Why payment card fees are biased against merchants

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1 Why payment card fees are biased against merchants Julian Wright November 2010 Abstract I formalize the popular argument that payment card networks such as MasterCard and Visa charge merchants too much and cardholders too little, resulting in excessive use of cards, a cost which is ultimately passed on to consumers paying by cash. To do this, I analyze a standard twosided markets model of a payment card network. With minimal additional restrictions, the model implies that the privately set fee structure is unambiguously biased against merchants in favor of cardholders, a result that continues to hold even if merchants are allowed to surcharge card payments and even under intense competition between payment networks. I explain how this bias is linked to the fact that merchants accept cards as a service to their customers, and argue the market failure arising is primarily a regulatory problem and need not raise any competition concerns. 1 Introduction MasterCard may be Priceless and Visa Everywhere You Want To Be but apparently only from the point of view of cardholders. These payment networks have increasingly found themselves under fire from merchant groups (led by large retailers) and policymakers, with regulatory and legal proceedings arising in more than thirty different countries. 1 Public authorities such as the Reserve Bank of Australia, the European Commission and the United States Government Accountability Office, together with a number of economists (e.g. Carlton and Frankel, 1995; Katz, 2001; Cabral, 2005; Vickers, 2005; Farrell, 2006) have argued that the fee structure in debit and credit cards are likely to be distorted, Department of Economics. National University of Singapore: 1 Recent or ongoing investigations include those in Argentina, Australia, Brazil, Canada, Chile, Colombia, Czech Republic, Denmark, the European Union, France, Germany, Honduras, Hong Kong, Hungrary, Israel, Italy, Mexico, the Netherlands, New Zealand, Norway, Poland, Romania, Singapore, Sourth Africa, Spain, Sweden, Switzerland, Turkey, Venezuela, the United Kingdom, and the United States. Bradford and Hayashi (2008) contain references for many of these investigations. 1

2 with merchants paying too much to accept payment cards and cardholders paying too little, resulting in excessive usage of payment cards by consumers, a cost which is ultimately passed on to consumers paying by cash. Their arguments rest on one of two themes: (i) merchant internalization: payment networks respond to merchants individual willingness to accept cards, but this is a poor indicator of the social benefits of card acceptance since merchants accept cards to attract customers from each other; and (ii) competitive distortion: that high merchant fees reflect the market power of issuers (i.e. the cardholders banks) over merchants through the setting of high interchange fees which are passed on to merchants through acquirers (i.e. the merchants banks). Despite the considerable interest of the various stakeholders, surprisingly to date no one has formalized these ideas to show how they lead to the conclusion that interchange fees (also known as swipe fees in the U.S.) are necessarily too high. The present paper fills this gap. It takes a fairly standard two-sided markets model of a payment card network from the literature, showing how this captures both of the above themes. With minimal additional assumptions it then establishes that privately set interchange fees are systematically too high, resulting in excessive usage of payment cards and inflated retail prices to the detriment of cash customers. Contrary to the claims in most previous works on the topic (including some of my own), these strong results do not depend on the particular nature of cardholder and merchant benefits of different payment instruments or the elasticities of demand on each side of the market. Rather, they arise primarily as a result of merchant internalization. A competitive distortion can increase or decrease the overall bias, although the effect of the two distortions together always results in excessive interchange fees. To understand the reason merchant internalization results in a biased fee structure, consider starting from a fee structure that maximizes profit and card volume, and then increase card fees and decrease merchant fees by a small and equal amount. This has no first order effect on the number of card transactions or profit but raises the average cardholder convenience benefit per transaction (and so welfare) since it means only consumers with higher convenience benefits of using cards will continue to use them. For a generic two-sided platform, there would be an offsetting bias on the other side of the platform, as merchants with lower convenience benefits of accepting cards would start accepting them. One could not say in general in which direction the overall bias goes. However, merchant internalization implies any offset on the merchant side is only partial. Given merchants internalize their customers benefits, they are insensitive to any change in the fee structure (their gain from lower fees is their customers loss through higher fees or lower rewards, which they internalize). The only offsetting effect that arises from the merchant side is an indirect effect. To the extent only consumers with higher convenience benefit of using cards continue to use them, merchants will more readily accept cards, meaning some merchants with lower convenience benefits of accepting cards will start accepting them, but this will necessarily be weaker than the original effect on cardholders. As a result, I show a small regulated reduction in interchange fees which increases card fees (or decreases rewards) and decreases merchant fees by an 2

3 equal amount would unambiguously increase user surplus, consumer surplus and total welfare. I show it would also decrease retail prices and the use of payment cards, although card customers would end up paying more. On top of the systematic bias arising from merchant internalization there is a possible competitive distortion which results if the pass-through rate by issuing banks is less than that of acquiring banks. This implies that increasing interchange fees charged to acquirers allows revenues to be shifted to the issuing side where they are not fully competed away, thereby raising total margins for banks. This provides a different reason why interchange fees may be set too high, although one which is based on card networks restricting the number of card transactions rather than encouraging excessively many card transactions. I show that to the extent that the pass through rate for issuers is less than for acquirers, the bias from merchant internalization is reduced, but the increased competitive distortion always implies that on balance, the fee structure remains distorted towards interchange fees being too high. The framework I adopt is based on the seminal work of Rochet and Tirole (2002) but differs from their benchmark model in that it allows for unobservable merchant heterogeneity (i.e. elastic merchant demand for card acceptance) and that merchants internalize the financial benefits their customers get from using their cards per transaction (e.g. through reward programs). Both of these features are incorporated in Wright (2004) and Rochet and Tirole (2010) 2, who show that when there is no competitive distortion, privately set interchange fees exceed the welfare maximizing level if and only if the average cardholder surplus per transaction exceeds the average merchant surplus per transaction. I am able to obtain an unambiguous result by adding the relatively mild assumption that the distribution of merchants convenience benefits has an increasing hazard rate and by exploiting a different decomposition of welfare. Furthermore, I extend the result to show it applies with non-constant bank margins provided the pass-through of costs on the issuing side is never higher than on the acquiring side, a property I will argue is consistent with the standard assumptions in the literature and the existing evidence. My findings show that, surprisingly, the main conclusion in Rochet and Tirole (2002), that the privately set interchange fee is never lower than the welfare maximizing level survives the generalization to elastic merchant demand for card acceptance. Indeed, their conclusion, which also relies on merchant internalization, is strengthened since I show the privately set interchange fee is now always too high. 3 By way of comparison with their results, in Section 4.1, I also consider a setting without unobservable merchant heterogeneity and obtain a new result. When issuing is monopolized, the card network sets the interchange fee 2 Rochet and Tirole s main focus is whether a proposed regulation for setting interchange fees (based on avoided cost) provides a good indicator of excessive interchange fees. Other papers that derive biases in privately set interchange fees include Bedre-Defolie and Calvano (2010) and Wang (2010), as discussed further below. 3 In a framework with elastic goods demand and heterogeneous issuers, but without merchant internalization, Wang (2010) also finds the privately set interchange fee is either equal to the efficient level or is too high. 3

