This paper provides a model for the well-known empirical phenomenon that houses of different quality experience different price developments. The typical pattern is that luxury houses appreciate more in boom periods and depreciate more during busts. The standard model of housing demand treats housing as a quantity of ?housing services?, an imaginary homogeneous commodity that is available in arbitrary quantities at a constant price per unit. This model is unable to explain differential development of house prices. However, a simple variant that treats the number of houses offering a given number of housing services as fixed is able to do this. This is shown by means of a formal analysis of a model in which households that differ in income are allocated over a given housing stock. In particular, the model predicts that the price of housing as a function of quality becomes more convex after a proportional increase in all incomes. Earlier explanations of this phenomenon relied on down payment effects, but since diverging house price developments are also observed in countries where these effects are negligible, this provides only a partial explanation. Empirical analysis of house prices in Amsterdam confirms the predictions of the model.