in the domestic welfare even t hough the total increase compared PAGE 23 23 to the free trade setting because of the savings in the fixed cost. If the fixed cost is high enough, the increase in the domestic firms profits due to the increase in the transfer payment from the foreign firm will be high enough to offset the de crease in the consumers surplus. Thus the domestic welfare will increase with a free trade alliance. Note also that it will be less costly for the fore ign firm to enter the market if the firm forms an alliance since it does not have to bear the full cost of setting up a new network. This will lead to increased product differentiation in the mark et when the market w ould not otherwise support direct entry. So if the fixed co st is sufficiently large that entry would not occur in the absence of an ISA, consumers benefit from the increased product differentiation supported by the ISA. Conditionally Restricted Alliances One potential motive for forming an ISA is to eliminate trade restrictions. Now suppose that country 1 imposes trade restrictions on the fore ign firm. Trade restrictions can take the form of tariffs or quotas. If country 1 is imposing a quota as a trade restriction, then the county is restricting the amount of good the foreign firm can sell to (1Q ) where Q (0, 1).8 If country 1 is using a tariff as a trade restriction, than the country is imposing a t percent ad valorem tax on each good the firm 2 sells in country 1.9 Assume also that the foreign fi rm would not be subject to tr ade restrictions when it forms an ISA with a domestic firm. In this setting, how ever, if the firm decides not to form an alliance it will have to comply with the trade restrictions For this type of cond itionally restricted ISAs, the threat levels will be the pr ofits the firms secure under trade restrictions. To be able to analyze the welfare effects of th e conditionally restricted alliances one first needs to look at the market in the absence of alliances. 8 The government imposes trade restrictions and they ar e considered to be exogenous throughout this essay. 9 The tariff is assumed not to be prohibitive, i.e. t is not high enough to prevent the firm 2 from selling its product. PAGE 24 24 First consider the case in which c ounty 1 imposes a quota restriction, Q on the foreign firm, firm 2. This restriction may change the firms profit function compared to the free trade case. In particular, if the ma rket demand for firm 2 exceeds (1Q ) at the established price, firm 2 cannot meet all of the demand. This gives firm 1 an opportunity to serve the segment of the market that it would not have se rved if it were competing with firm 2 in the absence of trade restrictions. However, if the market demand for firm 2 does not exceed (1Q ), firms compete in prices as if the quota were not imposed. The profits of firm 1 and 2 in the quota regime respectively are: } 2 max{ ] [1 2 1 1d d p p Q c pq ; (23) F d d p p Q c pq } 2 ), 1 min{( ] [2 1 2 2, (24) where the superscript q denotes the quota case. Assumption 2.1. The quota restriction is binding in market 1, i.e., 1Q <1x where x is the demand firm 2 faces without trade restrictions. Assumption 2.1 guarantees that the quota re strictions are bindi ng so that we can concentrate on the effects of trade restrictions. If the quota restriction were not binding, then the market equilibrium would be the same as free trade case. Lemma 2.5 summarizes the equilibrium outcome in the quota setting. Lemma 2.5. Suppose assumption 2.1 holds. Then in the quota setting, ] 1 [ ;2 1Q d r p dQ r pq q ; ] [1c dQ r Qq ; F c Q d r Qq ] ) 1 ( ][ 1 [2; and )] 1 ( 2 1 [ 2 Q Q d CSq. PAGE 25 25 Lemma 2.5 reveals that the quota limits the competition between th e two firms. The incumbent firm will recognize that no matter what pr ice firm 2 charges, the market share of firm 2 can never exceed 1Q. This will give firm 1 monopoly power over the fraction Q of the customers. Firm 1 might like to increase its ma rket share by lowering th e price beyond the price that leaves the consumer at location Q zero utility. If it were to do so, though, firm 2 would lower its price to ensure it continues to serve 1Q of the customers. If both firms charge the same price, consumers who are located at x [Q, 1] will always prefer to buy from firm 2 since they will get higher utility by doing so. Even if firm 1 charges p = c, firm 2 can charge p = c + d [2Q1], serve (1Q) of the customers and still make profit. This will leave firm 1 with zero profit, so firm 1 will choose not to compete for the whole market. Instead, firm 1 will set the price that will make the consumer at Q indifferent between buying the product and not buying. Hence, a quota effectively induc es two separate monopolies. Just as in the monopoly case, consumer surplus does not vary with the reservation price of the consumers in the quota setting. Firms have monopoly over their own segments, so they can exploit the consumers fully by se tting the price that extracts the reservation price less the disutility costs of the most distant customer. When assumption 1 holds, both firms secure higher profits when a quota is imposed than under free trade, because of the reduced price competition. Now assume that country 1 imposes a tariff, t, on firm 2 rather than a quota. In this case the consumers will have to pay ) 1 (2t p if they buy the product from firm 2. The actual price firm 2 gets is tp2, and the government of country 1 gets tariff revenue of ttp2. Lemma 2.6. In the tariff setting, ) 1 ( 3 2 3 3 ; 32 1t ct d c p ct d c pt t ; d ct dt18 ) 3 (2 1 ; F t d ct dt ) 1 ( 18 ) 3 (2 2; and d ct d ct d t c d r CSt36 ) 9 )( 3 ( ) 1 ( 2 1 PAGE 26 26 Lemma 2.6 reveals that even though the actual price firm 2 gets for its product is lower than in the free trade setting, the effective pric e the consumers face if they buy from firm 2 will be higher than in the free trade setting. T hus, the tariff increases the market share of the domestic firm. Because it has to lower its price, firm 2 receives lower profits. Domestic welfare is higher than in the free trade setting because of the increase in domestic firms profits in addition to the tariff revenues the domestic country secures from firm 2. However total welfare is lower than in the free trade setting because of the distortion caused by the tariff. Proposition 2.2. Suppose assumption 2 holds. If firm s form a conditionally restricted alliance, they will use transfer payments to secure the joint monopoly solution in both the quota and the tariff settings, just as in the case of free trade alliances. A conditionally restricted alliance increases total welfare by eliminating th e deadweight loss from trade restrictions in addition to the savings in the fixed cost. Even though the two types of trad e restrictions are distinct, they both lead to the same price in the presence of alliances. If alliances can be used to avoid trade restrictions, the trade restrictions only affect the thre at levels during the bargaining process. However, both firms always benefit by increasing the pe runit transfer price so that th e market price reaches the joint monopoly price. Thus, just as in the case of free trade alliances the market price will be the same as the joint monopoly setting, regard less of the nature of the trade re strictions. The nature of the trade restrictions only affects how the joint monopoly profit is distributed between the firms. Restricted alliances also preven t the inefficiencies associated with the deadweight loss, and assure welfare maximization in the market. In ad dition to preventing dead weight loss, restricted alliances increase the total welfare by eliminating the fixed cost. PAGE 27 27 Proposition 2.3. A conditionally restricted alliance increases domestic welfare if the foreign firm is subject to quota restrictions if it does not fo rm an alliance. However, the conditionally restricted alliance ma y reduce domestic welfare if the foreign firm is subject to a tariff if it does not form an alliance. When country 1 imposes a quota on the foreign firm, the market segmentation is exogenously defined. The domestic firm can s ecure monopoly profits fr om the portion (Q) of the market if firms cannot agree on a transfer price to form an alli ance. Consequently the foreign firm has to pay the domestic firm more to induce the domestic firm to forego its monopoly profits. Because of these payments domestic we lfare is higher than under a free trade alliance despite the decrease in consumers surplus. Ho wever if country 1 imposes a tariff on the foreign firm, firm 1 will have significantly lower pr ofit compared to a free trade alliance if the negotiations break down. So it is also in firm 1s in terest to form an alliance. Thus, even if firm 1s profit increases due to the increase in price, the transfer payment from firm 2 may not be high enough to offset the reduction in consumers surp lus. In addition the home country loses tariff revenue if the firms form an alliance. Restricted Alliances Now assume that the government imposes trade restrictions on the foreign firm whether it forms an alliance or operates independently. In th is setting, then, the foreign firm must always comply with the restrictions. Proposition 2.4. Suppose assumption 2.1 holds. Then in the quota setting, a restricted alliance increases total and domes tic welfare relative to trade re strictions case and leaves the consumers surplus unchanged. However in the ta riff setting, firms are able to increase the market price above the price in th e trade restrictions setting, and so consumers surplus declines. PAGE 28 28 If firm 2 is subject to quantity restrictions ev en if it participates in an alliance, the market shares of the firms do not change when firm 2 forms an alliance with the domestic firm. Therefore, the profitmaximizing firms do not gain by changing their prices if they form an alliance. This prevents the firms from increasin g the price compared to the prealliance setting by using a perunit transfer price. Thus the consumers will not be hurt by the restricted alliance in a quota setting. Domestic welfare increases becau se of the transfer payments from the foreign firm. However, note that the foreign firms only ga in from the alliance is the savings in the fixed costs, so the domestic firm ca nnot exploit the foreign firm as much as it can under the free trade alliances and the restricted alliances. If the foreign firm is subject to tariffs even if the firm is in an alliance, firms can still use the transfer payments to increase the market pr ice. Consumers will be harmed compared to prealliance case. Even though domes tic welfare increases compared to the prealliance case because of the transfer payments from the foreign firm, the domestic welfare will not be as high as in the case of conditionally restricted al liances. Because the foreign firm in a restricted alliance still has to comply with trade regulations, it is not willing to pay as high a transfer payment as it would in a conditionally restricted alliance. Theref ore, the transfer from the foreign firm to the domestic firm will be lower than in the case of conditionally restricted alliances. Conclusions and Extensions The welfare effects of ISAs depend on many f actors, including the market structure, regulatory policies, consumer pref erences, and the type of restri ctions (if any) imposed by the governments. Firms in an ISA generally are able to use the terms of their contract to coordinate their prices. In the settings analyzed here, the firms often are able to secure the joint monopoly profit. Note also that the type of trade restrictions (if any) generally do not change the effect of an ISA PAGE 29 29 on the market price. Regardless of the type of the trade restrictions, firm are often able to coordinate their prices. In these cases even t hough there are two firms in the market, there is effectively no competition. Consumers su ffer relative to the prealliance setting. However, note that alliances also have indir ect effects on consumers. A firm is more willing to enter a market via alliance than on its ow n. Even if direct independent entry is not profitable, a foreign firm may be willing to ente r the market by forming an alliance because it does not have to bear the full fixed cost of doing so. The effects of ISAs on the domestic welfare are le ss clear. The nature of trade restrictions and the size of the fixed costs are important in an alyzing the effects on ISAs. If the fixed costs are high enough, the foreign firm is more willing to form an alliance to avoid these costs. This leads to a higher transfer paymen t, which may increase the domestic welfare despite the loss in consumers surplus. An ISA is more likely to increase the domestic welfare if the foreign firm is subject to a quota restriction. This is because when there is a quota restriction, the foreign firm is limited in its ability to change the market price compared to a tariff setting. Therefore, it has stronger incentives to form an alliance, and it is willing to pay more to persuade the domestic firm to form an alliance. Note that even though the domestic firms have an incentive to lobby for trade restrictions for foreign firms, they also have an incentive to lobby to eliminate trade restrictions for their foreign alliance partners. If the foreign firm still has to comply with the quantity restrictions in an alliance, the foreign firms only gain from the alliance is avoiding the fixed costs since the market price depends on the quota level. Thus the domestic firm has no bargaining power. However if the alliance helps the foreign firm to avoid the quota, this will allow the domestic firm to exploit the foreign firm more, while charging the joint monopoly price to exploit PAGE 30 30 consumers. In the case of tariffs, even though the domestic firm still has an incentive to lobby for its alliance partner, the incentive is not as stro ng as in the quota setting. Despite the tariff, the firms can coordinate the payment schedule to in crease the market price above the competitive level in a restricted alliance. If the foreign fi rm in an ISA still has to comply with trade restrictions, the domestic firm receives some ba rgaining power (although not as much as in the restricted alliance case) to secure a higher shar e of the joint monopoly profits than the foreign firm. This essay suggests that anti trust agencies should examin e ISAs carefully; taking into account the compensation structur e employed within the ISA and prevailing trade restrictions. Government officials might also want to limit th e ability of ISA participants to employ high perunit transfer prices to coordina te prices and reach the joint mo nopoly price. This would make sure that the consumers are protected from high prices. This essay provides a basic understanding of IS As. Further investig ation of ISAs is required to understand more fully the welfare implications and the dynamics of ISAs. For simplicity, the present analysis assumes that c onsumer preferences, costs of firms and market size across countries are symmetric Relaxing these symmetries ma y affect firms profits, thus changing threat levels and th e transfer payments. Even though asymmetries may have a quantitative effect on equilibrium outcomes, the same qualitative welfare conclusions seem likely to arise. Also, an alliance does not affect the reservation price of the consumers in the model analyzed here. In reality alliances may cau se an increase in consumers valuation of the product because of benefits that may come with an alliance, such as rewards given by the firms for use of the alliance products. This may lead to an increase in consumer s surplus even though consumers face higher prices. PAGE 31 31 CHAPTER 3 INTERNATIONAL R&D ALLIANCES Introduction Research and development (R&D ) alliances are cooperative orga nizational structures that are designed to promote technolog ical progress. The parties to an R&D alliance continue to operate as separate entities. (In contrast, partie s to a research joint venture often operate as a single business entity.) R&D alliances may be formed by firms from the same country, or by firms from different countries. The last two decades have witnessed in creased collaboration on R&D among firms cross borders. Alliances among USEU, USJapan, and USChina firms have increased especially rapidly. 1 There has been extensive work on collabora tive R&D efforts by domestic producers within in a single country. One may think that the re sults in one country case trivially extend to alliances involving firms from more than one coun try. However, in an international alliance the foreign firm may be subject to trade restrictions. Because this limits the foreign firms ability to compete in the retail market, an international R&D alliance may lead to a different market outcome than a domestic alliance. The goal of this essay is to examine how investment incentives in international R&D alliances differ from the corresponding incentives a nd effects of purely domestic R&D alliances. This essay first analyzes R&D alliances with no restrictions on the foreign firm as a benchmark. It presents a setting in which two Cournot compe titors that are also competitors in cost reducing R&D can form an alliance to share the output s of their R&D invest ments by licensing each others innovations. Only one fi rm invests in this benchmark se tting, and firms can coordinate their production levels to secure the monopoly profit through strategic design of transfer prices. 1 See Moris (2004) and Science and Engineering Indicators (2006). PAGE 32 32 If trade restrictions are imposed on the foreign firm, the investment incentives in an alliance change significantly. When the foreign firm ha s the more advanced technology in an alliance, trade restrictions prevent the foreign firm fr om expanding its output to the profit maximizing level. This reduces the alliances ability to ex tract consumers surplus and increase profit. Therefore when the foreign firm is subject to trad e restrictions, the alliance will be better off if the domestic firm has the more adva nced technology. As a result, the foreign firm chooses not to invest at all, and all R&D inve stment is undertaken by the domestic firm. This essay also demonstrates that a regulator ca nnot achieve the socially optimal level of investment and keep the market price low simply by regulating the tran sfer prices with an R&D alliance. Additional policy instruments are require d to achieve this goal. Using a model in which two Cournot competitors in the retail market initi ally invest in cost reducing R&D, dAspremont and Jacquemin (1988) find that total R&D investment may be higher when firms share knowledge during the R&D stage if the R&D exte rnalities between the firms are sufficiently high. Kamien et al. (1992) demonstrate that if Cournot retail competitors coordinate their investments to maximize their join t profits by forming a joint venture, it leads to higher levels of R&D than the levels that arise in the absence of a joint venture. This essay extends dAspremont and Jacquemin (1988) and Ka mien et al. (1992) by allowing each firm to license its innovation to its competitor. The ab ility to license its innovation changes a firms R&D incentive due to the possibility of earning additional revenue from licensing compared to a setting where licensing is not possible. Also this allows firms to shar e output of their R&D efforts while retaining thei r identity as individual firms. Katz (1986) shows that if firms agree to share the costs and outputs of research before they undertake it without paying each other any royalty, then the overall investment level is lower than in the ab sence of such an agreement. PAGE 33 33 Katz and Shapiro (1985) show that fixedfee licensing across rival firms may increase or decrease the incentives to innovate. The model used in this essay allows firms to use both fixed licensing fees and royalties. Firm s may be able to use perunit fees to reduce the intensity of the retail market competition, which in turn changes R&D incentives. Model There are two firms in a country, the domestic fi rm (firm 1) and the foreign firm (firm 2). These firms produce a homogeneous good whose inverse demand function is p = a bQ, where p denotes the market price and Q denotes the total output in the market. Initially each firms marginal cost of production is c. Each firm has its own R&D facility. Each firms R&D is geared towards process innovation which reduces the marg inal cost of production by where 0 < PAGE 34 34 the stipulated interfirm transfer payments are made. If firms cannot agree on a payment schedule, no alliance is formed, and the firms i nvest in R&D independently and then choose their output levels simultaneously and independently The profits the firms secure under such independent operation determine the thre at levels for the Nash bargaining. Two different regulatory regimes will be considered. No trade restrictions are imposed in the free trade regime. Trade restrictions are imposed on the foreign firm in the restricted trade regime. As an initial benchmark, consider the first best setting in which a central planner can dictate the level of cost reducti on that must be implemented. S uppose the central pl anner acts to maximize total welfare. Lemma 3.1 identifies the optimal level of cost reduction f b in this setting. Lemma 3.1. In the first best setting, 21fbac b Lemma 3.1 simply reflects the fact that in order to maximize total welfare, the planner chooses the level of cost reduction that equates the marginal cost (2 b) and the marginal benefit (ac ) of cost reduction.2 As a second benchmark, consider the monopoly se tting where there is only one firm in the market. Lemma 3.2 identifies the market price, mp, the profit maximizing amount of cost reduction, m, and the profit, m in this setting. 