230 South LaSalle Street, Chicago, IL 60604

e-mail: sujit.chakravorti@chi.frb.org

411 Locust Street, St. Louis, MO 63102

e-mail: emmons@stls.frb.org

February 2001

Emerging Payments Occasional Paper Series

*We thank Lawrence Goldberg, Bob Moore, Ken Robinson, and participants at the 1998 Financial

Management Association meetings for comments on earlier drafts. We also benefited from conversations

with various network participants and industry experts. The views expressed are those of the authors and

should not be attributed to the Federal Reserve Banks of Chicago or St. Louis, or the Federal Reserve

System.

We model side payments in a competitive credit-card market. If competitive retailers

charge a single (higher) price to cover the cost of accepting cards, banks must subsidize

convenience users to prevent them from defecting to merchants who do not accept cards. The

side payment will be financed by card users who roll over balances at interest if their subjective

discount rates are high enough. Despite the feasibility of cross subsidies among cardholders,

price discrimination without side payments is Pareto preferred because of the costliness of the

by current convenience users.

Key words: credit cards, payments systems, consumer credit

JEL Classification: D11, D23, G21

1

I view credit cards, bank originated or other, as a temporary but probably unavoidable retreat in the campaign to develop an efficient domestic payments mechanism.

Credit cards serve not only as a source of revolving credit but also as a popular payment instrument among those who routinely pay off their balances in full each month. This is somewhat surprising because credit cards require an expensive supporting infrastructure. Do those who pay off their balances regularly pay for the services they receive? If they don't, who does?

First, a card-accepting merchant can serve the entire market by price-discriminating among consumers on the basis of payment method, but only liquidity-constrained customers will use credit cards.

In our model, a credit card equilibrium where liquid consumers use credit cards can only be supported if liquidity-constrained consumers subsidize their credit-card usage.

arrangement is feasible. Currently, Federal Reserve Regulation Z prohibits the banning of discounts to consumers

using other payment instruments. However, there are state laws and card association rules that prohibit imposing

surcharges for credit-card purchases. For a discussion of cash discounts and credit card surcharges, see Barron,

Staten, and Umbeck (1992), Kitch (1990), and Lobell and Gelb (1981).

of higher prices or fees and finance charges imposed by card issuers. However, if markets are not competitive

Finally, our model shows when credit-card usage can be welfare-enhancing. The key assumption in this regard is that at least a certain number of consumers face binding liquidity constraints. Intuitively, the value of consumer credit may outweigh the costliness of the payment instrument with which it is bundled.

The paper is organized as follows. Section I provides an overview of credit-card costs and usage. Section II discusses previous contributions to the literature on credit-card usage. In Section III, we develop a model of the interrelated downstream markets in a credit-card network.

We consider three pricing and subsidy schemes, including differentiated pricing and a single goods price with and without cross-subsidization within the credit-card network. Section IV compares the three schemes in terms of allocative efficiency and a simple utility-based measure of social welfare. Section V concludes.

Table 1 shows that credit cards are relatively expensive retail payment instruments for

merchants to accept. Compared to cash, which costs supermarkets only about 22 cents per $100

of purchases, credit cards appear to be extravagantly expensive, costing $2.41, nearly 11 times as

much (Food Marketing Institute, 1998). A large component of merchants' cost of accepting

credit cards is the merchant discount, the fraction of the face value of sales receipts that the

merchant's bank retains as its fee. From the standpoint of the economy as a whole, this is simply

a transfer payment, not a real resource cost. Taking these transfer payments into account and

netting them out, however, Humphrey and Berger (1990) concluded that credit cards are indeed

one of the most resource-intensive retail payment instruments. They calculate the total cost of

credit cards to be 88 cents compared to 4 cents for cash and 79 cents for checks (in 1988 dollars).

Despite relatively high costs, credit-card usage is growing rapidly in the United States.

The market share of credit cards increased from 14.5 percent to 21.4 percent in terms of the total

merchants and card issuers could also share in the costs. See Chakravorti and To (1999), Rochet and Tirole (2000),

and Schmalensee (1998) for models where markets are not assumed to be competitive.

