Price Rigidity and Means of Payment

Abstract

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 recordkeeping

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.