Scale economies and existence of sustainable monopoly prices

The size of the firm relative to market demand is crucial to a determination of whether there exist sustainable monopoly prices. In the one product case the size of the firm is its minimum efficient scale. In the multiproduct case size is defined by a set of outputs at which cost complementarities are present. The analysis shows that when the size of the firm is sufficiently large, there exist anonymously equitable Aumann-Shapley prices. Further, at these prices natural monopoly is sustainable against rival entry. The Aumann-Shapley price are also shown to be quantity sustainable in the sense of Brock and Scheinkman.