We present a dynamic model for the behavior of a developer who is assumed to be a profit taker. A conservation law in the housing market can be deduced by the classic calculus of variations, which explains spatial equilibrium of the housing market. We introduce the concept of infinitesimal transformations in the Lie group theory to describe the taste changes of households. By investigating invariant properties of dynamic model under infinitesimal transformations, the conservation law in the housing market is derived to explain invariant structure in the housing market under the taste changes of the households.
