Maximization of a Linear Utility Function over the Set of the Housing Market Short-Term Equilibria

AMS subject classification: 90C05, 90A14.

Some generalization of the housing market models published by Herbert and Stevens [4], Gustafsson et al. [2], and Wiesmeth [7] is suggested. The set of short-term equilibria in a housing market in the sense of Wiesmeth [7] is parameterized by Pareto-maximal integral points of some polyhedron. The problem of maximization of a linear utility function over the set of short-term equilibriums is studied. The problem is proved to be reducible (under some natural assumptions) to a linear programming problem (LPP), or to finite number of the LPPs in general case. The possible applications of the results and some related problems are pointed out.

This work was supported by the Research Support Scheme of the OSI/HESP, grant No. 934/1996.