Rapid paths in von Neumann-Gale dynamical systems

TL;DR

This paper proves the existence of rapid growth paths in von Neumann-Gale dynamical systems, advancing the mathematical understanding of economic growth models with random elements.

Contribution

It provides a general existence theorem for rapid paths in stochastic von Neumann-Gale systems, addressing a longstanding open problem.

Findings

Existence of rapid paths established under standard assumptions.

Addresses a problem open for over thirty years.

Extends deterministic growth theory to stochastic settings.

Abstract

The paper examines random dynamical systems related to the classical von Neumann and Gale models of economic growth. Such systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of convexity and homogeneity. A central role in the theory of von Neumann-Gale dynamics is played by a special class of paths called rapid (they maximize properly defined growth rates). Up to now the theory lacked quite satisfactory results on the existence of such paths. This work provides a general existence theorem holding under assumptions analogous to the standard deterministic ones. The result solves a problem that remained open for more than three decades.