2 It is assumed that 21 b PAGE 35 35 Lemma 3.2. In the monopoly setting, [21]2 41mabbc p b 1 4 b c am, and 2[] 41mac b Lemma 3.2 shows that a monopolist will choose a hi gh level of cost reduction if the cost of R&D is low and if the market price is not very sensitive to the output level (i.e., if b is low). Lower production cost allows the firm to expand its output level. This will cause the market price to be lower. If b is low, the loss in revenue due to a lower market price will not be high enough to offset the increase in revenue due to a higher output level, lead ing to higher profits. Therefore when b is low, the monopolist invests more in R&D. Note also that the monopolist chooses to invest less than the first best investment level. Now assume that the domestic firm and the fo reign firm decide to operate independently. Assume also that the foreign firm is not subject to any trade restrictions. In this free trade setting, if firms do not form an alliance, they pl ay a twostage game. In the first stage each firm determines its preferred level of cost reduction, ft i and carries out the investment required to secure this cost reduction. The outcomes of the R&D efforts are observed publicly. In the second stage the firms compete in the product ma rket by choosing output levels simultaneously and independently. Lemma 3.3 identifies the market price, ftp, the profit maximizing amounts of cost reduction, ft, and the profits, ftin the free trade setting. Lemma 3.3. In the free trade setting, [32]6 92ftabbc p b 122 92ftftftac b and 2 12 2[94][] [92]ftftbac b PAGE 36 36 Lemma 3.3 reveals that the market price and th e profits of the firms are lower in the free trade setting than in the monopoly se tting. It also shows that the level of cost reduction in the free trade setting, ft, declines as the cost of R&D ( ) increases and as the slope of the inverse demand curve ( b) declines, just as in the monopoly setting Proposition 3.1. Each firm chooses a lower level of cost reduction in the free trade setting than in the monopoly setting. To tal costreducing investment in th e free trade setting is higher than in the monopoly setting, but lower than in the first best setting. In the free trade setting, the firms face fierce competition in the retail market. Thus each firm wants to be more competitive by lowering its production costs. This causes total investment level in the free trade setting to be higher than in the monopoly setting. On the other hand, each firm knows that it will produce less than a reta il monopolist would produce. This lowers each firms benefit from R&D, reducing its incentive to innovate compared the monopoly setting and the first best setting. International R&D Alliances If firms form an R&D alliance, they play a threestage game. In the first stage, firms bargain over: (i) a perunit transfer price, pT, that the firm with th e less advanced technology will pay to the firm with the more advanced technology for each unit it sells for using the advanced technology in the production of th at unit; (ii) and a lump sum payment, Tthat the firm with the less advanced technol ogy will pay to the firm with th e more advanced technology for the rights to use its innovation. It is assumed that a firm can license its innovation to its competitor if it leads to at leas t the same level of cost reduction as the competitors technology.3 3 It is assumed that if a firm tries to license its compe titors inferior technology, the agreement will be blocked by antitrust authorities because of its po tential anticompetitive effects. The as sumption that a firm can license a technology that entails no strict cost reduction is adopted for analytic simplicity. PAGE 37 37 If a firm licenses its innovation, the licensee ge ts the full benefit of the innovation, i.e., the licensee enjoys the same cost reduction that th e licensor experiences. After negotiating the transfer payment schedule, the firms choose (s imultaneously and inde pendently) their profitmaximizing levels of cost reduction, given the esta blished transfer prices. Firms then carry out the investments required to achie ve the chosen cost reductions. After observing the outcome of the R&D process, the firms choose (simultaneous ly and independently) their profitmaximizing outputs, given the preva iling transfer prices. Free Trade Alliances Assume first that country 1 does not impose any trade restrictions on the foreign firm. Backwards induction will be used to find the subgame perfect equilib rium in this setting. The first step in this process is to characterize th e outcome in the retail competition stage given the prevailing transfer prices, and the R&D investments. There are three possible outcomes in the investment stage: ( i ) firm 1 invests more than firm 2; ( ii ) both firms invest the same amount; and ( iii ) firm 2 invests more than firm 1. First consider case ( i ). Only firm 1 can license it s technology in this case. Ther e are two different sources of profit for firm 1 in the retail competition stage: ( a ) revenue from selling its own product; and ( b ) revenue from collecting the transfer payments fr om firm 2. The transfer payment ensures the innovating firm (i.e., the firm that achieves the largest cost reduction) secures revenuepT for every unit the licensee sells. The pe runit transfer payment in this case acts just like an increase in the marginal cost of firm 2. The profits of firm 1 and firm 2 in the retail competition stage in this setting are: 2 1121121[()] [] ftaftaftaftaftaftafta pabQQcQTQT (31) PAGE 38 38 2 212122[()] [] ftaftaftaftaftafta pabQQcTQT. (32) In the last stage each firm chooses independe ntly and simultaneously the level of output that maximizes its profit. Given 12, f tafta ,pTand T Lemma 3.4 summarizes the market price, f ta p and the levels of output firm 1 and 2 produce, 1 f taQ and 2 f taQ in a free trade alliance when 12 f tafta. Lemma 3.4. Assume that 12 f tafta Then in a free trade alliance 1 13p ftaacT Q b 1 22 3p ftaacT Q b and 12[] 3p ftaacT p b Lemma 3.4 reveals that firm 1 secures a higher market share when it secures the greatest cost reduction. In this setti ng, even though both firms operate w ith the same marginal cost of production 1c the perunit transfer price,pT, increases the marginal cost of sales for firm 2. This offsets firm 2s incentive to increase produ ction due to the reducti on in production cost. Firm 1 exploits its effective cost advantage by expa nding its production. Rationally anticipating the profits they will ultim ately receive, firm 1 and firm 2 choose the level of cost reduction in the second st age to maximize thei r respective profits, 1 f ta and 2 f ta : 2 11 2 1 1[]2 [] [] 93pp fta pacTacT TT bb (33) 2 1 2 22[2] [] 9p ftaacT T b (34) Lemma 3.5. If 12 f tafta then 12[]5 2[91]p ftaacT b and 20fta in a free trade alliance. Lemma 3.5 reveals that if one party to a free trade alliance undertakes more R&D than its counterpart, then the former firm is the only firm that undertakes R&D. If firm 2 knows that PAGE 39 39 firm 1 is going to invest more, then firm 2 will end up licensing firm 1s technology. Any R&D that firm 2 will do will not change firm 2s revenue, or production cost.4 Therefore firm 2 will not invest at all to avoid bear ing additional cost of this ulti mately unproductive R&D. As a result firm 1 will be the only firm to undertake R&D. Because the firms are symmetric, case (iii) will lead to a similar outcome in which firm 2 does all the R&D and firm 1 does not invest at all. Now consider case (ii). In this case both firms can licen se their innovations. This allows both firms to secure additional revenues from its oppone nts sales. In this case the profits of firm 1 and firm 2 in the retail competition stage are: 2 1121121[()] [] ftaftaftaftaftaftafta ppabQQcTQTQ (35) 2 2122212[()] [] ftaftaftaftaftaftafta ppabQQcTQTQ (36) Given 12, f tafta ,pTandT, Lemma 3.6 summarizes the market price, f ta p and the levels of output firm 1 and 2 produce, 1 f taQand 2 f taQ, in a free trade alliance when 12 f tafta Lemma 3.6. Assume that 12 ftafta Then in a free trade alliance 2[]2 3p ftaacT p b and 123p ftaftaacT QQ b Lemma 3.6 reveals that if bot h firms reduce their costs by the same amount, both firms lower their production by the same amount. In this case, the market price for a given level of investment and perunit transfer price will be higher than if only one firm invests. In this case, both firms increase their effective marginal cost s by paying each other a transfer payment. However if one firm invests more than the ot her, only one firm is increasing its effective marginal cost by paying the other firm a tran sfer payment for the ri ght to use the better 4 Note that such investment may affect the threat points in alternative models. However in this model, the negotiations occur before the investments are undertaken. PAGE 40 40 technology. Therefore the market price in case (ii) is higher than the market prices in cases (i) and (iii). Rationally anticipating the profits they will get in the last stage, firm 1 and firm 2 choose the level of cost reduction in the second stage to maximize thei r respective profits, 1 f ta and 2 f ta which are given by: 2 1221 2 1 1[2]2 [] [] 93pp fta pacTacT T bb (37) 2 2112 2 2 2[2]2 [] [] 93pp fta pacTacT T bb (38) Lemma 3.7 If 12 ftafta then 124[]7 2[92]p ftaftaacT b in a free trade alliance. Lemma 3.7 reveals that, the total R&D investment in case ( ii ) is higher than the total R&D investment in cases ( i ) and ( iii ). Recall from Lemma 5 that for a given perunit transfer price, the market price in case ( ii ) is higher than the market price in cases ( i ) and ( iii ) if the R&D investments are the same in all cases. Thus for a given Tp, firms try to keep their costs lower in case ( ii ) to keep the market price from rising abov e the profit maximizing level. Therefore in this case firms choose to invest more compared to cases ( i ) and ( iii ). Anticipating the profits they will secure in the last stage of the game and the level of investment they will undertake in the second st age of the game, firms bargain over transfer payments in the first stage. The maximum to tal profit the alliance could get is the monopoly profit. When bargaining, the firms will first determine which of the three cases will allow them to capture the monopoly profit. Then Nash bargaining determines how the total profit from the alliance will be divided between the firms. Each firms share of the total profit depends on the amount of profit that it could secure if it operate d independently in the same setting, namely the PAGE 41 41 threat points. In the free trade al liance setting, each firms threat level is the profit it would get in the free trade setting. Once firms agree on an allocation, they will choose the transfer payments that will guarantee this allocation. Th e allocation of profits in a free trade alliance is the solution to the following problem: 121122 ,max ()()ftafta f taftftaft subject to: 12 f taftam (39) Lemma 3.8. In a free trade alliance, each firm ob tains onehalf of the monopoly profit. Because the firms are symmetric, the threat le vels in Equation 39 are the same for both firms, which leads to an equal division of industry profit. Afte r deciding how to split the final profit, the firms determine the transfer payments that will secure that allocation of profit. Proposition 3.2. In a free trade alliance, there is no pure strategy equilibrium in which both firms invest. In a free trade alliance, only one firm does R&D. Proposition 3.2 reveals that in a free trade alliance, firms do not choose identical investment levels in a pure strategy equilibrium. In the bargaining stage, firms realize that there is no transfer payment scheme that would lead both firms to invest the same amount and result in monopoly profit. In a free trade alliance when bot h firms innovate, each firm has an incentive to reduce its output in order to collect more transfer payments from the other firm. So even if firms are able to coordinate their i nvestments using transfer paymen ts, they cannot keep the output level in the market high enough to ensure the monopol y profit. In this stage firms also realize that they can find a transfer payment scheme that would lead to monopoly profits by inducing firms to invest different amounts. Therefore, firms choose transfer payments in the bargaining stage that induce asymmetric investments. Recall from Lemma 3.5 that if firms invest PAGE 42 42 asymmetrically then only one firm invests. Therefore Nash bargaining leads to two asymmetric equilibria in which onl y one firm invests. Proposition 3.3. In a free trade alliance, 2[] 41pbac T b and 2[] 2[41]ac T b The total level of investment in a free trade alliance is th e monopoly level of investme nt. Furthermore, the innovating firm produces the monopoly level of output and the noninno vating firm does not produce. To secure monopoly profits, firms agree on a pe runit transfer price that raises the noninnovating firms effective marginal cost to a leve l that makes it unprofitable for the firm to sell any output. This allows the innovating firm to behave as a monopolist and choose to invest and produce at the monopoly level, securing the mon opoly profit. The innovating firm employs the lumpsum transfer payment to share the monopoly pr ofit with its noninno vating counterpart. Proposition 3.4. A regulator cannot induce th e firstbest investment level in a free trade alliance and protect the consumers at the sa me time by only regulati ng transfer prices. If a regulator wants to protect consumers and keep the market price low when a free trade alliance is formed by regulating the transfer payments, the regu lator needs to cap the perunit transfer price. This will reduce the firms ability to increase the market price. However this also reduces the firms return on its investment by reducing the amount it will get from transfer payments. Therefore, a cap on the perunit transfer price leads to investment below its first best level. PAGE 43 43 Restricted Trade Alliances Now suppose that the government imposes a quot a on the foreign firm. In this restricted trade setting, the government limits the amount of good the foreign firm can sell to at most Q .5 First consider the case in which firms operate independently, so there is no R&D alliance. The quota restriction may change the firms profit functi on. In particular, if the market demand for the foreign firms product exceeds Q at the established price, the foreign firm cannot meet all of the demand. This gives the domestic firm an opport unity to serve the segment of the market that it would not have served if it were competing with the foreign firm in the absence of trade restrictions. In contrast, if the mark et demand for the firm does not exceed Q firms compete in prices as if the quota we re not imposed. Given 12,rtrt and Q the profits of firm 1 and 2 in the retail competition stage of the quota regime are: 2 112111[()] []rtrtrtrtabQQcQ (310) 2 212222[()] []rtrtrtrtabQQcQ ; (311) where the superscript rt denotes the restrict ed trade setting and2 rtQ 212 min{,} 3 ac Q b Lemma 3.9 summarizes the equilibrium outcome in the retail competition stage of the restricted trade setting given 1 rt and 2 rt that the firms chose in the investment stage. Lemma 3.9. In the restricted trade setting, [][21]2 41rtaQbbc p b ; 141rtacbQ b ; and 22rtQ 5 The realized trade restrictions are exogenous in the model. Furthermore, the quota is assumed to bind for the foreign firm, even if the foreign firm is a monopoly. PAGE 44 44 Lemma 3.9 reveals that the quota limits the co mpetition between the two firms, increasing the market price. In this sett ing, the domestic firm acts as a monopoly for the residual market demand ( p abQbQ ) after the foreign firm sells Q units. Therefore the domestic firm finds it optimal to reduce its cost by the sa me amount that a monopolist facing such demand would reduce its cost. The foreign firms incentive to reduce its cost is diminished by the limit on the amount of output it can sell in the domestic market. Proposition 3.5. In the quota setting, the foreign firm chooses a lower level and the domestic firm chooses a higher level of cost re duction than in the free trade setting. Total investment in the quota setting is le ss than in the free trade setting. A binding quota restriction reduces the market share of the foreign firm below its free trade level. This reduces the foreign firms incentive to reduce its cost, and so the firm invests less than in the free trade setting. On the other ha nd, the domestic firm has a higher market share in the quota setting than in the free trade setting. This guarantees the domestic firm a higher return from cost reduction than in the fr ee trade setting. Therefore, the domestic firm invests more than it would in the free trade setting. However, the increase in the domestic firms investment is less than the reduction in the forei gn firms investment, resulting in an overall reduction in industry investment. Now consider the setting where the firms form an R&D alliance. Backward induction is again employed to determine the market outcome. Proposition 3.6. Only the domestic firm invests in R&D in a restricted alliance. If the foreign firm is subject to quantity restric tions, the firms ability to produce is limited. In an alliance, if the foreign firm is the innovating firm, it will not be able to expand its production to the profit maximizing le vel for the alliance. Therefore the domestic firm will have PAGE 45 45 to produce the difference. However, the perunit transfer price that the firms agreed on in the bargaining stage will be too high for the domestic firm to in crease its production enough. Thus, the firms cannot secure monopoly profits if the forei gn firm is the firm that innovates. So in the bargaining stage firms choose transf er prices to ensure that the domestic firm is the firm that innovates. Extensions This essay has examined outcomes when two Cournot competitors collaborate in deterministic cost reduction by forming an R&D alli ance. It can be show n that the qualitative results presented in this essay continue to hol d for Bertrand price competition with sufficiently elastic demand, and for the Hotelling model of price competition for spatially differentiated products. The nature of the R&D process is important for the outcome of an alliance. Different results can emerge in settings w ith probabilistic R&D. When the R&D process is probabilistic, the model presented in this essay becomes analytically intractable.6 Simulations reveal that the optimal contract with stochastic R&D has some similar features to the one presented in this essay. 