Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem

Abstract

In this paper I consider the problem of determining best paths of economic growth, when the citerion of preference among paths focuses entirely upon the final state. This problem is considered within the framework of a model of a closed economy with constant returns to scale, of the type proposed by von Neumann in his paper on balanced growth equilibrium [5]. The main result (section 5) is that under certain conditions all best growth paths must be “close”to the von Neumann path of balanced growth, except possibly for a finite number of periods, which number is independent of the length of the path. Within the framework of this model of the closed economy, the two most restrictive conditions are (1) that the preference function on the final states be homogeneous, and (2) that the von Neumann balanced growth path be the unique profit maximizing direction of growth under the von Neumann equilibrium prices.

This research was supported by the Office of Naval Research under contract Nonr-222(77), project NR 049 029 with the University of California. Reproduction in whole or in part is permitted for any purpose of the United States government.