ABSTRACT STRATEGIES IN OLIGOPOLIES. This dissertation is part of the effort to contribute to our understanding of Price

Transcription

1 STRCT Title of Dissertation: ESSYS ON PRICE COMPETITION ND IRM STRTEGIES IN OLIGOPOLIES Heisnam Thoihen Singh, Doctor of Philosohy 007 Dissertation directed by: Professor Daniel Vincent Deartment of Economics University of Maryland, College Park This dissertation is art of the effort to contribute to our understanding of Price Cometition and irm Strategies in oligoolistic markets with certain characteristics. It comrises of three chaters. Chater rovides the introduction and background of the research and a brief summary of results. Chater : irms ractice oaching of their rival s customers in markets where they are able to identify between their own customers and those of the rivals. This ractice results in inefficiently high switching. In some of these markets firms also use strategies that make oaching by rival firms harder. In this chater I exlore the ractice of firms requiring customers to sign contracts that are of re-secified duration secifying early termination charges (or breach enalty). If contract with breach enalty is available,

2 firms find it rivately otimal to use it. However when all firms use it they are worse off and results in lower than efficient switching. Consumers may be better off or worse off. Chater 3: In this chater we examine the ricing decision of a tyical firm that sells more than one roduct in markets where roducts are strategic comlements and the firms have some market ower. We show that such a firm internalizes the strategic comlementarities when otimally choosing its rices leading to higher rices. We then emirically test and confirm in the US wholesale market for unbranded gasoline that a major refiner charges a higher wholesale rice for unbranded gasoline in cities where it also sells its brand gasoline at retail comared to cities where it does not. urthermore, in the cities where the refiner has brand resence at retail we find emirical evidence that its wholesale rice of unbranded gasoline is higher the higher is the market share of its brand in retail.

3 ESSYS ON PRICE COMPETITION ND IRM STRTEGIES IN OLIGOPOLIES y Heisnam Thoihen Singh Dissertation submitted to the aculty of the Graduate School of the University of Maryland, College Park in artial fulfillment of the requirements for the degree of Doctor of Philosohy 007 dvisory Committee: Prof. Daniel Vincent, Chair Prof. Roger etancourt Dr. Ginger Jin Prof. Peter Cramton Prof. John Horowitz

4 Coyright y Heisnam Thoihen Singh 007

5 DEDICTION To my arents for their constant suort. ii

6 CKNOWLEDGEMENTS I owe a big debt of gratitude to my advisor Professor Daniel Vincent, who has been a source of insirational insights and a brilliant guide. His guidance and insights were invaluable. I would also like to thank committee members Professor Roger etancourt, Professor Ginger Jin and Professor Peter Cramton for all their hel and encouragement. I would also like to thank Dr. Deborah Minehart for her helful comments and suggestions. I would also like to acknowledge Utsav Kumar, Piyush Chandra, bhishek Kashya for all the helful discussions. Last but not the least, I would like to thank my wife, Linthoi ngom who has been a constant source of strength and suort, esecially during my hardest times, and who has always believed in me and has heled make everything ossible iii

7 Contents Dedication ii cknowledgement..iii Contents...iv List of igures vii List of Tables viii. Chater : Introduction.. Motivation and Introduction to Chater.... Motivation and Introduction to Chater Chater : Countering Consumer Poaching: The case of Contracts with reach Penalties.9. Introduction..9. The Homogeneous Product Model... The ase Model.....a Second eriod Cometition.....b irst Period Cometition Contract with reach Penalty..7.3 Ex-ante Homogeneous Ex-Post Product Differentiation Model 0.3. No Contract with reach Penalty case 0.3.a Second Period Cometition....3.a Socially efficient Switching.5 iv

8 .3.b irst Period Cometition Contract with reach Penalty.9.3.a Second Period Cometition b Equilibrium Switching Outcome b irst Period Cometition Conclusions Strategic Comlementarities and the Incentive to Raise Prices: Evidence from the US Wholesale Gasoline Market Introduction The Model Case I Case II brief descrition of the US Wholesale Gasoline Industry Evidence from the US Wholesale Market for Unbranded Gasoline: Data and Emirical Estimation Conclusions 66. endix to Chater.69. Proof of Proosition 69. Proof of Proosition 7.3 Proof of Proosition Proof of Proosition Proof of Proosition Derivation of Otimal Penalty...85 v

9 . endix to Chater Matlab Codes and Results..86.a. Case I: The Three firm Case 86.b. Case II: The two firm Case..88 ibliograhy...00 vi

10 List of igures igure. ase Model: Cometition in s first eriod customers market segment. igure.. ase Model: Cometition in irm s first eriod customers market segment.3 igure.3 Efficient mount of Switching...6 igure.4. CWP: Cometition in s first-eriod customers segment...30 igure.5. CWP: Cometition in irm s first eriod customers market segment...3 igure 3.. Product Locations and Demand Regions.44 igure 3. US Gasoline Industry Structure.5 igure. United States PDD Ma.97 igure. Ma of City Terminals in the United States.98 igure.3 verage weekly rice of unbranded gasoline by refiner tyes 99 vii

11 List of Tables. Table Table Table Table.0 Equilibrium rices comarison of the two cases for different values of c..90 Table. List of City Terminals selling wholesale unbranded Gasoline During ugust Table. Refiners selling unbranded gasoline during ugust Table.3. City-Terminals where Marathon sells both unbranded and branded gasoline..95 Table.4. City terminals where Marathon sells only unbranded gasoline.96 viii