7 In the stochastic model, firms still choos e a perunit transfer pr ice to increase each others effective marginal cost, thereby reducing th e intensity of retail competition. Firms then use a lumpsum payment to distribute the additio nal surplus created. However, some qualitative results that emerge with probabilistic R&D are qu ite different. Even though firms can reduce the intensity of the retail competition, firms are not able to secure monopoly profits. Because the 6 This is also the case for the Bertrand and th e Hotelling models of price competition is used. 7 See the Appendix for a more detailed explanation of these simulations. PAGE 46 46 outcome of R&D is not a perfect signal of a fi rms investment level, each firm is likely to cheat which limits the ability of firms to license their innovation and in crease the market price compared to the deterministic setting. Thus in the probabilistic setting firms are not able to use transfer prices to increase th e market price to the monopoly leve l. An alliance in this setting leads to a market price above the competitive leve l, but below the monopoly price. In addition, in contrast to the deterministic R&D model, bot h firms invest at the e quilibrium when the R&D process is stochastic. Simulations also reveal that, the effects of an R&D alliance on investment incentives vary with the type of retail competition, the consum er demand and the cost of R&D if firms cannot reduce their costs with certainty. If the market demand for a produc t is relatively high compared to the production cost and R&D costs are relatively low, a firm in an alliance invests less than in either the free trade setting or the monopoly set ting. However, as the cost of R&D increases, firms invest more in the alliance setting compared to a monopolist. When the R&D cost is too high relative to the amount cost reduction the innova tion produces, a monopolist does not find it optimal to invest a lot. Howe ver the benefit of an alliance fr om an innovation is twofold; it lowers the production cost and allows firms to lo wer the intensity of th e price competition. Thus, a firms R&D incentive in an alliance settin g is not as sensitive to the cost of R&D as in the monopoly setting. In a Bertrand setting, the proportional increase in the profits of the alliance firms compared to the free trade levels is much higher than in Co urnot setting. Thus firms in Bertrand setting have increased incen tive to form an R&D alliance. Note also that even though the model presen ted in this essay focused on cost reducing R&D, one expects that the same qualitative resu lts hold for R&D that is geared towards product innovation. The source of collusive behavior in an alliance is th e firms ability to limit the PAGE 47 47 market output to the monopoly level by manipulati ng the terms of their licensing agreement. This depends only on the fact that at least one firm innovates, not on the type of innovation. Thus, firms can still coordinate their production by using the terms of their licensing agreements, when the result of R&D is a product innovation th at increases consumers valuation of the product. Conclusions Firms in a free trade alliance are able to use the terms of their contract to coordinate their prices and secure the joint m onopoly profit. Even though there are two firms present, the firms can employ licensing fees to eliminate compe tition and increase the market price to the monopoly level. Firms are also ab le to coordinate their R&D effo rts by using the terms of their contract. In a free trade alliance either the domestic or the fore ign firm invests at the monopoly level and the other firm does not invest at all. This essay also demonstrates that trade re strictions have sign ificant effects on R&D investments. If the foreign firm is subject to a quota restriction, the R&D incentives for the firms change compared to the free trade setting. Even if the foreign fi rm has a superior technology, the quota restriction prevents the firm from expandi ng its output level to th e monopoly level, which is the profit maximizing output level for the allian ce. In this setting, however, the firms cannot find licensing fees that would allow them to coordinate the output levels and induce profitmaximizing investment at the same time. Thus the existence of a quota restriction for the foreign firm eliminates any incentives for the forei gn firm to try to innovate in an alliance. In such a setting, only the domestic firm invests in an alliance. Furthermore, the firms can still employ transfer prices to coordinate th eir outputs and secure monopoly profit. PAGE 48 48 This essay suggests that antitr ust agencies should examine R& D alliances carefully. Even though they ostensibly compete in the retail market, firms can employ negotiated transfer payments to coordinate their R&D efforts and re duce retail market competition. Consumers are harmed by such activities. Regulating only transf er prices will not eliminate the anticompetitive effects of an R&D alliance. Although such re gulation can induce socially optimal investment levels, it will not eliminate the firms ability to coordinate their retail outputs. Additional instruments, such as retail price controls, ar e necessary to eliminat e such coordination. PAGE 49 49 CHAPTER 4 PRIVATELY NEGOTIA TED INPUT PRICES1 Introduction The Telecommunications Act of 1996 sought to increase competition in the provision of local telecommunications services.2 It did so in part by requiri ng incumbent suppliers to lease key elements of their networks to competitors, thereby eliminating the need for competitors to build their own networks from scratch.3 To date, the prices at which incumbent suppliers must lease key inputs to their competitors typically have been set by state regulators, following a pricing methodology established by the Fe deral Communications Commission (FCC).4 Recently, though, the chairman of the FCC has called upon all incumbent providers and their competitors to work earnestly to arrive at co mmercially negotiated rates for these inputs (Powell, 2004). SBC, a major in cumbent supplier of local teleco mmunications services, invited its competitors to join it in negotiating prices for these key inputs (Richtel, 2004). In addition, Qwest, another large incumbent s upplier, announced the successful ne gotiation of an input price agreement with MCI, a major buye r of key inputs (Latour, 2004). The purpose of this article is to consider some of the potential effects of privatelynegotiated input prices. Intuition might sugge st that, barring pronoun ced asymmetries in bargaining power, negotiations between incumbent suppliers and their competitors would produce reasonable input prices. The conflicting preferences of incumbents and competitors regarding the level of input pri ces could lead to negotiated pri ces that are neither unreasonably 1 This essay is a joint work with D. Sappington, and orig inally appeared in Journal of Regulatory Economics, Vol. 27 (3), pp. 263270. It is reproduced here with kind permission from Springer Science and Business Media. 2 Pub. L. No. 104104, 100 Stat. 56 (codified at 47 U.S.C. 151 et seq. ). 3 47 U.S.C., 251(c)(3). 4 See FCC (1996). Rosston and Noll (2002), among others, provide an accessible summary of the FCCs pricing methodology. PAGE 50 50 high nor unduly low. This simple intuition ignores the potential impact of i nput prices on retail competition, however. High input prices can i nduce an incumbent supplier to compete less vigorously for retail customers because the incu mbents retail success may come at the expense of competitors retail sales, and thus the profit the incumbent might otherwise derive from selling inputs to competitors. The reduced intensity of retail competition can harm consumers, even though privatelynegotiated input prices can, in principle, en sure industry cost minimization and increase aggregate welfare. We identify conditions under which this anti competitive effect of privatelynegotiated input prices can lead to the full exploitation of consumer s. We also identify a variety of factors that serve to ameliorate this effect of privatel ynegotiated input prices. The factors include retail price regulation, multiple input buyers, retail prod uct differentiation, and cost conditions that preclude the successful negotiation of input pr ices. We also examin e when input price negotiations will facilitate industry cost minimi zation, and when they will fail to do so. Our analysis draws upon insights developed else where in the literatur e. Armstrong et al. (1994), Sibley and Weisman (1998), Armstrong (1998, 2002), and Chen (2001), among others, observe that a verticallyintegra ted producer faces an opportunity cost that reflects changes in upstream profit when it expands its retail outpu t. Armstrong (1998, 2002), Laffont et al. (1998a, b), Vogelsang (2003), and Skreta (2004), among others, explain how high reciprocal interconnection tariffs can reduce the intensity of retail price competition. Armstrong (1998, p. 548) notes that firms are able to agree over th e choice of mutual access charges, something which cannot be expected to happen in oneway se ttings. The present analysis demonstrates that the insights developed in settings where co mpetitors set reciprocal interconnection tariffs may also be relevant in settings where retail competitors bargain over (o neway) input prices. PAGE 51 51 The insights extend to the latter oneway setti ngs because high input prices can reduce the intensity of retail price competition to the point where even the sole party that must pay the high input prices benefits from the high prices.5 Our analysis proceeds as follows. Section 2 analyzes a benchmark setting in which privatelynegotiated input prices result in the full exploitation of retail consumers. In this benchmark setting, the incumbent verticallyi ntegrated supplier faces a single potential competitor. The competitor has a downstream co st advantage, but the incumbent has a more pronounced upstream cost advantage. In additio n, the retail products of the two firms are homogeneous, and there is no retail price regulation. Section 3 explains how retail price regul ation can protect consumers from the full exploitation that arises in the benchmark setting.6 Section 4 notes that competition among multiple potential competitors also can preclude full exploitation of consumers. Section 5 demonstrates that private negotia tions may fail to produce mutually agreeable input prices when alternative cost structures prevail. The negot iations will fail, for example, if the incumbent supplier has lower downstream production co sts than the potential competitor. Section 6 examines the effects of retail product heterogeneity. When retail competition is characterized by Hotelling, rather than Bertrand, price competition, pr ivatelynegotiated input prices cannot be employed to exploit consumers fully. Furthermore, private negotiations will produce mutually agreeable input prices when, and only when, the incumbent can produce the input at lower cost than the competitor. Sect ion 7 provides concluding ob servations, including a 5 Unel (2004) provides related observations regarding the mutual benefits of high transfer payments in a model of international strategic alliances. 6 More generally, as the experience in Californias electricity sector has rev ealed, rigid retail prices coupled with substantial variation in input costs can lead to financial distress for regulated producers, to the ultimate detriment of consumers. For simplicity, we abstract from the insolvency of industry producers. PAGE 52 52 discussion of additional realworld considerations that may affect the results of private input price negotiations in practice. The proofs of all formal c onclusions are provided in the Appendix. The Benchmark Setting with No Retail Price Regulation Consider, first, the following benchmark setting. Two firms the incumbent and the entrant can produce a homogenous retail product, e.g., basic local telephone service. Each unit of the retail product is produced by combining one unit of an ups tream input and one unit of a downstream input. In the tel ecommunications context, the up stream input might include essential transmission and/or sw itching facilities; the downstream unit might include directory assistance or customer billing, for example. For simplicity, each input is assumed to be produced with constant returns to scal e. The incumbents and entran ts unit cost of producing the upstream input will be denoted I uc and E uc respectively. The corresponding downstream unit costs for the incumbent and entrant will be denoted I dc and E dc respectively. The incumbent is the leastcost supplier of the ups tream input and the entrant is th e leastcost downstream operator in this benchmark setting (so E u I uc c and I d E dc c ). The incumbents upstream cost advantage outweighs the entrants downstream cost advantage (so E d E u I d I uc c c c ). If the incumbent serves retail customers, it combines its own upstream input and downstream input to produce the re tail product. When th e entrant serves reta il customers, it can combine its downstream input eith er with its own upstream input or with the upstream input supplied by the incumbent. Thus, the entrant either can enter both the upstream and the downstream industry, or it can en ter just the downstream industry. If the entrant decides to operate exclusively in the downstream industr y, the entrant will buy the input from the PAGE 53 53 incumbent at unit price w. This upstream input price is de termined by Nash bargaining between the incumbent and the entrant (as explained further below).7 Each of N consumers is assumed to place value v (E d E uc c ) on one unit of the retail product. Consumers do not value additional units of the product. Therefore, each consumer will purchase one unit of the product if the product is available at a price that does not exceed v Consumers purchase the product from the firm that offers the lowest retail price. For simplicity, consumers are assumed to purchase the retail product from the entrant when the incumbent and entrant charge the same price for the product. The timing in this benchmark setting is as fo llows. First, the firms engage in Nash bargaining to determine the upstream input price, w.8 Second, the entrant determines whether it will use its own upstream input or purchase the upstream input from the incumbent, should the entrant prevail in the ensuing retail price comp etition. Third, simultaneously and independently, the incumbent and entrant each select the price they will charge for their retail product. Fourth, if the entrant has chosen to purchase the upstream input from the incumbent, the entrant procures from the incumbent (at unit price w) the quantity of the upstream input needed to fulfill the demand for the entrants retail produc t. Finally, the firms carry out the production required to fulfill customer demand for their retail products.9 7 For simplicity, the quality of the upstream inputs is assume d to be exogenous. As several authors have noted (e.g., Mandy, 2000; Beard et al., 2001; and Sappington and Weisman, 2005), in practice an incumbent supplier might choose the quality of the input it supplies to an entrant strategically in order to influence the quality for the entrants retail product and/or the entrants operating co st. In the present context, an incumbents willingness to negotiate an input price that is accep table to the entrant might vary with the (endogenous) quality of the incumbents upstream input. This issue merits additional research. 8 Nash bargaining is assumed in order to demonstrate that the identified anticompetitive effects of privatelynegotiated input prices can arise even when no party has disproportionate bargaining power. Extensions to the case of generalized Nash bargaining (e.g., Binmore et al., 1986; Roth, 1979) are discussed below. 9 This timing reflects the arguably realistic assumption that retail prices can be changed more quickly than can the source from which the entrant procures the upstream input. The time required to negotiate or establish new supply relationships typically justifies such an assumption in practice. PAGE 54 54 If the entrant could not purc hase the incumbents upstream input, the incumbent would employ its overall cost advantage to prevail in the retail price competition against the entrant. The incumbent could attract all customers in this hypothetical autarky regime by setting a retail price just below the entr ants unit cost of production (E d E uc c ). The incumbent would secure profit of (almost) N c c c cI d I u E d E u] ) ( [ by doing so. The entrant would earn zero profit. These profit levels in this autarky re gime constitute the threat points in the Nash bargaining that the incumbent and entr ant undertake in th e present setting.10 The primary results of this bargaining are repo rted in Proposition 4.1. Proposition 4.1. In the benchmark setting, the in cumbent and entrant will agree on a privatelynegotiated input price that ensures indu stry costs are minimized and the entrant serves all retail customers at price v pE so all consumer surplus is extracted. Proposition 4.1 reveals that the incumbent and entrant will negotiate an input price (I dc v w ) that serves to extract all surplus from consumers in the benchmark setting.11 As noted in the Introduction, when th e entrant purchases th e upstream input from the incumbent, the incumbent faces both a physical cost and an opport unity cost of expanding its retail sales. The physical unit cost (I d I uc c ) is simply the extra cost of producing more of the retail product. The opportunity cost is the reduction in profit the incumbent experien ces when its increased retail sales reduce the corresponding sales of the entran t, and thereby reduce the entrants demand for the incumbents upstream input. As long as the retail price is be low the consumers reservation 10 As explained more fully in the Ap pendix, the upstream input price resu lting from Nash bargaining in the benchmark setting is the value of w that maximizes ] [ ] [E A E I A I where i denotes the equilibrium profit of firm ) ( E I i in this setting and i A denotes the corresponding profit of firm i in the autarky regime. 