Infinite-Dimensional von Neumann Models

Abstract

In this paper we will give a generalization of the closed Leontieff model which can be considered as a linear model for an expanding economy with infinitely many commodities and productive processes. The general-zation of the Leontieff model, which we present here, is purely formal. It is done by substituting for the euclidean n-space ℝⁿ a partially ordered Banach-space and for the input matrix a positive compact operator. We are able to show, that the classical result on the existence of equilibrium remains valid for this generalized model. In particular, it turns out that many growth models which are described by ordinary differential equations are such generalized Leontieff models. As examples we shall present the Harrod-Domar model and the neo-classical growth model.