Optimal sizes and shapes of market areas of firms

Abstract

The purpose of this dissertation is to set forth a theoretical as well as empirical model on market sizes and shapes, and to investigate the sizes and shapes of market areas of firms in the United States. To fulfill the objective, the theory of the firm in economic space must be reexamined. This theory focuses attention on the fact that manufacturing plants sell to buyers who are scattered over an area rather than to consumers who are concentrated within a market center. The classical (nonspatial) theory is "in terms of realism" inadequate. Moreover, it is claimed to be inadequate in explaining economic relationships over space. This dissertation contends that the aggregate demand for the product of the spatial seller is much smaller than that of the spaceless firm when the cost of distance is included in the conception of product demand for the (spatial) firm. In fact, the equilibrium output and, therefore, the size of market depend on the distribution of buyers, the production cost function, and the pricing system presumed by the firm. This dissertation will establish the proposition that the circular market area is the most efficient and profitable shape for a monopolist, and the hexagonal shape the most profitable for competitive firms in the long -run. To find exact functional relationship between important market variables, two stage least squares will be used to obtain consistent estimates for the parameters. The size of market areas will then be tested. It will be found that the market area sizes of firms in general in the United States are quite small, smaller than the sizes crucial to the thesis advanced by Mills and Lav. These empirical results will then be evaluated on the basis of fixed cost analysis, threshold sensitive hypothesis, discriminatory pricing, and different individual demand curve types. This dissertation will contend that: (1) small size market areas prevail in the real world; (2) the level of fixed cost is relatively low and hence leads to small market areas; (3) threshold sensitivity gives rise to greater cost and requires larger market size; (4) market area size is so small as to eventuate in f.o.b. mill pricing, since this spatial price system is more profitable than discriminatory pricing, given small size market areas; and (5) convex individual demands lead to greater market size, and hence would promote spatial price discrimination. Ipso facto, demand curves in reality are probably not characterized by convexity.