11 Skreta (2004) provides a corresponding finding in a m odel where firms establish reciprocal interconnection fees. PAGE 55 55 value, v the entrants retail sales (and thus it s demand for the incumbents upstream input) decline by one unit for each extra unit of the retail product sold by the incumbent. Therefore, the incumbents unit opportunity cost of expanding its retail sales is I uc w the unit profit it earns from selling the upstream input to the entrant. The sum of the incumbent s unit physica l cost and unit opportunity cost is I dc w Consequently, when choosing it s profitmaximizing retail price, the incumbent acts as if its marginal cost is I dc w Because the en trants corresponding marginal cost is E dc w and because I d E dc c the entrant will serve all N retail customers at price I dc w and earn profit N c cE d I d] [ in equilibrium. The incumbents equilibrium profit, which is derived wholly from selling the upstream input to the entrant, will be N c wI u] [ .12 Notice that the entrants equilibrium profit in this benchmark setting is independent of the input price, w as long as all N consumers purchase the retail product. Notice also that the incumbents profit increases with w. Therefore, Nash bargaining will produce the highest input price that ensures all N customers purchase one unit of the retail product. Because the equilibrium price is I dc w the negotiated input price will be I dc v (so that v c wI d ). The key point here is that the incumbent and en trant both benefit from the reduced intensity of retail price competition that arises when the entrant buys the upstream input from the incumbent. Therefore, even though the entrant w ould value the cost reduc tion that a lower input price would secure, the entrant is willing to pay a relatively high price for the upstream input in 12 By considering both the physical cost and the opportunity cost of expanding downstream output, the incumbents analysis may be somewhat reminiscent of the analysis that underlies the e fficient component pricing rule (ECPR) for setting input prices (e.g., Baumol and Sidak, 1994). However, in the present setting, the incumbent considers the (upstream) opportunity cost of expanding its downstream output whereas the ECPR analysis considers the (downstream) opportunity cost of providing access to a competitor. Fu rthermore, whereas an access price that reflects the ECPR leaves the incumbent with the same pr ofit whether access is provided or is not provided, the input price in the present setting provides the incumbent with a portion of the incremental profit that arises from the successful negotiation of the input price. PAGE 56 56 order to reduce the intensity of retail price co mpetition. In equilibrium, the incumbent and entrant both secure higher profit wh en the entrant buys the upstream input from the incumbent at a relatively high privatelynegotiated input price. In contrast, cons umer surplus declines relative to the case where the entrant cannot purchase the upstream input from the incumbent. The reduced intensity of retail price competiti on causes the retail price to increase from E d E uc c (in the autarky regime) to v (the maximum amount consumers ar e willing to pay for the retail product). In summary, private negotiations always produc e a mutually agreeable input price in the benchmark setting. This input price ensure s that industry costs are minimized, and that consumer surplus is eliminated.13 It remains to determine wh ether these strong conclusions persist more generally. Setting with Retail Price Regulation Consider, first, the setting with retail price regulation. This setti ng is identical to the benchmark setting with one exception: the incumbents retail price is regulated. Let Ip (I d I uc c ) denote the regulated price at which th e incumbent must sell its retail product.14 This regulated price is set before the incu mbent and entrant negotiate the unit price (w) at which the entrant can purchase the upstr eam input from the incumbent. Next, the entrant decides 13 These conclusions persist when input prices are determined by generalized Nash bargaining. In particular, even when it has substantial bargaining power, the incumbent do es not employ the upstream input price to exclude the entrant from the industry under the conditions that ch aracterize the benchmark setting. Instead, the incumbent accommodates the entrants market particip ation in order to generate industry cost savings that serve to increase the profit of both the incumbent and the entrant. Generalized Nash bargaining simply alters the manner in which the extra surplus secured via the rationalization of industry production is divided between the producers. It does not ensure gains for consumers relative to the case wher e the entrant cannot purcha se the incumbents upstream input. 14 The incumbent is obligated to serve all retail demand at price Ip. The restriction Id I u Ic c p avoids settings where the incumbent may prefer to term inate operations rather than sell the retail product at the regulated price. PAGE 57 57 whether it will produce the upstream input itself or purchase the input from the incumbent. At this point, the entrant also sets the retail price for its product. Production is then carried out to meet realized consumer demand. The negotiated price for the upstream input is again determined by Nash bargaining between the incumbent and entrant. The firms profits in the regulated autarky regime where the incumbents retail price is set at Ip and the entrant cannot purchase the incumbents upstream input constitute their threat profit levels in th e Nash bargaining.15 Consumers preferences and purchasing behavi or are the same as in the be nchmark setting. Thus, the only substantive change in the present setting is the regulation of the incumbents retail price. Propositions 4.2 and 4.3 describe the effects of privatelynegotiated i nput prices in this setting with retail price regulati on. Proposition 4.2 considers the case where the regulated retail price (Ip ) is less than the unit cost of production ) (E d E uc c the entrant would incur in the (regulated) autarky regime. In this case, th e incumbent would serve all customers in the regulated autarky regime at the regulated price, Ip The incumbent would earn profit I RA = Ip [ N c cI d I u)] ( and the entrant would earn zero profit (0 E RA). Proposition 4.2. Suppose ) [E d E u I d I u Ic c c c p in the setting with retail price regulation. Then the incumbent and entrant will agree on a privatelynegotiated input price that ensures the entrant will serve all retail customers at priceIp, thereby securing consumer surplus N p vI] [ Relative to the regulated autarky regi me, the profit of each firm increases by 2 ] [ N c cE d I d and consumer surplus is unchanged. 15 Formally, the upstream input price th at arises from Nash bargaining in th e setting with retail price regulation is the value ofwthat maximizes ] ~ [ ] ~ [E RA E I RA I where i ~ denotes the equilibrium profit of firm i(=E I ,) in this setting and iRA denotes the corresponding profit of firmiin the regulated autarky regime. PAGE 58 58 Proposition 4.2 reveals that privatelynegotiate d input prices will agai n rationalize industry production in the setting with retail price regul ation. The incumbent will produce the upstream input and the entrant will pr oduce the downstream input. The negotiated upstream input price ( 2 ] [E d I d Ic c p w ) will divide evenly the extra surplus ( N c cE d I d] [ ) that arises when the entrant, rather than the incumbent, serves the retail market at the regulated price (Ip). Consumers do not gain from the rationalized industry structure in this setting because the entrant charges exactly the regulated retail price that would prevail in the re gulated autarky regime. Proposition 4.3 reports similar qua litative effects of privatelyne gotiated input prices in the case where the regulated price ex ceeds the unit production cost th e entrant would incur in the (regulated) autarky regime. In this case, the en trant would serve all reta il customers (at price Ip) in the regulated autarky regime, and would earn profit N c c pE d E u I E RA)] ( [ in doing so. The incumbent would earn no profit (so0 I RA). Proposition 4.3. Suppose ] [ v c c pE d E u I in the setting with retail price regulation. Then the incumbent and entrant will agree on a pr ivatelynegotiated input price that ensures the entrant serves all retail customers at price Ip thereby securing consumer surplus N p vI] [ Relative to the regulated autarky regime the profit of each firm increases by 2 ] [ N c cI u E u and consumer surplus is unchanged. Proposition 4.3 reveals that the incumben t and entrant again employ the privatelynegotiated input price to rationa lize industry production. The ne gotiated upstream input price ( 2 ] [I u E uc c w ) divides evenly the extra surplus ( N c cI u E u] [ ) that arises when the entrant procures the upstream input from the incumbent, rather than producing the input itself. The PAGE 59 59 entrant does not pass any of these industry cost savings on to retail customers, though, as the entrant charges the same price (Ip ) it would charge in the regulated autarky regime. Before proceeding to consider additional altern atives to the benchmark setting, notice that privatelynegotiated input prices also would benefit producers but not consumers if the incumbents regulated retail price were a price ce iling rather than an immutable price level. In fact, privatelynegotiated input pr ices can reduce consumer surplus in such a setting. To see why, consider the case where th e regulated price cei ling exceeds the entr ants unit cost of production (i.e., E d E u Ic c p ). In this case, if the entrant were not permitted to purchase the incumbents upstream input, competition between th e incumbent and the entrant would result in the incumbent serving retail customer s at the highest price (just belowE d E uc c ) that precludes profitable operation by the entrant. It is readil y shown that if privatel ynegotiated input prices were permitted in this setting, the incumbent and entrant would agree on an upstream input price (I d Ic p w ) that results in the entrant serving retail customers at the re gulated retail price ceiling, E d E u Ic c p Thus, in this setting, the reduc tion in the intensity of retail price competition induced by the privatelynegotiated input price serves to incr ease the retail price above the level that would ar ise in the absence of privat elynegotiated input prices. 16 Setting with Multiple Potential Entrants Propositions 4.2 and 4.3 reveal that retail pr ice regulation can preven t the use of privatelynegotiated input prices to exploit consumer s fully. Competition among multiple potential entrants can provide similar pr otection for consumers. Alt hough this conclusion holds more 16 In this case, then, privatelynegotiated input prices increase total surplus (by ensuring the rationalization of industry production), but reduce consumer surplus. PAGE 60 60 generally, it is readily demonstrated in the following simple setting, called the setting with multiple entrants. There are two potential entrants, labeled A and B in this setting. Each potential entrant has upstream unit cost E uc and downstream unit cost E dc Despite its downstream cost disadvantage (I dc > E dc ), the incumbent has lower overall costs than the entrants (i.e., I uc + I dc < E uc + E dc ), just as in the benchmark setting. In this setting with multiple entrants, the incu mbent first decides whether it will continue to serve retail customers as it has historically, or se rve exclusively as a supplier of the upstream input. The incumbent then enters into i nput price negotiations, first with entrant A to determine its unit input price (Aw ) and then with entrant B to determine its unit input price (Bw ). The input price negotiated with one entrant cannot be linked explicitly to the price negotiated with the other entrant.17 The incumbent and entrant B take Aw and entrant A s make or buy decision as given when they determine Bw via Nash bargaining. When they determine Aw via Nash bargaining, the incumbent and entrant A anticipate the input price (Bw ) that will subsequently be negotiated by the incumbent and entrant B After input prices are determined, the retail competitors set prices for their products simulta neously and independently. Because the retail products supplied by all firms are homogeneous, cons umers purchase from the firm that sets the lowest price. For simplicity, all consumers are assumed to pu rchase the product from entrant A whenever entrant A is one of the firms that sets the lowest retail price (and this price does not exceed v).18 17 This assumption may be reasonable when the term s of privatelynegotiated input price agreements are proprietary. The assumption rules out mostfavored custom er clauses, for example, which merit study in future research. 18 It is also assumed that entrant A will negotiate an input price with the incumbent whenever entrant A is indifferent between doing so and operating using its own inputs exclusively. The detailed proof of Proposition 4 (which is PAGE 61 61 Proposition 4.4. In the setting with multiple entrants, entrant A purchases the input from the incumbent and serves all retail customers at a price equal to the standalone cost of the entrants, E uc + E dc .19 Recall from Proposition 4.1 that when only one entrant is present (and when retail price regulation is not imposed), the incumbent and si ngle entrant will agree on a relatively high input price that allows the firms to split the incremental profit s ecured from the retail price (v) that extracts all consumer surplus. Proposition 4.4 re ports that multiple potential entrants can prevent such full exploitation of consumers. In the setting with multiple entrants, the incumbent and entrant A recognize that entrant B can profitably undercut any reta il price that exceeds its standalone cost of production. Anticip ating this relatively lo w retail price, the incumbent and entrant A are compelled to negotiate an input price be low the level that prevails in the benchmark setting. Thus, multiple potential entrants can ensure lower negotiated input prices and lower retail prices. Alternative Cost Structures The analysis to this point has assumed that potential competitors have lower downstream costs than the incumbent supplier. This assumption is nontriv ial. To understand why, consider a setting that parallels the benchmark setti ng with one key exception: the incumbents downstream unit cost of production is less than the corresponding downstream cost of the single available from the authors) allows for the possibility that the entrant might only agree to a negotiated input price if the price ensures entrant A strictly greater profit than it secures using its own inputs exclusively. 19 The incumbent earns less profit in the setting with multiple entrants than it secures in the benchmark setting. Similarly, entrant A earns less profit than the single entrant earns in the benchmark setting. Entrant B does not produce in the setting with multiple entrants, and so earns no profit. PAGE 62 62 entrant (so E d I dc c ). The setting with an incumbent downs tream cost advantage also allows for the possibility that the entrant is the least cost in dustry producer (so I d I u E d E uc c c c ). Proposition 4.5 reveals an important new effect that arises in this setting. Proposition 4.5. The incumbent and entrant will not negotiate a mutually advantageous input price in the setting with an incumbent downstream cost advantage. The firm that is the leastcost industry producer will serve all retail customers in this setting, and will employ its own upstream input to do so. Proposition 4.5 indicates that relative downstream costs can in fluence the success of private input price negotiations. When the incumbent ha s an upstream cost advantage and the entrant has a downstream cost advantage (as in the be nchmark setting), the two firms are able to negotiate an input price that en sures full extraction of consumer surplus and cost minimization at both stages of production. The two firms are una ble to reach such an agreement when the incumbent has a downstream cost advantage. In this case, as explained in section 2, any negotiated input price (w) induces the incumbent to act as if its marginal cost of production is I dc w and leads the entrant to act as if its marginal cost is E dc w Consequently, when E d I dc c the incumbent will undercut any profitable price set by the entrant, eliminating any prospect of positive profit for the entrant. Recogniz ing its inability to secure profit if it agrees to buy the input from the incumbent, the entrant will not do so. Instead, the entrant will serve the entire retail market at price I d I uc c using its own input if the entr ant is the least cost industry supplier (i.e., if I d I u E d E uc c c c ). If the entrant has both an overall cost disadvantage (so PAGE 63 63 I d I u E d E uc c c c ) and a downstream cost disadvantage (so I d E dc c ), the firm will not enter the industry at all, as it will be una ble to serve consumers profitably. Product Heterogeneity Recall that in the benchmark setting, the incumb ent and entrant are always able to negotiate an input price that extracts consumer surplu s fully. The full extraction is possible because consumers have identical, perfec tly inelastic demands for the s uppliers homogeneous products. More generally, privatelynegotiate d input prices will not allow industry suppliers to exploit consumers fully. This conclusion is reflected in Proposition 4. 6, which considers the setting with product differentiation. The cost structures and the timing of interactions are the same in this setting as in the benchmark setting. The key difference in the setting with product differentiation is that the firms engage in the form of retail price co mpetition considered by Ho telling (1929) rather than Bertrand competition. In the setting with product differentiation, N consumers are uniformly distributed on the unit interval, which represents product space. The incumbent is located at point 0 and the entrant is located at point 1 in this space. A consumer at location ] 1 0 [ L incurs transportation (e.g., disutility) cost L tI if she purchases the retail product from the incumbent. The consumer incurs transportation cost ] 1 [L tE if she purchases the product from the entrant. Each consumer buys at most one unit of the retail product, and secures gross value v from this unit. v is assumed to be sufficiently large that all N consumers buy one unit of PAGE 64 64 the retail product in equilibrium.20 Each consumer purchases the product from the firm that offers the smallest sum of retail price and transportation cost. Proposition 4.6. In the setting with product differ entiation, the entrant will buy the input from the incumbent when (and only when) the in cumbent can produce the input at lower cost than the entrant (i.e., when E u I uc c ). The input price that is nego tiated in this case will lead to equilibrium retail prices that: (i) extract all surp lus from the consumer who is indifferent between purchasing the product from the incumbent and purch asing it from the entran t; but (ii) leave all other consumers with strictly positive surplus. In the setting with product differentiation, the incumbent and entrant both serve retail customers in equilibrium. When all N customers always buy a unit of the product, the incumbents perceived unit production cost (which includes the relevant opportunity cost) is I dc w when the entrant commits to buy the input from the incumbent. The entrants corresponding unit cost is E dc w Thus, the entrants effectiv e unit cost advantage when it commits to buy the input is E d I dc c In contrast, when the entr ant decides to employ its own input, its unit cost is E d E uc c and the incumbents unit cost is I d I uc c The entrants corresponding cost advantage is E d I dc c[I u E uc c ]. Thus, the entrant secures a larger cost advantage (or a smaller cost disadvantage) by co mmitting to buy the input from the incumbent if and only if the incumbent can produce the input at lower cost than the entrant.21 20 Furthermore, transportation costs (It and Et) and the production costs of the incumbent and entrant are assumed to be sufficiently similar that both firms serve some of the N retail customers in equilibrium. 