On the shape and size of market areas

Abstract

How should the suppliers of a commodity be located so as to generate the greatest amount of welfare per unit area? Welfare is defined as consumers' surplus plus producers' profits. Costs of production are assumed to be linear functions of output identical for all firms and at all locations. Consumers are distributed in an unbounded two dimensional space at uniform density. They have identical linear demand functions. We determine both the optimal shape and the optimal radius of a representative firm's market area and compare them to those under free entry; the Loschian case of monopolistic competition. The general shape is that of rounded hexagons (or hexagonally flattened circles) with hexagons and circles as limiting cases. When fixed costs are high and firms are few, free entry creates fewer firms than is optimal, contrary to the well-known results for a free entry equilibrium in non-spatial monopolistic competition.