Issuer Competition and the Credit Card Interchange Fee Puzzle

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1 Issuer Competition and the Credit Card Interchange Fee Puzzle Jean-Charles Rochet and Zhu Wang February, 2010 Abstract This paper provides a new theory to explain the credit card interchange fee puzzle. Our model departs from the existing two-sided market theories by focusing on the impact of issuer competition (instead of network externality) on card industry performance. Considering a three-stage game in a four-party credit card system, we show that the consolidationamongmajorcardissuersisamain driving force of rising interchange fees and consumer card rewards. As a result, large issuers profits increase whereas merchant profits and consumer welfare are reduced. The theoretical findings are supported by empirical evidence and shed new light on the current regulatory policy debates. JEL classification: D4, L1, G2. Keywords: Credit cards, Issuer Competition, Interchange fees The views expressed herein are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System. Rochet: IDEI, Toulouse University. Wang: Economic Research Department, Federal Reserve Bank of Kansas City.

2 1 Introduction As credit cards become an increasingly prominent form of payments, the structure and performance of the industry have attracted great attention. One most controversial issue is the interchange fee the fee that merchants pay to card issuers (through merchant acquirers) for accepting card payments. Interchange fees are set by four-party credit card networks: Visa and MasterCard each set interchange fees collectively for their member financial institutions that issue and market their cards. 1 Nowadays, U.S. merchants pay about 1.75 percent of card transaction values for the interchange fees on average. This has generated significant revenues for card issuers. In 2007, the U.S. card issuers made a total of $42 billion interchange revenues. Merchants have been very critical of the interchange fees, claiming that the fees are excessively high. They pointed out that, despite of technology progress and cost reduction in the card industry, interchange rates in the United States have been rising in the past ten years and are among the largest and fast-growing costs of doing business. However, card networks disagree, arguing that the increasing interchange fees serve the needs of all parties in the card system, including funding better consumer reward programs that could also benefit merchants. In the meantime, competition authorities and central banks in many countries have started regulating or investigating interchange fees. 2 In the United States, interchange fees have been mainly challenged by private litigation. In the past few years, more than 1 Visa and MasterCard provide card services through member financial institutions (card-issuing banks and merchant acquiring banks). They are called four-party systems and account for approximately 80 percent of the U.S. credit card market. Amex and Discover handle card issuing and merchant acquiring primarily by themselves. They are called three-party systems and account for the remaining 20 percent credit card market share. In a three-party system, interchange fees are internal transfers and hence not directly observable. 2 The countries and areas that have taken actions on interchange fees include Argentina, Australia, Austria, Canada, Chile, Colombia, Denmark, European Union, France, Israel, Mexico, Norway, Panama, Poland, Portugal, South Korea, Spain, Switzerland and Turkey. Other countries that have started investigating interchange fees include Brazil, Hungary, New Zealand, Norway, South Africa and United Kingdom (Terri Bradford and Fumiko Hayashi 2008). 1

3 50 antitrust cases have been filed by merchants and merchant associations against the card networks and their large issuers regarding interchange fees. In addition, three bills are currently under consideration in Congress. If passed, the new legislation could open the possibility of regulating card fees in the United States. In order to understand and evaluate the card market structure and pricing issues, a large body of literature, called two-sided market theories, has been developed recently. Most of these models, following the pioneering work of Baxter (1983), emphasize the two-sided market externalities in card payment systems and suggest that interchange fees fulfill a special balancing purpose between consumers who use cards and merchants who accept cards. 3 Several factors are pointed out that may determine the level of interchange fees, including the issuing and acquiring costs, cardholders and merchants benefits of using cards, and bargaining power of the parties. However, these theories have not yet provided a clear answer to the following key questions: (1) What has driven up U.S. interchange fees for the past ten years? (2) Why have consumer card rewards been increasing with interchange fees? (3) How would the changing card fees affect merchants, consumers and card issuers? In the present paper, we provide a new theory to explain these puzzles surrounding credit card interchange fees. Our model departs from most existing two-sided market theories by focusing on the impact of issuer competition (instead of network externality) on card industry performance. We show that the increasing concentration of large card issuers is indeed a main driving force of rising interchange fees and consumer card rewards. As a result, large issuers profits increase whereas merchant profits and consumer welfare are reduced. The U.S. banking industry has been through a major consolidation since mid 1990s, largely driven by deregulation and technological changes. In the past ten years, the 3 For example: William Baxter (1983); Michael Katz (2001); Richard Schmalensee (2002); Jean- Charles Rochet and Jean Tirole (2002, 2003, 2006); Joshua Gans and Stephen King (2003); Julian Wright (2003, 2004); Marius Schwartz and Daniel Vincent (2006); James McAndrews and Zhu Wang (2008); Wilko Bolt and Sujit Charkravorti (2008); Oz Shy and Zhu Wang (2010); and Zhu Wang (2010a, b). 2