12 Chater. Introduction. Starting from the seminal aer by ertrand, which led to the introduction of the ertrand Paradox, rice cometition among oligoolistic firms has always been a rich area of research for both Industrial Organization Theory and lied Microeconomics. Unlike in erfect cometition or a monooly, firms in an oligoolistic market structure face an environment where rival firms anticiate their actions and counter them. irms therefore need to make strategic decisions based on the information available to them. In the short run, one of the most imortant strategic choice variables is the rice (others include advertising and sales intensity). The otimal choice of rice is often the most imortant strategic decision facing businesses and therefore the study of strategic rice cometition not only has a strong academic aeal but also a useful ractical side. However rice cometition never occurs in a vacuum. There always exist other instruments or conditions which either facilitate or hinder rice cometition. There is a vast economic literature, both theoretical and emirical which studies rice cometition in the resence of these other instruments or conditions dating back to Edgeworth (897) and Hotelling 3 (99). Edgeworth looked at rice cometition with firms facing caacity constraints in the sense that they cannot sell more than they are caable of roducing. ertrand, J Theory Mathematique de la Richesse Sociale. Journal des Savants, The Pure Theory of Monooly, in Paers Relating to Political Economy, volume, ed.. Edgeworth ( London: Macmillan, 95) 3 Hotelling, H. 99 Stability in Cometition Economic Journal

13 Hotelling introduced roduct differentiation in the form of transortation cost. Introducing these extra conditions led to the resolution of the ertrand Paradox! This dissertation is art of the effort to contribute to our understanding of rice cometition and firm strategies in oligoolistic markets with certain unique characteristics. It comrises of three chaters. Chater rovides the introduction and background of the research work. In chater we study rice cometition in markets where firms can identify between its own customers and rival firms customers and where switching costs are resent. In such markets, firms often comete for new and rival firm s customers by offering discounts to entice them to switch suliers, a ractice known as consumer oaching. This chater looks at the common ractice in the cellular hone service industry in the US of requiring customers to sign contracts with early termination fees as a means to counter consumer oaching. Chater 3 looks at rice cometition in markets where strategic comlementarities are resent and look at otimal ricing decisions of firms that sell two roducts that are strategic comlements. In a simle model we show that such a firm internalizes these comlementarities while otimally choosing rices and as a result charges a higher rice comared to a firm that sell only one roduct. We then find emirical evidence for the above in the wholesale market for gasoline in the United States. In such local wholesale markets for unbranded gasoline, we find that refiners that sell both branded and unbranded gasoline charge a higher rice for unbranded gasoline comared to refiners that sell only unbranded gasoline.. Motivation and Introduction to Chater :

14 Chater looks at markets that have a unique feature commonly observed in subscrition markets for services for examle, the credit card market, cable and longdistance telehone service, insurance market, etc. In such market, firms that rovide the services can usually identify between their own customers and rival firm s customers. irms in these markets ractice oaching, i.e., enticing the rival firm s customers to switch suliers by offering discounts. We examine rice cometition in such markets in which consumers incur costs to switch between firms and are thus artially locked in. irms on the other hand can rice discriminate between its locked customers and new customers (or rival firm s customers). Price Cometition in the resence of switching costs has received wide attention in the literature 4. Von Weiszacker 5 (984) first looked at a model with switching costs and showed that higher switching costs may make markets more cometitive. The reason is that higher switching cost combined with uncertain consumer future tastes makes consumers more farsighted. Current choices are influenced more by the future, making current references less imortant and therefore making the roducts less differentiated. Klemerer 6 (987) observes rightly that the above conclusion deends on the assumtion that firms would charge the same rices in subsequent eriods. In a model which allowed firms to charge a different rice in later eriods, Klemerer showed that the resence of switching costs make demand more inelastic in both the initial and subsequent eriods and may make market less cometitive in both eriods. Chen 7 (997) extends 4 See, for examle, Klemerer (987a, b), arrell and Shairo (988), eggs and Klemerer (99), Padilla (99, 995). Klemerer (995) rovides an excellent survey of the literature 5 Von Weizsacker, C. C. The Costs of Substitiution Econometrics, Vol. 5(984), Klemerer P. The Cometitiveness of markets with switching costs Rand Journal of Economics. Vol. 8 (987a) Chen, Y. Paying Customers to Switch, Journal of Economics and Management Strategies, vol. 6(997)

15 Klemerer s case to allow firms to rice discriminate between existing customers and new customers and showed in a two-eriod homogeneous good duooly model that firms are worse off engaging in this ractice of rice-discrimination (or oaching) and results in excessive switching in equilibrium. In his model however, switching is always inefficient because net of the switching costs consumers are identical and goods are homogeneous. Taylor 8 (003) looked at the case where there are more than two firms and showed that the market becomes fully cometitive only when there are more than two firms. Each firm earns economic rent on its customer base but zero economics rofit. The fully cometitive equilibrium leads to higher (inefficient) switching. The above aers miss one imortant feature that is common in the US cell hone service industry. Service roviders commonly require new customers to sign fixed length contracts secifying early termination charges (breach enalty) if they switch roviders before the end of the contract. This rovides an instrument to the firms to counter consumer oaching by rivals. Introduction of this new feature changes the structure of the rice cometition in two imortant ways, () switching costs become endogenous through contractual rovisions and () firms are able to commit to second eriod rices through the contract. I examine a two-eriod duooly model where firms are homogeneous in the first eriod but in the second eriod, firm secific tastes (in the manner of Hotelling) and switching costs emerge and where one or both firms offer a two eriod ricing contract along with a breach enalty. Note that desite ex ante homogeneity, firms earn ositive rofits because there is ex ost differentiation in the second eriod. I show that, when 8 Taylor, C Sulier Surfing: Cometition and Consumer ehavior in Subscrition Markets RND Journal of Economics, Vol. 34, no. Summer 003,

