Spatial variation of the marginal utility of income and unequal treatment of equals

In one of the most famous contributions to the “new” urban economics literature, Mirrlees [6] showed that a utilitarian planner, able to control the distribution of income (or endowments) across households, the consumption of land (or housing), and the distribution of population over space, would treat households with identical tastes unequally in the sense that utility levels would vary among them at the planner’s optimum. Similar results were obtained by Dixit [2], who showed that even more inequality-averse social welfare functions than the utilitarian one would result in unequal treatment. He concluded that only the Rawlsian maximin welfare function would produce the equal treatment outcome.2 This result has generated considerable attention (see, e.g., Mills and Mackinnon [5]) because of its apparently paradoxical nature. The purpose of this note is to present a new way of thinking about, and making plausible, the unequal-treatment result.3 To develop the intuition, recall that in monocentric city models where equals are treated equally, that is, where households have equal endowments, a market equilibrium with free mobility is characterized by equal utilities for all (assuming identical preferences). As is well known, in the absence of congestion or other market failures, this market equilibrium is Pareto-efficient, producing the maximum feasible common level of utility. Imagine now a Mirrlees planner, coming across such an equal-utility equilibrium. Under what conditions would the planner not want to disturb the market equilibrium? Clearly, a necessary condition for equal treatment to be utilitarian-optimal is that the marginal utility of income be the same for all households in the market equilibrium. Otherwise, freezing the allocation of resources in every other respect, social