4

dollar volume of consumer payments in the United States between 1990 and 1998, while market

share in terms of consumer transactions increased from 13.9 percent to 17.4 percent (Nilson

shares of credit and charge cards will rise further to 25.6 percent in terms of dollar volume, and

Several good sources of detailed historical and institutional background on the credit-card

market exist (Mandell, 1990; Evans and Schmalensee, 1993 and 1999; Nocera, 1994;

Chakravorti, 2000). In Figure 1, we diagram the set of bilateral interactions that comprise a

credit-card transaction. Prior to making credit-card purchases, consumers establish credit lines

with their banks that they access at the point of sale with their credit cards. If a credit card is

used, the merchant seeks authorization via the credit-card network. If a credit card is accepted

for payment, the merchant submits its receipts to its bank. The merchant’s bank presents the

credit-card receipts to the consumer’s bank. Then, the consumer’s bank sends funds to the

merchant’s bank, which credits the merchant’s account. At some later date, the consumer’s bank

bills the consumer for the credit-card purchases.

In Figure 2, we diagram the underlying fee structure of the transactions described above.

In today’s marketplace, consumers are not usually charged explicitly by merchants at the point of

sale for using their credit cards. However, merchants pay their banks a fee for each credit-card

transaction. The merchant’s bank is charged an interchange fee by the consumer’s bank. If

consumers pay for their credit-card purchases when billed, they receive benefits, most notably an

5

interest-free short-term loan, and often incur no usage costs. If consumers pay in installments

they pay an interest rate of which a part may be used to cover the costs associated with creditcard

processing.

We divide the analytical literature on credit cards into three main groups, corresponding

to the three sets of agents we study: consumers, merchants, the banks and the network

associations. As this classification scheme and our discussion should make clear, much of the

research to date on credit cards has focused on specific parts of the network, rather than

attempting to integrate the pieces into a coherent whole.

Many consumers value uncollateralized credit lines for making purchases when they are

illiquid (i.e., before their incomes arrive) at relatively high interest rates. Because few

alternatives to short-term uncollateralized credit exist, the demand for such credit may be fairly

consumers may not even consider the interest rate when making purchases because they do not

intend to borrow for an extended period when they make purchases; however, they change their

minds when the bill arrives.

Stavins (1996) argues that consumers are somewhat sensitive not only to changes in the

interest rate but also to the value of other credit-card enhancements such as frequent-use awards,

expedited dispute resolution, extended warranties, and automobile rental insurance. However,

she agrees with Ausubel (1991) and Calem and Mester (1995) that lowering interest rates may

attract less creditworthy consumers, therefore dissuading some credit-card issuers from lowering

their interest rates.

affect credit card use.

6

What is surprising is that even liquidity-unconstrained consumers use credit cards.

Industry sources estimate that convenience users comprise between thirty percent to forty percent

of credit-card users. Whitesell (1992) argues that the opportunity cost of holding cash and of

using checks in terms of lost float (especially for large transactions) exceeds that of credit cards.

In addition to float, there may be other advantages to credit cards such as dispute resolution and

limited consumer liability if the card is fraudulently used. Chakravorti (1997) argues that in

today’s marketplace, consumers have strong incentives to use credit cards for all purchases and

pay of their balances each month.

The consumer credit-card use literature suggests that liquidity-constrained consumers are

willing to pay relatively high interest rates partly because they have few alternatives and their

demand for these services is fairly inelastic. Their demand inelasticity may be partly due to their

relatively high discounting of future consumption. Card issuers could capture the difference

between the willingness to pay higher interest rates and the cost of providing such loans, and

Less research has focused on merchants' acceptance of credit cards. This omission is

perhaps surprising in light of the fact that the decision to accept credit cards appears to reduce

converting credit-card receipts into bank funds.

However, merchants may derive some offsetting benefits from accepting credit cards.

