Constrained or unconstrained price for debit card payment?

Retailers in the Netherlands and the U.K. can charge different prices for a commodity depending on whether cash or a debit card is used as payment, whereas retailers in the U.S. generally cannot. These two types of economies with and without a uniform pricing constraint for cash and debit card payments are compared in a microfounded monetary model. We place particular emphasis on the distinctive features of cash and debit cards as payment methods: the cost of a cash transaction for the seller is typically lower than that of a debit card, whereas the cost of cash holdings for the buyer is higher than that of a debit card. Our results suggest that a uniform pricing constraint makes cash-holding costs decline but consumption dispersion between the poor and the rich increase. Numerical examples show that the beneficial effect of the constraint dominates its negative effect.