The Welfare Implication of Lifting the No Surcharge Rule in. Credit Card Markets

Transcription

1 The Welfare Implication of Lifting the No Surcharge Rule in Credit Card Markets Hongru Tan November 5, 015 Abstract This paper investigates the welfare implications of banning the no surcharge rule (NSR) in the market to provide credit card payment services. Conventional wisdom indicates that banning the NSR may increase or decrease social welfare depending on the relative magnitudes of the distortion due to market power of issuers and the distortion of merchant internalization. Merchant internalization refers to the internalization of consumer surplus by merchants when they make the decision to accept credit card payments. However, this paper finds removing the NSR unambiguously decreases social welfare. This unambiguous conclusion for welfare holds regardless of the property of demand and the degree of competition among issuing banks. The only condition for the conclusion to hold is the existence of merchant internalization. The model of this paper also shows a reverse subsidization from card users to cash users instead of the conventional result that cash users subsidize card users under the NSR. By modifying and extending existing frameworks to better match reality and incorporating recent change in the market structure, this paper is able to explain the empirical regularities related to the various surcharging behavior of merchants. It also applies a difference in difference method to roughly estimate the change in payment value of credit cards resulted from the ban of the NSR in Australia in an attempt to verify which sub case of the model better mimics the practical situation in the real world. 1

2 Contents 1 Introduction 3 Background 8 3 Literature review 9 4 Model 11 5 Hotelling merchants Homogeneous merchants Unambiguous welfare implication Heterogeneous merchants Reverse cross subsidization Monopoly merchants Homogeneous merchants Heterogeneous merchants Surcharging behavior of merchants Conclusion 67 8 Appendix Hotelling competition Change in payment value Table Graph

3 1 Introduction The last five years have seen three cases have been investigated by government enforcement agencies against business provisions in the contracts between merchants and acquiring banks (in the case of Visa and MasterCard) or American Express. The provisions between acquiring banks and merchants are required under the contractual terms between Visa and MasterCard and their acquiring banks. These provisions restrict conduct by merchants to steer the choice of payment by consumers when completing their transaction. The two U.S. cases involve a complaint that these contractual terms violate Section 1 of the Sherman Act. The common complaint against the three credit card platforms resulted in a consent decree and settlement with Visa and MasterCard, 1 while American Express elected to go to trial and lost. Among all the business provisions implemented and enforced by the three credit card platforms, one provision, referred to as the no surcharge rule (NSR), has been particularly at issue in the antitrust cases. The no surcharge rule is a business practice that prohibits merchants from charging a higher price to purchases made using credit cards than to purchases made using other forms of payments (such as cash or debit cards). It is a precondition for merchants to accept credit card payments. The term surcharge refers to the potential price difference between consumers who pay with credit cards and consumers who pay with other forms of payments. After the antitrust investigation during last two decades, the no surcharge rule has been banned in the United States, Australia, Czech Republic, Denmark, Ireland, Hungary, Netherlands, New Zealand and the U.K. 3 Experts and economists in the relevant lawsuits against credit card companies doubt 1 See United States et al v. American Express Company et al, 10-CV-4496 Complaint, Proposed Final Judgment, and Competitive Impact Statement, 4 October 010, and Final Judgment, as well as Memorandum and Order, 0 July 011. All available online at United States et al v. American Express Company et al, 10-CV-4496 (Eastern District of New York) 19 February The details of regulation can be found in Weiner and Wright (005). 3

4 the NSR mainly for two reasons (as raised in the expert report of Prof. Ralph Winter for the lawsuit in Canada 4 ); namely: (i) the NSR suppresses competition between credit card companies, such as Visa and MasterCard, because it refrains Visa or MasterCard from competing on the basis of the level of surcharges, which could be used by merchants to cover their different costs of accepting each type of credit card; and (ii) the NSR induces a transfer of benefits from the consumers who use other forms of payment to consumers who pay with a credit card, since the cost of merchants to accept credit cards is built into the price of products under the NSR, and cash or debit card usingconsumers also pay for it. The phenomenon is referred to as cost externality in the literature, and it is essentially due to merchant s behavior to accept credit card payments to attract customers when the merchant fees are excessively high. This type of merchant behavior is called merchant internalization (MI) in literature and it simply implies that merchants internalize consumer surplus when making the decision to accept credit card payments or not. This paper first of all distinguishes itself by finding a different welfare implication of removing the NSR from the literature Rochet and Tirole(00) (RT00) in a similar setting. The welfare impact of lifting the NSR in RT00 is investigated in a context where a notfor-profit platform, consisting of oligopolistic issuers and perfectly competitive acquirers, provides credit card service to consumers and a sector of two Hotelling merchants. The welfare impact could be positive or negative depending on the relative magnitudes between the distortion from market power of issuers and the distortion of merchant internalization under the NSR. In the paper of RT00, they do not provide evidence or answer the question whether the credit card service is over or under provided in the real world. Therefore, no clear policy implication could be drawn from their model. However, a similar case in this paper, where a monopoly platform provides credit card 4 See the report at Expert%0Report%0of%0Ralph% 0A.%0Winter pdf 4

5 service to consumers and a sector of two Hotelling merchants through competitive issuing banks and competitive acquiring banks, shows that removing the NSR always decreases social welfare. This is because the monopoly platform, who is subject to the merchant acceptance condition or the condition of MI, acts as a social welfare maximizer when she maximizes her own profit under the NSR. As a result, the credit card service is always optimally provided. Alternatively, it means that the distortion due to MI always fully offsets the distortion due to market power of monopoly platform. The lifting of the NSR, which eliminates the condition of MI, always results in an under provision of credit card service and hence social welfare always decreases. Notably, the conclusion holds regardless of the property of demand and the degree of competition among issuing banks, and it implies the credit card service is optimally provided as long as there is merchant internalization among merchants. It also means that an unambiguous conclusion of welfare implication of lifting the NSR can be drawn even without empirical evidence. The only condition for the conclusion is the existence of merchant internalization. The result of optimal provision can also be applied in many other two-sided markets. In addition to find the above unambiguous welfare implication, the model of this paper is also extended and improved from the model of RT00 in three ways. First, the credit card platform is modeled as a monopoly platform rather than a not-for-profit association; second, an additional competition setting monopoly of merchants is considered; third, the heterogeneity of merchants is considered. The first extension of monopoly platform reflects the change in the structure of credit card industry over time: both Visa and MasterCard went public in the last decade which switches them from not-for-profit associations into for-profit platforms. The first extension also makes the model best fit the case of American Express where a monopoly platform directly provides the service to consumers and merchants. The second extension of monopoly merchants enables the model to explain the phenomenon of 5

6 excessive surcharges imposed by merchants, which could not be explained by models with Hotelling merchants. The third extension of heterogeneous merchants captures the reality that the platform serves many different sectors of industry. The second and third extensions together enable the paper to provide an explanation to the various merchant behaviors of surcharging observed in Australia, which have not been explained in the literature. To sum up, this paper investigates welfare implication of banning the NSR within a model where a monopoly credit card company provides credit card payment services to both consumers and merchants through competitive issuing banks and competitive acquiring banks. The competition among merchants could be monopoly and Hotelling competition, and heterogeneity of merchants is considered in either case. Credit card payment services provided to consumers in this paper refer to services that enable consumers to purchase a variety of products with credit cards, including account maintaining, fraud protection, transaction settlement and etc. Credit card payment services offered to merchants refer to services that allow merchants to accept payments by credit cards, which include the authorization, clearing and settlement of transactions conducted with credit cards. The benefits of the credit card payment services are the benefits that consumers or merchants obtain by paying with or accepting credit cards rather than cash. These benefits are called as transaction benefits in this paper for both consumers and merchants. The total transaction benefits of both consumers and merchants are the measure of social welfare. In general, this paper has identified three welfare effects of banning the NSR in the market to provide credit card payment services. The first welfare effect is that the removal of the NSR eliminates a market distortion due to merchant internalization, which decreases provision of credit card service below social optimal level and reduces social welfare. The second welfare effect is that the ban of the NSR leads to an institutional change in the market structure some merchants do not accept credit card payments under the NSR but 6

7 do accept them under surcharging. This market structure change increases the acceptance rate of credit cards among merchants and social welfare increases as a result. The third welfare effect of banning the NSR is to allow merchants to impose a surcharge in excess of their costs to accept credit card payments. The excessive surcharges discourage the use of credit cards, and therefore decrease social welfare. The negative effect of eliminating MI often dominates the positive effect of market structure change in the cases with Hotelling merchants, and therefore social welfare often decreases after the lifting of the NSR. Likewise, the negative effect of excessive surcharges dominates the positive effect of market structure change in the cases with monopoly merchants, and therefore social welfare decreases as well. For each competition setting among merchants, three sub cases including the sub case of one sector, the sub case of two sectors and the sub case of multiple sectors, have been discussed with examples and general comparisons. In all the cases with a few exceptions, social welfare under the NSR is greater than social welfare under surcharging. An additional but significant finding of this paper is that credit card users could potentially subsidize those who pay by cash under the NSR, which is in contrast with the finding in RT00. The new finding is due to the assumption that merchants are different in their transaction benefits, compared to the assumption that merchants have the same transaction benefit in RT00. When some merchants have a higher transaction benefit from accepting credit cards than the marginal merchants, they receive a negative cost to accept credit card payments, and they will build up this cost saving into the uniform price of products and the price of products for the cash user is decreased as a result. Credit card users therefore cross subsidize consumers who pay with cash. Moreover, this paper provides an explanation on surcharging behavior of merchants and a rough estimation of the change in payment value of credit cards as consequences of the removal of the NSR in the 003 reform of credit card market in Australia. 7

8 Background In addition to the credit card platform (for example Visa or MasterCard), there are often four parties in a payment system 5 : cardholders, merchants, issuers (or issuing banks), and acquirers (or acquiring banks). Issuers are the banks which issue credit cards to consumers, and acquirers are the banks which provide the machinery for merchants to accept credit card payments. Consider a typical payment transaction where a cardholder purchases a product worth $100 from a merchant. The payment flow is shown in Figure (3A) 6. The cardholder first pays $100 to the issuer, the issuer in turn pays to the acquirer, and finally the acquirer pays to the merchant. Figure(3B) shows the effective payment of fees in the transaction. The cardholder does not pay the fee directly. 7 The merchant pays the $1.60 merchant service fee (or merchant fee) to the acquirer. The acquirer pays $1.50 interchange fee (hereafter the fee) to the issuer. Both the issuer and acquirer pay $0.06 network fee to the credit card platform, e.g., Visa. Therefore, the merchant obtains $98.4 after fees; the acquirer obtains $0.04; the issuer obtains $1.44; the platform obtains $0.1. In the case of American Express, the credit card platform American Express directly charges the customer fee from consumers and the merchant fee from merchants. There are various payment methods include cash, credit card, debit card, personal cheque, stored-value card (gift card), among others. By accepting credit cards merchants enjoy various transaction benefits, including fraud protection, accounting facilities, time savings at the counter (relative to check payments), transaction enablement through credit and float. Consumers enjoy their own transaction benefits, including the ability to buy now and pay 5 In this paper, system, network and platform refer to the same or similar concept. 6 This figure is from the expert report of Professor Ralph Winter, see page 8 Expert%0Report%0of%0Ralph%0A.%0Winter pdf 7 In general, cardholders pay fees to issuers. If cardholders receive cash rewards, the customer fee is negative. 8

9 later (use credit) and eliminating the need to carry, count and the risk losing cash. 3 Literature review Rochet and Tirole (00) is the pioneer canonical study which investigates the welfare implication of removing the NSR. The welfare impact of lifting the NSR in their paper is investigated in a context where a not-for-profit platform, consisting of oligopolistic issuers and perfectly competitive acquirers, serves to consumers and a sector of two Hotelling merchants. Two distortions exist in their model under the NSR: the market power of issuers leading to an under provision of credit card services, and the merchant internalization leading to an over provision of credit card services. If the distortion of market power outweighs the distortion of merchant internalization, the credit card payment service is under provided, and the lifting of the NSR, which eliminates the distortion of merchant internalization, exaggerates the under provision and decreases social welfare. If the distortion of merchant internalization outweighs the distortion of market power, the credit card payment service is over provided, and the lifting of the NSR, which eliminates the distortion of merchant internalization, may increase or decreases social welfare. Wright (003) investigates the welfare effect of removing the NSR in a context where a not-for-profit platform, consisting of oligopolistic issuers and perfectly competitive acquirers, serves to consumers and a sector consisting of either a monopoly merchant or perfect competitive merchants. The paper finds that a monopoly merchant will surcharge excessively if she is allowed to impose a surcharge on credit card payments. The excessive surcharges will lead to too little use of credit cards and hence both the not-for-profit platform who maximizes the total transaction volume through credit cards and the regulator who maximizes social welfare prefer to operate under the no surcharge rule. However, the total transaction volume of credit card payments and social welfare are independent of the no surcharge 9

