This paper studies a centralized market with idiosyncratic uncertainty and money as a medium of exchange from a theoretical as well as an experimental perspective. In our model, prices are fixed and markets are cleared by rationing. We prove the existence of stationary monetary equilibria and of an optimum quantity of money. The rational solution of our model, which is based on the assumption of individual rationality and rational expectations, is compared with actual behavior in a laboratory experiment. The theoretical results are strongly supported by this experiment.