4 at the first-best level, while with sufficient issuer competition, interchange fees are always too high. This reinforces the view that merchant internalization is the primary source of the bias in interchange fee setting, and a distortion of competition is not needed to explain the bias. This conclusion is further supported in Section 4.3, when I allow for perfect inter- and intra-network competition and show the bias towards excessive interchange fees remains. This reflects that competing networks choose interchange fees to maximize their users private interests, resulting in cardholder surplus being counted twice once in attracting cardholders and once in attracting merchants who already internalize cardholder surplus. A standard assumption in the literature is that merchants set the same price for goods regardless of how consumers pay. This reflects either that card networks do not allow merchants to charge consumers more if they pay by card, or even where merchants are allowed to surcharge, that most merchants do not choose to do so. 4 As an extension of my main result, I consider in Section 4.2 what happens if merchants are able to surcharge but face transaction costs to do so. These transaction costs are assumed to vary across industries in a way the card network cannot perfectly observe. In equilibrium, interchange fees are set to take into account that higher interchange fees induce more merchants (i.e. those with low enough transaction costs) to surcharge. Despite this, I show privately set interchange fees remain inefficiently high due to merchant internalization for those merchants not surcharging and also due to the fact higher interchange fees result in additional transaction costs from surcharging, which a private card network does not internalize. There is one other recent paper (Bedre-Defolie and Calvano, 2010) that also shows in a general sense (i.e. allowing for elastic cardholder and merchant demand) that privately set interchange fees are excessive. Their mechanism relies on a key asymmetry that arises when cardholders face a membership decision of whether to hold a card in addition to how much to use it, whereas merchants make only an all or nothing decision of whether to accept cards. As a result, with unobservable merchant heterogeneity, a card network will set interchange fees too high since issuers fully extract cardholder surplus through two-part tariffs but fail to fully internalize the convenience benefits merchants obtain. The mechanism Bedre-Defolie and Calvano propose is complementary to the distortion highlighted in this paper since (i) they assume away merchant internalization by modeling merchants as monopolists facing unit demands and (ii) I assume away cardholders separate membership decision by making the number of cardholders exogenous (for instance, determined by whether they have a bank account rather than the level of interchange fees). 5 A challenge for future research is to combine these different mechanisms. The rest of the paper proceeds as follows. Section 2 lays out the benchmark 4 Frankel (1998) refers to this as price coherence that merchants are generally reluctant to set differential prices depending on the payment instrument used. 5 However, their framework does not fit the usual arguments put forward by policymakers and merchants in their framework, merchants that accept cards do so only because it lowers their (net) costs of receiving payment. 4

5 model, which is analyzed in Section 3. Section 4 considers several extensions, including to the case in which any heterogeneity in merchants convenience benefits are observable (Section 4.1), the case in which surcharging is allowed (Section 4.2) and the case in which there is competition between card networks (Section 4.3). Finally, Section 5 concludes with a discussion of policy implications. 2 Model The benchmark model I consider is basically the same as that in Wright (2004) which extends the seminal work of Rochet and Tirole (2002) to allow for unobserved merchant heterogeneity. 6 The assumptions on the costs and benefits of card payments are standard. There is a single card scheme (e.g. Visa) that provides the payment network and sets an interchange fee a, which is a per transaction payment from acquirers (the merchants banks) to issuers (the cardholders banks). Issuers face a per transaction cost of c I and acquirers face a per transaction cost of c A with c = c I +c A being the total cost per transaction. There is one or more symmetric issuer, resulting in an equilibrium per transaction fee p B, and one or more symmetric acquirer, resulting in an equilibrium per transaction fee p S. The per transaction fee p B can be negative, as is the case where consumers receive rewards and interest free benefits for using a payment card. I will put more structure on these equilibrium fees below. However, the particular model of competition in issuing and acquiring is left unspecified. Assume there is a continuum (measure one) of consumers. An exogenous fraction µ of consumers hold the payment card. Let b B be a cardholder s convenience benefit of using a card for a payment transaction rather than the alternative (say cash), which has benefits normalized to zero. b B is drawn on the interval [ ] b B, b B from the continuously differentiable distribution function H (b B ), with density h (b B ). The hazard rate λ B = h/ (1 H) is assumed to be increasing, a property which holds for uniform, normal, extreme-value and logistic distributions, among others (see Bagnoli and Bergstrom, 2005). Following Wright (2004) and the subsequent literature, cardholders are assumed to only observe their draw of b B at the time of purchase. This simplifies the analysis of merchants acceptance of cards without changing the equilibrium outcome. Initially, merchants are assumed to set a single price regardless of how consumers pay (i.e. price coherence). As a result, cardholders will use cards whenever they draw b B p B. The proportion of card payments at a merchant that accepts cards is denoted D (p B ) = Pr (b B > p B ) = 1 H (p B ). The expected (or average) convenience benefit to a cardholder using cards for a transaction is β B (p B ) = E[b B b B p B ] which is increasing in p B. The expected (or average) surplus to a cardholder from using their card for a transaction is v B (p B ) = β B (p B ) p B > 0. From the increasing hazard rate property, 6 Another difference is that Rochet and Tirole (2002) focus on the case the cardholder fee is a fixed fee, only discussing the case where it is a variable payment briefly on p.560 in their article. However, the fact that the rewards and interest-free benefits funded by interchange fees arise per transaction plays a key role in the analysis in this paper. 5

