Cost of Inflation in Inventory Theoretical Models

We show that the area under the long-run demand curve for money measures the welfare cost of inflation for a very large class of inventory theoretical models of money demand. The class of inventory models considered has a general stochastic structure of the net cash expenditures as well as of the fixed/variable cost of withdrawing and depositing money. Thus, our framework includes a large number of models that have been studied in the literature as special cases. The most important feature that is responsible for our result is the fact that private agents fully internalize all the costs and benefits associated with managing their inventory of money. As a result, the social costs and benefits of holding money, which are related to the welfare cost of inflation, are equal to the private costs and benefits of holding money, which are in turn captured by the area under the money demand curve.