Optimality of the Equilibrium Allocation

Abstract

In this chapter we introduce normative considerations using the framework developed in chapter two. Since no agent in the city has market power and since there are no external economies or diseconomies, one should expect that the first welfare theorem applies to the urban spatial context as well, that is, the equilibrium allocation of chapter two is Pareto efficient. As we show in the appendix this, indeed, is the case. Thus the spatial aspect of the model does not matter in that sense. But when we adopt the more restrictive concept of optimality using, say, a social welfare function which is concave and symmetrical in the commodities consumed by the individuals, the spatial aspect of the model does matter: whereas in a spaceless context the equilibrium allocation is optimal, in a spatial context it is not—excepting a special case. More specifically, whereas the equilibrium allocation of chapter two yields the same utility level for identical individuals everywhere, the optimal allocation of this chapter yields different utility levels for identical individuals at different locations unless the criterion for optimality is to maximise minimum welfare. In other words, optimality requires unequal treatment of equals.