Marginal Versus Average Cost Pricing in the Presence of a Public Monopoly - Brown, Donald J.; Heal, Geoffrey (American Economic Review, 1982)
The Arrow-Debreu analysis of decentralized resource allocation in a Walrasian economy assumes constant or decreasing returns to scale in production. Recently, several authors have extended this analysis to economies with a public monopoly, that is, a firm with increasing returns to scale. In this literature, the salient feature is the characterization of increasing returns to scale technologies as nonconvex production sets, so that under this definition both single and multiproduct firms may exhibit increasing returns. Here, our intended model is an economy with a competitive sector consisting of households and firms with convex technologies, and a public sector consisting of firms with nonconvex technologies. A special case is a single multiproduct firm which produces products for regulated markets (with a nonconvex technology) and produces products for unregulated markets (with a convex technology), for example, ATT firms with constant or decreasing returns are maximizing profits; the public monopoly is pricing at marginal cost, where potential losses are covered by the lump sum taxes; and all markets clear. An average cost-pricing equilibrium is a family of consumption plans, production plans and prices such that households are maximizing utility subject to their budget constraint; firms with constant or decreasing returns are maximizing profits; the public monopoly is pricing at average cost, that is, breaking even or making zero profits; and all markets clear. Unfortunately, all of the extant proofs of existence of a MCP or an ACP equilibrium are somewhat technical in nature and lack the transparency of counting equations and unknowns which many economists accept as an intuitive, if not formally correct, proof of existence. In view of this, one of the purposes of this paper is to demonstrate the existence of a MCP and an A CP equilibrium in a simple economy with increasing returns, where the equilibrium notions are characterized by systems of behavioral equations and market-clearing conditions. We give both an intuitive proof of existence by counting equations and unknowns, and a formal argument that these systems of equations have a solution by use of a simple fixed-point argument. In addition, we review several of the standard partial equilibrium prescriptions for the regulation of a public monopoly and show that in a general equilibrium model they can be interpreted as MCP or A CP equilibria.