16 contracts are feasible, not using contracts does not survive iterative elimination of dominated strategies. Offering a contract with breach enalty (CWP) is an otimal resonse. If the rival firm is not locking in customers, the other firm wants to. However in equilibrium when all firms use CWP first eriod cometition yields lower firm rofits than would occur if contracts were not feasible. lso comared to the revious literature, in the equilibrium with CWP there is less switching than is socially efficient. Contracts revent some efficient switching. The result is quite interesting because it has been often commented uon that this ractice disadvantage customers by locking them in and conversely, firms rofit by using this ractice. In fact, we find that the oosite is true.. Motivation and Introduction to Chater 3: Chater 3 looks at Price Cometition in markets with strategic comlements. The industry I study is the wholesale markets of gasoline in the United States where branded and unbranded gasoline are considered strategic comlements. In a seminal aer, ulow, Geanakolos and Klemerer 9 (985) introduced the concet of strategic comlements and substitutes. In oligoolistic markets the distinction between strategic comlements and substitutes is determined by whether a more aggressive strategy by one firm raises or lowers the other s marginal rofit from an increase in its own strategy. In short, two roducts are defined as strategic comlements in rice if an increase in rice of one roduct increases the marginal rofitability of raising the rice of the other roduct. The converse is true for strategic substitutes. We examine the ricing decision of a firm that sells more than one roduct in markets where roducts are strategic comlements and the firms have some market ower. In a simle theoretical model I 9 ulow, J., Geanakolos, J., Klemerer, P. Multimarket Oligoolies: Strategic Substitutes and Comlements, Journal of Political Economy, 985, vol. 93, no. 3 5

17 show that a firm that sells two roducts that are strategic comlements internalizes these comlementarities when otimally choosing the rices. It results in higher rices comared to a firm that sells only one roduct. In the emirical art of the chater, I find evidence of the above in the wholesale market for unbranded gasoline in the United States. There has been some amount of revious emirical literature on the wholesale gasoline industry in the United States (see Kaoor (003), Hastings 0 (004), etc). orenstein and Sheard (00) find that wholesale rices of gasoline resond with a lag to crude oil cost shocks due to the resence of adjustment cost in roduction and inventory. They also find that refiners have market ower in the wholesale markets and that those with more market ower adjust more slowly. Pinske, Slade and rett (003) finds that cometition is highly localized in the wholesale market for unbranded gasoline. The emirical art of chater 3 is closest to Gilbert and Hastings 3 (005) who examined the relationshi between vertical integration and wholesale rices of gasoline. They looked at the 997 acquisition by Tosco of Unocal s west coast refining and retailing assets and find evidence consistent with the strategic incentive to raise rivals cost. They concluded that, in the resence of ustream market ower, changes in vertical market structure can have substantial imact on ustream firm conduct and on equilibrium rices. In the United States wholesale market for gasoline, the sellers are the refiners who may be either Majors, like P, Shell, Chevron, etc. or Indeendent refiners who do not 0 Hastings, J. Vertical Relationshis and Cometition in Retail Gasoline Markets: Emirical Evidence from Contract Changes in Southern California merican Economic Review, March 004 orenstein, S. and Sheard,. Sticky Prices, Inventories, Market Power in Wholesale Gasoline Market Rand Journal of Economics vol. 33 no. Sring Pinske, J., Slade, M.E., rett, C. Satial Price Cometition: Semi Parametric roach Econometrica Vol. 70, No. 3 (May 00) Gilbert, R. and Hastings, J. Market Power, Vertical Integration and the Wholesale Price of Gasoline, Journal of Industrial Economics, vol. 53, no. 4 (December 005)

18 have a brand name at retail. Majors sell both branded and unbranded gasoline at many wholesale markets whereas Indeendent refiners sell only unbranded gasoline. So majors that sell both tyes of gasoline at a market have a strategic incentive to internalize the comlementarities when otimally choosing rice. In our emirical section we looked at the rice of unbranded gasoline charged by refiners that sell both branded and unbranded gasoline at the wholesale markets comared to rice charged by refiners selling only unbranded gasoline. We erform two tyes of emirical exercises deending on the scoe of the data available. The first exercise is for the whole set of refiners (firms) selling wholesale unbranded gasoline in the United States and for all city terminals located in the United States in the time eriod of our analysis. or this dataset we only have information on whether a refiner sells only unbranded gasoline (one roduct) or both unbranded and branded gasoline (two roducts) but no additional information on the market shares of the refiners. The main result of this exercise is that refiners that sell both unbranded and branded gasoline at a city terminal charge a higher rice for unbranded gasoline comared to refiners that sell only unbranded gasoline. The second emirical exercise is done for a major refiner, Marathon Petroleum, which oerates in 99 city terminals (wholesale markets). The wholesale dataset is augmented with the share 4 of Marathon brand retail stations. This share is a roxy for the market share of Marathon s branded gasoline. Marathon has retail brand resence in a little more than half of the 99 markets (city terminals) where it sells wholesale unbranded gasoline. The main results of this emirical exercise are the following. irst, we find that Marathon charges a significantly higher rice for unbranded gasoline in those markets 4 y share here, we mean the share retail stations selling Marathon rand gasoline to the total number of retail stations in the market. This is a roxy measure for the market share of Marathon rand Gasoline at the wholesale level. 7