6 it follows that v B (p B ) is a decreasing function of p B (see Prékopa, 1973), which also implies 0 < β B (p B) < 1. Assume there is a continuum (measure one) of industries. Consumer are exogenously matched with industries, and so, without loss of generality, each consumer is matched with each industry. Each industry contains two merchants that compete according to the standard Hotelling model, with the measure one of consumers uniformly distributed between the two merchants which are located at the extremes of a linear city of length 1. Consumers face linear transport costs tx to travel a distance x to the merchant of their choice, from which they wish to buy one unit of a good. Each unit of good costs d to produce and gives sufficiently high utility u that consumers always wish to purchase one unit of it. Let b S be a merchant s convenience benefit of accepting a card for a payment transaction rather than the alternative (say cash), which has benefits normalized to zero. b S is drawn on the interval [ ] b S, b S for each industry from the continuously differentiable distribution function G (b S ), with density g (b S ). The hazard rate λ S = g/ (1 G) is again assumed to be increasing. Given price coherence, by accepting cards a merchant is able to offer each of its card holding customers an additional expected surplus of φ B = D (p B ) v B (p B ), but faces an additional expected net cost of D(p B )(p S b S ) per cardholder from doing so. Under Hotelling competition, merchants will accept cards if this raises their customers expected surplus net of their own costs. This implies merchants in an industry with benefits b S accept cards if and only if p S b S + v B (p B ). (1) This acceptance rule is formally derived in Wright (2004) when all consumers hold cards. Rochet and Tirole (2010) show the same condition also holds for the Lerner-Salop model of competition with any number of merchants, while Wright (2010) shows the same condition holds for Cournot competition with elastic goods demand and any number of merchants. The extension to an exogenous fraction of cardholders, as is assumed here, is trivial. As a result of (1), all industries with b S b m S = p S v B (p B ) will accept cards. Let S (b m S ) = 1 G (bm S ) be the measure of such industries. The average convenience benefit to merchants accepting a card for a transaction is β S (b m S ) = E[b S b S b m S ], where 0 < β S (bm S ) < 1 follows as before. Since the interchange fee a acts as a per-unit tax for acquirers and a perunit subsidy for issuers, the relevant marginal cost for issuing is c I a and for acquiring is c A + a. All reasonable models of how issuers and acquirers behave imply p S c A + a and p B c I a, so they do not price below marginal cost. Assume that p B and p S are continuously differentiable functions of a, with p B < 0, p S > 0, p B + p S > c and p B p S. The assumption requires that there is always some pass-through of marginal costs into prices on both sides, that issuers and acquirers jointly derive positive margins, and that the passthrough on the issuing side is never higher than on the acquiring side. This is consistent with the standard assumption in the theoretical literature that there is 100% pass-through on the acquiring side (e.g. as in Rochet and Tirole,

7 and Bedre-Defolie and Calvano, 2010) reflecting the homogenous nature of price competition for merchants 7, while at the same time assuming that the issuing side is imperfectly competitive either with cost absorption (Rochet and Tirole, 2002) or constant margins (the benchmark case in Wright, 2004, Rochet and Tirole, 2010 and Rochet and Wright, 2010). The assumption also seems to be consistent with the limited empirical evidence that is available. 8 Katz (2005, p.132) writes Industry wisdom is... that acquirers generally pass through a higher percentage of fee changes to their customers than do issuers. The card network is assumed to set a to maximize the total of issuers and acquirers profit from card transactions, namely Π = (p B + p S c) T, (2) where T = µd (p B ) S (b m S ) is the number of card transactions. This objective function is the standard assumed in the literature. Possible justifications are that (i) historically, card networks such as MasterCard and Visa were associations representing the interests of their member issuers and acquirers; (ii) even after their initial public offerings, many of these members remain significant shareholders of the card networks, so their interests may still be considered; (iii) in practice card networks levy various fees on issuers and acquirers, and the amount they can extract from these fees may be closely related to issuers and acquirers profit from card transactions; (iv) card networks may actually maximize the volume of card transactions but if issuers and acquirers have equal pass-through rates, this is equivalent to maximizing Π in (2); and (v) if issuing is monopolized and acquiring is perfectly competitive so p S = c A + a, this specification also captures the fees that would be set by a closed payment network like American Express that directly chooses p B and p S. Social surplus is generated whenever consumers use cards for payment at merchants provided their joint convenience benefits exceed the joint cost of doing so (i.e. b B +b S > c). Thus, total welfare generated from the card network is the average social surplus per transaction multiplied by the number of card transactions, namely W = (β B + β S c) T. (3) Subtracting profit Π from W, total user surplus is the total surplus cardholders and merchants obtain from card transactions, namely U = (β B + β S p B p S ) T. (4) In the Hotelling model of merchant competition, equilibrium retail prices are higher by µd (p B ) (p S b S ) in an industry with convenience benefits b S in case 7 Indeed, acquirers often charge merchants interchange fee plus contracts, so they directly pass on interchange fees to merchants. 8 In an empirical study of issuing and acquiring in Europe, the European Commission (2006) found a pass-through rate of 0.4 for acquiring versus for issuing (based on their preferred fixed-effects specification). Studies of the regulatory experiment in Australia in 2003 in which interchange fees were reduced by 40 basis points in 2003 suggest a roughly 100% pass-through into lower merchant fees, but that cardholder fees (net of rewards and interest free benefits) have increased by a more modest amount (Chang et. al., 2005 and Shampine, 2010). 7

