Local labor markets with non-homothetic preferences

We study the effects on employment, costs of living, and income inequality of local shocks in the housing market or in the productivity of a tradable good. We construct a two-region search and matching model in which housing is considered a necessity good. Mobility of labor implies that any change in one region propagates into the other. The model is analytically tractable and provides some intuitive comparative statics results. We then calibrate the model on the basis of German data. Our simulations indicate that both types of shock produce limited employment gains but have a significant impact on housing prices and real income inequality: poorer, unemployed workers experience a larger increase in their cost of living index. This depends on the assumption of a non-homothetic utility function that generates a specific nominal wage to housing price positive relationship, partially safeguarding employed individuals against the rising cost of living.