10 rule and interchange fees if merchants are perfect competitors. This is because merchants will separate into two groups one group only accepts credit card payments and another group only accepts cash payments under either the no surcharge rule or under surcharging. Any changes in the interchange fee will be perfectly passed through by the merchants to consumers, making the interchange fee is irrelevant in either case. Some other literature also investigate the issue of the NSR. Economides and Henriques (working paper) explores the welfare impact of lifting the NSR in a context of competing payment platforms. They find that the imposition of the NSR increases the profit of platform if network effect from merchants to consumers is sufficient weak; and the imposition of the NSR increases social welfare if network effects from merchants to consumers is sufficiently weak and the demand of product of merchants is sufficiently inelastic. However, the competition between merchants is parameterized which implies the model can not be used to explain the surcharging behaviors observed in Australia. Schwartz and Vincent (006) find that the NSR benefits the platforms but harm the cash users and merchants in a context where the portion of consumers who pay by cash and consumers who pay with credit cards is fixed and exogenous. The welfare implication of lifting the NSR also depends on the predetermined portions between cash using consumers and card using consumers. The assumption of fixed portions of cash using consumers and card using consumers rules out the consumer s endogenous choice of payment methods which is the key to understand the payment choice in reality, and the key feature of this paper. Bourguignon et.al (working paper) discusses the optimal regulation of surcharging and cash discounts by incorporating behavioral elements into the model of RT00. However, the welfare implication of removing the NSR is not investigated in their paper. To sum up, the model of the paper is different from the literature in the following sense: (a) The heterogeneous merchants differ in their transaction benefits from accepting the credit 10

11 cards, while the merchants are assumed to have the same level of transaction benefit in RT00 and Wright (003); (b) The competition among merchants is explicitly modeled, and it could be monopoly or Hotelling competition, but in Economides and Henriques (working paper), the competition among merchants is parameterized; (c) Schwartz and Vincent (006) discuss the effect of allowing surcharges assuming the proportions of cash users and card users are fixed, while the proportions are determined endogenously in this paper. Nevertheless, none of them provides an unambiguous conclusion on welfare implication or explains the surcharging behavior of merchants in Australia. 4 Model In the model of this paper, a monopoly credit card company 8 selects two per transaction prices, which are the price charged to consumers namely customer fee p B and the price charged tomerchants namelythemerchant servicefeep S, to maximizeherprofit. 9 Underthe NSR, given the customer fee p B consumers choose to make payments with a credit card or by cash, and merchants choose to accept payment using a credit card or not given the merchant service fee p S. Under surcharging, consumers choose the methods of payments given the customer fee p B and the amount of surcharge s, and merchants always accept the payments made using credit cards since they can pass the cost to accept credit card payments onto consumers by imposing a surcharge. Two competition settings among merchants monopoly 8 This paper only considers the case of one credit card company, as an empirical study Rysman (007) finds that, even though most consumers hold more than one cards, they often use one of them. That is to say, the competition between credit card companies is small once a consumer decides which company she or he is loyal with. 9 In practice, the credit card company chooses the interchange fee, a, and charges the network service fee n I to issuing banks and the network service fee n A to acquiring banks. In effect, the platform, knowing the markup functions among issuers and acquirers, selects these three fees to affect the levels of customer fee p B and merchant fee p S, and hence the usage of the cards among consumers and among merchants. So we assume the credit card company chooses customer fee p B and merchant fee p S directly instead of choosing the interchange fee and network service fees. 11

12 and Hotelling competition are considered, and the competition among issuing banks and among acquiring banks is assumed to be perfectly competitive for exposition purpose. 10 The model best fit the case of American Express where a monopoly platform directly provides the service to consumers and merchants, and represents the case of Visa or MasterCard after their IPOs which switch them from not-for-profit associations into for-profit platforms. So, it reflects the change in the structure of credit card industry over time. In each case of competition among merchants, three sub cases are discussed; namely: the sub case where there is a single sector of merchants to provide a product to consumers; the sub case where there are two sectors of merchants to provide products to consumers; and the sub case where there are a continuum sectors of merchants to provide products to consumers. Merchants from different sectors have different transaction benefits b S from accepting credit card payments. In all the sub cases under either competition setting among merchants, social welfare levels under the NSR and under surcharging are compared. The markets of products are assumed to be fully covered, which means consumers always purchases a unit of product in each sector. This assumption implies that social welfare is always fully realized in the market of products under the NSR and surcharging, and it enables the welfare comparison to be focused on the credit card market. In all the cases, the approach of backwards deduction is applied to solve the two-stage games in the model. 5 Hotelling merchants In the case of Hotelling merchants, each sector is represented by two merchants competing a la Hotelling competition. Hotelling competition means that two identical merchants in each sector selling a same product are located at each end of a unit interval, and compete for the 10 In the real world, the competition among acquiring banks is close to be perfect, despite the competition among issuers is not the case. However, the assumption of perfect competition among issuing banks will not change the properties of the analysis. This point can be seen from the discussion of imperfect competition among issuing banks in the one sector case with Hotelling merchants. 1

13 consumption from consumers who are uniformly spread over the interval. Each consumer located at x incurstransportation cost xt travel to merchant i and transportation cost (1 x)t to merchant j, where the term t is transportation cost per unit distance for consumers. Each consumeralso has a transaction benefit from usingcredit cards b B independentlydrawn from the uniform distribution over the region [0, 1]. The utility from consumption of the good, u, is assumed to be large enough such that a consumer at least purchases from one merchant. 5.1 Homogeneous merchants Under the NSR with MI In the case of homogeneous merchants, there is a single sector within which two identical Hotelling merchants sell a same product to consumers. A monopoly platform under the NSR selects the customer fee p B and the merchant service fee p S to maximize her profit subject to merchant s acceptance of credit card payments. The term sector is referred to as the magnitude of transaction benefit b S of merchants within the sector. In the case with one sector in the model, merchants have one type of transaction benefit b S and merchants are homogeneous. In the case with more than one sectors in the model, merchants from different sectors have different transaction benefit b S and merchants are heterogeneous. But within one sector, two merchants share the same value of transaction benefits. To insure the Hotelling merchants to accept credit card payments, the platform cannot set a merchant service fee p S greater than the transaction benefit of Hotelling merchants b S plus a term v B (p B ) which stands for consumer s average net user surplus from enjoying the credit card payment services, and in this paper the term v B (p B ) is given by v B (p B ) = 1 p B (b B p B )db B 1 p B db B (1) 13

14 Therefore, the monopoly platform profit maximization problem is given by max π N = (p B +p S )D card () p B,p S s.t. p S b S +v B (p B ) (3) where D card = 1 p B is the amount of payments paid by credit cards. 11 The constraint of merchant s acceptance p S b S +v B (p B ) is derived from the condition for a Nash Equilibrium where both merchants prefer to accept credit card payments. The derivation for the constraint of merchant s acceptance, which has been derived in RT00 and Wright (004), is heavily involved in terms of calculation, and therefore is shown in the appendix I for interested readers. The condition (3), which is called merchant internalization, simply says merchants internalize consumer surplus when deciding to accept the card or not. In essence, the condition of merchant internalization holds for the case with Hotelling merchants because each merchant thought they would be able to attract more customers and earn an extra profit if she accepts credit card payments. But, they in effect are trapped in a prisonner dilemma in which they share the consumption of product equally without earning any extra profit than what they would abtain in the equilibrium where both of they decline the credit card payments. The condition of MI also incurs the phenomenon of cost externality which means the higher price due to MI is also born by the consumers who pay by cash, and they cross subsidize consumers who pay with credit cards by bearing the cost of it. As shown is appendix I, the following is solution to profit maximization problem of Hotelling merchants given the merchant fee p S which satisfies the MI condition p S b S + v B (p B ). p i = p j = p = [d+d B (p B )(p S b S )]+t (4) 11 The per transaction cost of operating the credit card platform is assumed to be zero as it is negligible in the real world. 14

15 π M i = π M j = π = t (5) where π is the equilibrium profit of merchants an p is the equilibrium price of product. In the equilibrium between Hotelling merchants, both merchants accept credit card payments, and the market of product is fully covered. Back to the problem of monopoly platform, her profit maximization problem can be rewritten as max p B π N = (p B +p S )(1 p B ) (6) s.t. p S b S + 1 p B (7) Solving the profit maximization problem of monopoly platform yields p B = b S +c p S = 3 b S + 1 c D card = 1+b S c D cash = b S +c p = d+t+ 1 (1+b S c) π N = 1 (1+b S c) CS card = ˆ 1 π M i = π M j = π = t p B (b B p B )db B = 1 (1 ( b S +c)) ˆ 1 CS product = (u p tx)dx = u d t 1 (1 ( b S +c)) 15

16 CS = CS card +CS product TS = π N +π M i +π M j +CS card +CS product The price of product p is obtained from (4) where the notation D B (p B ) from the appendix is equivalent to the notation D card here. Both notations stand for the payments made using credit cards. π stands for equilibrium profits of merchants. CS card is the consumer surplus in the market of credit card payment services; CS product is the consumer surplus in the market of product; CS is the total consumer surplus from both credit card market and product market; and TS is the total surplus from both product market and credit card market. In this general model, the value of parameters, b S and c are assumed to make sure the above solution are interior ones, i.e., the customer fee p B are over the region [0,1], and the demand of credit card payments D B is between [0,1]. Under the NSR without MI To clearly demonstrate the welfare implication, a middle case, where the phenomenon of MI is hypothetically eliminated among Hotelling merchants under the NSR, is discussed in this subsection. In particular, given the phenomenon of MI is hypothetically eliminated which implies the merchant acceptance condition is given by p S b S, the following is the solution to profit maximization problem of Hotelling merchants p i = p j = p = [d+d B (p B )(p S b S )]+t π i = π j = π = t 16

17 When the condition p S b S holds, both merchants accept credit card payments, and the market of product is fully covered. The monopoly platform profit maximization problem is then given as max p B π N = (p B +p S c)(1 p B ) (8) s.t. p S b S (9) Solving the profit maximization problem of monopoly platform yields p B = 1 b S +c p S = b S D card = 1+b S c D cash = 1 b S +c p = d+t π N = 1 4 (1+b S c) CS card = πi M = πj M = π = t (b B p B )db B = 1 ( 1 1 b ) S +c p B ˆ 1 ˆ 1 CS product = (u p tx)dx = u d t CS = CS card +CS product TS = π N +π M i +π M j +CS card +CS product 17

18 Under surcharging In the case where there is a single sector within which two Hotelling merchants sell a same product to consumers, a monopoly platform under surcharging selects the customer fee p B and the merchant service fee p S to maximize her profit subject to the amount of surcharge imposed by Hotelling merchants. In particular, the monopoly platform profit maximization problem is given by max π N = (p B +p S c)d card (10) p B,p S s.t. s = p S b S (11) where D card = 1 p B s is the amount of payments paid by credit cards. 1 The constraint of surcharges s = p S b S is derived from the equilibrium of profit maximization problems by the two Hotelling merchants. This result has been posed in Proposition 6 in RT00. It implies that the amount of surcharge equals the net cost of merchants to accept credit card payments, and the result is due to the property of perfect pass through of Hotelling model. In particular, two identical Hotelling merchants always perfectly pass by their extra cost onto consumers in a competitive equilibrium. Therefore, the solution of competition between Hotelling merchants is captured by p = d+t (1) s = p S b S (13) π M i = π M j = π = t (14) 1 The per transaction cost of operating the credit card platform is assumed to be zero as it is negligible in the real world. 18

