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

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 each consumer. In contrast, with a continuum of agents, average land rent goes up close to the central business district, is constant at some intermediate distance, and decreases for consumers farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.