More on scale economies and cities

Abstract

In this paper we develop a model of a closed economy with many types of traded (between cities) products of which the production functions are subject to scale economies internal to the industry as a whole. Workers are assumed to live in Muth type residential rings and commute to the center of the city where the industry is located. This setup leads to the creation of many types of cities. To each type of city, residential cost functions and output cost functions are constructed. From these cost functions all types of demand functions are derived. It is shown here that the introduction of cities into the economy leads to an equivalence between the demand for inputs and the demand for consumption goods, an equivalence which does not exist in models of economies without cities. Thus there are conditional-compensated, unconditional-compensated and Marshalian demand curves for both inputs and consumption goods. The efficiency conditions for this economy are in the short run marginal cost pricing, and for an interior solution in the long run, average cost pricing is also required. This last condition is equivalent to the Henry George rule. Marginal cost pricing remains an efficiency requirement in the case of natural monopoly cities. Next we investigate two cases of scale economies internal to the individual firms and to the industry as a whole. The first case is a model of regular products in perfectly competitive markets and the other model deals with differentiated products and monopolistic competition. These cases have been previously investigated in the literature. Here we generalize and expand previous results and gain additional insights.