Credit and the no-surcharge rule

A controversial aspect of payment cards has been the 'no-surcharge rule.' This rule, which is part of the contract between the card provider and a merchant, states that the merchant cannot charge a customer who pays by card more than a customer who pays by cash. In this paper we consider the design of an optimal card-based payment system when cash is available as an alternative means of payment. We find that a version of the no-surcharge rule emerges as a natural and advantageous feature of such a system.