19 and the constraint of surcharges for the monopoly platform is given by s = p S b S. By substituting the constraint into profit function of platform, the platform s problem becomes max ρ π N = (ρ c)(1+b S ρ) (15) where the price level ρ is given by ρ = p B +p S. The two fees always appear in pair in the profit function, and only the price level ρ matters in the profit optimization. Solving the profit maximization problem of monopoly platform yields ρ = 1+b S +c s = 1 3b S +c 4 p B = 1+b S +c 4 p S = 1+b S +c 4 D card = 1 p B s = 1+b S c D cash = p B +s = 1 b S +c p = d+t π N = 1 4 (1+b S c) CS card = ˆ 1 p B +s π M i = π M j = π = t (b B p B s)db B = 1 ( 1 1 b ) S +c ˆ 1 CS product = (u p tx)dx = u d t 19

20 CS = CS card +CS product TS = π N +π i +π j +CS card +CS product Without losing the generality, in the paper the customer fee and merchant fee are treated as to be allocated evenly when only the price level ρ matters under surcharging. In other words, they are equal in the result, i.e., p B = p S. The following subsection will provide a detailed comparison of results of each case. Welfare comparison Table I gives a summary of results in each equilibrium for the case of Hotelling merchants with one sector. The column one in Table I shows the results for the case under the NSR; column two shows the results for the case where the MI is hypothetically eliminated under the NSR; column three shows the results under surcharging. The results in column two and column three of Table I show that the profit of monopoly platform, the profit of merchants, the consumer surplus from credit card services, the consumer surplus from consumption of product, and the total surplus are the same in the case with no MI under the NSR and in the case under surcharging. These same results under either case indicate that the welfare impact of removing the NSR is to eliminate the effect of MI. In particular, the effect of MI in the problem is given by the followings π N NSRMI πn NSR = 1 4 (1+b S c) π M NSRMI πm NSR = 0 CS card NSRMI CScard NSR = 3 8 (1+b S c) CS product NSRMI CSproduct NSR = 1 (1+b S c) 0

21 CS total NSRMI CS total NSR = 1 8 (1+b S c) TS NSRMI TS NSR = 1 8 (1+b S c) The above comparison shows that MI has following effects in the case of Hotelling merchants under the NSR:(a) increase the profit of platform; (b) increase the consumer surplus of credit card service; (c) decrease the consumer surplus of product. MI decreases total consumer surplus but increases the total surplus. It implies that the lifting of the NSR, which eliminates the effect of MI, will increase total consumer surplus but decrease the total surplus. Notably, the profits of Hotelling merchants remains the same in each case. This is because, given the competitive equilibrium between Hotelling merchants, the monopoly platform is always able to set a merchant fee such that Hotelling merchants are are trapped in a Prisoner dilemma and obtain no extra profit by accepting credit card payments. The imposition of the NSR, which cultivates the effect of MI, enables the monopoly platform to increase her profit on top of the monopoly profit which she would obtain without the NSR. This extra profit obtained by the monopoly platform is realized by increasing the merchant fee and hence the price of the product. The consumer surplus from product market decreases as a result. At the same time, the monopoly platform reduces the customer fee to consumers, and the consumer surplus from credit card service market increases. The increase in consumer surplus from card market falls short of the decrease of consumer surplus from product, and therefore total consumer surplus decreases after the imposition of the NSR. However, the total social surplus increases because the increase in the profit of monopoly platform is greater than the decrease of total consumer surplus. This welfare comparison will be further clarified in the next subsection from a different respect, and the summary of results in Table I is provided by Proposition one as follows: Proposition one: In the case where a single sector is represented by two Hotelling 1

22 merchants, the profit of monopoly platform, total surplus are higher under the NSR than under surcharging, consumer surplus is higher under surcharging than under the NSR, and the profit of Hotelling merchants are the same under either case. 5. Unambiguous welfare implication This subsection demonstrates why the one sector case with Hotelling merchants yields a different welfare implication of removing the NSR from a similar situation in RT00. The previous subsection proves that lifting the NSR always decreases social welfare in the model because the effect of MI is eliminated. However, the model of RT00 indicates that lifting the NSR can increase or decrease social welfare. The fundamental reason lies in the difference of platform governance. In RT00, the platform is a not-for-profit association and consists of oligopolistic issuers; but, in this paper the platform is a monopoly and issuers are assumed to be perfectly competitive in the case of Visa and MasterCard (or neither issuer nor acquirer exists in the case of American express). In particular, the assumption one of RT00, which describes how competition among issuers determines the equilibrium customer fee p B given any level of interchange fee a, is given by the following two conditions: dp B /da < 0 dπ issuer /da > 0 where p B = p B (c I a) and a = p S c A. The terms c I and c A are the per transaction cost to issuers and acquirers. The above two conditions imply the equilibrium customer fee p B is decreasing in the interchange fee a, but the profit of issuers is increasing in the interchange fee a. The competition among acquirers is assumed to be perfect in their model. To give a

23 simple example, assume c A = 0, then p S = a, and assume the determination of customer fee is given by the following condition p B = c I αp S where α < 1 to insure the profit of issuers is increasing with interchange fee a or merchant fee p S. That is to say, for an increase in interchange feee and hence merchant fee, the issuers retain a portion of (1 α). Therefore, a lower value of α indicates a higher amount of retained by issuers and hence a higher market power of issuers. The condition of merchant acceptance implies p S b S + 1 p B As issuers prefer a higher level of interchange fee a and hence a higher merchant fee p S, the solution of the equilibrium fees is given by the solution to the following equation system p B = c I αp S which yields the equilibrium given as follows p S = b S + 1 p B p B = c I α b S +1 c I α p S = b S +1 c I α In the above equilibrium, the credit card services could be under or over provided. Take 3

24 c I = 1 as an example. The sum of transaction benefits of marginal consumer and merchant are greater than the cost if α < 3, or b B + b S = p B +b S c I if α < 3 & b S > 0 which implies the credit card service is under provided. The intuition is given as: a lower value of α implies a higher portion retained by issuers from an increase in merchant fee p S and hence a higher market power of issuers, which in turn implies a higher likelihood of the under provision of credit card services. Alternatively, it means that the under provision due to market power of issuers tend to outweigh the over provision due to MI when α is small. In the case that the credit card service is under provided under the NSR, the lifting of the NSR, which eliminates the over provision effect from MI, will further decrease provision of card service below social optimal level and definitely decrease social welfare. On the contrary, if α > 3, The sum of transaction benefits of marginal consumer and merchant are less than the cost, or b B + b S = p B +b S c I if α > 3 & b S > 0 It means the credit card service is over provided. The intuition is a higher value of α implies a lower portion retained by issuers for an increase in merchant fee p S and hence a lower market power of issuers, which in turn implies a higher likelihood of the over provision of credit card services. Alternatively, it means that the under provision due to market power of issuers tend to fall short of the over provision due to MI when α is large. In the case that the credit card service is over provided under the NSR, the lifting of the NSR, which eliminates the over provision effect of MI, will reduce the provision of credit card service. The welfare implication is then determined by the extent to which the provision of card service 4

25 is reduced. Therefore, welfare implication can be either positive or negative. In RT00 the competition among issuers has not been explicitly modeled, and the authors do not know the level of provision of credit card service in the real world. Yet no literature provides any empirical analysis on the level of provision of credit card service under the NSR. Therefore, no unambiguous policy advice can be inferred from their paper. However, the model of the previous subsection, where a monopoly platform provides credit card service to consumers and a sector of two Hotelling merchants through issuers and competitive acquirers, shows that removing the NSR always decreases social welfare. This is because the monopoly platform, who are subject to the merchant acceptance condition or the condition of MI, acts as a social welfare maximizer when she maximizes the profit. Alternatively, it means that the distortion due to MI always fully offsets the distortion due to market power of monopoly platform. As a result, the credit card service is always optimally provided under the NSR. The lifting of the NSR, which eliminates the condition of MI, always results in an under provision of credit card service and hence social welfare always decreases. The following example clearly shows the point. Generally, the equilibrium of the model is given by solving max p B,p S π N = (p B +p S c)d card (16) s.t. p S b S +v B (p B ) (17) or or max p B π N = (p B +b S +v B (p B ) c)d B (p B ) (18) ˆ 1 max π N = (b B +b S c)db B (19) p B p B 5

26 Again, both notation D Card and notation D B stand for the demand of credit card services, where D B is a notation from appendix. The above calculation shows that the monopoly platform turns into a social welfare maximizer after taking into account the constraint of MI, and the credit card service is always optimally provided under the NSR. Therefore, the lifting of the NSR, which eliminates the MI and turns the platform back to a profit maximizer, always decreases the provision of credit card service below social optimal level and social welfare decreases as a result. Although the above analysis only focuses on the credit card market, it does not affect the conclusion on the general welfare implication on both credit card market and product market. This is because the market of product is always fulled covered under the NSR and under surcharging. Then, soical welfare on the market of product is always achieved under either case, despite that the allocation of it may differ under either case. Therefore, the only difference in total social welfare is from the credit card market, and the above analysis reflects welfare implication on total social welfare for both credit card market and product market. Notably, this conclusion holds regardless of the property of demand, and it implies the credit card service is optimally provided as long as there is merchant internalization among merchants. In other words, it means that an unambiguous conclusion of welfare implication of lifting the NSR can be drawn even without empirical evidence. The only condition for the conclusion is the existence of merchant internalization. Another striking finding is that the conclusion of optimal provision of credit card service under the NSR holds regardless of the degree of competition among issuing banks. To see this point, consider the case where p B is the fee charged by the monopoly platform to issuing banks, and λ is the markup imposed by issuing banks. The value of λ indicates the degree of competition among issuing banks. A higher λ implies that the issuing banks can markup more and hence implies a less competition among them. In this case, the total customer fee 6

27 born by consumer is p B +λ, and the demand of card service is then D B (p B +λ) and the net consumer surplus is v B (p B +λ). The profit maximization problem of monopoly platform is given by max π N = (p B +p S c)d card (0) p B,p S s.t. p S b S +v B (p B +λ) (1) or or max p B π N = (p B +b S +v B (p B +λ) c)d B (p B +λ) () ˆ 1 max π N = (b B +b S c)db B (3) p B p B +λ which implies the monopoly platform still acts as a welfare maximizer when she maximizes her profit under the NSR. That is to say, the credit card service is always optimally provided under the NSR regardless of degree of competition among issuing banks. This optimal provision result also holds for general two-sided market, and it will has wide application and may take another paper to well discuss it. To be focused on the credit card market, Proposition two describes the conclusion of optimal provision as follows: Proposition two: In the case where a single sector is represented by two Hotelling merchants, the monopoly platform always maximizes social welfare and the credit card service is always optimally provided regardless of the property of demand of credit card service and the degree of competition among issuing banks. The lifting of the NSR always decreases social welfare. Proposition two indicates that the monopoly platform internalizes consumer surplus when she maximizes profit subject to MI condition, and all the welfare in credit card market is 7

28 achieved. However, this is not case in the model of RT00, the competition among issuers does not give them freedom to fully internalize consumer surplus. Also, the authors did not take into account the effect of equilibrium customer fees on the condition of MI. Therefore, the credit card service could be either under or over provided in their model. To sum up, the different welfare implication is driven by the difference assumption on platform governance. The assumption of monopoly platform captures the recent market structure change in credit card market: both Visa and MasterCard conducts their IPOs during last decade, and it can exactly represents the case of American Express. Therefore, the welfare implication of the model from this paper is more applicable in the current real world. 5.3 Heterogeneous merchants In the rest of the paper, the per transaction cost c is assumed to be zero since it is negligible in the real world. Likewise, the magnitude of b S is relative small in practice. 13 So, assume 0 b S 1 in the following parts of the paper. It can be verified that the assumption on the value of c and b S will not change the property of following analysis. Two sectors of merchants The previous subsection has discussed the case where there is one sector on the merchant side. This subsection discusses the case where there are two sectors. The term sector is referred to as the magnitude of transaction benefit b S of the merchant within the sector. In one sector the transaction benefit of merchants is b L S and in another sector the transaction benefit is b H S. 13 Jonker and Plooij (013) estimate that the magnitude of b S is under.5% of the value of the transaction payment. 8

