Capital accumulation in a stochastic decentralized economy

Abstract

Competitive equilibria in economies of overlapping generations are different from competitive equilibria in economies that have extended over finitely many periods, finite economies for short. These differences concern the properties of competitive equilibria, such as existence, optimality and determinacy or local uniqueness; and the phenomena compatible with competitive equilibria, such as net aggregate debt or fiat money with a positive price. The chapter discusses that all the variants of the model of overlapping generations allow for infinity of time periods and hence for infinitely many commodities. This infinity of time periods and commodities is not a mathematical curiosity, but rather is central to the economic significance of the model. Consider a pay-as-you-go system of social security. In economic models in which the rationality of individuals is presumed to be unlimited, the fact that no new generation would appear at some point in the very distant future would also lead to the immediate break down of the social security system. In an economy of overlapping generations, the temporal and demographic structure is explicit, which evidently enriches the study of problems such as the transfer of value over time. It also allows the claim that the inability of individuals to trade directly with individuals whose consumption and endowment spans commence after they have perished is the distinguishing feature of economies of overlapping generations.