Murphy and Ott (1977) suggest that merchants absorb some of the costs of credit-card use in

order to price-discriminate among customers. According to Ernst and Young (1996), 83 percent

of merchants surveyed thought that accepting credit cards would increase sales and 58 percent

thought accepting credit cards would increase profits. Note that according to the survey, an

increase in sales is not necessarily associated with an increase in profits. Another advantage of

accepting credit cards for merchants is that a third-party guarantees payment and the credit card

receipts are converted to good funds relatively quickly.

credit-card convenience use has two potential answers. Extending credit cards to convenience

users could be interpreted as banks buying options on future borrowing by consumers.

Alternatively, banks might be subsidizing convenience users simply to make their overall

portfolio performance look better in terms of lower chargeoffs and larger credit card volumes.

We do not model the bank’s motivation to cross-subsidize convenience users in our one-shot

static model; instead we explore market conditions where such cross-subsidization is possible.

Evidence on the subsidy to convenience users is difficult to quantify. However, the

existence of such a subsidy can be inferred from the following two observations. First, the

proportions of revenues and costs of card issuers, shown in Figure 3, indicate that the

interchange fee and annual fees are relatively small portions of a credit issuer’s revenue at 10.7

percent. Meanwhile, the cost of funds and operations is over two-thirds of the total. Second, the

interchange fee charged by American Express, primarily a charge-card issuer, is higher than

those of Visa, MasterCard, and Discover, which are primarily credit card issuers.

Any model that seeks to accurately depict credit-card pricing policies must study the set

of interrelated transactions as a whole. However, only a few researchers, such as Baxter (1983),

8

Chakravorti and To (1999), Rochet and Tirole (2000), and Schmalensee (1998) have investigated

the broad array of interlinking relationships among the participants in a typical credit-card

payment services need not generate the same level of output as generated by the demand for and

fundamentally interdependent, markets, Baxter suggests a system of side payments might be

necessary.

Our model follows Baxter (1983) by analyzing incentives and constraints facing creditcard

network participants interacting in distinct yet related markets. In contrast to Baxter, we

emphasize downstream credit-card markets (card issuance and card acceptance) instead of

This section of the paper is composed of four parts. First, we present the basic model.

The next subsection discusses a network in which merchants charge different prices to

consumers according to their means of payment, either credit cards or cash. In the third

subsection, we discuss the feasibility of a single-price retail environment. This discussion is

inspired by the stylized fact that we very seldom observe merchants explicitly charging different

prices according to the payment instrument used. Finally, we introduce the possibility of

cardholder benefits paid by card-issuing banks to convenience users of credit cards in a singleprice

retail environment.

network level. Certain networks such as American Express and Discover do not have two distinct institutions

serving consumers and merchants.

9

consumers, merchants, consumers' banks, and merchants' banks. Consumers receive a random

income and wish to purchase goods from merchants. Consumers may use their credit cards to

borrow from their banks in order to consume before their income arrives. If consumers use

credit cards to purchase the good, merchants must clear sales receipts through their own banks

back to consumers' banks.

two groups of consumers as "illiquid but solvent" Type 1s and "insolvent" Type 1s, respectively.

after banks set their credit card policies and merchants have chosen whether to accept credit

cards or not.

Department of Justice (1998, pp. 6-8).

10

thus measures the impatience of consumers; if this subjective discount rate is higher than the

consumers.

Only consumers' banks can lend to consumers. One could justify this assumption by

defining banks as entities that specialize in credit-screening and loan collection, so merchants

could conceivably own banks. This assumption is not critical for our analysis, which focuses on

pricing and subsidization in downstream credit-card markets.

We assume that interbank clearing and settlement of credit-card receipts occurs instantly.