8 cards are accepted. Averaged over all industries accepting cards, average retail prices are higher due to card acceptance by the amount (p S β S ) T. The impact of card payments on consumer surplus is therefore given by (β B p B ) T (p S β S ) T, which equals total user surplus from cards U. The relevant range of interchange fees for analysis is defined by the interval [a B, a S ], where p B (a B ) = b B, p B (a B ) = b B, b m S (a S ) = b S, bm S (a S) = b S and a S a B < a S a B. This is the simplest way to ensure that the privately and socially optimal interchange fee does not involve a corner solution (at a point where cardholders always want to use cards or merchants in all industries accept cards). It requires there be users on each side that are sufficiently resistant to the use of cards. As a result of this assumption, the number of card transactions (and so profit and welfare from cards) is zero for interchange fees outside the interval [a B, a S ], and is strictly positive for interchange fees within the range. The assumption also implies β B + β S > c for the relevant range of interchange fees (and so b B + b S > c) since β B + β S > β B + b m S = p B + p S > c, where the first inequality follows since b S < b m S (a) < b S for a (a B, a S ). Finally, I assume throughout that the possible objective functions T, Π, U, and W are log-concave in a over the relevant range of interchange fees, so that the first order conditions with respect to a characterize the respective maximums. The appendix shows that sufficient conditions for log-concavity of the objective functions are that each of p B, p S, β B and β S is sufficiently close to zero. An example satisfying these conditions arises if issuing and acquiring margins are linear in interchange fees (i.e. constant pass-through rates), and b B and b S are drawn from generalized Pareto distributions with increasing hazard rates (see the appendix). The timing of the game can be summarized into five stages. (i) The card network sets the level of the interchange fee a. (ii) Issuers and acquirers set equilibrium fees p B and p S. (iii) Based on their draw of b S, each merchant decides whether to accept cards and sets its (retail) price. (iv) Observing which merchants accept cards and their prices, consumers decide which merchant to purchase from (v) Cardholders receive their draw of b B and decide how to pay. 3 Results for the benchmark model A key question in the literature on payment cards is whether privately set interchange fees are too high compared to the welfare or consumer surplus maximizing levels. Previous results allowing for unobserved heterogeneity amongst both cardholders and merchants (Proposition 3 in Wright, 2004, and Proposition 11 in Rochet and Tirole, 2010) suggest that whether privately set interchange fees are too high is ambiguous. Rochet and Tirole (2010) write Proposition 11 8

9 shows that when the merchant homogeneity assumption is relaxed, the price structure chosen by a monopoly platform, in the absence of regulation, is no longer systematically biased in favor of cardholders. Indeed, these papers establish that assuming issuer and acquirer margins are both constant, privately set interchange fees will be too high if and only if β B p B > β B b m S (or equivalently, p S > β S given that b m S = p B + p S β B ) suggesting whether interchange fees are distorted upwards is an empirical matter that depends on the relative benefits of cardholders and merchants. Proposition 1 says this is not the case the distortion holds in general. Proposition 1 The privately set interchange fee strictly exceeds the interchange fees maximizing consumer surplus, total user surplus and welfare. Proof. Let a Π be the interchange fee maximizing Π and a W be the interchange fee maximizing W. These are uniquely defined by dπ/da = 0 and dw/da = 0. Combining (2) and (3), welfare from cards can be defined as W = ( βb + β S c p B + p S c ) Π. Differentiating welfare with respect to a and using that T = Π/ (p B + p S c) implies ( ) dw da = βb + β S c dπ p B + p S c da + T, where = dβ B da + dβ ( ) S da βb + β S c (p B + p p B + p S c S) (5) ( ( ) ) = β B (1 β S) p βb + β S c B + p B + p S c β S (p S p B ) (6) is strictly negative given p B p S, β B > 0, 0 < β S < 1, and β B + β S c > β B + b m S c = p B + p S c > 0. As a result, a small decrease in a from a Π which solves dπ/da = 0 must increase welfare compared to at a Π. Given log-concavity of W, this implies a W < a Π. (Note the same conclusion can be reached if Π is instead written as a function of W and dπ/da is evaluated at a W. In this case dπ/da = (p B + p S c) T / (β B + β S c) > 0, where is now evaluated at a W.) The same result applies with respect to consumer surplus and total user surplus. The contribution of cards to each surplus expression is given by (4), which can be written as U = W Π. The result follows given du/da = dw/da at a Π. Lowering interchange fees from the privately set level unambiguously raises consumer surplus and total welfare. Note this bias does not depend on the particular distribution of cardholder or merchant benefits (only that they involve increasing hazard rates), or the particular nature of issuing and acquiring competition (provided issuer pass-through is less than or equal to that of acquirers). 9

