Duality in comparative statics in rental housing markets with indivisibilities

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.