19 where it also sells branded gasoline (i.e., has retail brand resence). This results in similar to the result obtained from first exercise. Second, the share of Marathon brand retail stations has a ositive and significant imact on the rice Marathon charges for unbranded gasoline. This suggests that the gain from internalizing the strategic comlementarities is increasing in the market share of the second roduct. Third, in a non-linear secification of the reduced form estimation, we find that the rice of unbranded gasoline charged by marathon is concave in the share of its branded retail stations. inally, we find that the number of refiners selling unbranded gasoline in the wholesale market has a negative and significant imact on the rice of unbranded gasoline charged by Marathon. This result confirms the acceted view that cometition at the wholesale level is imortant for keeing rices low. 8

20 Chater. Countering Consumer Poaching: The case of Contracts with reach Penalty.. Introduction In many business settings firms are able to identify between their own customers and new (rival firm s) customers. In such settings firms often ractice ricing olicies where they offer discounts to new (rival firm s) customers in markets with switching costs. n examle of a market where such a ricing olicy is commonly observed is the market for long distance telehone services in the United States where rival firms routinely offer discounts (monetary or in the form of free long distance minutes of comarable monetary value) to rival firm s customers to switch. Others examles are the market for credit cards and the market for high-seed internet service. This tye of cometition where firms offer consumers enticement to switch suliers is common in subscrition markets for homogeneous goods [Taylor 003]. In a two eriod homogeneous good duooly model, Chen [97] showed that in equilibrium firms are worse off engaging in this ractice of oaching on rival firm s customers than if they can t discriminate between customers. urthermore consumers need not necessarily benefit from it. There is excessive switching in equilibrium. Since switching is never 9

21 efficient in a homogeneous goods model with switching cost the dead weight loss to society of switching is higher. Taylor [003] extended Chen s results for the case where there are more than two firms in the market and showed that the market becomes fully cometitive only when there are more than two firms. Each firm earns economic rent on its customer base but zero economics rofit. n interesting result that he showed was that the fully cometitive equilibrium leads to higher (inefficient) switching. It is interesting to note that the above aers have focused on only one art of the business ractice by the firms, viz. trying to oach on rival firms customers. However firms also develo strategies that make it harder for rival firms to entice their resent customers to switch or in the event they actually switch, the firm can extract some rent from their rivals. or examle it is common ractice in the US Cellular hone industry for customers to sign contracts (one year or two years) with the service rovider. Such a contract secifies rice for the length of the contract and an early termination fee (breach enalty) if the customer switches to a different rovider before the contract exires. This is an instrument, which increases the switching cost of the consumers. In the light of the results of the above aers my research questions are the following. Could the ractice of contracts with breach enalties be used by firms as an instrument to mitigate excessive oaching by rival firms? How does the equilibrium with contracts and enalties comare to the one when firms can t use this ractice? In articular how do firms rofits comare when they can use contracts with enalties? 0

22 I look at a model where firms are homogeneous in the first eriod but in the second eriod switching costs and ossibly, firm secific tastes emerge. I examine two cases. The ase Case is like Klemerer (987 a) and Chen (999), where firms comete in each eriod. irms can identify incumbent customers and charge them different rices. In the Contract with reach Penalty (CWP) case, one or both firms offer a two eriod ricing contract along with a breach enalty in the first eriod. Note that desite ex ante homogeneity, firms earn ositive rofits because there is ex ost differentiation in eriod. In the base case, firms rice below marginal cost in the first eriod, and comete vigorously in the second eriod for rival customers. Comared to the efficient outcome, there is excessive switching. In CWP, I show that offering a contract with breach enalty is rivately otimal. If the rival firm is not locking in customers, the other firm wants to. In CWP, there is less switching than is socially efficient. Contracts revent some efficient switches. lso I find that in CWP, first eriod cometition yields lower firm rofits than would occur if contracts were not feasible.. The Homogeneous roduct model.. The ase Model Consider the two eriod homogeneous good duooly model. There are two firms and selling a homogeneous good. oth firms roduce the good at a constant marginal cost c. There is a continuum of consumers with mass normalized to one. There are two eriods and each consumer demands a unit of the good in each of the two eriods. Consumers have high enough reservation value for the good that all consumers buy one unit of the good in each eriod. In the second eriod if a consumer switches

23 firms, she incurs a switching cost (exogenous), s, which she learns rivately at the beginning of the second eriod. We assume that s is distributed uniformly over the interval [0,]. irms have a discount factor δ and consumer have a discount factor, δ C. We assume that 0 δ δ. In the second eriod firm can tell whether a consumer is C its first eriod consumer or that of the rival. So the firm can oach (rice discriminate) on the consumers of the rival firm in the second eriod. s a benchmark case, let us consider the case where long term contract with breach enalty is not available as an instrument to the firms...a Second Period Cometition In the second eriod each firm has an established market share from the first eriod, α for and α for firm. irm i chooses two rices in the second eriod: a rice ii that it charges to its revious eriod customers and another rice, ij to the firm j s revious eriod customers who switch to i in the second eriod (i, j or ). Now consider the marginal consumer of firm who is indifferent between switching to or staying with. Her realization of switching costs, s is such that the following is true. s s Let q ij be the mass of consumers who bought from j in the first eriod and from i in the second eriod. Then,

