Poisson Price Dispersion

We study a competitive market for a homogeneous good, in which the only uncertainty concerns the number of identical sellers, who are sampled by a finite Poisson process from a continuum of potential participants. It is shown that, in equilibrium, there is price dispersion. Specifically, prices conform to a Poisson process on an interval, which is a proper subset of that between the sellers' cost and the buyers' reservation price. Although prices arbitrarily close to the latter may occur in equilibrium, they are less frequent than prices at the lower end of the pricing interval.