On the construction of general equilibria in a competitive economy

TL;DR

This paper provides a constructive approach to McKenzie's theorem on general equilibria, showing that under stronger preference conditions, approximate equilibria can be computed even though exact solutions cannot.

Contribution

It introduces a constructive method for finding approximate equilibria in a competitive economy under strengthened preference assumptions.

Findings

Approximate equilibrium points can be computed with arbitrary precision.

Strengthening preference conditions enables constructive solutions.

Full theorem remains non-constructive, but approximate solutions are feasible.

Abstract

This paper gives a constructive treatment of McKenzie's theorem on the existence of general equilibria. While the full theorem does not admit a constructive proof, and hence does not admit a computational realisation, we show that if we strengthen the conditions on our preference relation---we require $\succ$ to be uniformly rotund in the sense of Bridges [5]---then we can find `approximate equilibrium points,' points at which the collective profit may not be maximal, but can be made arbitrarily close to being maximal.