24 q α [ ( s)] α[ ] and, q α ( s) α[ ] Similarly, consider the marginal first eriod consumer of firm who is indifferent between switching to or staying with. She has an s such that the following is true, s s Then, q ( α)[ ( s)] ( α)[ ] and, q ( α ) ( s) ( α)[ ] The second eriod rofit of firm can then be written as: π ( ( c) q ( c) α[ c) q ] ( c)( α)[ ] The first term is the rofit from first eriod customers who choose to stay with in the second eriod and the second term is rofit from the rival firm s first eriod customers who switch to firm in the second eriod. Similarly, s second eriod rofit is given by: π ( ( c) q ( c)( α)[ c) q ] ( c) α[ ] 3

25 irm chooses and to maximizeπ taking second eriod rices of firm as given and firm chooses and to maximize π taking second eriod rices of firm as given. The first order conditions yields the following best resonse functions of firm and : ( c ) ( c ) ( c ) ( c ) The second order sufficient conditions are satisfied. Solving the above equations simultaneously yields the unique Nash equilibrium rices of the second eriod stage game. and c c 3 3 Note that in the equilibrium firms charge a lower rice to rival s first eriod customers to induce them to switch. There is second eriod switching in the equilibrium. In fact, onethird of the total customer oulation switch firms in the second eriod. Given that the roduct is homogeneous and switching is costly this is clearly inefficient Substituting the second eriod equilibrium rices in the firms second eriod rofit we can derive the following second eriod equilibrium rofits of the firms: 4

26 π π α 9 3 ( α) 9 3 Note that, the second eriod rofits of each firm is increasing in its first eriod market share. irms comete for market shares in the first eriod...b irst Period Cometition Consider consumer s choice of firms in the first eriod. Since both firms charge the same rice in equilibrium in the second eriod, consumer s choice of firms in the first eriod deends solely on the first eriod rices. Since consumers are ex-ante identical, all consumers will choose, ( i. e., α ) if the first eriod rice of is less than that of, i.e., <. Conversely all consumers will choose, ( i. e., α 0) if >. If, we assume that consumers choose and with equal robability. So if. Proosition. There exists a unique subgame erfect equilibrium of the game. The subgame α erfect equilibrium is characterized as follows. In the first eriod both firms charge the same rice: δ c 3 and in the second eriod each firm chooses rices ii and ij otimally as described in the revious section. 5

27 The formal roof is given in the aendix. The intuition is simle. ecause of the resence of switching cost in the second eriod, firms can charge a higher rice to its customers in the second eriod. irms earn ositive rofits in the second eriod which are increasing in first eriod market shares. So firms comete for market share in the first eriod. This leads to intense rice cometition in the first eriod yielding first eriod rices less than marginal cost. The firms earn the same two-eriod equilibrium discounted rofits given by: π π δ c 3 δ c δ > 0 Note that firms earn ositive rofits. This is because each firm can guarantee itself of at least the equilibrium rofit by not cometing in the first eriod and oaching on its rival firm s customers in the second eriod. So equilibrium rofits are not driven down to zero. This equilibrium rofit is however known to be lower 5 than that if firms were not able to oach on rival firm s customers in the second eriod. The exected surlus of a consumer who bought from firm i in the first eriod can be exressed as: i EU v ) δ [( v ) q ( v E[ s switch]) q ] ( i c ii ii ji ji The first term is first eriod surlus and the second term is discounted second-eriod exected surlus. The first term of which is surlus if the consumer stays with the same firm in the second eriod times the robability that she will stay and the second term is exected surlus of switching in the second eriod times robability of switching. In 5 Chen [97] has shown this to hold true. CHEN, Y. " Paying Customers to Switch " Journal of Economics and Management Strategies, Vol. 6(997),

28 equilibrium the exected consumer surlus of buying from firm is the same as that buying from firm and is given by: EU i ( v c)( δ ) c 3 5 δ c 8.. Contracts with reach Penalty (CWP) Definition : contract with breach enalty (CWP) is a 3-tule ( i, ii, τ i ) where i and ii are defined as before and τ i is a breach enalty to be aid by the first eriod customer if she switches to firm j in the second eriod. Consumer s first eriod choice: We assume that consumers are rational and they have a discount factor, δ c. rational consumer will choose over if her exected consumer surlus from choosing in the first eriod is greater than that from choosing., i.e., EU > EU where, i EU ( v i ) δ c[( v ii ) qii ( v ji E[ s switch]) q ji ] ssume that consumers discount future more than firms do, i.e., 0 δ δ c Proosition : If Contact with reach Penalty (CWP) is available as an instrument then no strategies that involve not using CWP survive iterative elimination of weakly dominated strategies. In other words if CWP is feasible then any strategy that involve not using CWP is not otimal. Conversely firms will always choose a strategy that involves using CWP. We 7

