The stochastic city

Abstract

This paper analyzes a simple model of an urban area with growth and uncertainty. Household income, rents, and prices for land follow stochastic processes. Even though investors are risk neutral, uncertainty affects both land rents and land prices in equilibrium because the conversion of land from agricultural to urban use is irreversible. Growth, on the other hand, affects urban and agricultural land prices but not the level of rents. We show that uncertainty (i) delays the conversion of land from agricultural to urban use, (ii) imparts an option value to agricultural land, (iii) causes land at the boundary to sell for more than its opportunity cost in other uses, and (iv) reduces equilibrium city size.