Introducing formalism in economics: The growth model of John von Neumann

Sandye Gloria-Palermo

doi:10.2298/pan1002153g

Abstract

The objective is to interpret John von Neumann's growth model as a decisive step of the forthcoming formalist revolution of the 1950s in economics. This model gave rise to an impressive variety of comments about its classical or neoclassical underpinnings. We go beyond this traditional criterion and interpret rather this model as the manifestation of von Neumann's involvement in the formalist programme of mathematician David Hilbert. We discuss the impact of Kurt G?del's discoveries on this programme. We show that the growth model reflects the pragmatic turn of the formalist programme after G?del and proposes the extension of modern axiomatisation to economics.

Highlights

It is first necessary to offer a brief overview of the growth model and of the controversy over the filiations; the variety of the comments is by itself an invitation to consider an alternative interpretation. We found such an alternative in von Neumann’s involvement in the formalist Hilbertian programme so that the classical/neoclassical demarcation line may well be replaced by the formalist/nonformalist criterion, as Blaug (2003) and Nicola Giocoli (2003) suggest
In the 1937 article, von Neumann characterises the equilibrium configuration of an economy expanding at a uniform rate
“God, it is said, speaks to each of us in our own language...”, Paul Samuelson (1989, p. 100) declared with reference to the 1937 paper, explaining further on that the genius of von Neumann’s contribution fitted any capital model. von Neumann (1945/46, p. 2) himself cleared the question of the filiations in a lapidary style: “It is obvious to what kind of theoretical models the above assumptions correspond”, as if this was not the issue at stake, drawing attention once more to the technical aspects and the nature of the mathematical approach itself

Summary

The 1937 Model and its Various Interpretations

In the 1937 article, von Neumann characterises the equilibrium configuration of an economy expanding at a uniform rate. Von Neumann’s model would offer proof that optimisation tools do not constitute a selective feature of neoclassical economics; Supporters of a neoclassical interpretation put to the fore more technical arguments to show that the model may be understood as a special case of the more general neoclassical framework Such generalisations entail, among others, the introduction into the model of the intertemporal preferences of consumers (Edmont Malinvaud 1953), the consideration of labour as a primary factor constrained by an exogenous growth rate (Michio Morishima 1964), a relaxation of the assumption of circularity according to which each production process uses or produces a given quantity of each good produced in the preceding period “God, it is said, speaks to each of us in our own language...”, Paul Samuelson (1989, p. 100) declared with reference to the 1937 paper, explaining further on that the genius of von Neumann’s contribution fitted any capital model. von Neumann (1945/46, p. 2) himself cleared the question of the filiations in a lapidary (and, after the fact, ironic) style: “It is obvious to what kind of theoretical models the above assumptions correspond”, as if this was not the issue at stake, drawing attention once more to the technical aspects and the nature of the mathematical approach itself

Von Neumann and the Formalist Programme of Hilbert

The Pragmatic Turn

From the Mechanical to the Mathematical Analogy