A Minimal Role of Government in Achieving Optimal Growth

Abstract

Paul Samuelson [5] [6] and Peter Diamond [2] have developed growth models in which the attempt by each economic unit to maximize its utility does not lead to a social optimum. It would be possible for all generations to consume more per capita, if economic growth were directed by an omniscient social planner. Their models are free from the usual sources of inefficiency encountered in price theory. They explicitly assume perfect competition, perfect foresight and no external economies or diseconomies. The purpose of this paper is to introduce government institutions which may have little foresight, which will not engage in central planning or use direct controls but whose existence will guarantee that the equilibrium solution will be optimal. I am interested in determining the minimal amount of government which is sufficient to produce long-run optimality. Our concern is with the Samuelson-Diamond model whose basic features may be briefly outlined. Two generations are alive at any time: a younger generation which works, and a retired generation. Population born at time t is (1 + n)t; and the participation rate is 100 per cent. of the younger generation. There are (1+ n)tl1 retired people who were born during the preceding period. The periods are of equal, but arbitrary, length. Savings of a worker are designed to maximize his lifetime utility; and his decision involves the substitution between future and present consumption, subject to a constraint. Let c1(t) be consumption of a worker during his youth and c2(t +1) his consumption during retirement one period later. Utility depends upon [c1(t), c2(t + 1)], the pattern of lifetime consumption. As an example, Diamond selected a utility function for the individual: