When worlds collide: Different comparative static predictions of continuous and discrete agent models with land

Abstract

Abstract:This paper presents a difference in the comparative statics of general equilibrium models with land when there are finitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb-Douglas utility, it is shown that with finitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by the consumer located at each fixed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each fixed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable. Abstract This paper presents a di¤erence in the comparative statics of general equilibrium models with land when there are …nitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb-Douglas utility, it is shown that with …nitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by the consumer located at each …xed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each …xed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative di¤erence between the two types of models, and this di¤erence is potentially testable.JEL Numbers: R13, D51, R14

Exploring the polycentric city with multi-worker households: An agent-based microeconomic model

“…The main difference with the analytical AMM model then lies in the discreteness of the simulated model, as opposed to the continuous analytical model. This provides an illustration of a discrete model converging to the continuous AMM model for large population sizes, which can be related to a discussion in the literature (Asami et al (1991); Berliant and Sabarwal (2008)). Let us now describe more precisely the hypotheses ensuring that the agent-based model reaches an equilibrium that is similar to the analytical one.…”

Tribute to Marcus Berliant: A pivotal matchmaker of general equilibrium and spatial economics

“…Marcus criticized the foundation of such density models, all developed by reformulating von Thünen's agricultural land use theory. Berliant (1985a) pointed out in clear manner the inherent basic difficulty with these models, and this was followed by a series of critical papers: , Berliant and ten Raa (1991), Berliant and McMillen (2006), Berliant and Kung (2006), and Berliant and Sabarwal (2008). The inherent basic difficulty of density models is summarized in the following self-contradiction theorem (Berliant 1985a, p. 328): the statement that there is a continuum of consumers, with each owning a parcel of land of positive area, is self-contradictory.…”

“…I G U R E 2 The equilibrium land price curve P x ( ) and lot sizes of the ALP model (N = 3)12 For further discussion of this issue, seeAsami et al (1990Asami et al ( , 1991,Berliant (1991),Berliant and Sabarwal (2008), andBerliant and Fujita (2019).…”