10 Indeed, since the inequality arising from the first term in (6) is strict, the result would continue to hold even if the pass-through rate for issuers was somewhat greater than that for acquirers. The extent of the initial welfare gain from lowering interchange fees can be measured by as given in (6). In (5), is decomposed into three terms. Assuming equal pass-through (i.e. p B = p S ) for the moment, the last term, which captures a competitive distortion, disappears and the first two terms are equal to {β Sp S β B p B } + { β S + β Bβ S} p B. (7) The first bracketed term in (7) captures distortions which arise because the card network does not internalize the effects of a change in its price structure on average cardholder and merchant convenience benefits β B and β S. A higher price on one side will increase the average convenience benefits of users on that side as only users with higher benefits make use of the platform. Welfare can be improved by shifting fees to the side where the average convenience benefit is more sensitive to fees, thereby raising benefits more on this side than they are reduced on the other side of the market without affecting the number of card transactions or profit at the margin. The net distortion could be positive or negative depending on the relative shapes of the two distribution functions. Without merchant internalization or a competitive distortion, this would be the only source of divergence between privately and socially optimal interchange fees, and the direction of the bias would be entirely an empirical matter. The second bracketed term in (7) shows how these distortions are partially undone by the fact that merchants internalize their customers surplus. Any attempt to raise welfare by increasing interchange fees and so merchant fees so as to increase the average convenience benefits of merchants will be to some extent undone by the fact cardholders will face lower fees which merchants internalize, so the decision of the marginal merchant will not actually be much affected by the change in interchange fees. Indeed, in the case with symmetric pass-through there will be no direct impact on the marginal merchants willingness to pay to accept cards as can be seen from the fact β S p S cancels with β S p B in (7). Merchants are, in this sense, insensitive to changes in interchange fees. There remains an indirect impact on the marginal merchant through the fact that lower interchange fees raise card fees and so the average convenience benefits of the remaining users of cards, which makes the marginal merchant willing to pay more to accept cards. However, this indirect effect only partially offsets the positive direct effect of lowering interchange fees on increasing the convenience benefits of cardholders, as can be seen from the fact (7) simplifies to β B (1 β S ) p B. Thus, with symmetric pass-through, the distortion on the cardholder side, which argues for lowering interchange fees, is only partially offset by the distortion on the merchant side, and lower interchange fees will unambiguously raise welfare. 9 9 As can be seen from (6), this depends on the increasing hazard rate property for the distribution of b S. In the special case that this distribution is exponential so that the hazard rate is constant and β S = 1, the indirect effect would fully offset the direct effect and merchant 10

11 The last term in (5) captures the competitive distortion which arises when pass-through is less on the issuing side than the acquiring side (i.e. p B < p S ) so that the card network can increase its profit margin by shifting revenue to the issuing side. At the same time, the difference in pass-throughs means that an increase in interchange fees now has a direct effect on merchant acceptance, since merchant fees will increase more than card fees will decrease. This means the average convenience benefits of merchants can be directly increased by increasing interchange fees, thereby reducing the extent of the distortion from merchant internalization. Nevertheless, the new competitive distortion means the net distortion always remains negative and privately set interchange fees remain too high. A competitive distortion by itself does not necessarily imply a bias against merchants. To see this, assume merchants only consider convenience benefits when deciding whether to accept cards. ( βb +β S c p B +p S c ) From (5), = β S p S β B p B (p S p B ), which can be positive if β S p S > β B p B, except in the 0. Merchant internalization is required to obtain an unambigu- limit as p B ous bias in privately set interchange fees. Further support for this view is given in Sections The bias in interchange fees induced by merchant internalization can be large. For example, consider the symmetric setting in which convenience benefits are drawn from the same uniform distribution over [ b, b ] for cardholders and merchants, issuing and acquiring costs are equal ( c = c I = c A ), and profit margins π are constant and arbitrarily close to zero for both issuers and acquirers. The relevant range of interchange fees is defined by [ c b + π, 3 ( b c ) 4 π ], with the requirement that 4b > 4 c + 5 π > b + 3b. Then instead of a W = a Π = 0, which would be true if there was no merchant internalization, a W a Π /3 > 0, so that moving to the welfare maximizing interchange fee requires privately set interchange fees be cut by nearly two-thirds. 10 To see this note that a Π = ( (b ) ) (b ) b c π and a W = a Π 2 /3 + 4 c + π c + 3 π 2 /3. As π 0, a W a Π /3 and a Π > 0 given b > c. Provided issuing and acquiring are symmetric, Proposition 1 implies a small reduction in interchange fees will not just raise consumer surplus, it will lower the average retail price set across all merchants. Proposition 2 Assuming that issuing and acquiring pass-through rates are symmetric, at the privately set interchange fee the equilibrium merchant fee exceeds the average merchant convenience benefit amongst merchants accepting cards. Lowering interchange fees from privately set levels will lower retail prices but raise prices (net of card fees and rewards) to card customers. internalization would not result in any bias. 10 The fact that the socially optimal interchange fee is positive despite both sides being completely symmetric is another implication of merchant internalization, as discussed in Wright (2004). 11

12 Proof. (5) can be rewritten as = (β B p B ) D p B D (β S b m S ) S db m S S da, where I have used that β B = (β B p B ) D /D, β S = (β S b m S ) S /S and p B + p S = 0 (given symmetric pass-throughs). Given < 0 at aπ from Proposition 1, this implies where I have used the first-order condition (β B p B ) + (β S b m S ) < 0, (8) D p B D + S db m S S da = 0 at a Π. Using (1), the inequality in (8) can be rewritten as p S > β S. (9) Since the change in average retail prices due to card acceptance is (p S β S ) T, (9) implies retail prices are higher as a result of card acceptance. Lowering interchange fees from the profit maximizing interchange fee decreases retail prices since d (p S β S ) /da = (1 β S ) p S + β S (1 β B ) p B > 0 and since dt/da = 0 at a Π given symmetric pass-throughs. The additional price paid by cardholders per transaction (net of rewards) due to card acceptance is (p B + p S β S ). Lowering interchange fees from the profit maximizing interchange fee increases the total price paid per transaction for card customers since d (p B + p S β S ) /da = β B β S p B < 0. By raising card fees or reducing rewards, lower interchange fees reduce the net cost of accepting cards to merchants and so result in lower retail prices. This is consistent with the view of policy makers that privately set interchange fees lead to inefficient card transactions that raise retail prices. 11 Regulating lower interchange fees will also have distributional effects. The fraction 1 µ of consumers not holding cards are better off with lower interchange fees due to lower retail prices. However, cardholders end up paying higher prices as the higher card fees (lower rewards) more than offset the effect of lower interchange fees on retail prices. While it is clear regulating lower interchange fees will mean consumers will use their cards less frequently at merchants that accept cards, it is not immediately obvious whether there will be more card transactions in total, taking into account that the number of merchants accepting cards will increase. The next proposition compares profit, welfare and output maximizing interchange fees to address this question. 11 With elastic demand for goods, inflated retail prices would presumably also introduce further allocative inefficiencies. 12

