Truncated Decision Rules and Optimal Economic Growth with a Fixed Horizon

Abstract

ONE OF TIlE MOST interesting characteristics of recent aggregative ino(dels of economic growth is perhaps the specification of optimal growth paths under varying assumptions and conditions defining optiinality. Assuming that an optimal growth path for a fixed horizon can be specified for a developed or an underdeveloped economy, difficult decision problems of macro-dyniamic policy-making arise, when appropriate governmental actions are needed to secure the convergence of the observed growth path to the optimal one. The solutions of these decision problems by simple mathematical models are considered here with special emphasis on their uncertainty and dynamic aspects. The implications of alternative preference functions are analyzed here to show how optimal decision rules can be derived under various orders of truncation2, where truncation refers to the (degree of incomplete sp)ecification of the probability distribution of the random elements of the problem, i.e., the risk preference function (or disutility function) of the problem. Our approach would be to analyze the concept of 'a linear decision rule' developed by Theil [71 and emphasized recently by Holt [6] who used a quadratic risk function in a simple aggregative Keynesian model based on the multiplicr, the income identity and private investment as the only random variable. For illustrative purposes, we would use the principle of optimality of Pontryagin [9] as a generalization of the extremum conditions of variational calculus to derive the optimal time