A Tractable Model of Monetary Exchange with Ex-Post Heterogeneity

Abstract

We construct a continuous-time, pure currency economy with the following three key features. First, our modelled economy incorporates idiosyncratic uncertainty—households receive infrequent and random opportunities of lumpy consumption—and displays an endogenous, non-degenerate distribution of money holdings. Second, the model is tractable: properties of equilibria can be obtained analytically, and equilibria can be solved in closed form in a variety of cases. Third, it admits as a special, limiting case the quasi-linear economy of Lagos and Wright (2005) and Rocheteau and Wright (2005). We use our modeled economy to obtain new insights into the effects of anticipated inflation on individual spending behavior, the social benefits and output effects of inflationary transfer schemes, and transitional dynamics following unanticipated monetary shocks.