4 Interchange Fee (%) Interchange Fee Issuer Concentration Issuer Concentration (Top 5) Figure 1: Issuer Concentration and Credit Card Interchange Fee number of commercial banks in the United States dropped by almost 30 percent. As a part of the banking consolidation wave, a sequence of mergers and acquisitions among top card issuing banks has led to a much more concentrated card issuing market. In 1996, the top five credit card issuers held 41 percent market share. By 2006, their share rose to 75 percent. 4 Figure 1 plots the market share of top five Visa and MasterCard issuers as well as the average Visa and MasterCard interchange fee. It shows close parallel changes between the issuer concentration and the interchange fee. In the paper, we construct 4 The merger wave of top card issuers began in 1996, when Chase purchased Chemical for $13 billion. The next year saw Bank One s acquisition of First USA for $23 billion, Citi s purchase of AT&T for $15 billion, and Fleet taking on Advanta for $11 billion. Then in 1998, Bank One purchased Chevy Chase for $5 billion and First Chicago for $18 billion, while Bank of America gobbled up Nations for $9 billion was the year MBNA bought First Union for $6 billion, while Citi picked up Associates for the identical sum. Bank One purchased Wachovia for $7 billion the following year. In 2002, Chase paid $8 billion for part of Providian. Next, HSBC acquired Household for $17 billion in 2003, the same year Citi got Sears for the price of $11 billion. In 2004, JP Morgan Chase purchased Bank One for $76 billion, while Bank of America acquired Fleet for $17 billion. Finally, Bank of America s $35 billion merger with MBNA took place in 2005, the same year that Washington Mutual bought Providian Financial for $6.5 billion. 3

5 Card Network (sets interchange I) pays p(1+f c ) (f c : consumer fee) Card Issuer pays p(1-i) (I: interchange) Merchant Acquirer pays p(1-f m ) (f m : merchant fee) Cardholder sells good at price p Merchant Figure 2: A Four-Party Credit Card System an industry equilibrium model that explains why the increasing issuer concentration may have driven up interchange fees and consumer card rewards. Based on the model, we also investigate the impact on merchant profits, issuer profits and consumer welfare. The paper is organized as follows. Section 2 sets up a model of a four-party card system. Section 3 solves for the industry equilibrium, including prices and outputs in both card and good markets. Section 4 investigates how increasing issuer concentration affects card fees and the impact on merchant profits, issuer profits and consumer welfare. Section 5 provides policy discussions. Section 6 concludes. 2 The Model A four-party card system is composed of five players: consumers, merchants, acquirers, issuers, and the card network, as illustrated in Figure 2. They are modeled as follows. 4

6 2.1 Consumers Consumers buy two types of goods. Let denote the consumption of goods for which consumers pay only with cash (cash goods in what follows). Let denote the consumption of goods for which consumers pay only with cards (card goods). 5 Consumers utility function is assumed to take the quasi-linear form given by = + 1, where (1) The price of card goods is denoted by. The price of cash goods is normalized to unity. Consumers budget constraint is given by + = (2) where denotes the consumers exogenously-given income. Substituting (2) for in (1), and maximizing with respect to obtains consumers isoelastic demand function for card goods =, where = (1 ) (3) The price that consumers pay for card goods is composed of two parts: (a) the retail price charged by merchants, denoted by, and (b) a percentage fee charged by card issuers (sometimes isnegativeandreferredtoasconsumercardreward). Hence, the overall price consumers pay for card goods is =(1+ ) (4) 5 We interpret cash as non-card payments which also include checks and bank transfers. Here we implicitly assume that the cost of using cash is too high for card goods. Alternatively, we could explicitly model consumers decisions regarding which payment instrument to use, but that would not affect our analysis. In fact, we may assume that each consumer has a unit demand for goods, but consumers are heterogenous with respect to the benefits they derive from using cards relative to cash. Assuming that consumers benefits from using cards follow a Pareto distribution would then generate the same isoelastic demand function (3) for card goods (see Wang 2010b). 5