21 If consumers transportation costs ar e sufficiently pronounced that not all customers purchase the product in equilibrium, then the incumbent and entrant will serve distinct market segments. Consequently, privatelynegotiated input prices can serve to lo wer industry costs without reducing the intensity of retail price regulation. PAGE 65 65 Extensions and Conclusions We have identified conditions under whic h industry producers can employ privatelynegotiated input prices to exploit consumer s severely. When these conditions (e.g., homogeneous retail products, no retail price re gulation, a single potential entrant, and a downstream cost advantage for the entrant) preva il, the firms will negotiate an input price that induces the incumbent producer to refrain from aggressive competition against the entrant because such competition would cause the incumben t to forfeit lucrative sales of the upstream input to the entrant. In turn, th e entrant is willing to pay a relatively high price for the upstream input in order to reduce the intens ity of retail price competition. We have also considered the effects of priv atelynegotiated input pr ices under alternative conditions. We have shown, for example, that re tail price regulation, multiple potential entrants, and retail product heterogeneity can limit the exte nt to which privatelynegotiated input prices can be employed to disadvantage consumers. We have also identified conditions under which firms should not be expected to conduct successful input pric e negotiations (e.g., when the incumbent has lower downstream costs than th e entrant). These findi ngs imply that although firms may be able to employ pr ivatelynegotiated input prices to disadvantage consumers under some conditions, they should not be expected to be able to do so under all relevant conditions. In practice, several ot her factors may reduce the likelihood that firms will readily negotiate input prices that disadvantage consumers. For example, the bargaining process itself can be costly and imperfect, in contrast to the si mplifying assumption maintained in the foregoing analysis. Furthermore, an incumbent that faces a stream of potential entrants may insist on The cost reductions can reduce equilibrium prices and increase consumer surplus. See Sappington (2005) for additional analysis of the effects of input prices on the make or buy decisions of potential entrants. PAGE 66 66 particularly favorable terms with early entran ts in order to develop a reputation as a tough bargainer. Such a policy may reduce the like lihood of successful negotiations with early entrants. The early entrants may be particularly unlikely to agree to unfavorable terms if they believe they can secure favorable treatment from regulators if private negotiations fail.22 In practice, an incumbent supplier also may pr efer that negotiations proceed slowly or fail altogether if the absen ce of an input price agreement harm s entrants more than it harms the incumbent. The differential harm arises naturally if entrants are unable to operate profitably without an input price agreement (perhaps be cause their limited customer base makes it uneconomic to incur the large fixed costs normally associated with networ k construction) or if entrants find the ensuing regul atory hearings to be differen tially burdensome, for example. Incumbents also may be reluctant to facilitate entry by firms that seek primarily to arbitrage regulated retail rates (i.e., engage in creamskimming) or by firms that will become particularly formidable competitors over time as they gain more experience in the industry. These considerations merit formal consideration in future research, as do the more complex negotiations that arise when multiple incumb ent input suppliers operate simultaneously.23 22 Thus, in practice, the relevant threat points in any private negotiations may entail regulated input prices rather than independent operation by the incumbent and entrants. 23 Future research also might consider the effects of nonlinear cost structures and nonlinear input prices. Laffont et al. (1998a), Carter and Wright (2003), and Dessein (2003), among others, demonstrate that the qualitative effects of interconnection fees can vary when nonlinear pricing st ructures are feasible. Notice that nonlinear input pricing structures may afford producers gr eater latitude to exploit retail consumers than do linear input prices. PAGE 67 67 APPENDIX A APPENDIX FOR CHAPTER 2 Proof of Lemma 2.1: It can easily be seen that the consumer at x=1 is indifferent between buying and not buying when.d r pm At this price monopolist se rves the whole market and earnsc d rm Consumer surplus is found by integrating the utility each consumer gets over [0, 1]: 1 0 1 0) ) ( ( ) ( dx x d d r r dx x d p r CSm m (A1) 2d Proof of Lemma 2.2: To characterize the competition be tween the two firms, it is useful to identify the location ( x) of the marginal consumer who is indifferent between buying from firm 1 and firm 2. The marginal consumer ge ts the same utility by buying the goods from the two firms, so: ] 1 [2 1x d p r x d p r (A2) where ip is the price that firm i charges. Equation A2 implies: d d p p x 21 2 (A3) Given this location, firm i will maximize its profit under direct exporting,e i where superscript e denotes direct exporting. x c pe] [1 1 ; (A4) F x c pe ] 1 ][ [2 2. (A5) PAGE 68 68 Since firms compete in prices, maximizing these profit functions with respect to price, and then solving the equation system simultaneously will give the equilibrium market price, ep. Firms maximize their profits with respect to prices The first order condition for a firm can be found by taking the derivatives of firms prof it function with respect to its own price. 0 ] [ 2 1 21 1 2 1 1 c p d d d p p p (A6) 0 ] [ 2 1 22 2 1 2 2 c p d d d p p p (A7) Solving Equation A6 for 1p and Equation A7 for2p, lead to: 22 1d c p p (A8) 21 2d c p p (A9) Equilibrium prices can be found by so lving Equation A8 and Equation A9 simultaneously: d c p p pe e e 2 1 (A10) At this price, it can easily be seen from E quation A3 that the firms will split the market equally. The profits of firm 1 and fi rm 2 are found by subs tituting price and x to Equation A4 and Equation A5. The consumer surplus is the sum of the surplus consumers who are located at x [0, 1/2] gets by buying firm 1s product and the su rplus consumers who are located at x [1/2, 1] gets by buying firm 2s product. 1 2 / 1 2 2 / 1 0 1)) 1 ( ( ) ( dx x d p r dx x d p r CSe PAGE 69 69 1 2 / 1 2 / 1 0)) 1 ( ) ( ( ) ) ( ( dx x d d c r dx x d d c r ) ) ( 4 ( 4 1d d c r (A11) In the free trade case, the domestic welf are for country one can be found by simply summing the consumers surplus and the profit of firm 1. 2 4 ) (1d d d c r CS DWe e e c d r 4 3 (A12) The full market coverage assures that: c d d r (A13) e mp p (A14) Full market coverage also assures that th e lower bound for consumer surplus under free trade is higher than the cons umer surplus under monopoly. This can be seen by comparing Equation A1 to Equation A11. ) 4 ( 4 1 ) ) ( 4 ( 4 1d d d d c r CSe mCS d d 2 4 3 Proof of Lemma 2.3: Firms maximize their profits, whic h are given by Equation 21 and Equation 22 with respect to prices. The first order conditions are given by: PAGE 70 70 0 2 ) ( 2 1 21 1 2 1 1 d T c p d d d p p pfta p fta (A15) 0 ) ( 2 1 22 2 1 2 2 fta p ftaT c p d d d p p p (A16) Solving Equation A15 for 1p and Equation A16 for2p lead to: 22 1 fta pT d c p p (A17) 21 2 fta pT d c p p (A18) Solving Equation A17 and Equation A18 simulta neously leads to the equilibrium price: fta p fta fta ftaT d c p p p 2 1 (A19) At this price, firms split the market equally which can easily seen by Equation A3. Substituting price and into Equation 21 and 22, we get the profits of firm 1 and firm 2 respectively for free trade alliances with lump sum transfer payment ftaT and per unit transfer payment fta pT. Proof of Lemma 2.4: Firms use Nash bargaining to find the values for the transfer payments. To find the outcome, one fi rst needs to find the threat points, fta that will be used in the Nash bargaining function. Each firm will use its profit it could get under free trade, which is PAGE 71 71 given by Lemma 2.2 as its threat point. Usi ng these values, Nash ba rgaining function for free trade alliances becomes: ) )( (2 2 1 1 fta fta fta fta ftaNash )] 2 ( ][ 2 [2 1F d dfta fta (A20) Note that substituting Equation A19 in to Equations 21 and 22 leads to: fta p fta ftaT d 2 1 (A21) Full market coverage guarantees that it is al ways more profitable if the whole market is covered. If the per unit transfer payment is higher than c d r 2 3 the consumer located around x = will not be able to buy the product. Thus while increasing the per unit transfer, firms will also make sure that the whole market is cove red. This imposes the following upper limit on firms total profit. c d rfta fta 22 1 (A22) Firms use Nash bargaining to split this total pr ofit. The outcome of the free trade alliances can be found by the solution to the following pr oblem as firms are maximizing Equation A20 subject to Equation A22 by choos ing the their re spective profits fta1 and fta2 )] 2 ][ 2 [ max2 1 ,2 1F d d Nashfta fta ftafat fat c d r t sfta fta 2 .2 1 (A23) The Langrangian for the above maximization is: ] 2 [ )] 2 ( ][ 2 [2 1 2 1c d r F d d Lfta fta fta fta (A24) PAGE 72 72 The first order conditions can be found by taking derivatives of Equation A24 with respect to fta1 fta2 and 0 22 1 F d Lfta ft (A25) 0 21 2 d Lfta ft (A26) 0 22 1 c d r Lfta fta (A27) Solving Equation A25, Equation A26 a nd Equation A27 simultaneously lead to: 2 2 4 21F c d rfta (A28) 2 2 4 22F c d rfta (A29) The per unit transfer payment for free trade alliances can be found by substituting Equation A28 and Equation A29 into the Equation A21. c d r Tfta p 2 3 (A30) The lump sum transfer payment for free trade alliances can be found by substituting Equation A29 into the profit function of firm 2, which was defined in Lemma 2.3. 2 2 / 3 2c d r F Tfta (A31) Proof of Proposition 2.1: First assume that rather than co mpeting, the firms operate as a joint monopoly. The main difference in this case is that firms will choose a price tat maximizes their joint profit. In the second stage rather than competing with each other, they will charge a PAGE 73 73 coordinated price. So under assumption 1, the profit function of the firms for a joint monopoly, jm where superscript jm denotes joint monopoly is: 1 ] [c pjm jm (A32) When firms form a joint monopoly they will ma ximize their combined profit. To find the equilibrium price, we differentiate join t monopolys profit with respect to price. 0 1 pjm (A33) So the joint monopoly will charge the highest possible price that will make all the consumers stay in the market. Assu me that it charges a price higher than 2d r pjm Then there will be some consumers located around x=1/2 who will not consume the good. Because of assumption 1, this is not optimal. Now assume that the joint monopoly charges a price lower than 2d r pjm Since its profit is increasing in price, and it can still increa se the price without losing any customer, this is not opti mal. Therefore price is equal to 2d r pjm Substituting this price into the joint monopol ys profit function, we get the equilibrium profit of the joint monopoly. c d rjm 2 (A34) The consumer surplus is the sum of the surplus consumers who are located at x [0, 1/2] gets by buying firm 1s product and the su rplus consumers who are located at x [1/2, 1] gets by buying firm 2s product. PAGE 74 74 1 2 / 1 2 / 1 0)) 1 ( ( ) (dx x d p r dx x d p r CSjm jm jm 1 2 / 1 2 / 1 0)) 1 ( ) 2 ( ( ) ) 2 ( (dx x d d r r dx x d d r r d4 1 (A35) This shows that the market price is the hi ghest under a joint monopoly. Firms use their ability to increase their prices to exploit consumers. Since there is greater differentiation in the market compared to monopoly case, firms can expl oit consumers reservation price even more. Consumer surplus is lower in the joint monopoly setting than in any other setting. Now consider a free trade alliance. The pr ice for free trade alliances can be found by substituting Equation A30 into Equation A19. 22 1d r p p pfta fta fta (A36) This is the price consumers pay in the joint m onopoly case. Thus the consumers surplus in the free trade alliance case is th e same as the consumers surp lus in the joint monopoly case. Consumers are hurt by the formation of alliance. This can easily be seen by comparing this consumer surplus with that in Lemma 2.2. 2 2 2 2 41F c d r d CS DWfta fta fta ) 2 ( 2 1F c d r DWfta (A37) PAGE 75 75 Note that for F d, Equation A37 will be always less then Equation A12. Thus a free trade alliance may increase the domestic welfare depending on the magnitude of the fixed cost. Proof of Lemma 2.5: When assumption 2.1 holds, the profits of firms under the quota setting are given by Equation 23 and Equation 24 become: Q c pq] [1 1 ; (A38) F Q c pq ] 1 ][ [2 2. (A39) Taking the derivative of firms profit func tions given by Equation A38 and Equation A39 leads to: 01 1 Q pq (A40) 0 12 2 Q pq (A41) Equation A40 and Equation A41 imply that each firms profit is increasing in its own price. So both firms would like to charge the highest possible price. Under full market coverage, it is optimal for firms to serve as many consumers as possible; hence both firms will charge a price that will make the consumer located at Q indifferent between buying and not buying. The prices firms will char ge under trade restrictions are: dQ r pq 1 (A42) PAGE 76 76 ] 1 [2Q d r pq (A43) Since Q (0,1), m qp d r dQ r p 1 (A44) m qp d r Q d r p ] 1 [2. (A45) Profits of firms can easily be found by substitu ting above prices in to Equation A42 and Equation A43. The consumer surplus is the sum of the surplus consumers who are located at x [0, Q] gets by buying firm 1s product and the su rplus consumers who are located at x [Q, 1] gets by buying firm 2s product. 1 2 0 1)) 1 ( ( ) (Q q q qdx x d p r dx x d p r CSQ )) 1 ( 2 1 ( 2 Q Q d (A46) For Q (0,1), m qCS d CS d 2 4 (A47) PAGE 77 77 Proof of Lemma 2.6: Assume that country 1 imposes a ta riff on firm 2. In this case the consumers who buy the product from firm 2 will have to pay ) 1 (2t pt where tp2 is the price firm 2 charges for its product in the tariff setti ng. This affects the lo cation of the indifferent consumer. d d p t p xt t2 ) 1 (1 2 (A48) Given this location, firm i will maximize its profit under direct exporting,t i where superscript t denotes tariff setting. x c pt t] [1 1 ; (A49) F x c pt t ] 1 ][ [2 2. (A50) The first order condition for a firm can be f ound by taking the derivativ es of firms profit function with respect to its own price. 0 ] [ 2 1 2 ) 1 (1 1 2 1 1 c p d d d p t p pt t t t t (A51) 0 ] [ 2 ) 1 ( 2 ) 1 (2 2 1 2 2 c p d t d d t p p pt t t t t (A52) Solving Equation A51 for tp1 and Equation A52 fortp2, lead to: 2 ) 1 (2 1d c t p pt t (A53) ) 1 ( 2 ) 1 (1 2t d t c p pt (A54) Equilibrium prices can be found by so lving Equation A53 and Equation A54 simultaneously: PAGE 78 78 3 3 31ct d c pt (A55) ) 1 ( 3 2 3 32t ct d c pt (A56) It can easily be seen from Equation A48 th at the domestic firm will serve the larger portion of the market. Even though the actual pri ce firm 2 gets is lowe r, the price consumers face if they buy from firm 2 is highe r than its price in the free trade setting. The profits of firm 1 and firm 2 are found by substituting Equation A55 and Equation A56 into Equation A49 and Equation A50. The consumer surplus is the sum of the surplus consumers who are located at x [0, d ct 6 2 / 1 ] gets by buying firm 1s product and the surplus consumers who are located at x [ d ct 6 2 / 1 1] gets by buying firm 2s product. 1 6 2 / 1 2 6 2 / 1 0 1)) 1 ( ) 1 ( ( ) (d ct t d ct t tdx x d t p r dx x d p r CS 1 6 2 / 1 6 2 / 1 0)) 1 ( ) ) 1 ( 3 2 3 3 ( ( ) ) 3 3 3 ( (d ct d ctdx x d t ct d c r dx x d ct d c r d ct d ct d ct d c r 36 ) 9 )( 3 ( 2 (A57) Proof of Proposition 2.2: Now assume that firms form a conditionally restricted alliance. Each firm will use the profit it could get under tr ade restriction setting as its threat point, cra PAGE 79 79 First assume that the foreign firm is subject to quota restrictions. In this setting the threat points are determined in Lemma 2.5. Using these values, Nash bargaining function for conditionally restricted alliances in the quota setting becomes: ) )( (2 2 1 1 cra cra cra cra craNash )] ) ) 1 ( )( 1 ( )][ ( [2 1F c Q d r Q c dQ r Qcra cra (A58) Just as in Lemma 2.4, the total profit is given by: cra p cra craT d 2 1 (A59) Full market coverage leads to the following constraint: c d rcra cra 22 1 (A60) The firms choose their respective profits to maximize Equation A58. The outcome of the conditionally restricted allian ces in the quota setting can be found by the solution to the following problem. )] ) ) 1 ( )( 1 (( )][ ( [ max2 1 ,2 1F c Q d r Q c dQ r Q Nashcra cra cracra cra c d r t scra cra 2 .2 1 (A61) The Langrangian for the above maximization is: )] ) ) 1 ( )( 1 (( )][ ( [2 1F c Q d r Q c dQ r Q Lcra cra ] 2 [2 1c d rcra cra (A62) The first order conditions can be found by taking derivatives of Equa tion A62 with respect to cra 1 cra 2 and 0 ) ) 1 ( )( 1 (2 1 F c Q d r Q Lcra cra (A63) PAGE 80 80 0 ) (1 2 c dQ r Q Lcra cra (A64) 0 22 1 c d r Lcra cra (A65) Solving Equation A63, Equation A64 and Equation A65 simultaneously lead to: 2 ) ( 41F c d r Q dcra (A66) 2 ) )( 1 ( 42F c d r Q dcra (A67) The perunit transfer payment for conditio nally restricted alli ances can be found by substituting Equation A66 and Equa tion A67 into the Equation A59. c d r Tcra p 2 3 (A68) The price for conditionally rest ricted alliances can be found by substituting Equation A68 into Equation A19. 22 1d r p p pcra cra cra (A69) This is the same price as free trade alliances, so conditionally restri cted alliances in the quota setting has the same effect on consumers as free trade alliances. The lump sum transfer payment for condition ally restricted alli ances can be found by substituting Equation A67 into the profit function of firm 2, wh ich was defined in Lemma 2.3. ] ][ 1 [ 4 2 c d r Q d F Tcra (A70) Total welfare in this case is the sum of the pr ofits of both firms and the consumers surplus. cra cra cra craCS TW1 1 PAGE 81 81 2 ) )( 1 ( 4 2 ) ( 4 4 F c d r Q d F c d r Q d d c d r 4 (A71) This is higher than the total welfare that is achieved in the quota setting. Hence compared to both the prealliance setting and the free trad e benchmark, total welf are is higher in the conditionally restricted alliance setting. Now assume that country 1 imposes tariff on the foreign firm. In this case the threat levels will be the profits firm will secure under the tariff setting which are given by Lemma 2.6. Using these values, Nash bargaining function for conditi onally restricted allian ces in the tariff setting becomes: ) )( (2 2 1 1 cra cra cra cra craNash ] ) 1 ( 18 ) 3 ( ][ 18 ) 3 ( [2 2 2 1F t d ct d d ct dcra cra (A72) Just as in the quota setting, the above function is subject to the following constraint: c d rcra cra 22 1 (A73) Thus the outcome of the conditionally restrict ed alliances in the tariff setting can be found by the solution to the following problem. ] ) 1 ( 18 ) 3 ( ][ 18 ) 3 ( [ max2 2 2 1 ,2 1F t d ct d d ct d Nashcra cra cracra cra c d r t scra cra 2 .2 1 (A74) The Langrangian for the above maximization is: PAGE 82 82 ] ) 1 ( 18 ) 3 ( ][ 18 ) 3 ( [2 2 2 1F t d ct d d ct d Lcra cra ] 2 [2 1c d rcra cra (A75) The first order conditions can be found by taking derivatives of Equa tion A75 with respect to cra 1 cra 2 and 0 ) 1 ( 18 ) 3 (2 2 1 F t d ct d Lcra cra (A76) 0 18 ) 3 (2 1 2 d ct d Lcra cra (A77) 0 22 1 c d r Lcra cra (A78) Solving Equation A76, Equation A77 and Equation A78 simultaneously lead to: ) 1 ( 36 ) 3 ( 36 ) 3 ( 2 4 2 22 2 1t d ct d d ct d F d c rcra (A79) ) 1 ( 36 ) 3 ( 36 ) 3 ( 2 4 2 22 2 2t d ct d d ct d F d c rcra (A80) The perunit transfer payment for conditio nally restricted alli ances can be found by substituting Equation A79 and Equa tion A80 into the Equation A59. c d r Tcra p 2 3 (A81) The price for conditionally rest ricted alliances can be found by substituting Equation A81 into Equation A19. 