Cities are physical structures, but the modern literature on urban economic development rarely acknowledges that fact. The elasticity of housing supply helps determine the extent to which increases in productivity will create bigger cities or just higher paid workers and more expensive homes, in this article, we present a simple model that provides a framework for doing empirical work that integrates the heterogeneity of housing supply into urban development. Empirical analysis yields results consistent with the implications of the model that differences in the nature of house supply across space are not only responsible for higher housing prices, but also affect how cities respond to increases in productivity.