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 face a strictly increasing rather than a constant marginal cost of production. The 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. The equilibrium is efficient if and only if the price distribution is degenerate and, hence, if and only if search frictions are small enough. In contrast, in Burdett and Judd (1983), the equilibrium price distribution is always non-degenerate and atomless and the equilibrium is always efficient. As in Burdett and Judd (1983), the equilibrium goes from monopolistic to competitive as search frictions decline.