Pricing and Matching with Frictions

TLDR

In a market where n buyers each demand one unit and m sellers each supply one or more units, sellers post prices and buyers choose sellers, leading to symmetric equilibrium but potentially more or fewer buyers than a seller can accommodate, creating frictions. The study aims to solve for prices and the endogenous matching function for finite n and m and analyze their asymptotic behavior. The authors solve for prices and the endogenous matching function for finite n and m and examine the limit as n and m grow. The matching function shows decreasing returns that converge to constant returns, and the authors argue that the standard matching function in the literature is misspecified, with implications for the Beveridge curve.

Abstract

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