A von Neumann Representation of Lonergan's Production Model

Abstract

A von Neumann growth model is adapted to illustrate an efficient transition for downward rigid consumption from one Schumpeterian stationary state to another. An arbitrary number of fixed capital goods can be accommodated in processes corresponding to a hierarchy of machines making machines. A cluster of innovations can be represented by a set of new processes which become available at some given time. Efficiency can be seen to entail the abandonment of some capital goods used in earlier processes. Algorithms for calculating numerical solutions involve only linear programming generalizations of vector difference equations.