Aggregation of Utility Functions

We are primarily concerned here with the question of integrability of the total demand in a model in which each consumer acts according to a cardinal utility function and has a fixed monetary income. It is well known that concavity of the various utilities is not sufficient to guarantee integrability, nor even to ensure rationality of the revealed preference. We show that if each personal utility function is homogeneous, in addition to satisfying the usual regularity conditions, then an aggregate utility function can be defined explicitly in terms of the given utilities. Furthermore, under the same assumptions we give a new characterization of equilibrium and show that equilibrium satisfactions are unique.