22 1d r p p pcra cra cra (A82) This is the same price as free trade alliances, so conditionally restri cted alliances in the tariff setting also has the same effect on consumers as free trade alliances. PAGE 83 83 The lump sum transfer payment for conditionally restricted alliances in the tariff setting can be found by substituting Equation A80 into the profit function of firm 2, which was defined in Lemma 3. ) 1 ( 36 ) 3 ( 36 ) 3 ( ) 3 ( 2 1 22 2t d ct d d ct d c d r F Tcra (A83) Total welfare in this case is the sum of the pr ofits of both firms and the consumers surplus. cra cra cra craCS TW2 1 c d r 4 (A84) Similarly this is higher than the total welfare in the tariff setting as well as the free trade setting. Proof of Proposition 2.3: In the quota setting domestic welfare if the firms form a conditionally restricted allian ce is found by adding the consumer s surplus and the domestic firms profit. 1 cracracraDWCS () 442 ddF Qrdc 2 ) ( 2 F c d r Q d (A85) Domestic welfare if firms do not form an al liance in the quota setting is given by: 1 qqqDWCS [1][] 2 d dQQQrQdc ) ( 2 c d r Q d (A86) PAGE 84 84 Note that Equation A85 is always greater than Equation A86 if fixed cost is positive; hence a conditionally restricted alli ance increases the domestic welfare. Now assume that country 1 impos es a tariff on the foreign firm, rather than a quota. If the firms form an alliance, the domestic welfare will be given by the sum of consumers surplus and firm 1s profit. cra cra craCS DW1 ) 1 ( 36 ) 3 ( 36 ) 3 ( 2 2 22 2t d ct d d ct d F c r (A87) If the firms do not form an alliance, the dom estic welfare will be given by the sum of consumers surplus, firm 1s profit and the tariff revenue, TR cra. t t t tTR CS DW 1 d d ct t d ct d c d r 6 ) 3 ( 18 ) 3 ( 4 32 (A88) If the fixed cost is not high enough, then Equa tion A88 will be higher than Equation A87. Thus an alliance may not always increase the domestic welfare. Proof of Proposition 2.4: First assume that the forei gn firm is subject to quota restrictions. In this case th e postalliance profit functions ra 1 and ra 2 of the firms will become: ra ra p raT T Q c dQ r Q ] 1 [ ] [1; (A89) ra ra p raT T c Q d r Q ] ) 1 ( ][ 1 [1. (A90) where raTis the lumpsum transfer payment and ra pTis the per unit transfer payment for restricted alliances. In this setting the threat points are determin ed in Lemma 2.5. Using these values, Nash bargaining function for restricted alliances becomes: PAGE 85 85 ) )( (2 2 1 1 ra ra ra ra raNash )] ) ) 1 ( )( 1 ( )][ ( [2 1F c Q d r Q c dQ r Qra ra (A91) Note that in this case d Q Q c d rra ra) 1 ( 22 1 This is a result of exogenously imposed quota restrictions. Since the government imposed quota determines the market partition and the market price, the total possible profits in this case are exogenously determined by the governments actions. The outcome of the restricted alliances can be found by the solution to the following problem. )] ) ) 1 ( )( 1 (( )][ ( [ max2 1 ,2 1F c Q d r Q c dQ r Q Nashra ra raa ra d Q Q c d r t sra ra) 1 ( 2 .2 1 (A92) The Langrangian for the above maximization is: )] ) ) 1 ( )( 1 (( )][ ( [2 1F c Q d r Q c dQ r Q Lra ra ] ) 1 ( 2 [2 1d Q Q c d rra ra (A93) The first order conditions can be found by taking derivatives of Equa tion A93 with respect to ra 1 ra 2 and 0 ) ) 1 ( )( 1 (2 1 F c Q d r Q Lra ra (A94) 0 ) (1 2 c dQ r Q Lra ra (A95) 0 ) 1 ( 22 1 d Q Q c d r Lra ra (A96) Solving Equation A94, Equation A95 and Equation A96 simultaneously lead to: PAGE 86 86 2 ) ( ) 1 (1F c d r Q d Q Qra (A97) 2 ) )( 1 ( ) 1 (2F c d r Q d Q Qra (A98) Above equations with Equation A89 and Equati on A90 lead to the perunit and the lump sum transfer payment for restricted alliances. 2 F Tra (A99) 0 ra pT. (A100) Note that because the quota restriction on the foreign firm, the per unit transfer price will not be enough for firms to raise th e market price. Thus the foreign firm is not willing to pay the domestic firm a per unit transfer price. Since th e market price is not affected by the formation of an alliance, the consumers surplus is unchanged. Domestic welfare increases compared to prealliance setting because of the lump sum transfer from the foreign firm to the domestic firm. The total welfare increases because of the savings in the fixed cost. Now assume that rather than a quota, country 1 imposes tariff on the foreign firm. In this case the postalliance profit functionsra 1 andra 2 will be different than the previous cases, since the foreign firm will still be subject to a tariff. So one first n eeds to find the profit functions of firms given the transfer payments, and find the market price in the second stage. In a tariff setting, the profit functions of fi rms in a restricted alliance will be given by: ra ra p ra raT T x x c p ] 1 [ ] [1 1; (A101) ra ra p ra raT T c p x ] ][ 1 [2 1, (A102) PAGE 87 87 where raTis the lumpsum transfer payment, ra pTis the per unit transfer payment for restricted alliances and d d p t p xt t2 ) 1 (1 2 The first order condition for a firm can be f ound by taking the derivatives of firms profit function with respect to its own price. 0 2 ] [ 2 1 2 ) 1 (1 1 2 1 1 d T c p d d d p t p pra p ra ra ra ra ra (A103) 0 ] [ 2 ) 1 ( 2 ) 1 (1 1 2 1 2 2 ra p ra ra ra ra ra raT c p d t d d t p p p (A104) Solving Equation A103 for rap1 and Equation A104 forrap2, lead to: 2 ) 1 (2 1 ra p ra raT d c t p p (A105) ) 1 ( 2 ) 1 ( ) 1 (1 2t t T d t c p pra p ra ra (A106) Equilibrium prices can be found by so lving Equation A105 and Equation A106 simultaneously: 3 ) ( 3 3 31c T t T d c pra p ra p ra (A107) ) 1 ( 3 ) ( 2 3 3 32t c T t T d c pra p ra p ra (A108) The location of the indifferent consumer can be easily found by substituting the above prices into x Note that the firms have the ability to use ra pTas a tool to increase the market price just as in free trade alliances. The profits functions of firms found by substituting Equation A107 and Equation A108 into Equation A101 and E quation A102. In this setting the threat PAGE 88 88 points are determined by Lemma 2.6. Using these values, Nash bargaining function for restricted alliances becomes: ) )( (2 2 1 1 ra ra ra ra raNash )] ) 1 ( 18 ) 3 ( ][ 18 ) 3 ( [2 2 2 1F t d ct d d ct dra ra (A109) Note that in this case: ) 1 ( 18 ) )( 2 ( ) 1 ( 3 ) )( 2 ( ) 1 ( 2 ) 2 (2 2 2 1t d c T t t t c T t t T t t dra p ra p ra p ra ra (A110) If the per unit transfer payment is higher than t t c d r 2 ) 1 ( 2 3 2 the consumer located around d T c t d xra p6 ) ( 3 will not be able to buy the product. Thus while increasing the per unit transfer, firms will also make sure that th e whole market is covered. This imposes the following upper limit on firms total profit. ) 1 ( 18 ) 3 2 )( 1 6 ( ) 2 ( 9 ) 1 ( 2 ) 1 ( 2 3 22 2 1t d ct d r d t t d t t c d rra ra (A111) The outcome of the conditionally restricted alliances can be found by the solution to the following problem. a raraNash2 1,max )] ) 1 ( 18 ) 3 ( ][ 18 ) 3 ( [2 2 2 1F t d ct d d ct dra ra ) 1 ( 18 ) 3 2 )( 1 6 ( ) 2 ( 9 ) 1 ( 2 ) 1 ( 2 3 2 .2 2 1t d ct d r d t t d t t c d r t sra ra (A112) The Langrangian for the above maximization is: )] ) 1 ( 18 ) 3 ( ][ 18 ) 3 ( [2 2 2 1F t d ct d d ct d Lra ra PAGE 89 89 ] ) 1 ( 18 ) 3 2 )( 1 6 ( ) 2 ( 9 ) 1 ( 2 ) 1 ( 2 3 2 [2 2 1t d ct d r d t t d t t c d rra ra (A113) The first order conditions can be found by ta king derivatives of Equation A113 with respect to ra 1 ra 2 and 0 ) 1 ( 18 ) 3 (2 2 1 F t d ct d Lra ra (A114) 0 18 ) 3 (2 1 2 d ct d Lra ra (A115) 0 ) 1 ( 18 ) 3 2 )( 1 6 ( ) 2 ( 9 ) 1 ( 2 ) 1 ( 2 3 22 2 1 t d ct d r d t t d t t c d r Lra ra (A116) Solving Equation A114, Equation A115 and Equation A116 simultaneously lead to: ) 1 ( 36 ) 1 6 )( 3 2 ( 2 2 ) 1 ( 4 )) 1 ( 2 3 2 (1t d d ct d r t d F t t c d rra ) 1 ( 36 6 ) 2 ( ) 1 ( 36 ) (2t d cdt t t d ct t (A117) ) 1 ( 36 ) 1 6 )( 3 2 ( ) 1 ( 2 2 ) 1 ( 4 )) 1 ( 2 3 2 (2t d d ct d r t t d F t t c d rra ) 1 ( 36 6 ) 2 ( ) 1 ( 36 ) (2t d cdt t t d ct t (A118) Above equations with Equation A101 and E quation A102 lead to the perunit and the lump sum transfer payment for restricted alliances. t t c d r Tra p 2 ) 1 ( 2 3 2 (A119) ) 2 )( 1 ( 36 ) 2 6 )( 3 2 ( ) 1 ( 4 )) 1 ( 2 3 ( 2 t t d t dt ct d r t t t c d r F Tra PAGE 90 90 2 2 2) 2 )( 1 ( 18 ) 3 2 ( ) 1 ( 36 ) 6 )( 2 ( ) (t t d ct d r t t d cdt t ct t (A120) Substituting Equation A119 into Equation A107 and Equation A108 shows that the actual price consumers face is hi gher than the trade restrictions. Hence compared to prealliance setting consumers are worse off. PAGE 91 91 APPENDIX B APPENDIX FOR CHAPTER 3 Proofs Proof of Lemma 3.1: The central planner chooses an amount of cost reduction that maximizes the total welfare. Thus f b is solution to the following problem: [()]/ 2 0argmax[()]acbabQcdQ (B1) Solving Equation B1, one gets 21fbac b Proof of Lemma 3.2: A monopolist chooses its production and investment levels to maximize its profit. m and mQ are solutions to the following problem: 2 ,argmax [()]QabQcQ (B2) Maximizing Equation B2 with respect to and Q one gets 1 4 b c am and 2() 41mac Q b The market price and the profit of the monopolist are found by substituting m and mQ into the inverse demand f unction and the monopolists prof it function, respectively. Proof of Lemma 3.3: In the free trade setting, the fi rms first choose their investment levels and then in the second st age they choose their production levels. The outcome in the free trade setting is found by backwards induction. The profit of firm i in the free trade setting is given by: 2[()()]ft iijiiiabQQcQ (B3) PAGE 92 92 In the retail market competition stage, firm i chooses its level of production, f t iQ to maximize its profit given the level of cost reduction, ft i, the firm has chosen in the previous stage. Equilibrium output levels 1 f tQ and 2 f tQ can be found by solving th e first order conditions for the maximization of Equation B3 with respect to f t iQ 12 12 3ftac Q b (B4) 21 22 3ftac Q b (B5) Anticipating the profits they will receive in the final st age, firms choose the profit maximizing level of cost reduction in the first stag e. Equilibrium levels of cost reduction in the free trade setting 1 f t and 2 f t can be found by solving the first order conditions for these maximizations simultaneously. 122() 92ftftftac b (B6) The market price and the profit of th e monopolist are found by substituting 1 f t, 2 f t, 1 f tQ and 2 f tQ into the inverse demand function and the monopolists profit function, respectively. Proof of Proposition 3.1: 2() 0 9241ftm iacac bb (B7) f tm i 124() 9241ftftmacac bb (72)() 0 (92)(41) bac bb (B8) PAGE 93 93 12 f tftm 124() 9221ftftfbacac bb (2)() 0 (92)(41) bac bb (B9) 12 f tftfb Proof of Lemma 3.4: Assume that 12 f tafta In this case only firm 1 can license its technology. Therefore the profit functions of the firms in the free trade alliance setting become: 2 1121121[()] [] ftaftaftaftaftaftafta pabQQcQTQT (B10) 2 212122[()] [] ftaftaftaftaftafta pabQQcTQT (B11) In the retail market competition stage, firm i chooses its level of production, f ta iQ to maximize its profit given the level of cost reduction, 1 f ta the domestic firm has chosen in the previous stage. Equi librium output levels 1 f taQ and 2 f taQ can be found by solving the first order conditions for the maximization of Equa tion B10 and Equation B11 simultaneously. 1 13p ftaacT Q b (B12) 1 22 3p ftaacT Q b (B13) The market price can be found by substituting Equation B12 and Equation B13 into the demand function. Proof of Lemma 3.5: Assume that 12 f tafta Rationally anticipating the profits they will ultimately receive in the retail stage, th e firms choose the levels of cost reduction to maximize their profits that are given by: 2 11 2 1 1[]2 [] [] 93pp fta pacTacT TT bb (B14) PAGE 94 94 2 1 2 22[2] [] 9p ftaacT T b (B15) Solving the first order conditions for the ma ximization of Equation B14 and Equation B15 lead to 12[]5 2[91]p ftaacT b and 20fta Substituting these into Equations B14 and B15 one can find the profits of the firms when 12 f tafta Proof of Lemma 3.6: Assume that *** 12 ftafta In this case both firms can license their technology. Thus the profit functions of the firm s in this setting become: *******2 1121121[()] [] ftaftaftaftaftaftafta ppabQQcTQTQ (B16) *******2 2122212[()] [] ftaftaftaftaftaftafta ppabQQcTQTQ (B17) In the retail market competition stage, firm i chooses its level of production, f ta iQ to maximize its profit given the level of cost reduction, f ta i it has chosen in the previous stage. Equilibrium output levels 1 f taQ and 2 f taQ can be found by solving the first order conditions for these simultaneously. ** 123p ftaftaacT QQ b (B18) The market price can be found by substituting E quation (B18) into the demand function. Proof of Lemma 3.7: Assume that *** 12 ftafta Rationally anticipating the profits they will ultimately receive in the retail stage, the firms choose the levels of cost reduction to maximize their profits that are given by: **2** 1221 *2 1 1[2]2 [] [] 93ftaftaftafta pp fta fta pacTacT T bb (B19) PAGE 95 95 **2** 2112 *2 2 2[2]2 [] [] 93ftaftaftafta pp fta fta pacTacT T bb (B20) Solving the first order conditi ons for the maximization of Equation B19 and Equation (B20) simultaneously leads to the equilibrium levels of cost reduction, 1 fta 2 fta 4[]7 2[92]pacT b Substituting these into Equations B19 a nd B20 one can find the profits of the firms when ** 12 f tafta. Proof of Lemma 3.8: The allocation of profits in a free trade alliance can be found by solving the following problem: 121122 ,max ()()ftafta f taftftaft subject to: 12 f taftam (B21) Maximizing B21 leads to 122m ftafta Proof of Proposition 3.2: In the bargaining stage, once the firms agree on an allocation of profits, firms choose transfer payments that will guarantee this allo cation. In particular firms will agree on transfer payments pT and T that solves 12m fta and 22m fta (B22) or 12m fta and 22m fta (B23) There is a unique pair of pT and T that solves equations that are depicted in B22. However there is no real solution to the equations shown in B23. This shows that firms cannot achieve monopoly profits if the firms choose the same investment level. Therefore in a subgame PAGE 96 96 perfect equilibrium, firms will choose a pair of pT and T that would force firms to choose asymmetric levels of investments. Lemma 3.5 show s that if this is the case, then only one firm will be investing. Hence in a subgame perf ect equilibrium only one firm invests. Proof of Proposition 3.3: Solving equations depicted in B22 simultaneously leads to 2[] 41pbac T b and 2[] 2[41] ac T b Substituting these transfer prices into 1 f ta, leads to 141ftaac b which is the monopoly level of investment When the transfer prices and the investment levels are substituted into e quilibrium output levels, one can see that 12() 41ftaac Q b and 20ftaQ. Proof of Proposition 3.4: 1 f ta is less than the first best investment level so a regulator would like increase the level of investment in an alliance. Recall from Lemma 3.5 that 12[]5 2[91]p ftaacT b Hence if the regulator wants to in crease the investment level, she should increase the per unit transfer pa yment. However an increase in the transfer payment would lead to an increase in the market price, thus hurting the consumers. Proof of Lemma 3.9: In the restricted trade setting, th e firms first choose their investment levels and then in the second st age they choose their production levels, just like the free trade setting. The outcome in the quota setting is al so found by backwards induction. In the second stage, the domestic firm chooses a level of pr oduction to maximize its profit that is given by the following equation. 2 112111[()()]rtabQQcQ (B24) The foreign firm, on the other hand maximizes its profit subject to the constraint that it PAGE 97 97 cannot sell more than the quota level which is exogenously determined by the government. Therefore the foreign firm solves the following problem. 22 221222max [()()]rt QabQQcQ (B25) subject to: 2QQ (B26) The Lagrangian for the above problem is given by the following expression 2 212222[()()]() LabQQcQQQ (B27) Note that we assumed the government imposes a quota restraint that bind s in the free trade setting. Thus solving the KuhnTucker conditions for Equation B27 leads to 1 12rtabQc Q b and 2 rtQQ. Anticipating the profits they will receive in the final st age, firms choose the profit maximizing level of cost reduction in the first stag e. This leads to equilibrium levels of cost reduction, 141rtacbQ b and 22rtQ Proof of Proposition 3.5: 12412rtrtacbQQ b 2(3) 2(41) acbQQ b (B28) Equation B28 is positive for a binding quota constraint, therefor e the domestic firm invests more than the foreign firm in the restricted trade setting. 114161rtftacbQac bb 2(3) 0 (61)(41) acbQbQ bb (B29) 11 rtft 22261rtftQac b 2(3) 0 2(41) acbQQ b (B30) PAGE 98 98 22 rtft 1222() 41261rtrtftacbQQac bb (21)(2(3)) 0 2(61)(41) acbQQ bb (B31) 122rtrtft Proof of Proposition 3.6: The proof of proposition 6 has a similar outline as the proofs of propositions 3.1 through 3.3. However note that when the foreign firm is subject to trade restrictions, the firms are no longer symmetric. Therefore at equilibrium firms will no longer split the monopoly profits equally. The allocation of profits in a restricted trade alliance can be found by solving the following problem: 121122 ,max ()()rtartartartrtart subject to: 12 rtartam (B32) The Lagrangian for the above optimization is given by: 112212[][][]rtartrtartrtartamL (B33) Maximizing (B33) leads to 12 122rtrt m rta (B34) 21 222rtrt m rta (B35) Once the firms agree on an allocation of profits firms choose transfer payments that will guarantee this allocation. To find these transfer payments, one first needs to identify the equilibrium levels of output and investment given transfer payments. Because the firms in the PAGE 99 99 restricted trade setting are no longer symmetric, all of the foll owing three possible outcomes should be analyzed separately. Case ( i ) firm 1 invests more than firm 2; Case ( ii ) both firms invest the same amount; and Case ( iii ) firm 2 invests more than firm 1. First assume that firm 1 invests more than firm 2. In this case only firm 1 can license its technology. Therefore the profit functions of the firms in the restricted trade alliance setting become: 2 1121121[()] [] rtartartartartartarta pabQQcQTQT (B36) 2 212122[()] [] rtartartartartarta pabQQcTQT subject to: 2 rtaQQ (B37) In the restricted alliance sett ing, the quota restriction may or may not be binding depending on the value of the transfer prices. If in the ba rgaining stage the firms choose transfer payments such that the quota is binding, then the output levels in the re stricted alliance setting when 12 rtartais given by: 1 12rtaacbQ Q b and 2 rtaQQ (B38) Rationally anticipating the profits they will ultim ately receive in the retail stage, the firms choose the levels of cost reduction to ma ximize their profits. This leads to: 141rtaacbQ b and 20rta. (B39) If in the bargaining stage, the firms choose tr ansfer payments such that the quota is not binding, then the output levels in th e restricted alliance setting when 12 rtarta is given by: 1 13p rtaacT Q b and 1 22 3p rtaacT Q b (B40) PAGE 100 100 Rationally anticipating the profits they will ultim ately receive in the retail stage, the firms choose the levels of cost reduction to ma ximize their profits. This leads to: 12()5 182p rtaacT b and 20rta. (B41) The firms will try to agree on transfer paymen ts such that the profits they will secure (whether the quota ends up being bi nding or not) will be the profits that are defined in Equations B34 and B35. However if the firms choose tran sfer prices such that the quota level ends up binding (i.e. if the equilibrium investment levels are given by Equation B39 and the equilibrium output levels are given by Equation B38), there is no pair of transf er payments that allows firms to reach these profits. Basically there are no transfer payments that satisfy equations depicted in Equation B42 and cause the quot a constraint to bind. 12 122rtrt m rta and 21 222rtrt m rta (B42) However there exists a pair of transfer paymen ts that satisfy equations depicted in Equation B42. These transfer payments lead the quota constraint to be non bi nding. The transfer payments that satisfy equations depicted in Equation B42 make it incentive compatible for the foreign firm not to produce at all and the domestic firm produces at the monopoly level. Now assume that both firms invest the same amount. In this case both firms can license their innovations. This allows both firms to secu re additional revenues from its opponents sales. In this case the profits of firm 1 and fi rm 2 in the retail competition stage are: *******2 1121121[()] [] rtartartartartartarta ppabQQcTQTQ (B43) *******2 2122212[()] [] rtartartartartartarta ppabQQcTQTQ subject to: 2 rtaQQ (B44) PAGE 101 101 Just like Case (i) the quota restriction may or may not be binding depending on the value of the transfer prices. Thus one needs to carry out a similar analysis in this case and look at two different scenarios depending on wh ether the quota constraint is bindi ng. In this case it turns out that there are no transfer payments that will satisfy equations give n in Equation B45 in either of these two scenarios. Thus firms cannot achie ve monopoly level of pr ofits if they end up investing the same amounts. 