General Equilibrium as a Topological Field Theory

TL;DR

This paper demonstrates that under certain conditions, general equilibrium theory can be formulated as a topological field theory, revealing potential for abrupt transitions between equilibrium states due to internal dynamics.

Contribution

It introduces a novel topological field theory framework for general equilibrium, capturing both equilibrium behavior and non-perturbative transitions.

Findings

Equilibrium corresponds to critical points in the topological field theory.

The theory admits instanton solutions linking different critical points.

Internal dynamics can cause abrupt, noise-driven transitions between equilibria.

Abstract

General equilibrium is the dominant theoretical framework for economic policy analysis at the level of the whole economy. In practice, general equilibrium treats economies as being always in equilibrium, albeit in a sequence of equilibria as driven by external changes in parameters. This view is sometimes defended on the grounds that internal dynamics are fast, while external changes are slow, so that the economy can be viewed as adjusting instantaneously to any changed conditions. However, the argument has not been presented in a rigorous way. In this paper we show that when conditions are such that: a) economies do respond essentially instantaneously to external influences; b) the external changes are small compared to the values that characterize the economy; and c) the economy's dynamics are continuous and first-order in time (as for Walrasian tatonnement), the resulting economic theory is equivalent to a topological field theory. Because it is a topological theory it has no dynamics in a strict sense, and so perturbatively---that is, when examining dynamics in the region of a critical point---the field theory behaves as general equilibrium posits. However, the field-theoretic form of the theory admits non-perturbative instanton solutions that link different critical points. Thus, in this theory, and in contrast to general equilibrium, the internal dynamics of the model occasionally make an appearance in the form of abrupt, noise-driven transitions between critical points.