A theory of credit cards☆

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Abstract

A two-period model is constructed to study the interactions among consumers, merchants, and a card issuer. The model yields the following results. First, if the issuer's cost of funds is not too high and the merchant's profit margin is sufficiently high, in every equilibrium of our model the issuer extends credit to qualified consumers, merchants accept credit cards and consumers face a positive probability of default. Second, the issuer's ability to charge higher merchant discount fees depends on the number of customers gained when credit cards are accepted. Thus, credit cards exhibit characteristics of network goods. Third, each merchant faces a prisoner's dilemma where each independently chooses to accept credit cards, however all merchants' two-period profits are reduced because of intertemporal business stealing across industries.

Section snippets

The Model

In our model, the five main credit card participants – the consumer, the consumer's financial institution or the issuer, the merchant, the merchant's financial institution or the acquirer, and the credit card network – have been condensed to three participants. The issuer, the acquirer, and the network operator are assumed to be a single agent and referred to as the issuer.
Assume that there is a continuum, say [0, 1], of indivisible goods exogenously priced at p. Each good is sold by a

Consumers

Starting with the second period, a consumer will always purchase the good she desires if she can afford it. If she had consumed with credit in the first period then she can afford to consume in the second period if Rω1 + ω2 ≥ 2p. That is, she earns a return R on her first period endowment, ω1. Her total cash balances in the second period must be used to pay off her debt from the first period, namely p. If Rω1 + ω2 < p then she defaults and the sum Rω1 + ω2 is seized by the issuer. Before the realization

Policy implications

Our model provides a benchmark for policymakers to consider when setting policies regarding credit card networks. We consider a credit card market where consumers are given rebates in the form of an interest-free short-term loan and merchants do not impose surcharges on credit card purchases. We also consider a monopolistic issuer and merchants that are monopolists but no single merchant has any bargaining power with the issuer. Under these conditions, we find under what conditions a credit

Conclusion

We constructed a model where we consider the various bilateral relationships in a credit card network. With the exception of Chakravorti and Emmons (2003), the literature on credit card networks ignores the cost and benefits of the extension of credit to network participants. We explain why merchants accept credit cards using the most restrictive possible environment — a single issuer, massless merchants, and no cost sharing by consumers either directly in the form of fees or finance charges or

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    ☆
    We benefited from comments on earlier drafts received from Gary Biglaiser, Catherine de Fontenay, Joshua Gans (the editor), Bob Hunt, Jamie McAndrews, Marius Schwartz, two anonymous referees and presentations at the Helsinki Conference on Antitrust Issues in Network Industries, Innovation in Financial Services and Payments Conference held at the Federal Reserve Bank of Philadelphia, the Economics of Payment Networks held at University of Toulouse, the Chinese University of Hong Kong, European University Institute, and Melbourne Business School. The views expressed are those of the authors and should not be attributed to the Bureau of Labor Statistics, the Federal Reserve Bank of Chicago or the Federal Reserve System.
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