On welfare theory and urban economics

This paper examines the welfare theorems in the context of urban economics. The standard model of urban economics, which involves a continuum of agents located in a continuous space, is first described. Next, examples are given where both potential theorems fail for variants of the standard model in which preferences depend explicitly on location. Namely, we point out that a Pareto-optimum may not be an equilibrium even though preferences are continuous, convex and locally non-satiated; and that an equilibrium may not be Pareto-optimal even though preferences are continuous and locally non-satiated. A reason for this failure might be found in the heavy requirements that the model imposes on the equilibrium price of land. Firstly, it must fully capture the hedonic pricing of location while, at the same time, it must prevent the movement of consumers between locations. Secondly, at each location, it must equal the marginal rate of substitution between land and the numeraire commodity. Our examples might be relevant to other spatial models, such as differentiated product and hedonic models, location theory models and models of political party competition.