Cash Burns: An Inventory Model with a Cash-Credit Choice

We present a dynamic cash-management model where agents choose whether to pay with cash or credit at every point in time. In the model credit usage depends on the current stock of cash, a novel result that matches recent micro evidence on household’s payment choices. The optimality of such decision rule is novel and cannot be obtained by models where cash-credit decisions are made at the “beginning” of each period. We discuss how to use the model to account for cross country-evidence on the intensity of credit usage and for several statistics on the size and frequency of cash withdrawals. We use the model to assess the household’s welfare cost of phasing out cash.