Association between Population Density and The Market Areas of Towns

This paper examines the relationship between population density and town spacing in four kinds of environment. These are: (1) linear curves of demand, transport and production costs and an even population distribution; (2) nonlinear transport cost curves over space; (3) variable population density within hinterlands; and (4) variation of transport costs with population density. Previously, it has been shown that the criterion of free entry does not uniquely determine town spacing. The implications of four stronger criteria are therefore examined in this paper. These location criteria are: (a) the number of towns is maximized; (b) the number of towns in minimized, subject to all consumers' being served; (c) the towns are all owned by one profit-maximizing monopolist; and (d) the average of some consumer utility function is maximized. In cases (a), (c), and (d) spacing decreases with density; in (b) spacing is an increasing function of density. Actual data are presented on the spacing of towns in Iowa and shopping centers in Chicago which indicate that spacing and population density are not associated. These results are consistent with the notion that entry is free but are not consistent with the stronger constraints employed in this paper.