29 show that if firm doesn t use CWP and it chooses rices otimally then firm can do better by using CWP which stos its first eriod customers from switching to firm in the second eriod. See aendix for the formal roof. Proosition states that in the game where contracts are feasible both firms will use contracts. The equilibrium outcome of the game turns out to be unique. oth firms use CWP and slit the market in the first eriod. The first eriod rice charged by both firms is c δ ( v ) and the second eriod contract rice and oaching rice are i c v and c resectively. The outcome however can be suorted by multile equilibrium strategies as shown in roosition 3 below. These strategies differ only in one asect, the enalty level. The rices remain the same. ny enalty, τ v c, comletely stos switching and hence any enalty level greater than that threshold are economically equivalent as it ertains to the outcome of the game. i Proosition 3: There exists a unique family of subgame erfect equilibria of the game (one equilibrium for each enalty level) in which both firms use CWP and the equilibrium strategies are as below: In the first eriod firm i offers the contract: i c δ ( v c) ii v τ v c i and in the second eriod, ij ij ( c τ ) jj c if τ j > jj j if c τ j jj c 8

30 The roof is given in the aendix. The second eriod rofit of firm can be exressed as: π α( c) α( c τ ) q ( α)( c) q The second term is firm s net loss arising from firm s oaching on its customers. We say net because loses sales revenue from consumer leaving it but receives rent in the form of enalties from the consumers who do leave. This net loss can be non-ositive only if τ c. ut then q 0. The intuition is simle. long the relevant range of rice where will rofitably oach, it is never rofitable for to let oach, i.e., its rent from enalties is always less than its loss from oaching. can assure itself of a non-ositive loss by choosing a enalty, τ c, which stos switching comletely. t the roosed equilibrium, the second eriod oaching rice is, ij c. There is no switching in equilibrium and since switching is costly, this is efficient. The second eriod equilibrium rofit for firm reduces to π α( ). This is c increasing in the first eriod market share, α. The two eriod discounted rofit for firm can be exressed as: π α[( c) δ ( v c)] The same argument is true for firm too. So firms comete for market share in the first eriod in the ertrand fashion. This drives down the first eriod rice and rofit until equilibrium discounted rofit is zero. So firms are worse off when CWP is feasible than when it is not. In equilibrium, the exected two-eriod discounted consumer surlus is 9

31 EU i ( v c)( δ ) Comaring with the exected discounted consumer surlus from the model with no CWP, we find that EU i 3 δ 8 i > EU if and only if δ c >. So, in this range of firm s 3 and consumer s discount factor, consumers are better off when firms use CWP. However firms are worse off. In the above model when roducts are comletely homogeneous, the equilibrium enalty is not unique. This is because equilibrium enalty so high that it stos switching comletely and so in the equilibrium, enalties do not affect switching at the margin..3 Ex-ante Homogeneous Ex-ost Product Differentiation Model. We enrich the revious model by allowing for horizontal roduct differentiation in the second eriod. The motivation is the following. Consumers are inherently heterogeneous in their references for the roduct. In the first eriod when a customer is considering urchasing the roduct from some firm, she does not have enough information to differentiate between the various roducts offered and hence view them as homogeneous roducts. However in the second eriod when she has exerienced one roduct for sometime, the true characteristics are revealed and she knows exactly how close the roduct is to her ideal roduct characteristics. ssumtion : Second eriod location of consumer, x is uniformly distributed over [0,] ssumtion : irm located at 0 and irm is located at. ssumtion 3: Second eriod switching cost is distributed over the unit interval, [0,]..3.. No CWP case. 0

32 Let us now look at the case when CWP is not available as an instrument to the firm..3.a: Second Period Cometition. The marginal first eriod customer of firm realizes a -tule (x, s) such that the following holds: x ( x) s Cometition in irm s first eriod customers market segment yields the following demands. igure. shows the demand regions for a tyical set of rices. q q rob(x s > q ) for 0 s, 0 x s q q 0 x x s igure.. Cometition in s first eriod customers market segment. The above shaded region reresents the s first eriod customers who switches to firm in the second eriod, for a given the set of rices,, ). In other words, s (

33 oaching in firm s first eriod customers market segment which is given below for different ranges of and. q ( ) [ ( )] ( 4 ) if if if if if 0 < > 0 Note that, the first two ranges reresent cases where the oaching rice by firm is greater than the second-eriod rice to own-customer by firm. Here, firm is not actively oaching, and switching may occur only due to extremely bad realization of the location random variable, x combined with a realization of a low enough switching cost, s. The last two ranges shows cases where the oaching rice by firm is too low comared to the second-eriod rice to own-customer by firm. It is shown in the aendix that it is never rofitable for firm to oach in these ranges. The relevant oaching region is given by the third range, i.e., 0. We will describe the equilibrium in this oaching range. Similarly for marginal first eriod customer of firm : ( x) x s nd cometition in s first eriod customers market segment yields the following demands: q q rob(x s > q ) for 0 s, 0 x

34 igure. shows the corresonding demand region for a tyical set of rices,, ). ( q s q 0 x x s igure.. Cometition in irm s first eriod customers market segment. nalogously, the shaded region reresents firm s oaching of firm s first eriod customers for a given set of rices,, ) and this is given below for all range of the rices,, ). ( ( q ( ) [ ( )] ( 4 ) if if if if if 0 < > 0 3

35 s before, irms and maximize their second eriod rofit by choosing a set of two rices, one for its own first eriod customers and another a oaching rice. The roblem is symmetric for both firms. Let us look at firm s maximization roblem. irm s second eriod rofit is: π α( c)( q ) ( α)( c) q The first term is rofit from s first eriod customers who stay with it in the second eriod and the second term is rofit from oaching on s first eriod customers. Let us focus on the relevant oaching region where 0 and 0. Plugging in the demands for the above regions, the second eriod rofit for firm is then given by: π α 4 { α( c) [ 3 ( )] ( )( c) [ ( )]} irm chooses and to maximize π which yields the following best resonse functions: R ( ) c 3 R ( ) c Similarly, s best resonse functions are: R ( ) c 3 R ( ) c 4

