The unitary elasticity property in a monocentric city with negative exponential population density

- This paper identifies a new property for a monocentric city with negative exponential population density.
- Unitary elasticity property: if a city is characterized by a constant density gradient, the sum of the elasticity of central density and the elasticity of land area with respect to population change will be approximately equal to unity.
- Topographic barriers and age of housing stock are the key factors explaining the deviation of the estimated sum of the elasticity of central density and the elasticity of land area with respect to population change from unity.

The central prediction of the monocentric city model is that real estate prices, density of development, population density, and land rent decline with the distance from urban center. The spatial pattern follows a negative exponential under the conditions derived by Brueckner (1982) and McDonald and Kim (1987). Research has demonstrated that these exponential density gradients have flattened over time due to rising income and falling transportation costs. This paper identifies a heretofore unknown property in a monocentric city with negative exponential population density, the “unitary elasticity property (UEP).” If a city is characterized by a constant density gradient, even if the slope of that gradient is changing over time, the sum of the elasticity of central density and the elasticity of land area with respect to population change will be approximately equal to unity. When this new prediction is tested, it fits US cities fairly well. Further analysis demonstrates that topographic barriers and age of housing stock are the key factors explaining the deviation from the UEP.