7 2.2 Merchants There are 1 merchants who sell card goods. Each merchant obtains the goods at a unit cost and sells them at a retail price. In addition, merchants pay a percentage fee for accepting card payments, usually referred to as the merchant discount. Let denote the output sold by merchant. Then, the total cost borne by each merchant ( =1 2)is ( )=( + ) Each merchant sets the output level taking the output by competing merchants = as given, and maximizes profit givenby ( )= ( ) (5) where can be extracted from (3) and (4), and expressed as a function of ( ). 2.3 Acquirers The acquiring market is competitive, where each acquirer receives a merchant discount fee from merchants and pays an interchange fee to issuers. For simplicity, we assume zero acquiring cost so acquirers play no role in our analysis but pass through the merchant discount as interchange fee to the issuers, i.e., = 2.4 Issuers The issuing market consists of two types of issuers: major issuers and marginal issuers. The former are large banks that capture most of the card issuing business. Compared with marginal issuers, major issuers have significant cost advantages and they dominate the pricing decision of the card network. 6

8 Accordingly, we assume there are 1 major issuers, and their marginal costs are normalized to be zero. In contrast, there are 0 1 marginal issuers who are less efficient. They incur a marginal cost 0 for serving each dollar value of card transaction. 6 Denote = as the total card transaction value in the market, which is also the total output of card issuers. Given the interchange fee set by the card network, each issuer chooses its output (i.e., its card transaction value) to maximize its profit taking the output of competing issuers = as given. Therefore, issuer s profit isdeterminedby ( + ) if is a major issuer, = ( + ) if is a marginal issuer. (6) where the consumer card fee is endogenously determined by the competition among issuers. 2.5 The card network and timing The card network is an association of card issuers, which collectively sets the interchange fee. Because of the dominance of major issuers in the network, the interchange fee is set in their favor. Without loss of generality, we assume the interchange fee is set so that + = Therefore, marginal issuers are driven away from the card issuing business. 7 The next section solves for a subgame perfect equilibrium of the following threestage game: 6 The card issuing cost includes the expenses for supporting cardholders accounts, offering credit float, providing fraud protection and so on. 7 MasterCard and Visa underwent structural changes recently, changing their status from non-profit bank associations to for-profit public firms in 2005 and 2008 respectively. However, top issuing banks still have strong control in both networks. 7

9 Stage I. The card network sets the interchange fee issuers. that drives away marginal Stage II. Each major issuer ( =1 ) takes as given and chooses its output to maximize profit (6), and issuer output levels satisfy the Nash-Cournot equilibrium in the card market. This determines the equilibrium consumer card fee. Stage III. Each merchant ( =1 ) takes card fees and as given and chooses output level to maximize profit (5), where merchant output levels satisfy the Nash-Cournot equilibrium in the good market. 3 The Market Equilibrium The consumer demand function is given by (3) and (4): (1 + ) =. (7) In Stage III, Each merchant takes card fees (, ) and competitors output as given, and chooses output to solve max = ( + ) = ( + ) (1 ) (8) 1+ where the retail price was substituted from (7). The first-order condition for the profit maximization problem (8) implies µ (1 ) (1 + ) ( + ) 1 = (9) + In a symmetric Nash-Cournot equilibrium all merchants sell the same amount, so that = for each merchant =1. Therefore, the total merchant output, =, 8

10 and retail price are = (1 + ) ( )(1 ) 1 and = ( )(1 ) (10) Observe that the retail price increases with the interchange fee,andthetotal merchant output decreases in (consumer card fee) and (interchange fee). In Stage II, each major card issuer takes the interchange fee and competitors output as given, and chooses output to solve max =( + ) (11) where can be derived from (10) as + = =( 1+ 1 ) ( )(1 ) 1 1 so that 1 = ( + ) 1 (12) ( )(1 ) The first-order condition for the issuer profit maximization problem (11) implies 1 ( + ) (1 ) (1 )=0 (13) ( )(1 ) + In a symmetric Nash-Cournot equilibrium, all major issuers have the same output so that = for =1. Therefore, the total card transaction value, = =, satisfies 1 (1 ( )(1 ) ) (1 )=0 (14) Equations (12) and (14) then pin down the equilibrium consumer card fee as (1 )(1 + )=1 (15) 9

