The exponential density function: First principles, comparative statics, and empirical evidence

It is well-known that the exponential density function can be derived using a compensated demand for bousing with a unitary price elasticity. We investigate how such an elasticity can arise from first principles and are thus able to identify the determinants of the density gradient. We then use these determinants, together with existing comparative statics, to examine unambiguously the relation between the density gradient and some exogenous variables. We conclude that our results are closely supported by existing empirical evidence—except for the effect of urban population size on the density gradient.