ARTICLE IN PRESS. Pricing in debit and credit card schemes. Julian Wright* 1. Introduction

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1 ARTICLE IN PRE Econoics Letters x (200) xxx xxx locate/ econbase Pricing in debit and credit card schees Julian Wright* Departent of Econoics, University of Auckland, Private ag 92019, Auckland, New Zealand Received 20 August 2002; accepted 19 February 200 Abstract This paper presents a odel of a debit or credit card payent schee, providing a siple deterination of the socially optial structure of fees between those charged to cardholders and those charged to erchants. 200 Elsevier.V. All rights reserved. Keywords: Credit cards; Payent networks; Interchange fees JEL classification: G21; L42; L1 1. Introduction When consuers use debit or credit cards for a purchase, an interchange fee is paid fro the erchant s bank (the acquirer) to the consuer s bank (the issuer). The level of this interchange fee deterines the relative fees faced by cardholders versus erchants. A higher interchange fee raises the costs of acquirers, who will charge erchants ore, and lowers the effective costs of issuers, who will charge cardholders less (or in fact, provide the with rebates). Frankel (1988), and ore recently policyakers such as the European Coission and the Australian Central ank have argued that card associations (MasterCard and Visa) have set interchange fees too high, the result being that erchants pay too uch for accepting credit card transactions, a cost which is ultiately passed on to their custoers who pay with cash. Consuers who pay by credit cards, it is argued, are subsidized by taxing cash paying custoers. everal odels exist in which these clais can be evaluated. axter (198) provides the seinal analysis of interchange fees in a payent schee, an analysis that was used to defend the legality of copeting banks collectively setting interchange fees in National ancard Corp. vs. Visa UA. His analysis relies on three underlying assuptions: (1) perfect copetition between issuers and between *Tel.: ; fax: E-ail address: jk.wright@auckland.ac.nz (J. Wright) / 0/ $ see front atter 200 Elsevier.V. All rights reserved. doi: / (0)0014-5

2 ARTICLE IN PRE 2 J. Wright / Econoics Letters x (200) xxx xxx acquirers, (2) erchants that accept cards do not attract custoers fro rivals who do not, and () all erchants get the sae benefits fro accepting cards. Assuption (1) iplies card schees are indifferent to the level of interchange fees. Assuption (2) leads to biased welfare conclusions, given that business stealing is not accounted for. Assuption () leaves unanswered how interchange fees should be set given heterogeneity across erchants. Recently, three papers have analyzed interchange fees, addressing these assuptions. Rochet and 1 Tirole (2002) relaxes assuptions (1) and (2), while chalensee (2002) relaxes (1) and (). In Wright (2001), I relax (1) () but without (1) I do not get the strong results obtained here. This paper analyzes socially optial interchange fees, relaxing instead assuptions (2) and (). Assuption (1), although not reasonable for a positive analysis of interchange fees, is a useful starting point for a 2 norative analysis. 2. The odel A transaction that is done using cards costs the issuer ci and the acquirer c A. Given perfect copetition between issuers and between acquirers, cardholder fees will be f 5 ci 2 a and erchant fees will be 5 ca 1 a, where a is the per-transaction interchange fee paid by acquirers to issuers. When a consuer (buyer) uses a card for a purchase, rather than cash, they are assued to get a net convenience benefit of b, where b is continuously distributed over consuers with a positive density h(b ) over the interval fb, b g. Consuers have inelastic deand, buying one good fro each industry. We assue each industry is ade up of two erchants, which copete according to a Hotelling odel of copetition. All goods have a cost d and erchants set a single price p. Consuers are randoly located in each industry according to the standard linear city version of the Hotelling odel, and the two erchants are located at the two extrees of the unit interval. Consuers draw an x for each industry fro the U [0, 1 distribution, and incur transportation costs of tx if they purchase fro fir 1 and t(1 2 x) if they purchase fro fir 2. When a erchant (seller) accepts a card for a purchase, rather than cash, the erchant gets a net convenience benefit of b, where b is continuously distributed over industries with a positive density g(b ) over the interval fb, b g. Given these assuptions, consuers wish to use cards if and only if b $ f. Denote the proportion of consuers who use cards for transactions as D, and the average transactional benefit to these consuers fro using cards as b. Note that D 5 Prfb $ fg is increasing in a, and b5 E[bub $ f is decreasing in a. Then it follows fro a straightforward odification of the proof of Proposition 1 in 4 Rochet and Tirole, that erchants will accept cards if and only if: 1 Wright (200) also relaxes (1) and (2), but in the context of a odel of perfect copetition between erchants. 2 For instance, it is not clear whether policyakers would want to use high interchange fees to subsidize issuing banks, so as to offset the effects of their high arkups, even though this ay be what is needed to axiize welfare. This can be justified by the presence of the no-discriination rule set by card associations, or by the observation of price coherence see Frankel (1988). 4 ee Appendix A of Wright (2001) for a proof.