11 In stage I, the card network takes (15) as given, and sets the interchange fee so that marginal issuers are competed away: + = (16) Therefore, (15) and (16) determine the equilibrium card fees and : =1 ( 1) = 1 (17) The resulting card network profit Π, equal to the total profit of all major issuers, becomes Π = =( + ) = 1 " ( )(1 ) # 1 1 (18) The equilibrium total merchant output and consumers price can be computed from (10) and (17) to be = " ( )(1 ) # 1 =(1+ ) = (19) ( )(1 ) Substituting (19) into (8) for = yields total profit ofallmerchants Π = =[(1 ) ] = " ( ) ( )(1 ) # 1 (20) Substituting (19) into consumers utility function (1) and (2) obtains the equilibrium consumer utility = + µ " # = ( )(1 ) (21) 10

12 Altogether, social welfare,defined as the sum of consumer utility, merchant profits and card issuer profits, is given by = + Π + Π = + 1 " # 1 1 µ 1 (1 )( ) (22) 4 Issuer Competition and Card Fees In this section, we conduct our main investigation on the following card fee puzzles: What has driven up the U.S. interchange fees in the past ten years? Why have consumer card fees (rewards) been decreasing (increasing) with interchange fees? How would card fee changes affect merchants, consumers and card issuers? 4.1 Theoretical Implications Recall that the market equilibrium card fees, satisfy (17) =1 ( 1) = 1 Accordingly, the effects of issuer competition are summarized in the following Proposition 1. Proposition 1 A decrease in the number of major issuers (i.e., an increase of issuer concentration) would 11

13 (a) increase the interchange fee, but decrease the consumer card fee, (b) increase the card network profits Π as well as each issuer s profit (c) decrease the total merchant profits Π as well as each merchant s profit, (d) increase consumers price, decrease consumption and utility and (e) decrease the social welfare Proof. Equations (17)-(22) imply (a) 0 0 (b) Π 0, 0 (c) Π 0 0 (d) 0 0, 0 and (e) 0 We can also investigate the effects of decreasing cost of marginal issuers, summarized in the following Proposition 2. Proposition 2 A decrease in the cost of marginal issuers would (a) increase the interchange fee, but decrease the consumer card fee, (b) not affect the card network profits Π as well as each issuer s profit (c) not affect total merchant profits Π as well as each merchant s profit, (d) not affect consumers price, consumption and utility and (e) not affect the social welfare Proof. Equations (17)-(22) imply (a) 0 0 (b) Π =0, =0 (c) Π =0 =0 (d) =0 =0, =0 and (e) =0 12

14 4.2 Empirical Evidence Consistent with our theoretical findings, Figure 1 shows close parallel changes between the issuer concentration and interchange fees in the data. In this subsection, we conduct regression analysis using the annual data from We ran the following two regressions, one using level data and the other using differenced data. The dependent variable is the interchange fee, and the independent variables include the issuer concentration and the time trend. = = ( 1) + + The interchange fee data that we use is the average Visa and MasterCard interchange rate for non-supermarket transactions. The issuer concentration is measured as the market share of the top five visa and MasterCard issuers. Table 1. Issuer Concentration and Interchange Fees Data Range ( ) Interchange Fee (Level) Interchange Fee (Difference) Issuer Concentration Time Trend Constant 074 (027) 003 (001) 090 (011) 080 (025) 002 (001) Adjusted Observations * Statistically significant at 5% level. The regression results, shown in Table 1, support our theoretical findings. The first regression using level data shows that interchange fee is positively affected by both 13

15 theissuerconcentration andthetimetrend,andbotheffects are strongly statistically significant. The regression fits data very well with an adjusted 2 of However, because the level regression may raise concerns on the nonstationarity issue of the data, we then ran the second regression using differenced data. The estimates turn out to be very similar, which again shows interchange fee is positively affected by both the issuer concentration and the time trend, and particularly the effect of issue concentration is strongly statistically significant. The regression also fits data well with an adjusted 2 of Our regression results allow us to quantify the contribution of different driving forces to the increase of interchange fee. As the data shows, interchange fee rose from 1.28% to 1.75% between Meanwhile, the issuer concentration rose from 0.41 to The estimates from our differenced regression then suggest that 58% of the increase of interchange fee could be explained by the increase of issuer concentration. The rest 42% increase of interchange fee may have been driven by other factors, including the reduced cost of marginal issuers as shown in our theoretical analysis. 5 Policy Discussions 5.1 Interchange Regulation By analyzing the strategic competition among card issuers, our theory sheds new light on policy debates regarding interchange fees. In several countries, public authorities have chosen to regulate down interchange fees. 8 Our analysis uncovers a novel channel through which the regulation might affect the market outcome. 8 For example, Reserve Bank of Australia introduced a price ceiling for credit card interchange fees in At the time, the interchange fees averaged around 0.95% of the card transaction value. The regulation required that the weighted-average interchange fee for both Visa and MasterCard systems could not exceed 0.5% of the transaction value. The regulation is currently due for review, and one notable finding is that card rewards have been effectively reduced. 14