13 Proposition 3 Lowering interchange fees from the profit maximizing level can decrease the volume of card transactions (equal pass-through case) or increase the volume of card transactions (asymmetric pass-through case). Provided passthrough rates are not too asymmetric, welfare maximization requires an interchange fee lower than the output maximizing level (otherwise, welfare maximization requires an interchange fee higher than output maximizing level). Proof. Writing the volume of card transactions T as a function of Π, we have ( dt da = 1 dπ p (p B + p S c) da Π S p B ), p B + p S c which is zero at a Π if p B = p S (symmetric pass-through) and is negative if p B < p S (pass-through less on the issuing side). With symmetric pass-through, a T and a Π coincide. Any change in interchange fee from the privately set level will reduce the volume of card transactions. With asymmetric pass-through, dt/da < 0 at a Π. A lower interchange fee will initially increase the volume of card transactions. Comparing dw/da and dt/da directly, note that dw = (β B + β S c) dt ( da da + dβb da + dβ ) S T da = (β B + β S c) dt da + ({β S (p S p B )} {β B (1 β S) p B }) T. Since dt/da = 0 at a T, welfare can be improved initially by lowering interchange fees below the output maximizing level if at a T, p B p S β S > β S + (1 β S ), (10) β B and by raising interchange fees if the inequality in (10) is reversed. Note the right hand side of (10) lies strictly between 0 and 1, so with symmetric (or nearly symmetric) pass-throughs the inequality holds and lowering interchange fees below the output maximizing level increases welfare, while if the asymmetry in pass-throughs is high enough, the inequality in (10) will always be reversed and raising interchange fees above the output maximizing level increases welfare. When pass-through on the issuing side is less than on the acquiring side, the volume of card transactions can be increased by lowering interchange fees from their profit maximizing level. This reflects that with asymmetric pass-through there is a competitive distortion, with transactions being sacrificed in order to shift revenues to the side where they are not competed away. As a result, regulations that lower interchange fees will initially increase card transactions and welfare This is the reason the effect of lowering interchange fees on average retail prices could be ambiguous when pass-through are asymmetric, since more transactions will be made on cards. 13

14 Proposition 3 implies that the concerns of policymakers and proponents of interchange fee regulation are fully consistent with the assumption that issuers and acquirers have roughly equal pass-throughs (i.e. a complete absence of a competitive distortion). This ensures that regulating lower interchange fees to maximize welfare results in some reduction in card volume. In contrast, if passthrough is sufficiently low on the issuing side, welfare maximization calls for a higher interchange fee than that which maximizes the volume of card transactions, reflecting that a higher interchange fee does not have much affect on the cardholder side but does raise the average convenience benefits of merchants that continue to accept cards Extensions The results from Section 3 show that even in a fairly generic setting, where the heterogeneity in cardholder and merchant benefits is not necessarily asymmetric to start with, there is a systematic bias in privately set interchange fees caused by the fact merchants internalize their customers surplus from using cards when deciding whether to accept cards. The above results also demonstrate that a competitive distortion is not required to explain why interchange fees are too high, although the bias against merchants remains in the presence of such a distortion. This section explores the robustness of these conclusions in several different dimensions. Section 4.1 shows a similar bias arises even if there is no unobservable heterogeneity across merchants. Remarkably, however, this bias disappears completely in the extreme case of a monopoly issuer, so that the privately set interchange fee is socially optimal. This result, which has not previously been noted in the literature, reinforces the view that the fundamental source of the bias in interchange fees is not a lack of issuing competition. Section 4.2 relaxes the assumption of price coherence. It allows merchants to surcharge for card payment but supposes they face some transaction cost for doing so which varies across different industries. It shows that interchange fees remain biased against merchants. Section 4.3 discusses the extension to competing payment cards, and draws on the existing literature to show that the bias continues to apply even in the presence of perfect inter- and intra-network competition. 4.1 Fully observable variation across industries Suppose any heterogeneity across different industries is observable to the card network. In particular, suppose there are n different industries, each of which may involve a different convenience benefit to merchants b S, along with a different distribution of cardholders convenience benefit H (b B ). Different industries 13 If b B and b S are uniformly distributed, then β B = β S = 1/2. From (10), welfare maximization calls for an interchange fee above that maximizing card transactions whenever the pass-through rate of issuers is less than two-thirds the magnitude of the pass-through rate of acquirers. 14

15 are indexed with a superscript i. Since these differences are observable to the card network, it can set different interchange fees a i for each such industry. However, consumers are assumed to face a single card fee p B that does not vary depending on the industry consumers purchase from. A special case of the model is when every industry is identical, or equivalently that there is just one industry. This was the assumption in the benchmark case of Rochet and Tirole (2002). Consider initially the special case in which the issuer is a monopolist and acquirers are perfectly competitive. I first show this implies the privately set interchange fee exactly maximizes welfare (and indeed is first-best). Proposition 4 If issuing is monopolized and acquiring is perfectly competitive, and if the card network can set a different interchange fee for each different industry, then privately set interchange fees result in maximum welfare. Proof. The card network chooses an interchange fee a i for each industry to maximize issuer and acquirer joint profit: max a 1,...,a n n µ ( p B + p i S c ) D i (p B ) s.t. p i S b i S + vb i (p B ) for i = 1,..., n. i=1 The monopoly issuer solves max p B (11) n µ ( p B + a i ) c I D i (p B ) s.t. p i S b i S + vb i (p B ) for i = 1,..., n. (12) i=1 Since p i S = c A + a i, the two objective functions can be combined as max p B,p 1 S,...,pn S n µ ( p B + p i S c ) D i (p B ) s.t. p i S b i S + vb i (p B ) for i = 1,..., n. i=1 (13) This is the same objective function as a closed card network that directly sets a single card fee and a different merchant fee for each different industry. Since profits are maximized by setting the highest possible merchant fee in each industry at which merchants still accept cards, the constraints p i S = b i S + vi B (p B) can be substituted into (13) so the objective becomes max p B n µ ( βb i + b i S c ) D i (p B ). (14) i=1 This is exactly the same objective as the social planner, which is to maximize total welfare. Thus, privately set interchange fees maximize welfare. The proposition shows that a profit maximizing card network with a monopoly issuer and competitive acquirers will set an efficient (indeed first-best) price structure. This result contrasts with the main result of Rochet and Tirole 15

