Competitive efficiency in an overlapping-generation model with endogenous population

Abstract

A puzzling result regarding market failure was obtained by Samuelson (1958) in his exact consumption-loan model. He showed that under the conventional assumptions on the economic environment, the fact that ‘each and every today is followed by a tomorrow’ [e.g. Samuelson (1958, p. 482)] may lead competitive markets to fail in achieving the standard Paretoefficiency objective. As the standard sources for market failure (externalities and non-convexities) are absent from Samuelson’s model, it was natural to ‘blame’ the infinity of the time horizon as such for the resulting inefficiency.’ Our purpose in this paper is to show that if certain exogenous features of the Samuelsonian model are treated as being endogenously determined by economic factors, the above-mentioned inefficiency, with its associated puzzles, does not arise. More specifically, in the model presented below, population is an endogenous variable with parental preferences determining the number and ‘quality’ (in a utility sense) of children. Importantly, endowments of children are viewed to be bequeathed to them by parents. Under the assumptions of perfect capital markets and perfect foresight, it is shown that every competitive equilibrium is Pareto-efficient (under any appropriate definition of