Constrained or unconstrained price for debit card payment?

•The effect of a uniform pricing constraint for cash and debit card is explored.•Cash holding is costly but saves transaction cost compared to debit card payment.•A uniform pricing constraint makes cash-holding costs decline.•But it magnifies consumption dispersion between the poor and the rich.•The beneficial effect of the constraint turns out to dominate its negative effect. 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.