29 Under the NSR The monopoly platform under the NSR has two options to serve the Hotelling merchants in each sector. To maximize her profit, the monopoly platform could choose to serve both sectors or choose to serve one sector with higher transaction benefit of merchants. The relative value of b L S and bh S determines which option yields a higher profit for the monopoly platform. In what follows, two examples will be posed to illustrate the welfare effect of removing the NSR. In the first example, the monopoly platform prefers to serve both sectors under the NSR, while the monopoly platform prefers to serve one sector under the NSR in another example. In the first example, the monopoly platform sets p S = b L S + 1 p B if she chooses to serve both sectors under the NSR, and her profit maximization problem is given by max p B π N = (p B +p S )(1 p B ) (4) s.t. p S b L S + 1 p B (5) The solution of the problem is p B = 0 p S = b L S + 1 π N = b L S +1 In the sector b L S, D card = 1 p B = 1 D cash = p B = 0 9

30 p L = d+t+d B (p B ) ( p S b L ) 1 S = d+t+ In the sector b H S, CS L card =ˆ 1 CS L product = ˆ 1 0 π L = t p B (b B p B )db B = 1 (u p L tx)dx = u d 5 4 t 1 D H card = 1 p B = 1 D H cash = p B = 0 p H = d+t+d B (p B ) ( p S b H ) S = d+t+b L S b H S + 1 CS H product = ˆ 1 CS H card =ˆ 1 0 π H = t p B (b B p B )db B = 1 (u p H tx)dx = u d 5 4 t 1 +bh S bl S The total consumer surplus and the total social welfare are CS NSR = CS L card +CSH card +CSL product +CSH product TS NSR = π N +π L M +πh M +CSL card +CSH card +CSL product +CSH product In the second example, the monopoly platform sets p S = b H S + 1 p B if she chooses to 30

31 serve only one sector under the NSR, and her profit maximization problem is given by max p B π N = (p B +p S )(1 p B ) (6) s.t. p S b H S + 1 p B (7) The solution of the problem is p B = 0 p S = b H S + 1 π N = b H S + 1 In sector b L S, D L card = 0 D L cash = 1 p L = d+t π L M = t CS L product = ˆ 1 0 CS L card = 0 (u p tx)dx = u d 5 4 t In sector b H S, D H card = 1 p B = 1 D H cash = p B = 0 p H = d+t+d B (p B ) ( p S b H S 31 ) = d+t+ 1

32 CS H card =ˆ 1 CS H product = ˆ 1 0 π H M = t p B (b B p B )db B = 1 (u p H tx)dx = u d 5 4 t 1 The total consumer surplus and the total social welfare are CS NSR = CS L card +CSH card +CSL product +CSH product TS NSR = π N +π L M +π H M +CS L card +CSH card +CSL product +CSH product The monopoly platform makes the choice to serve both sectors or to serve a single sector depending on her profitability under either choice. In particular, the monopoly platform choose to serve both sectors if 1+b L S 1 +bh S or equivalently b H S b L S 0.5 In the subsection of welfare comparison, two concrete examples will be shown to analyze the welfare impact of removing the NSR. Under surcharging In the case where there are two sectors within each of which two Hotelling merchants sell a same product to consumers, a monopoly platform under surcharging selects the customer fee p B and the merchant service fee p S to maximize her profit subject to the amount of 3

33 surcharge imposed by Hotelling merchants in each sector. Notably, the Hotelling merchants in each sector always accepts credit card payments as they can pass by the cost to do so onto consumers by levying a surcharge. In particular, the monopoly platform profit maximization problem is given by max p B,p S π N = (p B +p S ) ( 1 p B s H) +(p B +p S ) ( 1 p B s L) (8) where s H = p S b H S (9) s L = p S b L S (30) Surcharges s H and s L are derived from the equilibrium of profit maximization problems by the two Hotelling merchants. By substituting the constraint into profit function of platform, the platform s problem becomes max ρ π N = ρ ( 1+b H S ρ) +ρ ( 1+b L S ρ) (31) where ρ is the price level. Solving the profit maximization problem of monopoly platform yields ρ = +bh S +bl S 4 s L = +bh S 7bL S 8 s H = 7bH S +bl S 8 p B = +bh S +bl S 8 p S = +bh S +bl S 8 33

34 p L = d+t p H = d+t D L card = 1 p B s L = bh S +3bL S 4 D L cash = p B +s L = +bh S 3bL S 4 D H card = 1 p B s H = +3bH S bl S 4 D H cash = p B +s H = 3bH S +bl S 4 π N = 1 (1+ bh S +bl S) π L M = t CS L card =ˆ 1 CS H card =ˆ 1 π H M = t p B +s L ( bb p B s L) db B = 1 p B +s H ( bb p B s H) db B = 1 CS L product = ˆ 1 0 CS H product = ˆ 1 0 ( 1 1 ( +b H 4 S 3b L S) ) ( 1 1 ( 3b H 4 S +b L S) ) ( u p L tx ) dx = u d 5 4 t ( u p H tx ) dx = u d 5 4 t CS SR = CS L card +CSH card +CSL product +CSH product TS SR = π N +π L M +π H M +CS L card +CSH card +CSL product +CSH product 34

35 Welfare comparison In this subsection, two examples are given to compare social welfare under the NSR and under surcharging. In the first example, the transaction benefits of merchants are given as b H S = 0.7 and bl S = 0.1 and the monopoly platform prefers to serve a single sector with higher transaction benefit of merchant under the NSR; in the second example the transaction benefitsareas b H S = 0.5andbL S = 0.1 andthemonopolyplatformpreferstoservebothsectors under the NSR. Table II provides a summary of solutions under the NSR and surcharging when the values of parameters are given as {u = 0,d = 0,t = 10,b S = 0.5}. The results in Table II show that the monopoly platform prefers to run her business under the NSR than under surcharging in both cases. The total surplus under the NSR is lower than the total surplus under surcharging in the case with b H S = 0.7 and bl S = 0.1, but otherwise in the case with b H S = 0.5 and bl S = 0.1. Two fundamental market forces drive the results behind the scene. First force is a change in market structure during the transition from under the NSR to under surcharging. The change in market structure refers to the fact that the merchants who did not accept credit card payments under the NSR do accept credit card payments under surcharging as the merchants in the sector b L S do in the example with { b H S = 0.7,bL S = 0.1}. This move brings about some new payments made using credit cards and also brings down the total price level charged by the monopoly platform. Social welfare in providing credit card payment service increases as a result. The second force is elimination of the merchant internalization, which decrease the payments using credit cards decreasing social welfare. In the example with { b H S = 0.7,bL S = 0.1}, both forces exist and the force of market structure change dominates the force of elimination of MI, and hence lifting the NSR increases socialwelfare. Intheexamplewith { b H S = 0.5,bL S = 0.1},theforceofmarketstructurechange does not exit because the merchants in both sectors accept credit card payments under the 35

36 NSR. The only market force is elimination of the merchant internalization. Therefore, lifting the NSR in this example decrease social welfare. In the general case, if the monopoly platform serves two sectors, the difference in total surplus and consumer surplus are given by TS NSR TS SR = 1 16 CS NSR CS SR = 1 16 ( 4+4b H S 7 ( b H ) S +4b L S 7 ( b L ) S +b H S bs) L ( 4+1b H S 5 ( b H ) S 0b L S 5 ( b L ) S +6b H S bs) L and TS NSR TS SR 0 if 0 b L S b H S 1 CS NSR CS SR 0 Therefore, the social welfare under the NSR is greater than social welfare under surcharging, and it is because the market force of elimination of the merchant internalization decreases social welfare during the lifting of the NSR. However, the sign of the difference in consumer surplus is uncertain. Take the case with b L S = 0 as an example. The difference in consumer surplus is given as CS NSR CS SR b L S =0 = 1 ( 4+1b H S 5 ( b H ) ) S = 1 ( )( ) +b H S +5b H S and CS NSR CS SR 0 if 0.4 b H S 1 CS NSR CS SR 0 if b H S 0.4 The intuition is that under the NSR a higher value of b H S reduces the price of product in the highsector b H S and thereforereducesthe monopolyplatform s expropriation of theconsumers 36

37 surplus from credit card payment service by way of increasing price of product. Therefore, a higher b H S implies a higher total consumer surplus under the NSR through the effect of MI. Hence, Proposition three is given as Proposition three: In the case where there are two sectors with two Hotelling merchants in each sector and the monopoly platform prefers to serve both sectors under the NSR, the profit of monopoly platform, total surplus are higher under the NSR than under surcharging, the profit of Hotelling merchants are level off under surcharging and under the NSR. Consumer surplus may be higher or lower under the NSR than under surcharging depending on the relative magnitude of transaction benefit of merchants of two sectors. 14 If the monopoly platform prefers to serve one sector under the NSR, the difference in total surplus and consumer surplus are given by and TS NSR TS SR = 1 16 ( 4+4b H S 7( b H ) S 1b L S 7 ( b L ) S +b H S bs) L CS NSR CS SR = 1 ( 1 4b H S 5 ( b H ) S 4b L 16 S 5 ( b L ) S +6b H S bs) L TS NSR TS SR 0 if 0 b L S b H S 1 CS NSR CS SR 0 if 0 b L S b H S 1 Therefore, proposition four is given as Proposition four: In the case where there two sectors with two Hotelling merchants in each sector and the monopoly platform prefers to serve one sector under the NSR, total surplus and consumer surplus are lower under the NSR than under surcharging. The profit of Hotelling merchants are level off under surcharging and under the NSR. The profit of 14 It can be easily shown that the profit of platform is higher under the NSR when she prefers to serve two sectors or when the condition b H S b L S 0.5 holds 37

38 monopoly platform is higher under the NSR than under surcharging. 15 Again the intuition of Proposition four lies in the fact that when the monopoly platform serves one sector under the NSR, two market forces exist during the lifting of the NSR, and the force of market structure change dominates the force of elimination of MI, which increases social welfare. A continuum sectors of merchants The previous subsection has discussed the case where there are two sectors on the merchant side. This subsection discusses the case where there are uncountable many sectors with their transaction benefit of merchants b S uniformly distributed in the region [0,1]. As the market of product is assumed to be fully covered under the NSR and under surcharging, total surplus from product market is always achieved under either case. The only difference is the allocation of total surplus from product market under either case. Therefore, what matters, in the comparison of total surplus, is the credit card market. So, the following comparison of welfare will be focused on the market of providing credit card payment services abstracted from product market. Under the NSR To maximize her profit, a monopoly platform under the NSR selects the customer fee p B and the merchant service fee p S subject to merchant s acceptance of credit card payments. In particular, the profit maximization problem of platform under the NSR is given by 15 It can be easily shown that the profit of platform is higher under the NSR when she prefers to serve one sector or when the condition b H S b L S 0.5 holds 38

39 ˆ 1 ˆ 1 max π N = (p B +p S ) db B db S = (p B +p S )(1 p B )(1 (p S v B (p B ))) p B,p S p S p B v B (p B ) (3) where 1 (p S v B (p B )) is the amount of sectors within which Hotelling merchants accept credit card payments. In each of those sectors, the purchases of product made by credit cards is given by 1 p B. Therefore, the total transaction volume of purchases made through credit card platform T = (1 p B )(1 (p S v B (p B ))) is given by the product of the credit card payments made in each sector 1 p B and the number of sectors within which Hotelling merchants accept credit card payments. The consumer surplus term is given by v B (p B ) = 1 p B in the case of uniform distribution. Social welfare in the market of providing credit card payment service is given by W = ˆ 1 ˆ 1 p S p B v B (p B ) (b B +b S )db B db S (33) The solution to the profit maximization problem is given as follows p B = 0 p S = 0.75 π N = T = 0.75 W =

40 Under surcharging In the case where there are a continuum of sectors within each of which Hotelling merchants sell a same product to consumers, a monopoly platform under surcharging selects the customer fee p B and the merchant service fee p S to maximize her profit subject to the amount of surcharge imposed by Hotelling merchants in each sector. In particular, the monopoly platform profit maximization problem is given by max π N = (p B +p S ) p B,p S ˆ 1 ˆ 1 0 p B +s db B db S (34) where s = p S b S (35) Social welfare in the market of providing credit card platform service is given by W = ˆ 1 ˆ 1 p S p B +s (b B +b S )db B db S (36) Surcharges s is derived from equilibrium of profit maximization problems of Hotelling merchants in each sector. By substituting the constraint into profit function of platform, the platform s problem becomes max ρ π N = ρ ˆ 1 ˆ 1 0 ρ b S db B db S (37) Solving the profit maximization problem of monopoly platform yields 16 ρ = p B = In the actual calculation, the profit function is given byπ N 1 1 = ρ ρ db 0 ρ b S Bdb S+ρ 1 dbbdbs because ρ 0 ρ b S 0 if b S is in the region [ρ,1]. 40

