• No results found

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

N/A
N/A
Protected

Academic year: 2021

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

Copied!
84
0
0

Loading.... (view fulltext now)

Full text

(1)

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

Hongru Tan November 25, 2015

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 distor-

tion 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 con-

ventional 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.

(2)

Contents

1 Introduction 3

2 Background 8

3 Literature review 9

4 Model 11

5 Hotelling merchants 12

5.1 Homogeneous merchants . . . . 13

5.2 Unambiguous welfare implication . . . . 22

5.3 Heterogeneous merchants . . . . 28

5.4 Reverse cross subsidization . . . . 42

6 Monopoly merchants 43 6.1 Homogeneous merchants . . . . 44

6.2 Heterogeneous merchants . . . . 51

6.3 Surcharging behavior of merchants . . . . 64

7 Conclusion 67 8 Appendix 71 8.1 Hotelling competition . . . . 71

8.2 Change in payment value . . . . 76

8.3 Table . . . . 79

8.4 Graph . . . . 83

(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. 2

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 pur- chases 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 2010, and Final Judgment, as well as Memorandum and Order, 20 July 2011 . All available online at http://www.justice.gov/atr/cases/americanexpress.html.

2

United States et al v. American Express Company et al, 10-CV-4496 (Eastern District of New York) 19 February 2015.

3

The details of regulation can be found in Weiner and Wright (2005).

(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 using consumers 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 (2002) (RT2002) in a similar setting.

The welfare impact of lifting the NSR in RT2002 is investigated in a context where a not- for-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 RT2002, 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 http://www.ct-tc.gc.ca/CMFiles/CT-2010-010 Expert%20Report%20of%20Ralph%

20A.%20Winter 251 45 3-12-2012 1262.pdf

(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 RT2002 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

(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

(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 poten-

tially subsidize those who pay by cash under the NSR, which is in contrast with the finding

in RT2002. 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 RT2002. 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 2003 reform of credit card

market in Australia.

(8)

2 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 $0.12. 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 http://www.ct- tc.gc.ca/CMFiles/CT-2010-010 Expert%20Report%20of%20Ralph%20A.%20Winter 251 45 3-12-

2012 1262.pdf

7

In general, cardholders pay fees to issuers. If cardholders receive cash rewards, the customer fee is

negative.

(9)

later (use credit) and eliminating the need to carry, count and the risk losing cash.

3 Literature review

Rochet and Tirole (2002) is the pioneer canonical study which investigates the welfare im- plication 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 mer- chants. 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 lead- ing 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, ex- aggerates 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 (2003) 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 com-

petitive 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 maxi-

mizes 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 transac-

tion volume of credit card payments and social welfare are independent of the no surcharge

(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 plat- form 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 suffi- ciently 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 (2006) find that the NSR benefits the platforms but harm the cash users and merchants in a con- text 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 RT2002. 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

(11)

cards, while the merchants are assumed to have the same level of transaction benefit in RT2002 and Wright (2003); (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 (2006) 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 to merchants namely the merchant service fee p S , to maximize her profit. 9 Under the 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 (2007) 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.

(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.

(13)

consumption from consumers who are uniformly spread over the interval. Each consumer lo- cated at x incurs transportation 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 consumer also has a transaction benefit from using credit cards b B independently drawn 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)

(14)

Therefore, the monopoly platform profit maximization problem is given by

p max

B

, p

S

π N = (p B + p S ) D card (2)

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 Equilib- rium where both merchants prefer to accept credit card payments. The derivation for the constraint of merchant’s acceptance, which has been derived in RT2002 and Wright (2004), is heavily involved in terms of calculation, and therefore is shown in the appendix I for in- terested 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 be- cause 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 prison- ner 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.

(15)

π M i = π M j = π = t

2 (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

2 (7)

Solving the profit maximization problem of monopoly platform yields

p B = −b S + c

p S = 3 2 b S + 1

2 − c 2 D card = 1 + b S − c

D cash = −b S + c p = d + t + 1

2 (1 + b S − c) 2 π N = 1

2 (1 + b S − c) 2 π M i = π M j = π = t

2 CS card =

ˆ 1 p

B

(b B − p B ) db B = 1

2 (1 − (−b S + c)) 2

CS product = 2 ˆ

12

0

(u − p − tx) dx = u − d − 5 4 t − 1

2 (1 − (−b S + c)) 2

(16)

CS = CS card + CS product

T S = π N + π M i + π j M + 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 T S 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

2

(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 2 p S = b S

D card = 1 + b S − c 2 D cash = 1 − b S + c

2 p = d + t

π N = 1

4 (1 + b S − c) 2 π M i = π M j = π = t

2 CS card =

ˆ 1 p

B

(b B − p B ) db B = 1 2



1 − 1 − b S + c 2

 2

CS product = 2 ˆ

12

0

(u − p − tx) dx = u − d − 5 4 t CS = CS card + CS product

T S = π N + π M i + π j M + CS card + CS product

(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

p max

B

, p

S

π N = (p B + p S − c) D card (10)

s.t. s = p S − b S (11)

where D card = 1 − p B − s is the amount of payments paid by credit cards. 12 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 RT2002.

