  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.
