They consider the design of an optimal card-based payment system when cash is available as an alternative means of payment, and derive conditions under which cards will be preferred to cash. The authors find that a feature akin to the controversial no-surcharge rule may be necessary to ensure the viability of the card payment system. This rule, which is part of the contract between a 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.

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