Merchants' banks purchase these receivables from merchants and sell them to the consumers’

banks that issued them. As before, our assumption that consumers' and merchants' banks are

distinct entities is not critical for our story because interbank-clearing arrangements are part of

the upstream credit-card market.

dollar of credit-card receipts sent through the network; in other words, consumers' banks own the

are the real incremental resource costs of operating the network compared to an all-cash

economy (which we assume has zero transaction costs). We assume for ease of exposition that

then sold by merchants' banks to consumers' banks for the face value of the receivables less a

11

liabilities that clear back to them.

only purchase with credit in period 1. Because banks are unable to discriminate between

creditworthy and uncreditworthy consumers, they extend the same level of credit to all

In what follows, we consider two pricing features of credit cards that are universally

level of cardholder benefits in the form of float, cash rebates, airline miles, loyalty points,

record-keeping convenience, status enhancement, use as a form of identification, peer-group

every card-issuing bank "pays" the type-2 consumers on each dollar of purchases made with the

number of general-purpose credit-card networks. While these are clearly important issues, our focus is on pricing

and subsidization within a single competitive network.

only available to consumers who pay their bills in full each month.

card-issuers. The qualitative results would not change if benefits were not fungible with cash as long as consumers'

utility is increasing in the level of benefits.

12

unit of the good. That is, the consumption good serves as the numeraire in our model. A

merchant, like a consumer, is impatient. Unlike a consumer, a merchant values only money

what follows, we assume that merchants operate in a competitive market so their sales revenue

cannot exceed their cost of doing business.

determined by competition in the credit-card market. Consumers' banks bear consumer default

costs, so they must earn enough on solvent borrowers to cover loan losses and network costs.

In what follows, we study credit arrangements that come as close as possible to the firstbest

level of consumption given liquidity, incentive, and information constraints, as well as the

riskiness of extending consumer credit and the cost of clearing the resultant claims back to the

issuer. We consider three different schemes for pricing goods and credit-card use. In the first

bank revenues and the fact that providing payment services to convenience users is costly.

13

benefits. In the second, merchants charge a uniform price to all consumers, regardless of how

scheme we consider, merchants charge a single price to all consumers but banks pay benefits to

convenience users to compensate them for the higher retail prices necessary to cover the cost of

the credit-card network. Table 2 summarizes these schemes.

First, we consider the case in which the two types of consumers are served at potentially

Intuitively, this should be allocatively efficient because a merchant's effective costs of selling to

the two types of consumers can be met exactly.

markets for merchants (M), merchants' banks (MB), and consumers' banks (CB), so none of

these firms expect to make a positive profit in equilibrium:

s.t.

Income-output identity

[ ] [( ) ]

1

2

1

+ − − ≥

= − − + −

α

π α β β

V.P. of consumer bank

14

The strategy for solving program P1 is based on our assumption of competitive markets:

so the costs incurred to operate the interbank payment network must be borne by consumers.

credit-card infrastructure that does not benefit them.

We now determine retail prices. When consumers use cash, merchants' cost of serving

they pay a higher retail goods price for the privilege (finance charges are discussed below).

15

rewrite problem P1 as problem P1.1:

s.t.

the default risk of his type; he pays a retail goods price that reflects the extra cost of providing

consumers (one unit) both because his expected income is lower and because his purchasing

power is reduced in the face of a higher retail goods price. All consumption of goods in this

consumers and the variable cost of the payment system, respectively), the lower is

16

the greater is the increase in social welfare when liquidity constraints can be relaxed. Finally, the

retail settings, which could be due to consumer resistance to differentiated pricing; to menu or

calculation costs for the merchant; to a desire by the merchant to effectively price-discriminate

by choosing not to pass through the costs of serving some customers; or perhaps to contractual

arrangements between merchants and their banks preventing surcharges on credit card purchases.

merchants and/or banks.

The simple message of this section is that a merchant cannot serve both consumer types

The argument is straightforward. In order to break even on type-1 consumers who buy on credit,

who accepts credit cards. This drives away consumers who do not need to borrow, since they

resource cost of the credit-card network is positive but does not eat up all of the economy's resources.

17

can purchase the good at a price of one from a merchant who does not accept credit cards. Thus,

only type-1 consumers use credit cards.

Finally, we consider bank-provided cardholder benefits, which can be thought of as side

payments contingent on credit-card use. Intuitively, side payments from banks may allow

merchants to cover the costs of credit cards while ensuring that type-2 consumers use cards.