36 Solving the above best resonse functions yields the unique Nash equilibrium rices of the second eriod sub-game. 7 c and c The second eriod equilibrium rofits are: 5 5 π α and π ( α) It is easy to check that the above set of equilibrium rices are indeed in the relevant oaching regions discussed earlier and that there is switching in the equilibrium. In articular the roortions of first eriod customers who switch firms in the second eriod for both firms are the same given by: q q 5 So in equilibrium a little less than half of the customers switch firms. Comared to the case with no second eriod roduct differentiation, equilibrium switching is higher. This is not surrising. In the first case, since the roducts are homogeneous, switching by a customer is solely motivated by the difference in the second eriod offered by its first eriod firm and the second eriod oaching rice of the rival firm. With roduct differentiation there is another incentive for consumers to switch that arises due to the realization of their true references in the second eriod. Socially Efficient mount of Switching. In this model switching is not altogether inefficient as was the case with the first model when any switching is socially inefficient. This is because for consumers with realizations of low enough switching cost, s and strong reference for the rival firm, it is 5

37 efficient to switch. However we will show that there is excessive switching in equilibrium. Efficient switching arises when switching is solely motivated by the relative trade-offs between the switching cost, s and the second eriod reference arameter, x and not due to difference in second eriod rices. This imlies that socially efficient switching occurs when and. Plugging these values in the demands we get the socially efficient amount of switching, q q 4, i.e., social efficiency entails that one-fourth of the market switches firms in the second eriod. See figure.3. So there is excessive switching in equilibrium. s q s q o x s x o x x s igure.3. Socially efficient switching. Note that, similar to the first model, the second eriod rofit is increasing in first eriod market share. This will have imlications for first eriod rices as firms comete for market share in the first eriod. 6

38 .3.b: irst Period Cometition. We assume that consumers are rational in the following sense. consumer will choose the firm that gives the highest exected consumer surlus for the two eriod given first eriod rices. Since the second eriod rices for the two firms are the same in equilibrium consumers will choose firms solely on the basis of the first eriod rices. nd since all consumers are ex-ante identical all consumers will choose over if the first eriod rice of is lower than that of and vice versa, i.e., α if < and α 0 if >. s before we assume that consumers choose and with equal robability if they charge the same first eriod rice, i.e., α if. Proosition 4: There exists a unique symmetric sub-game erfect equilibrium of the game in which contracts(cwp) are not feasible. The strategies are as follows: In the first eriod firm i chooses δ i c and in the second eriod it chooses 3 ii and ij otimally as described in the last section. The firms slit the market in the first eriod, i.e., α. The equilibrium two-eriod discounted rofit of the firms is: π π 5 δ 7 The formal roof is similar to that of roosition and is given in the aendix. heuristic exlanation follows. The two-eriod discounted rofit for firm and can be written as: 7

39 π π ( ( 5 c) α δ π δ ( ) 7 c δ α 3 5 c)( α) δ π δ ( ) δ ( α) 7 c 3 Notice that the rofits are increasing in the resective first eriod market shares. So firms comete for market shares in the first eriod by cutting first eriod rices in the ertrand fashion. Note also, that firm i can assure itself of a ositive rofit equal to 5 δ 7 by choosing not to comete in the first eriod and then oaching on its rival firm s market in the second eriod. or any first eriod rice above the roosed equilibrium rice, ertrand cometition in the first eriod rices drives down equilibrium rofit to this reservation value. If firm i chooses a first eriod rice below the equilibrium rice, it catures the entire market but its rofit is less than rices indeed constitute equilibrium. 5 δ. So the roosed equilibrium 7 Comared to the equilibrium of the model with no ex-ost roduct differentiation in the second eriod, the firms earn a higher equilibrium rofit. irst eriod rices and market shares are the same however second eriod rices are higher. This is intuitive. Product differentiation in the second eriod imarts some market ower to the firms. irms exloit this ower by charging a higher rice in equilibrium. more subtle oint is that the amount of switching in equilibrium is also higher. This is because now switching is driven by two factors. irst, as before, by the second eriod oaching by rival firms and secondly, by the realization of consumers relative reference between the firms. 8

40 .3.. Contract with reach Penalty model: ssume that contracts of the following form are available to the firms. In the first eriod, firm i can offer a contract which secifies a first eriod rice, i ; a second eriod rice, ii ; and a breach enalty, τ i which is to be aid by its first eriod customer if she leaves the firm in the second eriod. In the second eriod firm i can offer a new rice, ij, to the first eriod customers of the rival firm, j who switch to firm i. Proosition 5: If Contact with reach Penalty (CWP) is available as an instrument then no strategies that involve not using CWP survive iterative elimination of weakly dominated strategies. The roof is similar to that of roosition given in the aendix. Proosition 6: There exists a unique sub-game erfect equilibrium of the game where both firms use CWP and the strategies of each firm involves: In the first eriod firm i offers the following contract, i c δ ( v c) v τ v c i ii nd in the second eriod firm i chooses, δ ij ij ( 3 ( jj jj c τ ) c τ j j ) if if 0 jj jj ij ij τ 0 τ j j 9