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 (12)

s = p S − b S (13)

π M i = π M j = π = t

2 (14)

12

The per transaction cost of operating the credit card platform is assumed to be zero as it is negligible in

the real world.

(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 2

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 2 D cash = p B + s = 1 − b S + c

2 p = d + t

π N = 1

4 (1 + b S − c) 2 π M i = π M j = π = t

2 CS card =

ˆ 1 p

B

+s

(b B − p B − s) db B = 1 2



1 − 1 − b S + c 2

 2

CS product = 2 ˆ

12

0

(u − p − tx) dx = u − d − 5

4 t

(20)

CS = CS card + CS product

T S = 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 N SRM I − π N SR N = 1

4 (1 + b S − c) 2 π M N SRM I − π N SR M = 0

CS N SRM I card − CS N SR card = 3

8 (1 + b S − c) 2 CS product − CS product = − 1

(1 + b S − c) 2

(21)

CS total N SRM I − CS N SR total = − 1

8 (1 + b S − c) 2 T S N SRM I − T S N SR = 1

8 (1 + b S − c) 2

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

(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.

5.2 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 RT2002. 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 RT2002 indicates that lifting the NSR can increase or decrease social welfare.

The fundamental reason lies in the difference of platform governance. In RT2002, 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 RT2002, 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

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

2

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

p S = b S + 1 − p B

2 which yields the equilibrium given as follows

p B = c I − α 2b S + 1 − c I 2 − α

p S = b S + 1 − c I

2 − α

In the above equilibrium, the credit card services could be under or over provided. Take

(24)

c I = 1 as an example. The sum of transaction benefits of marginal consumer and merchant are greater than the cost if α < 2 3 , or

b c B + b b S = p B + b S ≥ c I if α < 2

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 > 2 3 , The sum of transaction benefits of marginal consumer and merchant are less than the cost, or

b c B + b b S = p B + b S ≤ c I if α > 2

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

(25)

is reduced. Therefore, welfare implication can be either positive or negative. In RT2002 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

p max

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

max p

B

π N = (p B + b S + v B (p B ) − c) D B (p B ) (18)

or

max p

B

π N = ˆ 1

p

B

(b B + b S − c) db B (19)

(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

(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

p max

B

, p

S

π N = (p B + p S − c) D card (20)

s.t. p S ≤ b S + v B (p B + λ) (21)

or

max p

B

π N = (p B + b S + v B (p B + λ) − c) D B (p B + λ) (22) or

max p

B

π N = ˆ 1

p

B

(b B + b S − c) db B (23)

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 mer- chants, 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

(28)

achieved. However, this is not case in the model of RT2002, 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 (2013) estimate that the magnitude of b

S

is under .5% of the value of the transaction

payment.

(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 b H 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 2

B

if she chooses to serve both sectors under the NSR, and her profit maximization problem is given by

max p

B

π N = 2 (p B + p S ) (1 − p B ) (24)

s.t. p S ≤ b L S + 1 − p B

2 (25)

The solution of the problem is

p B = 0 p S = b L S + 1

2 π N = 2b L S + 1

In the sector b L S ,

D card = 1 − p B = 1

D cash = p B = 0

(30)

p L = d + t + D B (p B ) p S − b L S 

= d + t + 1 2 π L = t

2 CS card L =

ˆ 1 p

B

(b B − p B ) db B = 1 2

CS product L = 2 ˆ

12

0

(u − p L − tx) dx = u − d − 5 4 t − 1

2 In the sector b H S ,

D card H = 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 2 π H = t

2 CS card H =

ˆ 1 p

B

(b B − p B ) db B = 1 2

CS product H = 2 ˆ

12

0

(u − p H − tx) dx = u − d − 5 4 t − 1

2 + b H S − b L S The total consumer surplus and the total social welfare are

CS N SR = CS card L + CS card H + CS product L + CS product H

T S N SR = π N + π M L + π H M + CS card L + CS card H + CS product L + CS product H

In the second example, the monopoly platform sets p S = b H S + 1−p 2

B

if she chooses to

(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 ) (26)

s.t. p S ≤ b H S + 1 − p B

2 (27)

The solution of the problem is

p B = 0 p S = b H S + 1

2 π N = b H S + 1 2 In sector b L S ,

D L card = 0

D cash L = 1 p L = d + t

π L M = t 2 CS card L = 0 CS product L = 2

ˆ

12

0

(u − p − tx) dx = u − d − 5 4 t In sector b H S ,

D card H = 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 + 1

2

(32)