41 p S = π N = T = W = Welfare comparison The comparison of the above results indicates that social welfare under the NSR is greater than social welfare under surcharging. As in the case with two sectors, two market forces drive the welfare impact of removing the NSR; namely: (a) the change in the market structure; (b) the elimination of MI. The merchants in sectors with b S p S v B (p B ) or b S 0.5 in this case do not accept credit card payments under the NSR, but do accept credit card payments under surcharging. This change in market structure generates new payments made using credit cards in those sectors and increase social welfare as a result. However, the elimination of the merchant internalization, decreases the payments using credit cards decreasing social welfare. The total effects of the two market forces of removing the NSR is negative which means removing the NSR decreases social welfare when there are a continuum of sectors b S [0,1] within each of which Hotelling merchants sell a same product to consumers. Therefore, Proposition five are given as Proposition five: In the case where there are a continuum sectors with their transaction benefit of Hotelling merchants b S uniformly distributed in the region [0,1], the profit of monopoly platform, total surplus are higher under the NSR than under surcharging, and the profit of Hotelling merchants are level off under surcharging and under the NSR. 41

42 5.4 Reverse cross subsidization This section will state a finding on cross subsidization in model with Hotelling merchants, which is opposite to result in RT00 and the prevailing argument against the NSR. In RT00, The Proposition six in RT00 states that: for a given interchange fee, allowing card surcharges raises the merchant price for cardholders and lowers it for noncardholders. Put it differently, the consumers who make purchasing using cash bear a part of cost to providing credit card payment services, and they cross subsidize those consumers who pay with credit cards under the NSR. This conclusion is also true in our model within sector[p S v B (p B ), p S ]. Remember that in the model with Hotelling merchants, the uniform prices of goods under NSR and the cash price and the card price under surcharging are respectively given by p = [d+d B (p B )(p S b S )] + t, p cash = t + d and p card = t + d + p S b S, where the p card is the sum of the cash price p cash and surcharge s. In the sectors with transaction benefits b S between [p S v B (p B ), p S ], allowing surcharges raises the prices for card users while it lowers the prices for cash users. This is because the uniform price under the NSR is less than the cash price and greater than the card price p cash < p < p card, which implies cash users cross subsidize the card users under NSR. This is one of the central arguments against the NSR in the antitrust lawsuit. However, the result within sector [p S,1] is opposite, where allowing surcharges lowers the prices for card users while raises the prices for cash users, or p card < p < p cash. It means card using consumers cross subsidize cash using consumers under the NSR. No literature has found this result and therefore it is stated in the following proposition. Proposition six: In the case where there are a continuum sectors with their transaction benefit of Hotelling merchants b S uniformly distributed in the region [0,1], removing NSR raises the prices for card users while it lowers the prices for cash users in sector 4

43 [p S v B (p B ), p S ], and lowers the prices for card users while it raises the prices for cash users in sector [p S v B (p B ),1]. Proposition six identifies a situation where card users could cross subsidize the cash users under the NSR. This is because when some merchants have a higher transaction benefit from accepting credit cards than the marginal merchants, they receive a negative cost to accept credit card payments, and they will build up this cost saving into the uniform price of products and the price of products for the cash user is decreased as a result. Credit card users therefore cross subsidize consumers who pay by cash. 6 Monopoly merchants The previous section discusses the welfare implication in the case with Hotelling merchants. The merit of the case with Hotelling merchants is that it can capture the phenomenon of MI, or the interaction between merchants when they make the decision to accept credit card payments or not. However, the assumption of Hotelling merchants handicaps the model to provide an explanation to the various surcharging behaviors of merchants in Australia after the 003 reform of credit card industry. More specifically, the excessive surcharges observed in the real world can not be explained by the equilibrium of Hotelling competition where amount of surcharges are just a perfect passthrough of merchant s net cost to accept credit card payment. No excessive surcharges exists in the Hotelling model. Therefore, the monopoly merchants are considered in this section, which will provide an explanation to what have been observed in Australia. In the case of monopoly merchant, each sector is represented by a monopoly merchant who is located at the origin of a unit interval [0,1] with consumers uniformly spread over the interval. Each consumer has utility u to consume the product sold by the monopoly merchant, and the consumer who is located at x incurs transportation cost xt traveling to 43

44 the merchant s store to purchase the product. Each consumer also has a transaction benefit from using credit cards b B drawn from the uniform distribution over the region [0,1]. Under the assumption of full coverage of the market of product, a monopoly merchant under the NSR, regardless of payment methods, sets the price of product p equal to u t the utility of consuming the product u netting the transportation cost of the consumer who is located at x = 1. Under the assumption of full coverage of the market of product in the cases without the NSR, a monopoly merchant sets the price of product purchased in cash p cash equal to u t, and sets the price of product purchased with credit cards p card equal to u t + s. The demand of credit card payment services from consumers under the NSR is given by D card = 1 p B because consumers make purchases using credit cards when their transaction benefits are greater than the customer fee or p B > b B. Likewise, the demand of credit card payment services from consumers under surcharging is given by D card = 1 p B s. 6.1 Homogeneous merchants Under the NSR In the case where there is a single sector within which a monopoly merchant sells a product to consumers, a monopoly platform under the NSR selects the customer fee p B and the merchant service fee p S to maximize her profit subject to merchant s acceptance of credit card payments. To insure the monopoly merchant to accept credit card payments, the platform cannot set a merchant service fee p S greater than the transaction benefit of monopoly merchant b S, and the monopoly platform profit maximization problem is given by max π N = (p B +p S )D card (38) p B,p S s.t. p S b S (39) 44

45 where D card = 1 p B is the amount of payments paid by credit cards. 17 The constraint of merchant s acceptance p S b S is derivedfromthecomparison of merchant s profitswhenshe accepts credit card payments and when she does not. In particular, the profit of merchant when she accepts credit card payments given the merchant service fee p S and customer fee p B is πac M = (p d+b S p S )D card +(p d)d cash (40) where p is the price of product, d is the cost of product, b S is the transaction benefit of merchant to accept credit card payments, D card is the demand of product by consumers who pay by credit cards, and D cash is the demand of product by consumers who pay with cash. By substituting p = u t, D card = 1 p B, D cash = p B, the profit is given by π M AC = u t d+(b S p S )(1 p B ) (41) while the profit of merchant when she does not accept credit card payments is π M NA = u t d (4) π M AC πm NA if b S p S 0 as the demand, 1 p B, is non negative. Therefore, the constraint of merchant s acceptance is given by p S b S. The monopoly platform will set the merchant service fee to the highest possible level, i.e., p S = b S, and the monopoly merchant accepts credit card payments. Therefore, the profit maximization problem of merchants becomes max p B π N = (p B +b S )(1 p B ) (43) 17 The per transaction cost of operating the credit card platform is assumed to be zero as it is negligible in the real world. 45

46 Solving the profit maximization problem of monopoly platform yields p B = 1 b S p S = b S p = u t D card = 1 p B = 1+b S D cash = p B = 1 b S π N = 1 4 (1+b S) π M = u t d and the consumer surplus in the market of credit card payment services, the consumer surplus in the market of product, the total consumer surplus and the total surplus are given respectively by CS card = ˆ 1 p B (b B p B )db B = 1 (1 p B) = 1 CS product = ˆ 1 0 (u p tx)dx = t CS = CS card +CS product ( 1 1 b ) S TS = π N +π M +CS card +CS product Notably, the interior solution in this problem is supported by the condition that b S 1 as the solution of customer fee is given by p B = 1 b S. If b S 1, the monopoly platform will 46

47 set p B = 0 as the demand D card = 1 p B can not exceed one which is the maximum level of possible demand in this model. Again, this section only consider the case where b S is over [0, 1]. Under surcharging In the case where there is a single sector within which a monopoly merchant sells a product to consumers, a monopoly platform under surcharging selects the customer fee p B and the merchant servicefeep S tomaximizeherprofitsubjecttotheamountof surchargeimposedby the monopoly merchant. In particular, the monopoly platform profit maximization problem is given by max π N = (p B +p S )D card (44) p B,p S s.t. s = 1 b S p B +p S (45) where D card = 1 p B s is the amount of payments paid by credit cards. 18 The constraint of surcharges is derived from profit maximization problem of the monopoly merchant. In particular, the profit of the merchant is π M = (p cash d+b S p S )D card +(p cash d)d cash (46) After substituting p cash = u t, D card = 1 p B s, D cash = p B +s, the profit maximization problem of the merchant when she accepts credit card payments given the merchant service 18 The per transaction cost of operating the credit card platform is assumed to be zero as it is negligible in the real world. 47

48 fee p S and customer fee p B is given by maxπ M = u t d+(b S +s p S )(1 p B s) (47) s The solution to profit maximization problem of merchant is s = 1 b S p B +p S (48) Therefore,theconstraintofsurchargesforthemonopolyplatformisgivenbys = 1 b S p B +p S, and by substituting the constraint into profit function of platform, the platform s profit maximization problem becomes max ρ π N = ρ 1+b S ρ (49) where ρ is the price level. The two fees always appear in pair in the profit function, and only the price level ρ matters in the profit optimization. Solving the profit maximization problem of monopoly platform yields ρ = 1+b S s = 1 b S p B = 1+b S 4 p S = 1+b S 4 p cash = u t D card = 1 p B s = 1+b S 4 D cash = p B +s = 3 b S 4 48

49 π N = 1 8 (1+b S) π M = u t d (1+b S) Again, without losing the generality, in the paper the customer fee and merchant fee are treated as to be allocated evenly when only the price level ρ matters under surcharging. In other words, they are equal in the result, i.e., p B = p S. The consumer surplus in the market of credit card payment services, the consumer surplus in the market of product, the total consumer surplus and total surplus from both markets are given respectively by CS card = ˆ 1 p B +s (b B p B )db B = 1 (1 p B s) = 1 CS product = ˆ 1 0 (u p cash tx)dx = t CS = CS card +CS product ( 1 3 b ) S 4 TS = π N +π M +CS card +CS product where p B +s = 3 b S 4. The solution indicates that the monopoly platform make a choice of total price level of the customer fee and merchant service fee to maximize her profit without worrying about the decomposition between the two fees. The interior solution of the above problem is supported by the condition b S 3. If b S 3, the above demand of card payments D card has a corner solution and equals to one, and all the consumers make purchases using credit cards and the market of credit card payment service is fully covered and the associated social surplus is realized. However, the comparison will be focused on the cases where b S is over [0, 1], which will not change the property of the analysis. 49

50 Welfare comparison Table III gives a summary of solutions under the NSR and surcharging when 0 b S 1. The results of anecdotal example with parameter values as {u = 0,d = 0,t = 10,b S = 0.5} in Table III shows that the monopoly platform prefers to run her business under the NSR than under surcharging, while the monopoly merchant prefers to operate her business under surcharging than under the NSR. The total surplus under the NSR is generally greater than the total surplus under surcharging. In particular, if the transaction benefit of merchant b S takes value between [0,1] the difference of total surplus under either case is given by TS NSR TS SR = 5 3 (1+b S) 0 Likewise, if the transaction benefit of merchant b S takes value between [0,1], the consumer surplus under the NSR is also greater than the consumer surplus under surcharging as CS NSR CS SR = 3 3 (1+b S) 0 Therefore, the Proposition seven is given as follows: Proposition seven: In the case where a single sector is represented by a monopoly merchant, the profit of monopoly platform, total surplus and consumer surplus are higher under the NSR than under surcharging, but the profit of monopoly merchant is higher under surcharging than under the NSR. The intuition of Proposition seven is that under the NSR only the distortion of market power of monopoly platform exists in the credit card market, but under surcharging both the monopoly platform and merchant exercise their market power in the credit card market. Therefore, the exercise of market power by the merchant increases her own profit but drives down the consumer surplus, social surplus and the profit of monopoly merchant. 50

