Existence of Competitive Equilibrium in a General Overlapping-Generations Model*

In the companion paper [2], Balasko and Shell establish existence of competitive equilibrium for a pure-distribution, overlapping-generations economy without money (see, especially, Propositions (3.10) and (3.11) in Section 3). That argument is remarkably simple, but depends critically on some strong hypotheses concerning individual tastes and endowments. In particular, it is assumed that, in any given period, every living consumer has a utility function which is strictly increasing in every available commodity, as well as an endowment which is strictly positive in every available commodity. These two assumptions are especially difficult to rationalize in an intergenerational context. How many teen-agers do you know who are eager viewers of Lawrence Welk? How many “middle-agers” who are likely users of Clearasil? So much for increasing (much less strictly increasing) utility functions! Regarding strictly positive endowments, we invite the reader to dream up his/her own counterexamples. (Another hint: How do you respond to the commonly heard lament, “What I wouldn’t give to be young again!“?) In the present paper, we do away with such unrealistically severe hypotheses. And we do more. Following the Arrow-Debreu tradition, we postulate fairly mild conditions on individual tastes and endowments. Of course, in line with the same tradition, we must then impose some further conditions on the potential economic interrelationships among consumers. This additional structure is an application to the overlapping-generations model of McKenzie’s basic concept of irreducibility.