Reglonal Science and Urban Economics 20 (1990) 473-508 North-Holland zyxwvutsrqponmlkjihgfedcbaZY ON THE FOUNDATIONS OF LAND USE THEORY Discrete Versus Continuous Populations* Y ASAMI zyxwvutsrqponmlkjihgfedcbaZYXWVUTS Unmersrty of Tokyo, Tokyo, Japan M FUJITA and T E SMITH Unwerslty of Pennsylvama, Phdadelphra, PA 19104, USA Received May 1988, final version received January 1990 Urban economists and location theorists have long employed land use models with a contmuum of agents dlstnbuted over a contmuum of locations However, these contmuous models have been cntlclzed on behavioral grounds in that mdlvldual households can consume only zero amounts of land m equlhbrmm Hence the central purpose of this paper IS to propose an alternatlve mterpretatlon of these contmuous models as hmltmg approxlmatlons of discrete population models In particular, it IS shown that for large population sizes, the population dlstnbutlons of the classical contmuous model umformly approximate the equlhbnum popula- tion dlstnbutlons generated by an appropriately defined class of discrete population models 1. Introduction Since the classic work of Alonso (1964), Mills (1967), Beckmann (1969) and Muth (1969), urban economrsts and locatton theorists have employed land use models with a contmuum of agents distributed over a continuum of locattons These classical continuous models of land use have been shown to be analytically tractable and empn-really rich, thus, they have been widely used m the literature But from the very outset, people have also questioned the logical foundations of such models As Alonso ortgmally observed ‘ we are still plagued by the problem that we are dealing with the user of land as rf he located at a pomt, while the necessity of equating supply and demand quantities requn-es that we extend this point so that tt will have an area’ [Alonso (1964, p 99)] More recently, the precise mathematical nature of this dtfficulty has been clarrfied by Berhant (1985), Berhant, Papageorgrou and Wang (1987) and *This research has been supported by NSF grants SES85-02886 and SES87-09312 which are gratefully acknowledged The authors are indebted to Marcus Berhant, ThlJs ten Raa, Jacques- Franpols Thlsse and an anonymous referee for a number of helpful comments on an earlier draft of this paper 0166-0462/90/$03 50 0 199GElsevler Science Publishers B V (North-Holland)