51 6. Heterogeneous merchants Two sectors of merchants The previous subsection has discussed the case where there is one sector on the merchant side. This subsection discusses the case where there are two sectors. The term sector is referred to as the magnitude of transaction benefit b S of the merchant within the sector. In one sector the transaction benefit of merchant is b L S and in another sector the transaction benefit is b H S. The motivation to discuss the case with two sectors is from the practical situation where a monopoly platform can not perfectly price discriminate the merchants according to their type b S. Under the NSR The monopoly platform under the NSR has two options to serve the monopoly merchant in each sector. To maximize her profit, the monopoly platform could choose to serve both sectors or choose to serve one sector with higher transaction benefit of merchant. The relative value of b L S and bh S determines which option yields a higher profit for the monopoly platform. In what follows, two examples will be posed to illustrate the welfare effect of removing the NSR. In the first example, the monopoly platform prefers to serve both sectors under the NSR, while the monopoly platform prefers to serve one sector under the NSR in another example. In the first example, the monopoly platform sets p S = b L S if she chooses to serve both sectors under the NSR, and her profit maximization problem is given by max p B π N = (p B +p S )(1 p B ) (50) s.t. p S b L S (51) 51

52 The solution of the problem is p B = 1 bl S π N = 1 p S = b L S ( 1+b L S ) In the sector b L S, D L card = 1 p B = 1+bL S D L cash = p B = 1 bl S p = u t CS L card =ˆ 1 π L M = u t d p B (b B p B )db B = 1 ( ) 1 1 bl S =ˆ 1 CSproduct L (u p tx)dx = t 0 In the sector b H S, D H card = 1 p B = 1+bL S D H cash = p B = 1 bl S p = u t πm H = u t d+( b H 1+b S S) L bl S =ˆ 1 CScard H (b B p B )db B = 1 ( 1 1 bl S p B ) 5

53 =ˆ 1 CSproduct H (u p tx)dx = t The total consumer surplus and total social welfare are 0 CS NSR = CS L card +CSH card +CSL product +CSH product TS NSR = π N +π L M +π H M +CS L card +CSH card +CSL product +CSH product In the second example, the monopoly platform sets p S = b H S if she chooses to serve only one sector under the NSR, and her profit maximization problem is given by max p B π N = (p B +p S )(1 p B ) (5) s.t. p S b H S (53) The solution of the problem is p B = 1 bh S π N = 1 4 p S = b H S ( 1+b H S ) In sector b L S, D L card = 0 D L cash = 1 p = u t π L M = u t d 53

54 CS L card = 0 =ˆ 1 CSproduct L (u p tx)dx = t 0 In sector b H S, D H card = 1 p B = 1+bH S D H cash = p B = 1 bh S p = u t CS H card =ˆ 1 π H M = u t d p B (b B p B )db B = 1 ( ) 1 1 bh S =ˆ 1 CSproduct H (u p tx)dx = t The total consumer surplus and total social welfare are 0 CS NSR = CS L card +CSH card +CSL product +CSH product TS NSR = π N +π L M +π H M +CS L card +CSH card +CSL product +CSH product The monopoly platform makes choice to serve both sectors or to serve a single sector depending on her profitability under either choice. In particular, the monopoly platform choose to serve both sectors if 1 ( ) 1+b L 1 ( ) S 1+b H 4 S 54

55 or roughly equivalent to b H S 1.414b L S In the subsection of welfare comparison, two concrete examples will be shown to analyze the welfare impact of removing the NSR. Under surcharging In the case where there are two sectors within each of which a monopoly merchant sells a product to consumers, a monopoly platform under surcharging selects the customer fee p B and the merchant service fee p S to maximize her profit subject to the amount of surcharge imposed by the monopoly merchant in each sector. Notably, the monopoly merchant in each sector always accepts credit card payments as they can pass the cost to do so onto consumers by levying a surcharge. In particular, the monopoly platform profit maximization problem is given by max π N = (p B +p S ) ( 1 p B s H) +(p B +p S ) ( 1 p B s L) (54) p B,p S where s H = 1 bh S p B +p S s L = 1 bl S p B +p S (55) (56) Surcharges s H and s L are derived from profit maximization problem of the monopoly merchant in each sector. Specifically, the profit maximization problem of the merchant in sector b H S is maxπ H s M = ( p cash d+b H ) S p S (1 pb s)+(p cash d)(p B +s) (57) 55

56 and the profit maximization problem of the merchant in sector b L S is maxπ L s M = ( p cash d+b L S p S) (1 pb s)+(p cash d)(p B +s) (58) where the price of product p cash in both sector is given by p cash = u t. Following the step in the case with one sector, the solutions of the above two problems can be easily obtained as s H = 1 bh S p B +p S s L = 1 bl S p B +p S (59) (60) Therefore, the constraints of surcharges for the monopoly platform are as given. By substituting the constraint into profit function of platform, the platform s profit maximization problem becomes max ρ π N = ρ 1+bH S ρ +ρ 1+bL S ρ (61) where ρ = p B +p S is the price level. Solving the profit maximization problem of monopoly platform yields ρ = +bh S +bl S 4 s L = 1 bl S s H = 1 bh S p B = +bh S +bl S 8 p S = +bh S +bl S 8 p L cash = ph cash = u t 56

57 CS L card =ˆ 1 CS H card =ˆ 1 D L card = 1 p B s L = bh S +3bL S 8 D L cash = p B +s L = 6+bH S 3bL S 8 D H card = 1 p B s H = +3bH S bl S 8 D H cash = p B +s H = 6 3bH S +bl S 8 π N = ( 1 + bh S +bl S) 4 π L M = u t d π H M = u t d p B +s L ( bb p B s L) db B = 1 p B +s H ( bb p B s L) db B = 1 ( b H S +3b L S) ( +3b H S b L S) =ˆ 1 CSproduct L ( u p L cash tx ) dx = t 0 =ˆ 1 CSproduct H ( u p H cash tx ) dx = t 0 ( 1 1 ( 6+b H 8 S 3b L S) ) ( 1 1 ( 6 3b H 8 S +b L S) ) CS SR = CS L card +CSH card +CSL product +CSH product TS SR = π N +π L M +π H M +CS L card +CSH card +CSL product +CSH product Welfare comparison In this subsection, two examples are given to compare social welfare under the NSR and under surcharging. In the first example, the values of merchant transaction benefits within each sector are given as b H S = 0.7 and bl S = 0.1 and the monopoly platform prefers to serve a 57

58 single sector with higher transaction benefit of merchant under the NSR; in the send example the values are given as b H S = 0.5 and bl S = 0.1 and the monopoly platform prefers to serve both sectors under the NSR. Table IV provides a summary of solutions for either case. The results of two examples in Table IV show that the monopoly platform prefers to run her business under the NSR than under surcharging, and the total surplus under the NSR is greater than the total surplus under surcharging. The motivation to pose the case where b H S = 0.7 and bl S = 0.1 is to show a fundamental market force which is effective during the process of removing the NSR. The fundamental market force is a change in market structure which means the merchants who did not accept credit card payments under the NSR do accept credit card payments under surcharging as the merchant in the sector b L S does in the example with { b H S = 0.7,bL S = 0.1}. This move brings about some new payments made using credit cards in the sector b L S which increases social welfare. However, the second market force, which is excessive surcharges imposed by monopoly merchants leading to an under provision of credit card payment service, decreases social welfare. In the example with { b H S = 0.7,bL S = 0.1}, both forces exist and the force of excessive surcharges dominates the force of market structure change, and hence lifting the NSR decreases social welfare. In the example with { b H S = 0.5,bL S = 0.1}, the force of market structure change does not exit because the merchants in both sectors accept credit card payments under the NSR. The only market force is the excessive surcharges imposed by merchants in each sector, and lifting the NSR in this example decrease social welfare as a result. In the general case, if the monopoly platform serves two sectors, the difference in total surplus and consumer surplus are given by TS NSR TS SR = 1 64 ( 0 15 ( b H ) S +36b L S 3 ( b L ( ) S) ) +8b H S 1+5b L S 58

59 CS NSR CS SR = 1 ( 1 ( b H ) S +8b L 64 S +11 ( b L ) S +4b H S bs) L and TS NSR TS SR 0 if 0 b L S bh S 1 CS NSR CS SR 0 if 0 b L S bh S 1 Therefore, the social welfare under the NSR is greater than social welfare under surcharging, and Proposition eight is given as Proposition eight: In the case where there are two sectors with one monopoly merchant in each sector and the monopoly platform prefers to serve two sectors under the NSR, the profit of monopoly platform, total surplus and consumer surplus are higher under the NSR than under surcharging. The profit of monopoly merchant in the sector b L S is higher under surcharging than under the NSR. The profit of monopoly merchant in the sector b H S can be higher or lower under surcharging than under the NSR. Similar to Proposition seven, Proposition eight states that the exercise of market power by the merchants drives down the consumer surplus, social surplus and the profit of monopoly platform. The profit of monopoly merchant in the sector b L S increases during the lifting of the NSR, because the merchant obtains no net gain by accepting credit card payments under the NSR but earns extra profit by imposing an excessive surcharge under surcharging. The monopoly merchant in the sector b H S does obtain net gain of ( b H S bl S) 1+b L S by accepting credit card payments under the NSR because the monopoly platform set merchant fee at p S = b L S. Whether the profit of merchant in the sector bh S increase or decrease during the lifting of the NSR depend on the magnitude of rent obtained under the NSR and the amount of extra profit obtained by imposing an excessive surcharge under surcharging. If the monopoly merchant serves one sector under the NSR, the difference in total surplus 59

60 if the monopoly merchant serves one sector under the NSR is given by and TS NSR TS SR = 1 ( 4+7 ( b H ) S 8b L 64 S 19 ( b L ( ) S) ) +8b H S 3+b L S CS NSR CS SR = 1 ( 4+7 ( b H ) S 4b L 64 S 5 ( b L ( ) S) ) +4b H S 4+b L S TS NSR TS SR 0 if 0 b L S b H S 1 and b H S 1.414b L S CS NSR CS SR 0 if 0 b L S b H S 1 and b H S 1.414b L S Therefore, proposition nine is given as Proposition nine: In the case where there are two sectors with one monopoly merchant in each sector and the monopoly platform prefers to serve one sector under the NSR, the profit of monopoly platform, total surplus and consumer surplus are higher under the NSR than under surcharging, but the profits of monopoly merchants in both sectors are higher under surcharging than under the NSR. Proposition nine states that the excessive surcharges imposed by merchants discourage too much credit card payments in each sector, and make only a few credit card payments generated in the sector b L S in the switch of market structure during the lifting of the NSR. Therefore, social welfare decreases after the removal of the NSR. In this case, the profit of merchant in sector b H S also increases with no doubt, because the merchant obtains no rent under the NSR, but earns extra profit by imposing a surcharge under surcharging. A continuum sectors of merchants The previous subsection has discussed the case where there are two sectors on the merchant side. This subsection discusses the case where there are uncountable many sectors with their 60

61 transaction benefit of merchants b S uniformly distributed in the region [0,1]. As in the case with Hotelling merchants, the following comparison of welfare will be focused on the market of providing credit card payment services. Under the NSR A monopoly platform under the NSR selects the customer fee p B and the merchant service fee p S to maximize her profit subject to merchant s acceptance of credit card payments. In particular, the profit maximization problem of platform under the NSR is given by ˆ 1 ˆ 1 max π N = (p B +p S ) db B db S = (p B +p S )(1 p B )(1 p S ) (6) p B,p S p S p B where 1 p S is the amount of sectors within which a monopoly merchant accepts credit card payments, as only in sectors with b S p S the monopoly merchant accepts credit card payments. In each of those sectors, the purchases of product made by credit cards is given by 1 p B. Therefore, the total transaction volume of purchases made through credit card platforms T = (1 p B )(1 p S ) = 1 p S 1 p B db B db S is given by the product of the credit card payments made in each sector 1 p B and the number of sectors within which a monopoly merchant accepts credit card payments. Social welfare in the market of providing credit card service is given by W = ˆ 1 ˆ 1 p S p B (b B +b S )db B db S (63) The solution to the profit maximization problem of platform under the NSR is given by p B = p S =

