Duality in comparative statics in rental housing markets with indivisibilities

Abstract

We present certain duality results on comparative statics on competitive rent vectors in the rental housing market model. In the model, apartments as indivisible goods are classified into a finite number of categories, and are traded for one composite commodity. Our concern is about certain general properties of the behavior of rents with parameter changes. In particular, the rent changes are intimately related to the boundary income changes of the categories of apartments. Both changes are endogenously determined in equilibrium. We will show that these changes exhibit nice dual structures. We will also apply our model and comparative statics to a rental housing market in the Tokyo metropolitan area.  2005 Elsevier Inc. All rights reserved.JEL classification: R31; R30; D58

Effects of quality changes in rental housing markets with indivisibilities

“…The above result will be compared with another comparative statics result, which is a variant of an earlier result in Kaneko et al (2006). In this comparative statics, all the h t 's remain unchanged, but only the income of the household choosing the k-th apartment increases.…”

“…We follow a simpli…ed version of the rental housing market model (M; N ) of Kaneko et al (2006). The symbols M and N denote the set of households, M = f1; : : : ; mg, and the set of landlords, N = f1 0 ; : : : ; n 0 g. Each household i 2 M having income I i > 0 will rent at most one unit of an apartment.…”

“…is discussed in Kaneko et al (2006). Here, we give an example to illustrate the housing market model described above.…”

“…In this paper, we consider comparative statics in the rental housing market model of Kaneko-Ito-Osawa (2006), where apartments are treated as indivisible goods and are exchanged with one composite good. In particular, we consider the comparative statics of apartment rents when the quality of a certain apartment class is improved.…”

“…However, the literature re ‡ects almost no interactions with urban economics, except for Kaneko (1983) and Gerber (1985). Recently, Kaneko et al (2006) gave a more systematic application of the approach to urban rental housing markets, and also studied various properties arising from comparative statics. The present paper is a further study in this line of research.…”