Pricing and matching with frictions

Suppose that n buyers each want one unit and m sellers each have one or mor e units of a good. Sellers post prices, and then buyers choose sellers. In symmetric equilibrium, similar sellers all post one price, and buyers rando mize. Hence, more or fewer buyers may arrive than a seller can accommodate. We call this frictions. We solve for prices and the endogenous matching fu nction for finite n and m and consider the limit as n and m grow. The match ing function displays decreasing returns but converges to constant returns. We argue that the standard matching function in the literature is misspeci fied and discuss implications for the Beveridge curve.