16 Recall that the market equilibrium card fees derived in (17) =1 ( 1) = 1 Under this fee schedule, major issuers deter the entry of marginal issuers and dominate the card market. Now let us consider a policy experiment that the interchange fee is regulated down to a lower level so that 1 ( 1) Our model suggests that this would trigger the entry of marginal issuers. To see how this work, let us consider the Cournot competition among all issuers, including both major and marginal ones. A major issuer takes the interchange fee and other issuers output as given, and chooses its profit-maximizing output. The first-order condition implies that 1 ( + ) (1 ) (1 ( )(1 ) + )=0 (23) Similarly, a marginal issuer 0 takes the interchange fee and other issuers output 0 as given, and chooses its profit-maximizing output 0. The first-order condition implies that 1 ( 0 + 0) (1 0 ) (1 + ( )(1 ) 0 + )=0 (24) 0 In a symmetric Nash-Cournot equilibrium, all major issuers have the same output = for =1; and all marginal issuers have the same output 0 = 0 for 0 =1 0. Therefore, the aggregate card transaction value, = + 0 0,satisfies 1 (1 ( )(1 ) ) (1 )=0 (25) 15

17 1 (1 0 ( )(1 ) ) (1 + )=0 (26) Note that we have derived in (14) that Therefore, (25)-(27) determine that 0 = Basedon(28),weestablishthat 1+ = [ ( )(1 ) ] 1 (27) + + = + 0 ( + 0 ) (28) = iff 1 ( 1) (29) Hence, we verify that, under the regulation, marginal issuers now make positive profit by entering the market at the Nash-Cournot equilibrium. Meanwhile, consumer card fee becomes higher. Note that = 1 is the upper bound of the consumer card fee in the unregulated case, and we now have = + 0 ( + 0 ) iff 1 ( 1) (30) Furthermore, we can show that, compared with the unregulated case, both the retail price and the consumers price are lower, merchants output and profits Π are higher, major issuers profits Π is lower, but consumer utility and social welfare are higher under the regulation. In contrast to the findings in Propositions 1 and 2, we also found that changing the number of major issuers and marginal issuers cost yield different results under the regulation. Particularly, a decrease in the number of issuers (i.e., an increase of issuer concentration) would increase (instead of decreasing) the consumer card fee 16

18 , though other results in Proposition 1 still hold. We also found that a decrease in marginal issuers cost would yield real effects under the regulation. Namely, it would decrease the consumer card fee, increase the profits of both card issuers and merchants, and also increase consumers consumption and social welfare. 5.2 Further Issues Our policy discussion suggests that regulating down interchange fees may improve the card market outcome by encouraging entry of marginal issuers. While this sheds new light on understanding the structure and performance of card markets, we recognize there are limitations of the analysis. First, we treated the issuers costs as exogenous in the model. Based on this, regulating down interchange fees appears to be desirable. However, it is possible in reality that the cost advantages of major issuers are due to endogenous investment efforts. Moreover, the extra profits of major issuers may also provide incentives for marginal issuers to improve their efficiency and to catch up. All these endogenous and dynamic factors may make the welfare results of interchange regulation less clear and obvious. Second, our analysis has abstracted from the question whether card fees fulfill a special balancing purpose in two-sided markets. While this might be a reasonable assumption for studying a mature card market, it may not adequately characterize an emerging card market. Rochet (2007) discusses some broad issues on horizontal integration in two-sided payment markets. Third, it is important to recognize that price regulation is not the only option, or necessarily the best option, for policymakers to improve market outcomes. Other policy options are worth exploring, such as reforming the payment card market structure or supporting the technology progress of competing payment services. In addition, increasing public scrutiny and regulatory threat may also be effective policy measures. 17

