A model of money with multilateral matching

We develop a model of decentralized monetary exchange to examine the distributional effects of inflation across heterogeneous agents. The agents have private information about their productivity, preferences, or money holdings. Matching is multilateral and each seller is visited by a stochastic number of buyers. The good is allocated according to a second-price auction in money. In equilibrium, homogeneous buyers hold different amounts of money leading to price dispersion. We find the closed-form solution for the distribution of money holdings. Entry of sellers is suboptimal except at the Friedman rule. Inflation acts as a regressive tax.