Income, spatial competition and welfare

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




John Yinger


Income, Spatial competition, Welfare, Wage inequality, Land allocation, Commuting

Subject Categories

Economic Theory | Labor Economics | Urban Studies and Planning


This dissertation is comprised of four essays. Chapter II develops a new way to present standard urban models and a new rent function called the rent-commuting cost function. The rent-commuting cost function represents the relationship between rent and total commuting cost, and is advantageous because it is independent of the functional form of the commuting cost function and its gradient falls as household income rises. However, the gradient of the rent-distance function may not fall as income grows if: (1) the income elasticity of marginal commuting cost is greater than the income elasticity of land demand; (2) congestion is considered; and (3) commuting cost is a function of income and distance. Therefore, the gradient of the rent-commuting cost function is an appropriate measure of suburbanization, and the gradient of the rent-distance function is not.

Chapter III examines comparative statics and derives the effects of income on urban characteristics using a closed model. The commuting cost is assumed to be a function of income and distance. As income grows household utility increases but less than it would in the standard model where the commuting cost is solely a function of distance. Also, the length of the border of the city becomes elongates as income grows. In contrast to the Alonso-Wheaton model, land rent at the central business district (CBD) rises as income grows if the time cost of commuting is greater than the operating cost. If an increase in income causes total commuting cost to increase significantly, households' willingness to bid more for land closer to the CBD will be strengthened since they can save more money by doing so. As income grows land demand rises and population density falls at the CBD.

Chapter IV also uses comparative statics to derive the effects of a median preserving increase in wage inequality on the welfare of households. It uses the same model as in Chapter III but with two income classes. An increase in income of the wealthy living in the suburban area can either hurt or improve the welfare of the poor depending on the relative magnitudes of operating cost and time cost. In contrast, an increase in the income of the poor living in the central area of the city always hurts the rich. Generally, if an increase in income of one class intensifies competition for land at the boundary of two classes, it hurts the other. Alternatively, if competition for land at the boundary is reduced, the welfare of the other class is enhanced.

Chapter V assumes a commuting network made up of dense circular streets and finite radial roads. Based on the assumed commuting network, the market and optimal commuting cost functions are derived. Using the Alonso-Wheaton model equipped with new commuting cost functions, the optimal and equilibrium allocations of land between residential and public uses are derived. If households are freely mobile and a city is small, a local government can attain the optimal allocation of land by maximizing population. The optimal allocation of land for roads is the same as the equilibrium allocation.


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