Externalities and Interdependence in a von Neumann Growth Model

Abstract

In a von Neumann growth model, all inputs for the production during one period must be produced (or possibly bought in a market) by the economic agent who will use them. Externalities are introduced here in the sense that an agent may use some inputs (e. g. public services) without buying them or providing them by himself. Similarly, some outputs (beneficial or harmful) may not accrue to the producer, but to other agents in the economy. The resulting situation is a game between various agents in an economy. A particular solution of such a game (the Nash equilibrium) is derived. Various forms of interdependence between economic agents will be briefly discussed.

It is shown how a von Neumann growth model can be viewed as a competitive equilibrium model and how this explains the formation of prices and intensities of the various processes, both in the presence and absence of externalities.

If no externalities are present, then the individual profit maximization by a multitude of economic agents leads to the globally optimal solution (the maximal possible growth rate). But if there are externalities, the muopic profit-maximization by competing individuals will generally lead to a less than optimal growth rate, and some form of cooperative planning is needed to achieve an optimal solution.