THE OPTIMAL SIZE DISTRIBUTION OF CITIES

Properties of the optimal size distribution of cities are derived by using the hierarchy model explicitly considering the productivity of cities. Properties are (i) in allocating workers to the same industry in cities with different hierarchies, it is optimal to allocate so that marginal effects upon the GNP are the same; (ii) in allocating workers to different industries in the same city, it is optimal to allocate so that the direct marginal effects upon that city's GRP are the same; (iii) at optimum, all hierarchies have the same weight in a national economy. Based upon these properties, an optimality index for the size distribution of cities is constructed. Values of this optimality index are estimated for U.S. and Korea. The construction and estimation of an optimality index make it possible to investigate the degree and major sources of departures from the optimum. © 1991.