Search theory of imperfect competition with decreasing returns to scale

I study a version of the search-theoretic model of imperfect competition by Burdett and Judd (1983) in which sellers operate a production technology with decreasing rather than constant returns to scale. Equilibrium exists and is unique, and its structure depends on the extent of search frictions. If search frictions are large enough, the price distribution is non-degenerate and atomless. If search frictions are neither too large nor too small, the price distribution is non-degenerate with an atom at the lowest price. If search frictions are small enough, the price distribution is degenerate. Equilibrium is efficient if and only if the price distribution is degenerate. Generically, neither the structure nor the welfare properties of equilibrium are the same as in Burdett and Judd (1983). As in Burdett and Judd (1983), however, equilibrium outcomes span the spectrum from pure monopoly to perfect competition as search frictions decline.