12 122rtrt m rta and 21 222rtrt m rta (B45) Finally assume that the foreign firm invests mo re than the domestic firm. In this case only the foreign firm can license its innovations. Ther efore the profit functions of the firms in the restricted trade alliance setting become: **************2 1122111[()] [] rtartartartartartarta pabQQcQTQT (B46) **************2 2122212[()] [] rtartartartartaftarta pabQQcQTQT subject to: ** 2 rtaQQ (B47) The outcome in this case is the same as Case (i i). There are no transfer payments that will satisfy equations given in Equati on B48, the quota constraint bi nding or not. Thus firms cannot achieve monopoly level of profits if the forei gn firm invests more than the domestic firm. ** 12 122rtrt m rta and ** 21 222rtrt m rta (B48) The preceding analysis shows that the firms cannot achieve monopoly profits in any case except for Case (i) Therefore in a subgame perfect equilibrium, firms will choose a pair of pT and T that would guarantee that only the domestic fi rm invests. Hence in the subgame perfect equilibrium only the domestic firm invests. PAGE 102 102 Simulation Results In a stochastic R&D model, the difference compared to a deterministic R&D model is that rather than choosing the level of cost reduction, a firm chooses the probability of successful innovation, s which would reduce its consta nt marginal cost of production c by which is an exogenously determined parameter. Th e cost of such innovation is given by s2. The timing of the model and the demand function remain the same. This model becomes analytically intractable if probabilistic R&D is used. Thus, simulations are employed to analyze the effects of R&D alliances. The simulations presented in this essay are ca rried out using Mathema tica 5.2. The model is still solved using backward induction. For a ll values of parameters within a given range, the last stage retail competition and the second stage investment decision can be solved analytically given the outcome of the bargaining stage. Using these analytical results, first Nash bargaining function is first calculated as a f unction of the per unit transfer price pT and the lump sum payment T Then this function is maximized using nu merical estimation. To ensure that this process yields the true maximum, it is re peated 100 times for different values of pT and T in a feasible region as initia l values and the maximum of these 100 iterations is selected as the true maximum. Cournot Model First assume that firms compete in quantities. Simulations show that the firms are able to increase the market price above competitive level. However they cannot coordinate their prices effectively enough to reach monopoly level (Figure B1). Simulations also reveal that both firms increase their profits significantl y compared to the free trade setting, but the firms cannot achieve PAGE 103 103 the monopoly level of profits (Figure B2). If the market demand for a product is relatively high compared to the production cost and if R&D costs ar e relatively low, a firm in an alliance invests less than in the free trade sett ing and the monopoly setting (Figur e B3). Conversely if the demand is not high enough, an alliance firm invest s more than to a monopolist. An increase in the cost of R&D lowers a monopolists R&D incen tive significantly, but the investment level in an alliance is not altere d drastically. Thus as increases, a firm in an alliance starts undertaking more R&D compared to a monopolist (Figure B4). Bertrand Model Now assume that firms compete in prices. The results are similar in nature to the results derived under Cournot competition. Just as in C ournot setting, the market price in the alliance setting is higher than the fr ee trade setting but lowe r than the monopoly setting (Figure B5). Firms are able to increase thei r profits; however their total profits are significantly below the monopoly level of profits (Figure B6). In Bertrand setting, th e alliance leads to a higher proportionate increase in profits compared to the free trade leve ls than the firms in Cournot setting. Thus, firms in Bertrand setting have higher incentive to try to form an alliance. Similar to the Cournot setting, a firm in an alliance invests less than in the monopoly and free trade settings when the demand is high enough compared to the cost of pr oduction (Figure B7). However as increases, firms invest more compared to both settings (Figure B8). PAGE 104 104 0 20 40 c 0 20 40 a 0 20 40 Price alliance monopoly freetrade 0 20 40 c Figure B1. The market prices under differe nt scenarios with Cournot competition when = 15, = 2, and b = 2. PAGE 105 105 0 20 40 c 0 20 40 a 0 25 50 75 100 Profit monopoly alliance freetrade 0 20 40 c Figure B2. The total profits firms would secure under different scenario s with Cournot competition when = 15, = 2, and b = 2. PAGE 106 106 0 20 40 c 0 20 40 a 0 0.2 0.4 0.6 0.8 Probability alliance monopoly freetrade 0 20 40 c Figure B3. The success probabilities each firm would choose under different scenar ios with Cournot competition when = 15, = 2, and b = 2. PAGE 107 107 0 20 40 c 0 20 40 a 0 0.1 0.2 0.3 0.4 Prob alliance freetrade monopoly 0 20 40 c Figure B4. The success probabilities each firm would choose under different scenar ios with Cournot competition when = 30, = 2, and b = 2. PAGE 108 108 0 20 40 c 0 20 40 a 0 20 40 Price alliance monopoly freetrade 0 20 40 c Figure B5. The market price under different scenarios with Cournot competition when = 15, = 2, and b = 2. PAGE 109 109 0 20 40 c 0 20 40 a 0 5 10 15 20 Profit monopoly freetrade alliance 0 20 40 c Figure B6. The total profits firms would secure unde r different scenarios with Bertrand competition when = 15, = 2, and b = 2. PAGE 110 110 0 20 40 c 0 20 40 a 0 0.2 0.4 0.6 0.8 Prob alliance monopoly freetrade 0 20 40 c Figure B7. The success probabilities each firm would choose under different s cenarios under Bertrand competition when = 15, = 2, and b = 2. PAGE 111 111 0 20 40 c 0 20 40 a 0 0.1 0.2 0.3 0.4 Prob a llianc e freetrade monopoly 0 20 40 c Figure B8 The success probabilities each firm would choose unde r different scenarios Bertrand competition when = 30, = 2, and b = 2. PAGE 112 112 APPENDIX C APPENDIX FOR CHAPTER 4 Proof of Proposition 4.1: 0 E A and N c c c cI d I u E d E u I A)] ( [ since E d E u I d I uc c c c When the entrant is expected to bu y the input from the incumbent at unit price w ~ the incumbent faces opportunity cost N c wI u] ~ [ and physical production cost N c cI d I u] [ when it, rather than the entrant, serves all retail customers. The sum of the incumbents unit opportunity cost and physical production cost is I dc w~ The entrants unit cost of serving retail customers is E dc w~ Therefore, because E d I dc c, price competition will drive the retail price to I dc w ~ and the entrant will serve the N retail customers. Consequently, the profit of the incumbent and entrant, respectively, will be: N c wI u I] ~ [ (C1) N c c N c w c wE d I d E d I d E] [ )] ~ ( ~ [ (C2) Under these circumstances, Nash bargaining will produce an upstream input price given by: ] [ ] [ max arg~E A E I A Iww (C3) It follows from Equation C1 and Equation C2 that I A I is strictly increasing in w ~ and E A E is independent of w ~ Consequently, the product in Equation C3 is maximized when w ~ takes on the highest value consistent with all N consumers purchasing one unit of the retail product. Since the entrant charges price I dc w ~ in equilibrium, the value of w as determined in Equation C3 is I dc v w Finally, notice that when this price is set for the upstream input, the entrant prefers to buy PAGE 113 113 the upstream input from the incu mbent (and there by secure profit N c cE d I d] [) rather than produce the upstream input itself (in wh ich case it earns ze ro profit). Proof of Proposition 4.2: 0 E RA and N c c pI d I u I I RA)] ( [ since E d E u Ic c p Therefore, when the entrant is expected to purchase the upstream input from the incumbent, Nash bargaining will produce an upstream input price given by: ] ~ [ ] ~ [ max argE RA E I RA Iww (C4) where I I d I u I E I u IQ c c p Q c w ] [ ] [ ~ and (C5) E E d I EQ c w p ] [ ~ (C6) where EQ and IQ denote the equilibrium retail sales of the entrant and incumbent, respectively. The entrant will in deed purchase the upstream input from the incumbent if doing so secures nonnegative profit for the entrant (since 0 E RA). If the entrant buys the upstream input from the incumbent, then Equation C4 through Equation C6 reveal that when N QE and 0 IQ: 2] [ ] [ max argN c w p c p w wE d I I d Iw (C7) Maximizing the product in Equation C7 provides: 2 ] [E d I d Ic c p w (C8) Equation C8, Equation C5, and Equation C6 reveal: 2 ] [ ] 2 ) ( [ ~ N c c N c c c pE d I d I RA I u E d I d I I and (C9) 0 2 ] [ 2 ] [ ~ N c c N c cE d I d E RA E d I d E. (C10) PAGE 114 114 Equation C10 reveals that the entrant will (weakly) prefer to purchase the upstream input from the incumbent and set price Ip in order to serve all retail cu stomers rather than set a higher price or employ its own upstream input (and thereby earn zero profit). Proof of Proposition 4.3: 0 I RA and N c c pE d E u I E RA)] ( [ since E d E u Ic c p Therefore, when the entrant is expected to purchase the upstream input from the incumbent, the upstream input price determined by Nash bargaining will be as specified in Equation C4 through Equation C6. The entrant will indeed purchase the upstream input from the incumbent if doing so secures profit in excess of E RA for the entrant. When the entrant serves all N retail consumers at priceIp it follows from Equation C4 through Equation C6 that: 2] [ ] [ max argN w c c w wE u I uw (C11) Maximizing the product in Equation C11 provides: 2 ] [I u E uc c w (C12) It follows from Equation C5, Equa tion C6, and Equation C12 that 2 ] [ 2 ] [ ~ N c c N c cI u E u I RA I u E u I and (C13) E RA I u E u E RA E d I u E u I EN c c N c c c p 2 ] [ ] 2 ) ( [ ~ (C14) Equation C14 reveals that the entrant will purc hase the upstream input from the incumbent and set price Ip in order to serve all retail consumers rather than set a hi gher price (in which case its profit is zero) or employ its own upstream input (in whic h case its profit is E RA). PAGE 115 115 Proof of Proposition 4.4: The setting with multiple entrants is one in which there is no retail price regulation. In addition, the incumben t faces two entrants, entrant A and entrant B. The firms produce a homogeneous retail product. E ach unit of the retail product is produced by combining one unit of the downstr eam input and one unit of the ups tream input. Each firm has a constant unit cost of producing th e inputs. Furthermore, for simp licity, the two entrants have the same production costs. The entrants upstr eam and downstream unit costs are denoted by E uc and E dc respectively. The incumbents upstream and downstream unit costs are denoted by I uc and I dc respectively. The incumbent is the leas tcost supplier of th e upstream input (so E u I uc c), and the entrants are th e leastcost suppliers of the downstream input (so I d E dc c). When each firm uses its own inputs exclusively, the incumbent is the least cost supplier (i.e., I d I uc c < E d E uc c), as in the benchmark setting. An entrant can produce the retail product by comb ining its downstream input either with its own input or with the incu mbents input. If entrant i buys the input from the incumbent, it pays the incumbent unit price iw for i = A, B. The incumbent negotiates these prices sequentially, first with entrant A and then with entr ant B. The input price paid by entrant i cannot be linked explicitly to the input price paid by entrant j where j i and i, j = A, B. The input prices are determined by Nash bargaining. The timing in this setting with multiple entrants is as follows. First, the incumbent makes a binding commitment as to whether it will con tinue to serve retail customers (as it has historically) or it will pr ovide wholesale services exclusively. Second, the incumbent engages in Nash bargaining with entrant A. If the bargaining is successful the two parties agree on input price Aw. Third, the incumbent bargains with entrant B. If this Nash bargaining is successful, PAGE 116 116 the two parties agree on input price Bw If an entrant fails to negotiate an input price with the incumbent, that entrant will compete for reta il customers using exclusively its own inputs. Fourth, after all negotiations have been completed, the firms choose their retail prices simultaneously and independently. Because th e firms products are homogeneous, consumers purchase (at most one unit of) the product from the firm that offers the lowest price. For simplicity, all consumers are assumed to purchase th e product from entrant A as long as it is one of the firms that sets the lowest reta il price (and this pr ice does not exceed v). Finally, if an entrant has chosen to buy the input from the incumbent, the entrant procures the quantity of the upstream input required to meet the equilibrium demand for its retail product. The incumbents market participation decision, the negotiated input prices, and the entrants decisions to make or buy the upstream input are all known publicly. The solution to this problem is determined via backward induction, determining the outcome of the bargaining between the incumben t and entrant B first, taking as given the outcome of the bargaining between the incumbent and entrant A. Consider first the case where the incumbent decides to provide wholesale services exclusively. In this case, if both entrants successfully negotiate an input pr ice with the incumbent, the equi librium retail price will be the higher of the unit costs of the two entrants, } { maxE d B E d Ac w c w Entrant Bs profit function when it buys the input from the incumbent is B = } { [maxE d B E d Ac w c w B E d BQ c w )] ( where BQ is the equilibrium demand for en trant Bs retail product when both entrants successfully negotiate an input price with the incumbent. In equilibrium, entrant B will either serve all retail customer s or it will not produce at all. If the incumbent and entrant B cannot agree on an input pr ice, entrant B produces the upstream input itself. In this case, entrant Bs (sta ndalone) unit cost of producing the retail PAGE 117 117 product is E d E uc c and the equilibrium retail price will be } { maxE d E u E d Ac c c w when entrant A has successfully negotiated input price Aw with the incumbent. Entrant Bs profit will be B = B E d E u E d E u E d AQ c c c c c w )] ( } { [max where BQ is entrant Bs retail sales when it does not buy the upstream input from the incumbent. This profit will be en trant Bs threat point in its negotiations with the incumbent, follo wing a successful negotiation of input price Aw for entrant A. The incumbents profit following successful negotiation with both entrants is I = A AQ w + ] [B A I u B BQ Q c Q w where AQ is the entrant As retail sales when it buys the upstream input from the incumbent and entrant B buys th e input from the incu mbent at input price Bw.1 If the negotiation between the incumbent and en trant A is successful but the incumbent and entrant B do not agree on an input price, the incumbents profit will be I = A I u AQ c w ~ ] [ where AQ ~ is the level of entrant As retail sales when the incumbent and entrant A successfully negotiate an input price, but the incumbent and entrant B fail to do so. This profit is the incumbents threat level when it negotiates with entrant B, following successful negotiation with entrant A. The input price, Bw that arises from Nash bargaining in the second stage is the input price that maximizes the following function: BZ ] [ ] [I I B B (C15) 1 This is the maximum profit the incumbent can secure by nego tiating with the entrants. If this profit is less than the profit the incumbent can secure by refusing to negotiate with the entrants, the incumbent will not agree to negotiate. The incumbent always prefers to negotiate with both entrants than with just one entrant because the ability to negotiate with the second entrant should negotiatio ns with the first entrant fail allows the incumbent to secure a larger portion of the available surplu s in its negotiations with the first entrant. PAGE 118 118 BZ is not differentiable, but can be analyzed graphically. Figure C1 below plots the difference between the profit entrant B secures wh en an input price is negotiated successfully and its corresponding profit absent such su ccessful negotiation as a function of Bw. To derive Figure C1, observe that: B E d B E d B E d A B BQ c w c w c w )] ( } { max [ B E d E u E d E u E d AQ c c c c c w ] ) ( } { max [ (C16) To explore how B (entrant Bs profit if its negotiati ons with the incumbent fail) varies with Aw (the input price negotiate d by entrant A), first suppose Aw is less than the entrants upstream unit cost, E uc In this case, entrant B cannot comp ete profitably against entrant A in the retail market when entrant B produc es the input itself because entr ant As cost of producing the retail product is less than entrant Bs standalone cost. Consequently, if the input price negotiations between entrant B and the incumbent fail, entrant B will not serve any retail customers, i.e., 0BQ In this case, entrant A will serve all retail customers, so ~ N QA Substituting these values into Equation C2 provides: B E d B E d B E d A B BQ c w c w c w ] ) ( } { max [ when E u Ac w. (C17) Entrant B can profitably serve all retail customers at priceE d Ac w if it can secure a lower input price than entrant A has secured. Therefore, N QB if A Bw w, and so it follows from Equation C17 that: PAGE 119 119 N w w N c w c wB A E d B E d A B B] [ ] ) ( [ when E u A Bc w w (C18) If entrant B cannot secure a lo wer input price than entrant A has secured, entrant B cannot compete profitably against entrant A in the retail market, i.e., 0BQ for A Bw w. The equilibrium retail price in this case will be E d Bc w, and entrant A will serve all