19 6 Conclusion This paper provides a new explanation for puzzles surrounding credit card interchange fees. Our model departs from most existing two-sided market theories by focusing on the impact of issuer competition (instead of network externality) on industry performance. Considering a three-stage game in a four-party credit card system, we show that the consolidation among major card issuers is a main driving force of rising interchange fees and consumer card rewards. As a result, large issuers profits increase whereas merchant profits and consumer welfare are reduced. The theoretical findings are shown to be supported by empirical evidence, which suggests that more than half the increase of interchange fees in the past ten years could be accounted for by the increase of issuer concentration. By analyzing the strategic competition among card issuers, our theory sheds new light on policy debates regarding interchange fees. In some countries, public authorities have chosen to regulate down interchange fees. Our analysis suggests that this may improve the card market outcome by encouraging entry of marginal issuers. While this provides a novel perspective to understand the structure and performance of card markets, we also discuss potential limitations of policy interventions. 18

20 References [1] Baxter, William (1983), Bank Interchange of Transactional Paper: Legal Perspectives, Journal of Law and Economics 26: [2] Bolt, Wilko and Alexander Tieman (2008), Heavily Skewed Pricing in Two-sided Markets, International Journal of Industrial Organization, 26(5), [3] Bolt, Wilko and Sujit Charkravorti (2008), Economics of Payment Cards: A Status Report, Economic Perspectives, 32 (4), 15-27, Federal Reserve Bank of Chicago. [4] Charkravorti, Sujit and Roberto Roson (2006), Platform Competition in Twosided Markets: The Case of Payment Networks, Review of Network Economics, 5 (1), [5] Evans, David and Richard Schmalensee (2005), Paying with Plastic: The Digital Revolution in Buying and Borrowing, 2nd Ed., MIT Press, Cambridge, MA. [6] Gans, Joshua S. and Stephen P King (2003), The Neutrality of Interchange Fees in Payment Systems, Topics in Economic Analysis & Policy: 3(1), Article 1. [7] Hayashi, Fumiko (2006), A Puzzle of Card Payment Pricing: Why Are Merchants Still Accepting Card Payments? Review of Network Economics 5: [8] Hayashi, Fumiko and Stuart Weiner (2006), Interchange Fees in Australia, the UK, and the United States: Matching Theory and Practice, Economic Review, Third Quarter, Federal Reserve Bank of Kansas City. [9] McAndrews, James and Zhu Wang (2008), The Economics of Two-Sided Payment Card Markets: Pricing, Adoption and Usage, Working Paper, Federal Reserve Bank of Kansas City. [10] Katz, Michael (2001), Reform of Credit Card Schemes in Australia II: Commissioned Report, RBA Public Document, August. 19

21 [11] Rochet, Jean-Charles (2007), Some Economics of Horizontal Integration in the Payments Industry, Federal Reserve Bank of Kansas City conference proceedings: Nonbanks in the Payments System: Innovation, Competition and Risk. [12] Rochet, Jean-Charles (2003), The Theory of Interchange Fees: A Synthesis of Recent Contributions, Review of Network Economics, 2: [13] Rochet, Jean-Charles and Jean Tirole (2002), Cooperation among Competitors: Some Economics of Payment Card Associations, RAND Journal of Economics 33: [14] Rochet, Jean-Charles and Jean Tirole (2003), An Economic Analysis of the Determination of Interchange Fees in Payment Card Systems, Review of Network Economics 2: [15] Rochet, Jean-Charles and Jean Tirole (2006), Externalities and Regulation in Card Payment Systems, Review of Network Economics 5: [16] Schwartz, Marius and Daniel Vincent (2006), The No Surcharge Rule and Card User Rebates: Vertical Control by a Payment Network, Review of Network Economics 5: [17] Shy, Oz and Zhu Wang (2010), Why Do Payment Card Networks Charge Proportional Fees? American Economic Review, forthcoming. [18] Wang, Zhu (2010a), Market Structure and Payment Card Pricing: What Drives the Interchange? International Journal of Industrial Organization, 28: [19] Wang, Zhu (2010b), Regulating Debit Cards: The Case of Ad Valorem Fees. Economic Review, First Quarter, Federal Reserve Bank of Kansas City. [20] Wright, Julian (2003), Optimal Card Payment Systems, European Economic Review 47: [21] Wright, Julian (2004), Determinants of Optimal Interchange Fees in Payment Systems, Journal of Industrial Economics 52:

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