62 π N = T = W = Under surcharging Inthecase wherethere areacontinuum of sectors withineach of which amonopoly merchant sells a product to consumers, a monopoly platform under surcharging selects the customer fee p B and the merchant service fee p S to maximize her profit subject to the amount of surcharge imposed by the monopoly merchant in each sector. In particular, the monopoly platform profit maximization problem is given by max p B,p S π N = (p B +p S ) ˆ 1 ˆ 1 0 p B +s db B db S (64) where s = 1 b S p B +p S (65) Social welfare in the market of providing credit card payment service is given by W = ˆ 1 ˆ 1 p S p B +s (b B +b S )db B db S (66) Surcharges s is derived from profit maximization problem of the monopoly merchant in each sector. In particular, the profit maximization problem of the merchant in sector b S is maxπ M = (p d+b S p S )(1 p B s)+(p d)(p B +s) (67) s 6

63 The solution of the problem is s = 1 b S p B +p S (68) Therefore, the constraint of surcharges for the monopoly platform is as given. By substituting the constraint into profit function of platform, the platform s problem becomes max ρ π N = ρ ˆ 1 ˆ b S +ρ db B db S (69) where the price level is given asρ = p B + p S. Solving the profit maximization problem of monopoly platform yields ρ = 0.75 p B = 0.35 p S = 0.35 π N = T = W = Welfare comparison The comparison of the above results indicates that social welfare under the NSR is greater than social welfare under surcharging if b S is uniformly distributed in the region [0,1]. As in the case with two sectors, two market forces drive the welfare impact of removing the NSR; namely: (a) the change in the market structure; (b) the excessive surcharges imposed by merchants. Themerchantsinsectorswithb S p S orb S inthiscasedonotaccept 63

64 credit card payments under the NSR, but do accept credit card payments under surcharging. This change in market structure generates new payments made using credit cards in those sectors and increase social welfare as a result. However, the monopoly merchants in each sector imposes excessive surcharges which leads to a under provision of credit card payment services and therefore decreases social welfare. The total effects of the two market forces of removing the NSR is negative which means removing the NSR decreases social welfare when there are a continuum of sectors b S [0,1] within each of which a monopoly merchant sells a product to a continuum of consumers. Therefore, Proposition ten is given as Proposition ten: In the case where there are a continuum sectors with their transaction benefit of monopoly merchants b S uniformly distributed in the region [0,1], the profit of monopoly platform, total surplus are higher under the NSR than under surcharging, but the profit of monopoly merchant is higher under surcharging than under the NSR. 6.3 Surcharging behavior of merchants This subsection provides an explanation on surcharging behavior of merchants observed in Australia. A 011 report from the Reserve Bank of Australia 19 documents surcharging behaviors of merchants almost a decade later since the ban of the NSR in 003. The report had mainly recorded four surcharging behaviors of merchants as of December, 010; namely: (i) around 30 percentage of merchants had imposed a surcharge on a certain credit card; (ii) about 40 percent of large merchants imposed a surcharge while only approximately 0 percent of small merchants surcharged 0 ( see Figure 1); (iii) the average rates of surcharges among all merchants surcharging were much higher than the costs of merchants to accept 19 See Review of Card Surcharging: A Consultation Document June 011, Reserve Bank of Australia, review-card-surcharging.pdf 0 large (small) merchants are those with annual revenue more than $530 million (between $1 million and $0 million) 64

65 credit card payments 1 ( see Figure ); and (iv) blended surcharging, i.e., imposing a same level of surcharges on transactions paid by different types of credit cards with different costs to merchants, was quite common among merchants. Only about 10 percent of merchants have imposed a surcharge on a certain credit card in other countries without the no surcharge rule. In the explanation of this paper, two forces the heterogeneity in merchant s transaction benefits (or cost saving) to accept credit cards and the heterogeneity in the market power of merchants to provide credit card payment services at the point of sale drive the most surcharging behaviors of merchants. The following equation of surcharges is used to explain the above behaviors, i.e., s = p S b S + D card D card (70) Note that the surcharge equation of monopoly merchants is an expression derived in a general form. In particular, the profit maximization problem of monopoly merchant is given by maxπ M = (p cash d+b S p S )D card +(p cash d)(1 D card ) (71) s By substituting p cash = u t, the problem is given by maxπ M = u t d+(b S +s p S )D card (7) s and the first order condition yields (70). Basically, four types of surcharging behaviors are observed; including: (a) some merchants surcharge while some do not; (b) excessive surcharges prevail; (c) the prevalence of 1 In December 010, the average rates of surcharges for MasterCard, Visa and Diners Club credit cards were 1.8, 1.9 and 4 percent respectively. The merchant fees for MasterCard and Visa cards are around 0.6 percent, and. percent for Diners Club cards. See Review of Card Surcharging: A Consultation Document June 011, Reserve Bank of Australia for more details. See Wright (01) p, footnote 17 65

66 surcharging is higher among large merchants and lower among small merchants; (d) some merchants have a blended surcharge. The first type of surcharging is explained by the expression of surcharging. For example, surcharges are positive if p S +D card /D card > b S. That is to say, for any given merchant fee p S, merchants with lower transaction benefit b S tend to surcharge. The second type of surcharging excessive surcharge is explained by the market power term D card /D card. The term of market power could be exceptionally high when consumers have inelastic demand of credit card payment services at the point of sale, and hence merchants tend to impose an excessive surcharge in this case. To give an example, in the businessof air ticket online bookingwhere consumers have to pay with a type of credit cards, the amount of surcharges are extraordinary high: a family paid a $100 surcharges on top of the base price $36.80 of a family air ticket from airline Jetstar in The excessive amount of surcharges are therefore explained by the inelastic demand of consumers of credit card payment services the driving force of the mentioned market power of merchants. The third type of surcharging on the prevalence is explained by the variations of the two variables the market power of merchants and the transaction benefits. For a given merchant fee p S, a larger market power term indicates merchants are more likely to surcharge (as surcharges are given by(70)) when the transaction benefits b S varies. The large merchants 4 in Australia are those with a high volume of sales, and the high volume of sales, D card, often translates into high market power in providing credit card payment services. This explains the fact that the prevalence of surcharges is higher among larger merchants, when they tend to have higher market power. 3 This anecdote can be found at 4 The larger merchants refer to the merchants have a higher turnover in the market to sell goods and products. The merchants with higher turnovers tend to have a larger consumer base, and the market power in providing card services is positively related to the volume of consumer base. Thus, larger merchants in good markets also tend to have a higher market power in providing card services. often have a larger consumer base and less elastic demand of card services. 66

67 The fourth type of blended surcharging can be explained by the difference in transaction benefits of merchants and the difference of demand of each type of credit cards. Consider a merchant who accepts both American Express (Amex) credit cards and Visa credit cards. The merchant s cost to accept Visa credit cards is typically lower than the cost to accept Amex credit cards. In other words, Visa often charges a lower merchant fee than Amex does. But the number of consumers who use Visa credit cards are generally much higher than the number of consumers using Amex credit cards, and the larger number of Visa credit card users can indicates a greater market power of the merchant in providing Visa credit card payment services at the point of sale. The merchant therefore tends to have blended surcharges: impose a same level of surcharge on both Amex and Visa credit cards because the two factors the higher cost of Amex credit cards and the heightened market power of providing Visa credit card network services offset each other. 5 7 Conclusion The controversy of the no surcharge rule is world-wide and has been ongoing for more than two decades. Since the introduction of credit cards in the 1950s in the United States, 6 the no surcharge rule has played a critical role in fostering and protecting the credit card network. When credit cards prevail nowadays, people start to doubt their legitimacy. In strong contrast with public understanding and conventional wisdom, this paper provides a theory which strongly supports the existence of the NSR. In particular, this paper shows that in the cases of homogeneous merchants, social welfare under the NSR is always greater than social welfare under surcharging. This is because, in the case with Hotelling merchants, the NSR fosters a market force from merchant internal- 5 American Express provides more corporate cards, and Visa more household cards. So, these two different type of cards can be seen from different markets. 6 the detailed history background can be found at page 10 in Adam (006). 67

68 ization which offsets the market distortion due to market power of monopoly platform, and in the case with monopoly merchant, the NSR prevents merchants from imposing an excessive surcharge. In the case with heterogeneous merchants, another market force of market structure change is generated during the lifting of the NSR, and it always favors allowing surcharges. However, the positive effect from market structure change is relative small compared to two other negative market forces during the removal of the NSR. Therefore, social welfare often decreases after the ban of the NSR. It is also worthwhile mentioning that the unambiguous welfare implication in the case with homogeneous merchants does not rely on any assumptions on the parameters of market and the degree of competition among issuing banks. The NSR is always better if MI exists among merchants in the case with Hotelling merchants; and the NSR is always better in the case with monopoly merchants because it prevents another markup by merchants. This unambiguous understanding regarding welfare implication is crucial. It provides a new benchmark for policy intervention regarding the current institutional structure of credit card markets, which has not been updated for more than a decade, despite the fact that significant institutional changes take place in the credit card market. However, this paper does not consider the impact of removing the NSR in a setting with platform competition which could be a worthwhile topic for future research. Nevertheless, the lack of platform competition will not affect the welfare implication of lifting the NSR nowadays. This is because consumers often use one type of credit cards despite the fact that they often hold multiple cards, which is documented in the empirical study Rysman (007). 68

69 References [1] Adam J. Levitin, 005 The Antitrust Super Bowl: America s Payment System, No- Surcharge Rules, and the Hidden Costs of Credit, 3 Berkeley Bus. L.J. 65 (005). [] Bradford, T. and Hayashi, F. Developments in Interchange Fees in the United States and Abroad. Working Paper, Federal Reserve Bank of Kansas City, 008. [3] Baxter, W Bank Interchange of Transactional Paper: Legal and Economic Perspectives, Journal of Law and Economics. Volume 6, No. 3 pp; [4] Bourguignon, Hlne, Gomes, Renato, and Tirole, Jean Shrouded Transaction Costs. Mimeo [5] Economides, N. and D. Henriques (working paper). To surcharge or Not to Surcharge? A Two-sided Market Perspective of the No-surcharge Rule, Working paper series No 1388, European Central Bank. [6] Farrell, J Efficiency and competition between payment instruments, Review of Network Economics 5, [7] Gans, J. and S. King The Neutrality of Interchange Fees in Payment Systems, Topics in Economic Analysis & Policy, Volume 3. Article 1. [8] Rochet, J.-C. and J. Tirole 00, Cooperation among Competitors: Some Economics of Payment Card Associations, RAND Journal of Economics 33: [9] Rochet, J.-C. and J. Tirole Platform Competition in Two-Sided Markets. Journal of the European Economic Association, 1(4): [10] Rochet, J.-C. and J. Tirole (011) Must-take cards: merchant discounts and avoided costs, Journal of the European Economic Association 9(3),

70 [11] Rysman, M An Empirical Analysis of Payment Card Usage, Journal of Industrial Economics, 55, [1] Schwartz, M, and D. R. Vincent, 006. The No Surcharge Rule and Card User Rebates: Vertical Control by a Payment Network. Review of Network Economics, Vol.5. No.1. March, pp [13] Vickers, J Public policy and the invisible price: Competition law, regulation and the interchange fee, Competition Law Journal 4, [14] Weiner, S. and J. Wright Interchange Fees in Various Countries: Developments and Determinants, Review of Network Economics, 4(4), Article 3. [15] Wright, J Optimal Card Payment Systems. European Economic Review, Vol. 47, pp [16] Wright, J Determinants of Optimal Interchange Fees, Journal of Industrial Economics, 5, 1-6. [17] Wright, J. (01) Why Payment Card Fees are Biased against Retailers, RAND Journal of Economics. 70

71 8 Appendix 8.1 Hotelling competition For a given merchant fee p S, the Hotelling merchants in one sector could both accept, both decline and one accepts and one declines the credit card payments. The following will show that under condition (3) both merchants accept credit card payments is a Nash equilibrium in the sector under the NSR. First consider the case where both merchants, merchant i and merchant j, accept credit card payments. They set the uniform prices of the product p i and p j respectively to compete for the consumers. Consumers could pay in cash or with credit cards. A consumer located at x decides which merchant to purchase from according to the relevant price and transportation cost regardless of her drawn of the transaction benefit b B as she can enjoy transaction benefit from either merchant if she has a transaction benefit b B greater than the customer p B or can not enjoy it from neither of the merchant if otherwise. In other words, the value of the transaction benefit b B of a consumer does not affect the choice of which merchant to purchase, but it does affect how she makes the payment. Therefore, consumers with transaction benefits greater than the customer fee (b B > p B ) purchase with credit cards and consumers with transaction benefits less than the customer fee (b B < p B ) purchase with cash, and the demand of merchant i and merchant j are respectively given by x i = 1 + p j p i t and x j = 1 + p i p j t The above two are standard Hotelling demand functions which are obtained by first finding the marginal consumer who is indifferent between purchasing from either merchant, and then demand of merchant i or j is given by aggregating consumption of those consumers who is located closer to merchant i or j than the marginal consumer is. The location of 71

