A turnpike theorem for a non-stationary Gale economy with limit technology. A particular case

Abstract

This paper is a continuation of the work by Panek [2013a], [2013b] and Panek and Runka [2011], with direct reference to [2013b]. The difference between this paper and paper [2013b] reveals when applying a different optimality criterion with the help of which growth processes are assessed. The optimality criterion in [2013b] is the value of production in the last period of a fixed planning horizon T = {0, 1, …, t1} measured in von Neumann equilibrium prices. In this paper we take the total value of output (also measured in von Neumann prices) produced in the whole horizon T as a growth criterion. The aim of the paper is to prove that a change of growth criterion does not deprive the economy of its turnpike properties. It was pointed out that a Gale economy with a changeable technology convergent to the limit technology also preserves similar properties if we accept the social utility function (with standard properties) as a growth criterion. The paper consists of three sections. In Section 1 we present a non-stationary Galetype model with a limit technology. Section 2 contains proof of the so-called ‘weak’ turnpike theorem, whilst in Section 3 we prove a ‘strong’ version of the turnpike theorem for the economy under investigation. The paper closes with final comments.