retail customers. Consequently, from Equation C17: 0 B B when A Bw w. (C19) Equation C18 and Equation C19 ar e reflected in Figure C1. The corresponding difference between the in cumbents profit when it successfully negotiates an input price with entrant B and its threat le vel of profit is: ] [B A I u B B A A I IQ Q c Q w Q w ] ~ ~ [A I u A AQ c Q w (C20) If entrant A is able to secure an input price below its upstr eam unit cost of production (i.e., if E u Ac w), entrant A will serve all retail customers if the negotiations between the incumbent and entrant B fail. Consequently, N QA ~ in this case. Equation C20 simplifies according to which en trant secures the lower input price. If entrant B secures an input price belo w entrant As input price (i.e., if A Bw w), entrant B will serve all retail customers. Consequently, 0AQ and N QB in this case. Substituting these values into Equation C20 provides: I I N w wA B] [ < 0 when A Bw w (C21) PAGE 120 120 If entrant B cannot secure a lo wer input price than entrant A has secured, then entrant A will serve all retail customers, and so 0BQ and N QA. Consequently, from Equation C19: 0 I I when A Bw w (C22) Equation C21 and Equation C22 ar e reflected in Figure C2. Equilibrium outcomes when E u Ac w can be determined by comparing Figure C1 and Figure C2. If entrant B s ecures a lower input price than entrant A has secured (so Bw < Aw ), entrant B will serve all retail customers in equilibrium, and the incumbents profit will be N c wI u B I] [ When Bw < Aw, this profit is lower than the profit the incumbent would secure if it did not negotiate an input price with entrant B, a nd so entrant A se rved all retail customers. Therefore, the incumbent will not agr ee on an input price for entrant B that is below Aw Consequently, entrant Bs unit production cost will exceed entrant As unit production cost, whether entrant B buys the upstream input from the incumbent or employs its own upstream input. Therefore, entrant B will not be able to operate profitab ly in the retail market when E u Ac w, and so will be indifferent among all input prices that are at least as high as Aw In summary, if entrant A secures an input price below E uc the incumbent and entrant B will subsequently negotiate an input pr ice that is at least as high as Aw Formally: A Bw w when E u Ac w. (C23) As noted, when Equation C23 holds, entrant A will serve all retail customers (so N QAand 0BQ ) by setting a price equal to entrant B s unit cost of production. Thus, if entrant B and the incumbent negotiate input price Bw, the equilibrium retail price in this case will be: PAGE 121 121 E d Bc w p (C24) Because entrant B is indifferent among all i nput prices that are at least as high as Aw when E u Ac w, Nash bargaining could produce multiple values for Bw. To account for these multiple values, let 0 x denote the difference between Bw and Aw Formally: x w wA B (C25) Equation C24 and Equation C25 imply that when E u Ac w the profits of the three firms will be: N x N w w N c w c wA B E d A E d B A ] [ ] ) ( [ ; (C26) N c wI u A I] [ ; and (C27) 0 B (C28) If the negotiated input price for entrant A exceeds E uc and the negotiations between entrant B and the incumbent fail, entrant B can profitably drive entrant A from the retail market when entrant A has committed to purchase the input from the incumbent. This is because entrant Bs standalone cost will be lower than entrant As un it cost under these circumstances. Consequently, from Equation C16: B E d B E d B E d A B BQ c w c w c w ] ) ( } { max [ N c c c wE d E u E d A] ) ( [ = B E d B E d B E d AQ c w c w c w ] ) ( } { max [ N c wE u A] [ when E u Ac w. (C29) If entrant B secures an input price below Aw, it will be able to serve all retail customers profitably (so N QBand 0AQ ). Consequently, from Equation C29: PAGE 122 122 N c w N c w c wE u A E d B E d A B B] [ ] ) ( [ N c w N w wE u A B A] [ ] [ = N w cB E u] [ when A Bw w. (C30) In contrast, if entrant B ne gotiates an input price above Aw, entrant A will serve all retail customers (and so N QAand 0BQ ). Consequently, from Equation C29: N c wE u A B B] [ when A Bw w. (C31) Equation C29 and Equation C30 ar e reflected in Figure C3. Now consider the corresponding payoffs for the incumbent. It follows from Equation C20 that: ] [B A I u B B A A I IQ Q c Q w Q w when E u Ac w. (C31) If B Aw w, entrant B will serve all retail customers in equilibrium. Therefore, in this case, Equation C31 becomes: N c wI u B I I] [ when } { maxB E u Aw c w (C32) In contrast, if B Aw w, entrant A will serve all retail customers. Consequently, from Equation C31: N c wI u A I I] [ when B A E uw w c (C33) Equation C32 and Equation C33 ar e reflected in Figure C4. A comparison of Figure C3 a nd Figure C4 reveals that BZ is negative except on the interval ] [E u I uc c Consequently, the value of Bw that maximizes Equation C15 in this interval will be the outcome of the Nash bargaining between the incumbent and entrant B when E u Ac w. Substituting Equation C30 and Equation C32 into Equation C15 provides: PAGE 123 123 2 B][][Z NcwwcI u BB E u= when E u Acw > (C34) Setting the derivative of Equation C34 equal to zero and solving for Bw provides: 0] [2= += Nwccw w ZBE u I u B B B => 2/][E u I u Bccw += (C35) Equation C35 reveals that the negotiated input price for entrant B will be the average of its upstream unit cost and the incumbents corresponding cost when E u Acw > Furthermore, because entrant B will serve all retail customers in equilibrium: NccwNcwcwE u I u A E d B E d A B2/)( ])( [ += ++=P ; (C36) 2/][][I u E u I u B IccNNcw ==P ;and (C37) 0 =PA. (C38) These second stage outcomes inform the determination of the first stage outcomes. The Nash bargaining between the incumbent and entrant A will produce an input price, Aw that maximizes: ] ][ [ZAI IA APPPP= (C39) AZ is not differentiable, but can be analyzed graphically. To do so, notice first that when the incumbent and entrant A agree on input price Aw entrant As profit, AP will be: APAE d A E d BE d AQcwcwcw ])(},{max[ +++ = (C40) The threat level for entrant A, AP in its Nash bargaining with the incumbent is the level of profit entrant A can secure if it competes using its own upstream and downstream inputs: A E d E u E d BE d E u AQcccwcc ])(} ,{max[ ++ + =P (C41) PAGE 124 124 Recall from the discussion preceding Equation C23 that if the incumbent and entrant A agree on an input price that is less than entrant A s upstream cost (i.e., if E u Ac w), entrant A will serve all retail customers and entrant B will not operate in equilibrium. Substituting 0BQ N QA and x w wA B into Equation C40 and Equation C41 provides: A E d E u E d B B d E u A B A AQ c c c w c c N w w ] ) ( } { max [ ] [ A E d E u E d A E d E uQ c c c x w c c N x ] ) ( } { max [ for E u Ac w. (C42) If x the difference between Bw and Aw is sufficiently small compared to entrant As upstream cost, entrant A will not be able to serve retail customers profitably if its negotiations with the incumbent fail. In particular, if x w cA E u the equilibrium retail price will be the stand alone cost of entrant A, AQ will be zero, and BQ ~ entrant Bs retail output when it successfully negotiates an input price but entrant A fails to do so, will be N. In this case, Equation C42 becomes: N xA A when x w cA E u (C43) In contrast, if x is sufficiently large, then even if the negotiations between the incumbent and entrant A fail, entrant B will not be able to operate profitably. In particular, if x w cA E u then N QAand 0 ~ BQ Consequently, from Equation C42: N c w N w wE u B A B A A] [ ] [ N w cA E u] [ when x w cA E u (C44) Recall from the discussion leading up to Equa tion C38 that if entrant A and the incumbent agree on an input price that is higher than the entrants upstream cost (i.e. if E u Ac w), entrant PAGE 125 125 A will not be able to serve retail customers profitably in equilibrium. Consequently, AQ and AQ both will be zero. Substituting 0AQ and 0AQ into Equation C40 and Equation C41 provides: 0 A A when E u Ac w (C45) Equation C43, Equation C44, and Equation C45 provide the relationship depicted in Figure C5. If the negotiations between the incumbent and entrant A fail, the incumbent is still able to negotiate with entrant B. The incumbents threat level in its Nash bargaining with entrant A, I, is the profit the incumbent can secu re from bargaining with entrant B: B I u B IQ c w ~ ] [ (C46) Recall from the discussion leading up to Equa tion C28 that if the incumbent and entrant A agree on an input price below E uc entrant B will not be able to produce profitably in equilibrium, and so entrant A will serve all retail customer s. Consequently, the difference between the incumbents profit and its threat level will be: N c wI u A I I] [ B I u BQ c w ~ ] [ when E u Ac w. (C47) BQ ~ varies with x the difference between Bw and Aw Recall from the discussion preceding Equation C43 that entrant A will not be able to serve retail customers profitably if x is sufficiently small (i.e., if x w cA E u ), and so 0AQ and N QB~ Consequently, from Equation C35: N c wI u A I I] [ N c wI u B] [ = N x N w wB A ] [ when x w cA E u (C48) PAGE 126 126 In contrast, recall from the discussion preceding Equation C31 that entrant B will not be able to serve retail customers profitably if x is sufficiently large (i.e., if x w cA E u ). Consequently, 0 ~BQ and Equation C47 reveals: N c wI u A I I] [ when x w cA E u (C49) Recall from the discussion leading up to Equa tion C35 that if the incumbent and entrant A initially agree on an input price above E uc entrant A will not be able to compete profitably against entrant B in equilibrium. Therefore, if E u Ac w, it follows from Equation C35 that the incumbent and entrant B will negotiate input price Bw = 2 / ] [E u I uc c. Substituting this value for Bw into Equation C47 reveals: N c c c N c wI u E u I u I u A I I] 2 [ ] [ N c c wE u I u A)] 2 ( [ when E u Ac w (C50) Equation C48 through Equation C50 provide Figure C6: Figure C5 and Figure C6 reveal that AZ is strictly negative when Aw x cE u, and zero when Aw E uc Therefore, Nash bargaining will pr oduce an input price in the interval [) ,E u E uc x c. The value of Aw that maximizes AZ in this interval will vary with the magnitude of x If x is sufficiently large compared to the in cumbents upstream cost advantage (i.e., if x 2 / ] [I u E uc c), Equation C39 implies: 2 A] [ ] [ Z N c w w cI u A A E u when x 2 / ] [I u E uc c (C51) In this case, the negotiated i nput price is determined by: PAGE 127 127 0 ] [2 N w c c w w ZA E u I u A A A => 2E u I u Ac c w (C52) If x 2 / ] [I u E uc c and so the input price for entrant A is as specified in Equation C52, 2 / ] [E u I u Bc c x w entrant A will serve all retail customers at price p = x cE d + 2 / ] [E u I uc c, and the profits of entrant A and the incumbent will be: N xA ; and (C53) 2 / ] [ N c cI u E u I when x ] [I u E uc c/2 (C54) Entrant B will not agree to an input price below its standalone upstream unit cost of production. Therefore, the largest feasible value for x is 2 / ] [I u E uc c. At this value of x the profits of the incumbent and entrant A are gi ven by Equations C53 and C54, respectively. If x 2 / ] [I u E uc c, the value ofAw identified in Equation C52 will lie outside the interval [E u E uc x c ,). Consequently, AZ is negative at Aw = 2 / ] [E u I uc c. AZ is decreasing in Aw at Aw = E uc x and so Nash bargaining will not produce an input price above E uc x AZ is negative when x c wE u A Therefore, the negotiated input price for entrant A will be Aw = E uc x if x < 2 / ] [I u E uc c. From Equation C25, this input price for entrant A will lead to a negotiated input price of E u Bc w for entrant B. The corresponding equilibrium retail price will be E d E uc c p Entrant B will earn zero profit under these circumstances, and the equilibrium profits of entrant A and the incumbent will be: N xA ; and (C55) PAGE 128 128 N x c cI u E u I] [ when x 2 / ] [I u E uc c (C56) The discussions leading to E quation C53 and Equation C55 reve al that in equilibrium, entrant B is never able to secure an input price below Aw. Because entrant B does not serve any retail customers in equilibrium in this case, it will be indifferent among feasible values of x Furthermore, because x cannot exceed 2 / ] [I u E uc c, the value of I in Equation C56 will exceed the corresponding value in Equation C54. Recall from the discussion following Equation C54 that the largest possible value of x is 2 / ] [I u E uc c. At this value of x E u Bc w (since 2 / ] [E u I u Bc c x w ) and E u Ac w x (since 2 / ] [E u I u Ac c w ). Also recall from the discussi on leading to Equation C55 that when x < 2 / ] [I u E uc c, E u Bc w and Aw = E uc x Therefore, in equilibrium, for every feasible value of x (i.e., for all x ] 2 / ) ( 0 [I u E uc c), the incumbent will negotiate input price E u Bc w with entrant B and input price Aw = E uc x with entrant A. Furthermore, the equilibrium retail price will be E d E uc c p for every x in the interval ] 2 / ) ( 0 [I u E uc c. Equation C56 reveals that the incumbent will prefer the smallest value of x that induces entrant A to negotiate with the incumbent. It remains to consider the possibility that th e incumbent might choose not to negotiate with the entrants. When the incumbent competes against the entrants in the retail market and all firms employ their own inputs, the equilibrium retail price will be E d E uc c, the entrants standalone unit cost. Due to its overall unit cost advantage, the incumbent will serve all retail customers and earn profit I = N c c c cI d I u E d E u] [ If E d I dc c x this profit will exceed the level of profit identified in Equation C56, and so the in cumbent will choose not to negotiate with the PAGE 129 129 entrants. In this case, industry costs will not be minimized because the incumbent will serve retail customers even though its downstream unit cost exceeds the downstream unit cost of the entrants. However, if entrant A will negotiate an input price with the incumbent whenever doing so ensures entrant A at least the profit it can secu re by refusing to negotiate with the incumbent, x will be zero in equilibrium, th e incumbent will negotiate with the entrants, and industry costs will be minimized. Proof of Proposition 4.5: If the entrant commits to buy the incumbents input at unit price w, the incumbents profit will be: I I d I u E I u I BN c c p N c w )] ( [ ] [ (C57) where EN and IN are the equilibrium outputs of the entrant and the incumbent, respectively, and p is the prevailing retail price. If th e incumbent sets a retail price above E dc w, the entrant will find it profitable to se t a lower price, thereby ensuring that 0IN and N NE. Consequently, from C57, the incumbents profit will be: N c wI u I B] [ (C58) Among all retail prices at or below E dc w, the most profitable price for the incumbent is E dc w. At this price, the incumbents profit is: N c w N c c c wI u I d I u E d I B] [ )] ( [ N c cI d E d] [ (C59) Because I d E dc c, C58 and C59 imply that the incumbent will always set retail price E dc w. This price precludes the entrant from making any profit when it commits to buy the input from the incumbent. Consequently, if I d I u E d E uc c c c the entrant will strictly prefer PAGE 130 130 to make the input itself rather than purchase the input from the incumbent. The same preference will hold weakly if I d I u E d E uc c c c (and strictly if input price ne gotiations entail any costs for the entrant). When the firms both produce their own input, the firm with the lowest overall unit cost of production will prevail in the marketplace and serve all N retail customers. Proof of Proposition 4.6: Let ) 1 0 ( L denote the location of the customer that is indifferent between purchasing from th e incumbent and the entrant. Thus: ] 1 [ L t p L t pE E I I (C60) where Ip is the retail price charged by firm ) (E I i Solving Equation C60 for L provides: ] [ / ] [ I E E I Et t t p p L (C61) It follows from Equation C61 that when the entrant decides to employ its own input, the profit of the entrant and incumbent are, respectively: [][]/[]EEEEIEIEI Aud p ccpptNtt and (C62) [][]/[]IIIIEIEEI Aud p ccpptNtt. (C63) Maximizing Equation C62 with respect to Ep and maximizing Equation C63 with respect toIp and then solving the resulting equations simultaneously provides: ] 2 2 2 [3 1 E d E u I d I u I E E Ac c c c t t p and (C64) ] 2 2 2 [3 1I d I u E d E u E I I Ac c c c t t p (C65) Substituting the equilibrium prices in Equa tion C64 and Equation C65 into Equation C62 and Equation C63 provides: )] ( 9 [ / ] 2 [2I E E d E u I d I u I E E At t c c c c t t N and (C66) PAGE 131 131 )] ( 9 [ / ] 2 [2I E I d I u E d E u E I I At t c c c c t t N (C67) When the entrant commits to buy the i nput from the incumbent at unit price w the incumbents profit will be: I B I d I u I B E B I u I BN c c p N c w ] [ ] [ (C68) where I Bp is the price set by the incumbent in this regime and E BN and I BN are the number of retail customers served by the entrant and th e incumbent, respectively. Equation C61 can be employed to determine E BN and I BN and thus I B, as functions of E Bp and I Bp Maximizing I B with respect to I Bp to obtain an Equation for the incumben ts profitmaximizing retail price as a function of E Bp performing an analogous exercise to deri ve the entrants profitmaximizing retail price as a function of I Bp and then solving the two equations simultaneously provides: 3 / ] 2 2 [E d I d I E E Bc c t t w p and (C69) 3 / ] 2 2 [I d E d E I I Bc c t t w p (C70) Substituting these equilibrium prices into Equation C68 and the corresponding Equation for the entrants profit provides the following equa tions for the equilibriu m profit of the entrant and the incumbent, respectively: )] ( 9 [ / ] 2 [2I E E d I d I E E Bt t c c t t N and (C71) N c w t t c c t t NI u I E I d E d E I I B] [ )] ( 9 [ / ] 2 [2 (C72) It follows from Equation C66 and Equation C69 that as long as 0 2 E d I d I Ec c t t and 0 2 E d E u I d I u I Ec c c c t t the entrant will prefer to buy the input from the incumbent (i.e., E A E B ) if and only if E u I uc c. PAGE 132 132 Also notice from Equation C69 and Equation C70 that E B is independent of w and I B is strictly increasing in w. Therefore, the input price determ ined by Nash bargaining will be the largest value of w that ensures the marginal customer (at locationL) will purchase the product. Consequently, this marginal customer will secu re no surplus, but other customers (with lower equilibrium transportation costs) wi ll secure positive surplus. Figure C1. The difference between the profit entrant B secures when an input price is negotiated successfully and its corresponding profit ab sent such successful negotiation as a function of Bw whenAw is less than the entrants upstream unit cost, E uc B B Bw N wA Aw PAGE 133 133 Figure C2. The difference between the profit the incumbent secure s when it negotiates an input price with the entrant B successfully and its corresponding profit absent such successful negotiation as a function of Bw whenAw is less than the entrants upstream unit cost, E uc I I Bw N wA Aw PAGE 134 134 Figure C3. The difference between the profit entrant B secures when an input price is negotiated successfully and its corresponding profit ab sent such successful negotiation as a function of Bw whenAw is higher than the entrants upstream unit cost, E uc B B N w cA E u] [ BwE ucAw PAGE 135 135 Figure C4. The difference between the profit the incumbent secure s when it negotiates an input price with the entrant B successfully and its corresponding profit absent such successful negotiation as a function of Bw whenAw is higher than the entrants upstream unit cost, E uc I I Aw Bw N cI u N c wI u A] [ I uc PAGE 136 136 Figure C5. 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In 2008, she began employment at Bo azii University. 