However, increasing the use of credit cards means there is an unambiguous increase in the real

resource costs of the payments system. This raises the questions of who pays to "bribe" type-2

consumers to use the credit card, and why? Several (not mutually exclusive) explanations are

plausible:

borrowing resulting in reduced consumption. The decision to cross-subsidize is dependent

on the consumers’ bank’s ability to charge a higher than risk-adjusted interest rate to Type

1s. This is the explanation we adopt in this paper.

believe that absorbing type-2 consumers' credit-card costs is a worthwhile marketing

expense. For example, merchants may be able to sell goods with higher profit margins to

type-2 credit-card users. However, if markets are competitive, this is not a feasible long-run

strategy.

18

model is unable to capture this phenomenon.

In this section, we assume interest revenue from type-1 consumers subsidizes all costs associated

with type-2 credit card purchases; neither merchants nor banks earn positive profits that could be

given to type-2 consumers. Alternative assumptions about the source of subsidy (or empirical

investigation) are clearly interesting topics for future research.

We assume that merchants and/or banks prefer a single goods price for some reason(s) so

all consumers will shop in the same stores. Benefits are paid in goods in period one only to type-

2 consumers who use a credit card. These benefits are a proxy for a wide range of actual

cardholder benefits.

To conserve space, we relegate detailed analysis of the model to the Appendix. One key

point arising from the analysis is that, in order to provide a cross-subsidy to type-2 consumers to

profits, there is no other surplus to transfer. The "tax revenue" could be raised through higher

interest rates on borrowing.

required to bring Type 2s into the credit card network. That is, their consumption is the same

whether they participate in the credit-card network or not. In the previous case, we found that

single-price merchants could serve either Type 1s or Type 2s but not both. In the appendix, we

*

1

1

19

To calculate the interest rate charged on consumer loans, as before, we set the consumers’

banks’ voluntary participation constraint to zero. The equilibrium interest rate is:

( )

1

(1

1

1

−

+ −

−

=

α β

α

β

β

,

which exceeds the interest rate charged under the two other schemes. The first term on the righthand

side of this expression is the familiar risk-adjusted required return for the bank. The second

term reflects the additional cost to Type 1s of participating in a credit-card network in which

Type 2s are rewarded for credit-card use. Banks must recover from type-1 consumers the

reflects both type-1 default risk and the per-capita subsidy provided to Type 2s.

α

α

α

1 *

= − − −

c .

scheme, goods are not being purchased by Type 2s with the least expensive payment instrument

available to them, cash, but instead with credit cards resulting in reduced consumption for Type

1s. Type 2s face higher prices but remain at the same level of consumption as before. The

Thus, only certain parameter values will result in such a pricing scheme being feasible.

This pricing scheme demonstrates that convenience users may be indifferent between

using credit cards or cash in competitive goods and credit markets. In other words, we present

the minimum level of benefits required to entice Type 2s to participate. We further demonstrate

20

that if Type 1s sufficiently discount future consumption, they are willing to participate in such a

pricing scheme.

Consumer credit allows liquidity-constrained households to consume before their income

arrives, but a credit-card infrastructure is costly to operate. How do the various pricing and

cross-subsidy schemes compare in terms of a simple measure of social welfare that incorporates

both the utility gains from borrowing and the resource use of a credit-card network? This section

evaluates each of the schemes discussed above by comparing them to an economy with no credit

cards as a benchmark.

of social welfare is the weighted sum of consumption by all agents, where period-two

We showed above that uniform pricing and price discrimination according to the payment

instrument used are equivalent schemes when there are no cardholder benefits. Notice from

Table 3 that, with credit cards, Type-1 consumption is lower in amount but is not discounted

21

resource costs, are in the range of two percent of sales, then the condition becomes 0.25 -

Finally, if merchants set a uniform goods price and cardholder benefits are paid to Type

2s, then the amount of Type 1s’ consumption decreases relative to the benchmark case and

relative to the uniform pricing/price discrimination case, as well. This is because the Type 1s

pay for Type 2s to participate at unchanged consumption levels. Our measure of social welfare

network eats up more resources. However, such a scheme could be welfare-enhancing to an

economy without credit cards if Type 1s sufficiently discount future consumption. As noted in

the discussion above, however, such a credit-card pricing and cross-subsidization scheme may

operate if competition from other networks can be resisted (or they are co-opted).

Credit cards are a rapidly growing part of the retail payments and consumer-finance

system in the United States. Yet credit-card pricing and apparent cross-subsidization among

users defy easy explanation. We develop a model of interrelated downstream markets in a

pays for credit cards.

We show that, if no cardholder benefits are paid, uniform pricing by merchants and price

discrimination are equivalent: consumer types separate themselves. Liquidity-constrained

consumers are the only ones who use (and pay for) credit cards. If liquid consumers are

compensated for decreased consumption resulting from higher goods prices and card-issuers are

economy is 25 percent per annum (Brayton, et. al., 1997, p. 236). See the Food Marketing Institute (1998) for estimates of the costs of accepting credit cards.

22

able to charge sufficiently high interest rates to a sufficiently large pool of creditworthy

borrowers, it may be possible to charge a single price and serve all consumers with a credit card.

Card-issuers pay a direct benefit to liquidity-unconstrained consumers, which they collect from

liquidity-constrained consumers via higher interest rates.

Thus, our model shows how credit-card borrowers could be induced to pay for the entire credit-card network. Our results are critically dependent on our assumption of competitive markets. If merchants and card issuers earned rents, other explanations of who pays for credit cards would exist. Future research should seek to identify and quantify why card-accepting merchants and card-issuing banks perceive some cross-marketing benefits arising from convenience users of credit cards.

23

Economic Review 81(1), 50-81.

Barron, John M., Michael E. Staten, and John Umbeck (1992), “Discounts for Cash in Retail

Baxter, William F. (1983), “Bank Interchange of Transactional Paper: Legal and Economic

Brayton, Flint, Eileen Mauskopf, David Reifschneider, Peter Tinsley, and John Williams (1997),

227-45.

Brito, Dagobert L., and Peter R. Hartley (1995), “Consumer Rationality and Credit Cards,”

Journal of Political Economy 103(2), 400-33.

Calem, Paul S., and Loretta J. Mester (1995), “Consumer Behavior and the Stickiness of Credit-

Industry Issues, First Quarter.

_______ (2000), “Why Has Stored Value not Caught On?,” Federal Reserve Bank of Chicago,

Emerging Issues Series S&R-2000-6.

_______ and Ted To (1999), “A Theory of Merchant Credit Card Acceptance,” Federal Reserve

Industry (Cambridge, MA: National Economic Research Associates, Inc.).

(Cambridge, MA: The MIT Press).

(Washington, D.C.: Food Marketing Institute).

May, 279-93.

Humphrey, David B., and Allen N. Berger (1990), “Market Failure and Resource Use: Economic

24

Risk and the Role of the Federal Reserve, ed. David B. Humphrey (Boston: Kluwer

Academic Publishers), 45-86.

Kitch, Edmund W. (1990), “The Framing Hupothesis: Is It Supported by Credit Card Issuer

Spring, 217-33.

December, 1-4.

Murphy, Michael M., and Mack Ott (1977), “Retail Credit, Credit Cards and Price

Nilson Report (1997), Issue 653, October.

Nilson Report (1999) Issue 706, December.

(New York: Simon & Schuster).

Rochet, Jean-Charles, and Jean Tirole (2000), “Cooperation among Competitors: The Economics

Toulouse.

Stavins, Joanna (1996), “Can Demand Elasticities Explain Sticky Credit Card Rates,” Federal

United States Department of Justice, Antitrust Division (1998), "United States of America,

Plaintiff, v. Visa U.S.A. Inc., Visa International Corp., and MasterCard International

http://www.usdoj.gov/atr/cases/f1900/1973.htm).

