A Study on the Problem of Optimum Economic Growth

Abstract

<p>The theory of optimum economic growth has centred around the 1928 paper of Ramsey and extensively developed by subsequent authors. Samuelson and Solow extended Ramsey's analysis to a world involving multiple capital goods. Following Ramsey's formulation of his problem in terms of constrained maximization of an integral over infinite time, Tinbergen, Koopmans, Cass, Weizacker and Mirrlees worked in an infinite time horizon, allowing for certain modifications. Chakravarty pointed out that the integral need not converge even if the policy proposed by Ramsey (as being optimal) were adopted. Since there is considerable difficulty in demonstrating convergence in an infinite time horizon, Chakravarty and Goodwin tackled this problem in a finite time horizon. In our thesis, we are concerned with the problem of investigating the existence of an optimum savings programme in a finite time horizon. We provide a rigorous proof of the existence of such an optimum savings programme. We also demonstrate the uniqueness of the optimal programme. Furthermore, we have given a rigorous characterization of an optimal savings programme as being efficient. Rigorous proof of uniqueness of an optimal savings programme and the property that it is efficient, have nowhere appeared in the literature either in the context of an infinite or in that of a finite time horizon model.</p>