16 (2002) obtained with homogenous merchants. In their paper, the only reason an interchange fee could be efficient is if it was constrained efficient that is, a higher interchange fee would be needed to obtain the right card fee but this was not possible since then merchants would no longer accept cards. In contrast, the outcome from (14) implies the first-best level of a single card fee n p i=1 B = c hi (p B ) bi S n i=1 hi (p B ), (15) which equals c b S in the case with homogenous merchants. This ensures cardholder correctly internalize the cost of acquiring and the (weighted average) convenience benefits to merchants when deciding whether or not to use cards. The corresponding interchange fees are defined by a i = b i S c A + v i B (p B), (16) which equal a = b S c A + v B (c b S ) in the case with homogenous merchants. This interchange fee is set above Baxter s (1983) proposed interchange fee b S c A to ensure that the issuer s monopoly markup is appropriately offset. Merchant internalization plays a key role in the above result. If merchants instead only consider their own convenience benefits, accepting cards only when p S b S, then p B would be set to maximize n i=1 µ ( p B + b i S c) D i (p B ). Card fees would be set inefficiently high due to the issuer s monopoly pricing and there would be too few card transactions. The internalization of cardholders average surplus by merchants ensures that fully extracting all surplus from merchants also extracts cardholders convenience benefits. As a result, the perfectly discriminating monopolist issuer has the right incentives with respect to setting interchange fees from a welfare perspective. The above result implies that lowering interchange fees from their privately set level will necessarily lower welfare since it will raise card fees above the efficient level without affecting merchant acceptance given all merchants already accept cards. However, less obviously, there may also be no gain in user surplus associated with a lowering of interchange fees. For simplicity, take the case where there is just one industry (i.e. merchants convenience benefits are homogenous). Then total user surplus U = (β B + b S p B p S ) µd (p B ) will be equal to zero since the card network sets the interchange fee to the point where merchants just accept (i.e. p S = b S +v B (p B ) = b S +β B p B ). If the interchange fee is lowered from this level, p S will decline so it raises the possibility that U will become positive. However, for a general interchange fee, the monopoly issuer maximizes its profit (p B + a c I ) µd (p B ) subject to p S b S + v B (p B ). As the issuer increases p B in response to a lower a, the merchant acceptance constraint is tightened, and so even though p S is lowered, the constraint may remain binding. Indeed, this will be true in general for a small decrease in interchange fee since the constraint is strictly binding at the privately set interchange fee. To see this note λ = µ (D + (p B + a c I ) D ) / (1 β B ) is the solution of the Lagrange multiplier on the constraint in the monopoly issuer s profit maximization problem. Evaluating at the privately optimal interchange 16

17 fee a = b S c A +v B (c b S ) and using the property that β B D = (β B p B ) D implies λ = µd > Thus, it could take a considerable reduction in interchange fees (and welfare) for user surplus to be increased in this case. Now suppose instead issuers are competitive. In this case, the card network will no longer generally have the same incentives as the social planner since issuers no longer extract all of the end user surplus. The finding from Proposition 1 that interchange fees are excessive is restored. Proposition 5 If issuing is subject to sufficient (but not perfect) competition, acquiring is perfectly competitive, and if the card network can set a different interchange fee for each different industry, then the privately set interchange fees strictly exceed the interchange fees maximizing welfare. Proof. Starting from the efficiently set interchange fees defined by (16), consider introducing competition to issuing. Holding interchange fees constant initially, assume competition in issuing lowers the card fee p B below p B defined in (15). This will be true if competition is sufficient to overcome the constraint on the issuers card fees at the initial interchange fee. This will increase vb i in each industry, thereby causing the card network to increase interchange fees in each industry to capture this additional surplus. This increase in interchange fees will reinforce the reduction in the equilibrium card fee. As a result, ( n ) dw da i = µ ( ) c b i S p B h i (p B ) i=1 dp B da i, which equals zero at p B under a monopoly issuer will become negative at the privately set interchange fee under sufficient issuer competition. In other words, welfare can be increased by lowering the interchange fee in each industry. Proposition (5) reinforces the view that the problem of excessive interchange fees is not necessarily due to insufficient issuer competition. Indeed, in this setting in which merchants all accept cards, competition among issuers is necessary for interchange fees to be excessive. The result that greater issuer competition increases equilibrium interchange fees is the opposite of the result found in Rochet and Tirole (2002). In my setting greater issuer competition leads to higher interchange fees reflecting the increasing willingness of merchants to accept cards when rewards and interest free benefits are high given merchants care about the surplus their customers get from using cards. In contrast, in Rochet and Tirole (2002), merchants do not internalize the surplus their customers get from rewards and interest-free benefits since these are included in the net card fee which is assumed to be a fixed fee in their model. 14 For example, if b B follows the Generalized Patero distribution given in the Appendix, then the constraint will remain binding unless interchange fees are lowered by ε 2 v B (c b S ) / ( 1 + ε + ε 2). Only if interchange fees are lowered more than this amount will total user surplus become positive. 17

