Who pays for credit cards?

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 payments 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 card network--unless banks have other motives, such as purchasing options on future borrowing by convenience users.