72 the marginal user is obtained by equating the benefits of purchasing from either merchant, or u (p i +tx i ) = u (p j +t(1 x i )), and the location of the marginal consumer is x i = 1 + p j p i t. Therefore, the demand of merchant i is x i = 1 x j = 1 + p j p i t and demand of merchant j is x j = 1 + p i p j t. Hence, the profit maximizing problem of merchant i and j are given respectively by max p i {[p i (d+d B (p B )(p S b S ))]x i } max p j {[p j (d+d B (p B )(p S b S ))]x j } where x i = 1 + p j p i t and x j = 1 + p i p j t. The term D B (p B ) stands for each merchant serves D B (p B ) unit of transaction payments paid by credit cards, and the expression p S b S means each payment incurs a cost equal to merchant fee nets her own transaction benefit p S b S. The solution of the profit maximization problems is: p i = p j = p = [d+d B (p B )(p S b S )]+t π i = π j = π = t (73) Second consider the situation where merchant i does not accept credit card payments, and merchant j continue to accept credit card payments. If merchant i deviates to reject credit card payments, a portion of consumers who used to make purchases using credit cards from merchant i now switch to merchant j to enjoy the transaction benefit from paying by credit cards. In particular, among the population of consumers with the realized transaction benefit b B greater than the customer fee p B, the demand of merchant i is given by x i = 1 + p j p i (b B p B ) t, which is a standard Hotelling demand. The location of the marginal user is obtained by equating the benefits of purchasing from either merchant, or u (p i +tx i ) = u (p j +t(1 x i ))+(b B p B ), and the location of marginal user is x i = 7

73 1 + p j p i (b B p B ) t. Finally, the total demand of merchant i from consumers with transaction benefit greater than the customer fee (b B > p B ) is obtained by taking an aggregate for any value of b B, and it is given as follows: ˆ bb ˆ bb ( 1 x card i = x i (b B )db B = p B p B + p ) j p i (b B p B ) db B t ( 1 x card i == D B (p B ) + p ) j p i v B (p B ) t (74) where v B (p B ) is the consumer s average user surplus per transaction as defined in (1). Likewise, the total demand of merchant j from consumers with transaction benefit greater than the customer fee (b B > p B ) is given by ˆ bb ˆ bb ( 1 x card j = x j (b B )db B = p B p B + p ) i p j +(b B p B ) db B t ( 1 x card j == D B (p B ) + p ) i p j +v B (p B ) t (75) The consumers with transaction benefit less than the customer fee (b B < p B ) will not pay with credit cards. Among consumers with transaction benefit less than the customer fee (b B < p B ), the demand of merchant i is simply given by x i = 1 + p j p i t. Therefore, the total demand of merchant i from consumers with transaction benefit less than the customer fee (b B < p B ) is obtained by taking the aggregate for any value of b B, and it is given by ˆ pb ˆ pb ( 1 x cash i = x i db B = b B b B + p ) ( j p i 1 db B = (1 D B (p B )) t + p ) j p i t (76) Likewise, the total demand of merchant j from consumers with b B < p B is given by ˆ pb ˆ pb ( 1 x cash j = x k jdb B = b B b B + p ) ( i p j 1 db B = (1 D B (p B )) t + p ) i p j t (77) 73

74 Finally, the profit maximization problems are: ( maxπ i = (p i d) x cash p i i ) +x card i maxπ j = (p j d)x cash p j +(p j d (p S b S ))x card j j Merchant i merely incurs the cost of selling the product and has a uniform markup p i d Merchant j serves bothtypes of consumers, incurringacost dwhenshesells to consumers who pay in cash and incurring an extra cost to provide card service p S b S when she sells to consumers who pay with credit cards. Solving the problem yields prices and profits given by p i = t+d+ 1 3 D B (p B )(p S b S v B (p B )) (78) p j = t+d+ 1 3 D B (p B )((p S b S )+v B (p B )) (79) π j = t π i = t [ 1 1 3t D B (p B )(v B (p B ) (p S b S ))] (80) [ 1+ 1 ] 3t D B (p B )(v B (p B ) (p S b S )) 1 t (p S b S )v B (p B )D B (p B )(1 D B (p B )) By comparing (73) with (80), it can be seen that merchant i will not deviate to decline credit card payments when π > π i, which is equivalent to (81) b S p S v B (p B ) where v B (p B ) is the consumer surplus. Hence, when the condition (3) holds which is called the condition for merchant internalization in the literature of credit card markets, neither merchant will deviate to decline credit card payments when they start the competition by 74

75 accepting credit card payments. Next consider the situation starting with competition where both merchants reject credit card payments. In doing so, a condition, under which both merchants will deviate from rejecting credit card payments to accepting credit card payments, is derived. If both merchants reject credit card payments, the profit maximizing problems of merchants are given by { ( 1 max (p i d) p i + p )} i p j t { ( 1 max (p j d) p j + p )} i p j t Solving them yields p i = p j = p = d+t π i = π j = π = t (8) Suppose merchant j deviates to accept credit card payments and merchant i still rejects credit card payments, the profit maximizing problems of the two merchants are given as ( maxπ i = (p i d) x cash p i i ) +x card i where x cash i maxπ j = (p j d)x cash p j +(p j d (p S b S ))x card j j, x cash j, x card i and x card j are given by (76), (77) (74) and (75) respectively. Solving the problem yields the same solution as the above π i = t [ 1 1 3t D B (p B )(v B (p B ) (p S b S ))] (83) 75

76 π j = t [ 1+ 1 ] 3t D B (p B )(v B (p B ) (p S b S )) 1 t (p S b S )v B (p B )D B (p B )(1 D B (p B )) Merchant j doesnotdeviatetoaccept creditcardpaymentsifherprofitwhenshedeviates is less than her profit when she remains to reject credit card payments if π j π or if p S b S + v B (p B ) by the comparison of (84) and (8); merchant j will deviate to accept credit card payments if π j π. The condition π j π requires p S b S. However, when b S p S b S + v B (p B ), both π > π j and π < π j could be the case, which means the condition (3) may not sufficient for a Nash equilibrium where both merchant accept credit payments when starting from both merchant declining credit card payments. This paper will treat condition (3) as the sufficient condition for the Nash equilibrium by following the assumption in RT00 and Wright (004) that where multiple equilibria with identical profits exist, the card company or merchants will choose the equilibrium where both merchants accept credit card payments. 7 To sum up, Hotelling merchants accept credit card payments if condition (3) holds. The condition, which is called merchant internalization, simply says merchants internalize consumer surplus when deciding to accept the card or not. In essence, the condition of merchant internalization holds for Hotelling merchants because each merchant is able to attract more customers if she accepts credit card payments. (84) 8. Change in payment value This section estimates the change in value of credit card payments due to surcharges in Australia, and finds that the reform of Reserve Bank of Australia (RBA) in 003 contributes to up to 40% value decline in credit card payments over 7 years. 7 Moreover, the competition could also start from one merchant accepts credit card payments and another does not. As stated in Wright (004), it is possible to show there is no such equilibrium where one merchant accepts credit card payments and the other rejects, given t is not too small. Therefore, this paper does not consider such an equilibrium here. 76

77 In 003 reform, RBA capped the average weighted interchanges fee from 0.95% to 0.5% percent, and removed the prohibition on surcharges. The reform brings about some consequences. First, the cash rewards programs have declined but the annual fees increased. Second, some consumers substitute away from swiping a credit card to a debit card due to the surcharge with credit card payments. This point can be seen from the relative annual growth in value of credit card payments and debit card payments. 8 As is shown in Figure 4, 9 in a six year period before the reform, the annual growth in value of credit card and debit card payments are around 5% and 15% respectively; in the decade after the reform, the growth rates are around 8% and 1% respectively. To reveal how the surcharges affect the transaction value of credit card payments, a rough econometric exercise is conducted. Before the reform, the annual growth rates in credit and debit card payments are given by x B credit and xb debit as follows: x B credit = time trend+credit growth x B debit = time trend+debit growth The term time trend represents the common factors that affect both growth rates. These factors include technological progress, economic expansion or recession, the demand of card payments due to the online shopping and etc. The credit growth and debit growth stand for the individual growth rates of card payments. Before the reform, it can be seen that the individual growth rate of credit card is larger than that of of debit card. This is partly due to more functionality of credit cards (e.g. people can borrow) and the issuing effort by 8 The NSR rule is still applied to the debit card transactions after the reform. 9 The figure is the graph one from a report called The personal credit card market in Australia: pricing over the past decade. This report can be reached at 77

78 banks. Thus, the individual growth difference is debit growth credit growth = x B debit xb credit (85) After the reform, the annual growth rates are x A credit = time trend+credit growth switch x A debit = time trend+debit growth+switch The switch stands for the value of payments switching from credit cards to debit cards. In this context, the debit card is deemed to be the second best alternative to the credit card. When consumers do not swipe their credit cards when merchants surcharge the payments, they swipe the debit card with which the payment is not surcharged. Therefore, the decline in the value of credit card payments is the switch which is given by switch = 1 ( x A debit x A credit (debit growth credit growth)) or switch = 1 ( x A debit x A credit ( x B debit xb credit)) after substituting equation (85). Plugging into the figures, we have switch = 1 (1% 8% (15% 5%)) = 7% Suppose the industries fully absorb the effect of surcharges on payment methods over 7 years till 010. The switch away value of credit card payments over 7 years is around 40%. 30 That 30 The change in value is 1 (1 7%) 7. =

79 is the reform contributes to up to 40% value decline in credit card payments over 7 years. 8.3 Table Table I: the summary of results for the case of Hotelling merchants with one sector NSRMI NSR SR p B b S +c 1 (1 b S +c) 1 4 (1+b S +c) p S 3 b S + 1 c b S 1 4 (1+b S +c) p d+t+ 1 (1+b S c) d+t d+t D card 1+b S c 1 (1+b S c) 1 (1+b S c) D cash b S +c 1 (1 b S +c) 1 (1 b S +c) ρ 1 (1+b S +c) 1 (1+b S +c) 1 (1+b S +c) s na na 1 4 (1 3b S +c) π N 1 (1+b S c) 1 4 (1+b S c) 1 4 (1+b S c) π M t CS card 1 (1 ( b S +c)) 1 CS product u d 5 4 t 1 (1 ( b S +c)) t ( 1 1 b S+c u d 5 4 t t ) 1 ( 1 1 b S+c u d 5 4 t ) Table II: the summary of results for the case of Hotelling merchants with two sectors { b L S = 0.1,b H S = 0.7} { b L S = 0.1,bH S = 0.5} NSR SR NSR SR p B p S p L

80 p H D L card D L cash D H card D H cash ρ { s L,s H} na {0.5, 0.35} na {0.5, 0.175} π N πm L πm H CScard L CScard H CSproduct L CSproduct H T S Table III: the summary of results for the case of monopoly merchant with one sector General case {u = 0,d = 0,t = 10,b S =.5} NSR SR NSR SR p B 1 (1 b S) 1 4 (1+b S) p S b S 1 4 (1+b S) p u t u t D card 1 (1+b S) 1 4 (1+b S) D cash 1 (1 b S) 1 4 (3 b S)

81 ρ na 1 (1+b S) na.75 s na 1 (1 b S) na.5 π N 1 4 (1+b S) 1 8 (1+b S) π M u t d u t d (1+b S) ( ) ( ) 1 CS card 1 1 b S b S CS product t t 5 5 T S na na Table IV: the summary of results for the case of monopoly merchant with two sectors { b L S = 0.1,b H S = 0.7} { b L S = 0.1,bH S = 0.5} NSR SR NSR SR p B p S p D L card D L cash D H card D H cash ρ { s L,s H} na {0.45,0.15} na {0.45,0.5} π N π L M π H M

82 CScard L CScard H CSproduct L CSproduct H T S

83 8.4 Graph Figure 1 Figure Figure 3 83