A random bidding and supply land use equilibrium model

A model of the static equilibrium in the real estate market is studied in this paper and a solution algorithm is proposed. Consumers and real estate suppliers are assumed to have idiosyncratic differences, which are described by the discrete choice theory with random-utility and profit-behavior. Consumers are differentiated into clusters by socioeconomic characteristics while suppliers are differentiated by production technology. Consumer behavior is subject to budget constraints (with fixed income), a quasi-linear utility function, and is affected by neighborhood externalities (households) and agglomeration economies (firms). The suppliers’ behavior is restrained by zone regulations and affected by scale and scope economies. Total households by cluster are exogenous and total supply fits total demand. Real estate combined with location options is assumed to be discrete and differentiated, then transactions are modeled as auctions. Equilibrium prices are the result of auctions and the market clearing condition. These conditions generate a discontinuous non-linear location equilibrium problem where convexity is obtained by applying the MNL logit in all decisions. The equilibrium is described by a fixed-point equation system that, under some specified conditions, has a unique and stable solution; such conditions are analytically defined and represent a minimum degree of choice dispersion in the model. A fixed-point algorithm is proposed to solve the equilibrium, along with the conditions that assure convergence. This real estate equilibrium model can be applied to the highly complex reality of urban environments at a relatively low computational cost.