Price Rigidity and Means of Payment

The trade-off between cash and a debit card as a means of payment is incorporated into a search-theoretic model. A buyer incurs the proportional cost of carrying cash into the decentralized goods market, and a seller accepting a debit card bears a fixed record-keeping cost. In an equilibrium, the price of a cash good turns out to be relatively sticky compared with that of a debit-card good. With money supply increasing at a constant rate, the carrying cost of cash proportional to its amount causes the cash balance net of cost to increase at a rate less than the money growth rate. Consumption smoothing also leads to a relatively small decrease in quantity traded in comparison with the increase in cash balance, implying rigid price. Further, the means-of-payment mechanism underlying price rigidity yields an additional distortionary effect of inflation on relative price between cash trade and debit-card trade, which implies higher welfare cost of inflation than that in the standard search-based model.