41 To illustrate the above roosition let us solve the game by backward induction. irst consider second-eriod stage game..3.a Second Period Cometition. The marginal first-eriod customer of firm gets a realization of s and x such that, x ( x) s τ Cometition in irm s first-eriod market segment yields the following demand: q q rob( x s > τ q ) for 0 s, 0 x q s q 0 x x s τ igure.4. Cometition in s first-eriod customers segment. 30

42 The above shaded region reresents the s first eriod customers who switches to firm in the second eriod, for a given the set of rices and enalty,,, τ ). irm s ( oaching demand in firm s first eriod customers market segment: q 0 ( 4 4 [ ( τ )] ( 4 τ τ ) ) if if if if if 0 τ τ < τ τ τ > 0 Similarly for firm, the marginal first-eriod customer realizes, s and x such that, ( x) x s τ Cometition in its first eriod customers market segment yields q q rob( x s > τ q ) for 0 s, 0 x s q q 0 x x s τ 3

43 igure.5. Cometition in s first eriod customers market segment. igure.5 shows the demand region for a tyical set of rices and enalties, (,, τ ). The shaded region reresents customers, who switch to firm in the second eriod. Generally, firm s oaching in s first-eriod market segment is given by: q 0 ( 4 4 [ ( τ )] ( 4 τ τ ) ) if if if if if 0 τ τ < τ τ τ > 0 Now let us look at the second eriod maximization exercise of the two firms. Since the roblem is symmetric we can look at firm s roblem. s second eriod is given by: π [( c)( q ) τ q ] ( )( c) q α α irm chooses to maximize it second eriod rofit. Note that the first term comrises of rofit from firm s first eriod customers who stay and rent (enalties) from those who leave in the second eriod. This does not deend on its second eriod choice,. s second eriod otimization can therefore be written as: max( c) q w. r. t The best resonse in the relevant oaching region is 3

44 3 ( c τ ) c τ if if 0 τ τ 0 t the roosed equilibrium, the otimal second eriod oaching rice for firm is c 9. It is easy to verify that this (given otimal enalty and otimal second eriod contract rice of firm ) satisfies the first range above. In fact at the roosed equilibrium 5 τ. This means that firm finds it otimal not to 9 comletely subsidize the consumer of the switching enalty. Combined with the existence of the consumer secific inherent switching cost, s this in turn means that only consumers with very strong enough dislike of firm and low enough switching cost will find it better-off to switch. Equilibrium Switching Outcome: t the roosed equilibrium we obtain ositive switching as an equilibrium outcome. t the roosed equilibrium q 4 8, i.e., close to one-twentieth of the first eriod customers of firm switch to firm in the second eriod. Since the equilibrium is symmetric the same amount switches from firm to. i.e., at the roosed equilibrium 4/8 of the total market switches firms in the second eriod. So comared to the socially efficient switching amount there is too little switching in the equilibrium. The intuition is simle. When there is a second motivation for consumers to switch (other than just the rice differential) it is no longer otimal to sto switching comletely. Some consumers are willing to ay high enough enalties and switch to the other firm even though the enalty of breach is not comletely comensated by the rice differential. t the margin, 33

45 the firm finds it more rofitable to let such consumers switch and earn the rent from the enalties rather than sto switching all together by charging a very high enalty..3.b irst Period Cometition and otimal choice of contract: irst let us look at consumer s choice of firms in the first eriod. consumer will choose firm over if her exected surlus from choosing in the first eriod is greater than that of choosing. Exected surlus from choosing firm in the first eriod is given by: EU [ rob( stay)( v ) E( x stay) rob( switch) {( v ) E[ x s ]}] ( v ) δ τ switch c nd that of choosing is EU [ rob( stay)( v ) E( x stay) rob( switch) {( v ) E[ x s ]}] ( v ) δ τ switch c Since all consumers are ex-ante identical s first eriod market share, α if EU > EU and 0 α if EU < EU. s before we make the assumtion that all consumers choose and with equal robability if they get the same exected surlus from both firms, i.e., α if EU EU. Now let us derive firm s otimal choice. The two-eriod discounted rofit for firm can be written as: π ( ( c) α δ π c) α δ [ α( c) α{ ( c) τ } q ( α)( c) q ] The first term is the first eriod rofit and the second term is the discounted second eriod rofit. Consider the second term. The first term within the square brackets is 34

46 second eriod rofit from its first eriod customers base. The middle term is loss of rofit less rent from enalties due to customers switching from in the second eriod. This reresents s net loss from s oaching on its first eriod customers. The last term reresent s rofit from oaching on s first-eriod customers. The roosed equilibrium strategy for firm involves choosing 4 ( ) δ, v and 79 c δ v c τ v c in the first eriod. The 3 exlanation is as follows. irm s otimal enalty is chosen so as to maximize its second-eriod rofit for any second eriod contract rice and given that s second-eriod oaching rice in s customer segment, τ c 3 is otimally chosen This results in the otimal enalty,. The derivation of the otimal enalty is given in the aendix. s long as firm discounts the future less than consumers, δ < δ, it would find it rofitable to cross subsidize first eriod rice, with second eriod rice, c. So firm charges the highest ossible second eriod rice, v. Since the roblem is symmetric the same is true for firm. Now consider the otimal choice of first eriod rice by. t the roosed equilibrium the two eriod discounted rofit for firm shown above can be exressed just as a function of first eriod rice, and its market share, α : π 4 ( c) α δ α v c ( α) Note that the second term which reresents second-eriod rofit is increasing in first eriod market share. irms comete for market share in the first eriod. This cometition drives down first eriod rice. Note however that firm can assure itself of a ositive rofit 35