A model of debit card as a means of payment

This paper provides an explanation for both the rapid growth in the use of a debit card over time and the cross-sectional difference in the use of a debit card using a search-theoretic model. The trade-off between cash and a debit card as means of payment is incorporated such that a buyer incurs disutility cost proportional to the amount of cash holdings, while a seller accepting a debit card bears a fixed record-keeping cost regardless of transaction amount. As record-keeping cost decreases with the development of information technology over time, disutility cost of cash holdings required for pairwise trade eventually exceeds record-keeping cost so that all the agents with different wealth levels choose to use a debit card as a means of payment. Also, disutility cost of cash holdings required for pairwise trade would be higher for the rich than for the poor, implying the cross-sectional feature of payment pattern that the rich use a debit card more frequently than the poor. There are two distinct mechanisms that improve welfare as record-keeping cost decreases: one is to reduce deadweight loss from holding cash and the other is to reduce its distortionary effect on output produced in pairwise trade.