18 4.2 Allowing merchants to surcharge A fundamental assumption in most of the existing literature is that merchants cannot pass the costs of accepting cards to their customers (e.g. through a surcharge for using cards). This reflects that such surcharging is banned by card networks in most countries. If surcharging is allowed, existing theories imply interchange fees will be completely passed through to consumers and so the level at which they are set becomes irrelevant from a policy perspective, as well as from the perspective of consumers, merchants and card networks (see Gans and King, 2003 for a very general neutrality result). 15 However, the neutrality of interchange fees does not accord well with reality. In countries where the card networks no-surcharge rules have been banned (e.g. Australia, Netherlands, New Zealand, Sweden, and the U.K.), the vast majority of merchants continue not to add any surcharge for consumers paying by card. This suggests there is some other reason why surcharging will not be widespread even when it is allowed. The simplest explanation is that doing so involves transaction costs. In this section I consider what happens if merchants are allowed to surcharge for card transactions. Merchants that set a surcharge for card transactions incur a positive transaction cost k of doing so, the level of which is assumed to vary across different industries in a way which is not observed by card networks. To simplify the model, like Section 4.1, I assume merchants are otherwise homogenous, including in their convenience benefit of accepting cards. This provides a different way to introduce unobservable merchant heterogeneity, in which all merchants accept cards but some will surcharge. For simplicity I also focus on the case in which issuers and acquirers have constant margins, which shows the bias obtained below does not rely on any competitive distortion. Let the transaction cost k associated with collecting the surcharge be drawn on the interval [0, ) for each industry from the continuously differentiable distribution function G (k), with density function g (k) everywhere positive. Let the level of the surcharge in an industry where merchants surcharge be denoted r. The objective functions are again assumed to be log-concave over the relevant range of interchange fees. Proposition 6 If merchants are homogenous in the convenience benefits of accepting cards but are heterogeneous in the transaction costs of surcharging for card acceptance, the privately set interchange fee strictly exceeds the interchange fees maximizing consumer surplus, total user surplus and welfare. Proof. I first characterize when merchants will surcharge for cards and when they will set uniform prices. With uniform pricing, equilibrium retail prices in the Hotelling model assuming card acceptance equal p = d + t + µd (p B ) (p S b S ), where d is the unit cost of goods and t is the Hotelling transportation cost parameter. Under surcharging, it is straightforward to show that the equilibrium retail price will be the usual Hotelling price p = γ + t with 15 See also Rochet and Tirole (2002), Schwartz and Vincent (2006) and Wright (2003) for analyzes comparing welfare with and without surcharging. 18

19 a surcharge for card payment of r = p S b S + k. The equilibrium level of the surcharge equals the additional net costs of accepting cards and surcharging. Consider the equilibrium where both merchants in an industry set surcharges. Now suppose merchant 1 sets uniform prices instead. Then its market share is and its profit is s 1 = µ (φ B (p B ) φ B (p B + p S b S + k)) + γ + t p 1 2t π 1 = (p 1 d + µ (D (p B ) (b S p S ))) s 1. Merchant 1 s deviation (uniform) price is p 1 = d + t + µ (φ B (p B ) φ B (p B + p S b S + k) D (p B ) (b S p S )), 2 so that its profit after the deviation is where t ( 1 µρ ) 2, 2 2t ω = D (p B ) (p S b S ) (φ B (p B ) φ B (p B + p S b S + k)) = bb p B +p S b S +k (b B + b S p B p S k) dh (b B ) bb p B (b B + b S p B p S ) dh (b B ) is a measure of the additional net cost to merchants (less cardholder surplus) of setting uniform prices rather than passing through the additional costs of accepting cards to cardholders. Therefore, there is an equilibrium where both merchants set surcharges if ω 0. Similarly, it can be shown that there is an equilibrium where both merchants set uniform prices if ω 0. Assume initially that the card network chooses an interchange fee such that b S < p S < b S + v B. This means if k is arbitrarily close to 0, then ω > 0 so that there will be surcharging. It also means for k high enough (k = b B +b S p B p S will do), then ω = (β B (p B ) + b S p B p S ) D (p B ) < 0 given p S < b S + v B. As k increases, ω decreases since dω/dk = D (p B + p S b S + k) < 0. These properties imply there exists 0 < k < b B (p B + p S b S ) at which ω (k ) = 0. All industries with higher k will involve uniform pricing and all industries with lower k will involve surcharging. The number of card transactions is ( ) k T = µ 0 D (p B + p S b S + k) dg (k) + D (p B ) (1 G (k )), 19

20 where k is defined implicitly by ω (k ) = 0. Card transactions consist of two types transactions made by consumers who face a surcharge to use cards but that receive sufficiently high convenience benefits that they still wish to use cards, and transactions made at merchants who do not surcharge. For b S < p S < b S + v B we have and dt da = µ dk da = (p S b S ) h (p B ) D (p B + p S b S + k ) > 0 ) ((D (p B + p S b S + k ) D (p B )) g (k ) dk da D (p B ) (1 G (k )). (17) Higher interchange fees increase the number of merchants that will surcharge, thus reducing card transactions at these merchants, but increase the usage of cards at the remaining merchants who continue to set uniform prices. I now show that a is indeed set so that b S < p S < b S + v B. Note first that if p S b S + v B, then no merchants will want to set uniform prices since ω > 0 for all k > 0. Indeed, all merchants will surcharge for card acceptance since p S > b S k. Interchange fees will be neutral in this range. However, starting from p S = b S + v B, a small reduction in a will increase T since the first term in (17) is negative and the second term is zero. In contrast, at p S = b S, no merchants surcharge and a small increase in a will increase T since the first term in (17) is zero and the second term is positive. Given our assumption that T is log-concave over the relevant range of interchange fees, T (and so Π) is maximized at an interchange fee for which b S < p S < b S + v B. As before, welfare from cards can be written as a function of Π, so that W = ( ) βb + b S c k Π µ kd (p B + p S b S + k) dg (k), p B + p S c 0 where the additional term reflects the transaction costs of surcharging. Differentiating welfare with respect to a implies ( ) dw da = βb + b S c dπ p B + p S c da T β B µk D (p B + p S b S + k ) g (k ) dk da, (18) where the last two terms in (18) are negative since β B > 0 and dk /da > 0. As a result, a small decrease in a from a Π which solves dπ/da = 0 must increase welfare compared to at a Π. Given the log-concavity of W, this implies a W < a Π. The same result applies with respect to total user surplus since U = W Π and so du/da = dw/da at a Π. To obtain the result on consumer surplus note equilibrium retail prices are higher by ( k µ D (p 0 B + p S b S + k) (p S b S + k) dg (k) +D (p B ) (p S b S ) (1 G (k )) ) 20

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