3 ARTICLE IN PRE I A J. Wright / Econoics Letters x (200) xxx xxx b $ b ; 2sb 2 fd5 c 1 c 2 b (1) In parallel to the consuer side, the proportion of erchants accepting cards is 5 Prfb $ b g, and the average transactional benefit to these erchants fro accepting cards is b 5 Eb f ub $ b g. Note that b is increasing in a, is decreasing in a, and b is increasing in a.. The welfare axiizing interchange fee Given the assuption of inelastic consuer deand, total welfare is: b b W 5EEb s 1 b2 ci2 cad gsbdhsbddb db (2) f b Proposition 1. The welfare axiizing interchange fee equates the erchant fee with the average transactional benefits obtained by erchants that accept cards. It is defined by a* 5 b 2 c. Proof. The welfare axiizing interchange fee is characterized by: dw dd d 5sf 1 b2 ci2 cad 1sb 1 b2 ci2 cad D5 0. () da da da ubstituting (1) into (), the first order condition siplifies to: dw 5sb2 ca2 adh( f ) 5 0 (4) da which has its solution characterized by: A a* 5 b 2 c A (5) A sufficient condition for a unique solution to exist is that db /da, 1. ufficient conditions to ensure the solution axiizes welfare are E(b ) 1b. ci1 c A, b1 E(b ). ci1 c A, b 1b # ci1 c A, and b1b # ci1 c A. These rule out the possibility of a boundary solution, whereby welfare could be higher when no erchant accepts cards, when no consuer uses cards, when all consuers use cards, or when all erchants use cards. h Welfare is axiized by setting a fee structure so that as any transactions where joint transactional benefits (b 1 b ) exceed joint costs (c I1 c A) take place using cards, and as any transactions where b1 b, ci1 ca take place using cash. Using a single interchange fee, this objective is best achieved if erchants only accept cards when the su of their transactional benefit fro accepting cards (b ) and the average transactional benefits of their card paying custoers ( b ) exceed joint costs, and if consuers only use cards when the su of their transactional benefit fro using cards (b ) and the

4 ARTICLE IN PRE 4 J. Wright / Econoics Letters x (200) xxx xxx average transactional benefits fro erchants they purchase fro which accept cards ( b ) exceed 5 joint costs. The first condition will be true at any interchange fee in this odel, given that erchants, through copetition to attract custoers, will already internalize the average benefits their card paying custoers get fro using cards (net of any fees cardholders pay for using cards). This can be seen in (1). At a* the second condition will also be true. ince consuers face fees of f 5 ci 2 a, absent any interchange fee they will pay issuing costs. At a* consuers will face the fee f 5 ci1 ca2 b, thus they will also face acquiring costs and will internalize the average erchant benefits their card usage generates. This socially optial interchange fee has several interesting properties. First, it is straightforward to show that the cardholder and erchant fees iplied by this interchange fee also correspond to the fees an unconstrained central planner would choose. At these fees, the card schee (just) covers its costs, so the fees also correspond to those chosen by a constrained central planner. econd, the socially optial interchange fee is higher than a naive interpretation of axter s optial interchange fee (a ) in the face of unobserved erchant heterogeneity. This follows since a* 5 b 2 c A. E(b ) 2 ca5 a. Third, given that the erchant fee equals the average transactional benefits that erchants obtain fro accepting cards, the average price of goods in the econoy will be neither higher nor lower as a result of card acceptance. Cash custoers pay ore in soe industries but less in others. Fourth, if b Uf2 s, 1 sg and b Uf2 s, 1 s g, so that consuer and erchant deand is linear in fees, then: 2s1 s2 cad2s1 s2 cid a* 5. Even if costs and benefits of cards are syetric between the cardholder side and the erchant side of the network, the socially optial interchange fee will be positive and erchant fees will exceed cardholder fees, reflecting the underlying asyetry between consuers and erchants. Merchants accept cards, in part, to attract custoers fro one another. This eans that it is efficient, other things 6 equal, to place a greater burden of cost recovery on erchants than on consuers. Finally, note the socially optial interchange fee bears little relation to issuing costs. 4. Conclusions This paper deterines the welfare axiizing interchange fee under a different set of assuptions copared to the existing literature. The ain finding is that the socially optial interchange fee 5 Clearly this iplies soe inefficient card transactions will take place (where b1 b, ci1 c A) but it also iplies soe efficient card transactions will not take place (where b1 b. ci1 c A). In contrast to the fraeworks used by axter (198) and Rochet and Tirole (2002), with a single interchange fee soe inefficient transactions are inevitable, reflecting the fact that each different erchant has to ake an all-or-nothing acceptance decision. 6 Intuitively, given syetry, distortions are iniized when an equal proportion of users on both sides of the network want to ake use of the network. This will occur when b 5 f. ince b 5 2 (b2 f ), this requires that a. 0 and f,.

5 ARTICLE IN PRE J. Wright / Econoics Letters x (200) xxx xxx 5 equates the erchant fee with the average transactional benefits obtained by erchants that accept cards, thereby odifying axter s original rule. The resulting optial fee structure between cardholders and erchants tends to favor cardholders, who unlike erchants, will not otherwise internalize the benefits obtained by users on the other side of the card transaction. Despite this, the optial fee does not distort average retail prices. Acknowledgeents I would like to thank seinar participants at Northwestern University, University of California erkeley, and University of Toulouse for their helpful coents. Any errors are ine. References axter, W.F., 198. ank interchange of transactional paper: legal perspectives. Journal of Law and Econoics 26, Frankel, A.., Monopoly and copetition in the supply and exchange of oney. Antitrust Law Journal 66, Rochet, J., Tirole, J., Cooperation aong copetitors: soe econoics of payent card associations. Rand Journal of Econoics, chalensee, R., Payent systes and interchange fees. Journal of Industrial Econoics 50, Wright, J., Deterinants of optial interchange fees in payent systes. University of Auckland Working Paper No Wright, J., 200. Optial card payent systes, European Econoic Review, forthcoing.