π H M = t 2 CS card H =

ˆ 1 p

B

(b B − p B ) db B = 1 2

CS product H = 2 ˆ

12

0

(u − p H − tx) dx = u − d − 5 4 t − 1

2 The total consumer surplus and the total social welfare are

CS N SR = CS card L + CS card H + CS product L + CS product H

T S N SR = π N + π M L + π H M + CS card L + CS card H + CS product L + CS product H

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 + 2b L S ≥ 1 2 + b H S or equivalently

b H S − 2b 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

(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

p max

B

, p

S

π N = (p B + p S ) 1 − p B − s H 

+ (p B + p S ) 1 − p B − s L 

(28)

where s H = p S − b H S (29)

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 = 2 + b H S + b L S 4 s L = 2 + b H S − 7b L S

8 s H = 2 − 7b H S + b L S

8 p B = 2 + b H S + b L S

8 p S = 2 + b H S + b L S

8

(34)

p L = d + t

p H = d + t

D L card = 1 − p B − s L = 2 − b H S + 3b L S 4 D L cash = p B + s L = 2 + b H S − 3b L S

4

D card H = 1 − p B − s H = 2 + 3b H S − b L S 4 D cash H = p B + s H = 2 − 3b H S + b L S

4 π N = 1

2 (1 + b H S + b L S 2 ) 2 π L M = t

2 π H M = t 2 CS card L =

ˆ 1 p

B

+s

L

b B − p B − s L 

db B = 1 2

 1 − 1

4 2 + b H S − 3b L S   2

CS card H = ˆ 1

p

B

+s

H

b B − p B − s H 

db B = 1 2

 1 − 1

4 2 − 3b H S + b L S   2

CS product L = 2 ˆ

12

0

u − p L − tx 

dx = u − d − 5 4 t

CS product H = 2 ˆ

12

0

u − p H − tx 

dx = u − d − 5 4 t CS SR = CS card L + CS card H + CS product L + CS H product

T S SR = π N + π M L + π M H + CS card L + CS card H + CS product L + CS product H

(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 b L 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 benefits are as b H S = 0.5 and b L S = 0.1 and the monopoly platform prefers to serve both sectors under the NSR.

Table II provides a summary of solutions under the NSR and surcharging when the values of parameters are given as {u = 20, 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 b L S = 0.1, but otherwise in the case with b H S = 0.5 and b L 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, b L 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, b L S = 0.1

, both forces exist and the force of market struc- ture change dominates the force of elimination of MI, and hence lifting the NSR increases social welfare. In the example with 

b H S = 0.5, b L S = 0.1

, the force of market structure change

does not exit because the merchants in both sectors accept credit card payments under the

(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

T S N SR − T S SR = 1 16

 4 + 4b H S − 7 b H S  2

+ 4b L S − 7 b L S  2

+ 2b H S b L S 

CS N SR − CS SR = 1 16



−4 + 12b H S − 5 b H S  2

− 20b L S − 5 b L S  2

+ 6b H S b L S  and

T S N SR − T S SR ≥ 0 if 0 ≤ b L S ≤ b H S ≤ 1

CS N SR − 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 N SR − CS SR | b

L S

=0 = 1

16

 −4 + 12b H S − 5 b H S  2 

= − 1

16 −2 + b H S 

−2 + 5b H S 

and

CS N SR − CS SR ≥ 0 if 0.4 ≤ b H S ≤ 1 CS N SR − 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

high sector b H and therefore reduces the monopoly platform’s expropriation of the consumers

(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 mer- chants 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

T S N SR − T S SR = 1 16

 −4 + 4b H S − 7 b H S  2

− 12b L S − 7 b L S  2

+ 2b H S b L S 

CS N SR − CS SR = 1 16



−12 − 4b H S − 5 b H S  2

− 4b L S − 5 b L S  2

+ 6b H S b L S  and

T S N SR − T S SR ≤ 0 if 0 ≤ b L S ≤ b H S ≤ 1

CS N SR − 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

HS

− 2b

LS

≤ 0.5 holds

(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

HS

− 2b

LS

≥ 0.5 holds

References

Related documents

In view of the importance of aryloxy tetrazoles and aryloxy imidoylazides [38-43], we want to report a facile, effective and less hazard method for synthesis the 5-aryloxy

Field experiments were conducted at Ebonyi State University Research Farm during 2009 and 2010 farming seasons to evaluate the effect of intercropping maize with

Experiments were designed with different ecological conditions like prey density, volume of water, container shape, presence of vegetation, predator density and time of

In theory, FRET is a radiationless energy transfer process, so ideally, a single emission spectrum of the output fluorophore should be observed, as illustrated in Fig.2.7

effort to develop few novel hybridized derivatives of murrayanine (an active carbazole derivative) by reacting with various small ligands like urea, chloroacetyl chloride,

Recently, we reported that the activity of cAMP-dependent protein kinase A (PKA) is de- creased in the frontal cortex of subjects with regres- sive autism

This study is a systematic review and meta- analysis that was performed in clinical trial about the effect of vitamin D copmpared with placebo on CD4 count of