Wells, Kirsten E. (1996), “Are Checks Overused?” Federal Reserve Bank of Minneapolis,

Quarterly Review, Fall, 2-12.

Money, Credit and Banking 24(4), November, 246-50.

25

Merchants solve program P2 (below), in which a merchant charges a single goods price,

cost of accepting credit cards. Note that type-1 consumers use credit cards for all purchases,

while type-2 consumers will use a combination of cash and credit cards. Because card-issuers

cannot distinguish the different types of consumers, they grant each consumer the same level of

credit. Each Type 1 receives less than a $1 credit line because of default risk and the subsidy to

lowers the equilibrium price because of the zero profit constraint on merchants. The equilibrium

consumers.

{p}

s.t.

26

Most of program P2 is familiar from the previous discussion. The additional elements here are

cardholder benefits and an additional voluntary participation constraint of Type 2s using credit

cards for part or all of their purchases. Type 2s will purchase goods with cash and credit, and

Type 2s will only participate in the credit card scheme if their total consumption with

credit cards is no less than their total consumption without cards. In other words, their voluntary

participation constraint(s) must be satisfied. Substituting a Type 2's budget constraint into his

second voluntary participation constraint yields:

1

consumption resulting from higher goods prices.

( )

1

1 (

1

1

−

+ −

−

=

α β

α

β

β

.

The first term is the risk associated with lending as before. The second term captures the

additional cost of enticing Type 2s to use their credit cards.

27

yields:

α

α

α

1

= − − −

c .

Type 1s consume less under such an arrangement because they pay for the additional cost of

processing credit card transactions for type-2 consumers, even though they benefit from lower

prices. Comparative statics are relatively straightforward, with type-1 consumption decreasing

merchants operate in a competitive market, their profits are zero which means total revenue

equals total cost. Total revenue and total cost can be expressed as:

and

1 1

1

(1 )

(1 )

+ − −

= + −

α α

α α

.

which leads to the following quadratic expression:

) (1 ) 0

(1 )

(1

α

αβ αβ

α

α

.

2 (1 )

1

*

α

α αβ

−

= − − − + Δ

p ,

where:

2

1

2 2 2 2 2 2 2 3 2 3 4 2 2 3

1

Note that only certain parameter values will support a credit card equilibrium for this specific

pricing scheme. The following relationship must hold:

1

equilibrium values for these variables.

29

Consumer Merchant

Consumer’s Bank Merchant’s Bank

Purchases Good or Service

Credits

Account

Sends

Receipt

Establishes Sends Bill

Credit Line

Sends Funds

Presents Receipts

Authorize

Adapted from Evans and Schmalensee, 1993.

Network

30

Consumer Merchant

Consumer’s Bank Merchant’s Bank

Fixed price

Credit card

receipts

discounted

Pays

benefits if

nonrevolving

Pays interest

if revolving

Interchange Fee

Regardless of

instrument used

31

Chargeoffs

32.8%

Operations

32.8%

Cost of

Funds

33.9%

Fraud 0.5%

Source: Credit Card News, April 15, 1999.

Cash Advance Fees 5.4%

Interest

75%

Interchange 10.7%

Penalty Fees 6.3%

Annual Fees 1.9%

Enhancements 0.7%

32

Cost per

transaction*

$0.08 $0.45 $1.07 $0.29 $0.80

Cost per $100 of

purchases

$0.22 $0.82 $2.41 $0.70 $2.43

*The average purchase amount varies by payment instrument.

Source: Food Marketing Institute, 1998, p. 3.

33

Uniform pricing with no

subsidies

Single price for all

purchasers, p

None

Price discrimination with no

subsidies

Different for cash and credit

None

Uniform pricing with

subsidies

Single price for all

purchasers, p

Paid by banks to type-2

consumers

34

Benchmark case:

No credit cards

(in period two)

(in period one)

+

1

1

Uniform pricing or

price discrimination

with no cardholder

subsidy

(in period one)

(in period one)

Uniform pricing

with cardholder

subsidy

(1 )

1

(in period one)

1

= −αβ

consumption, reflecting impatience.