Weak Axiomatic Demand Theory.

This paper gives a unified and simple treatment of three related questions in the demand theory of the weak axiom: (i) Is there an elementary, i.e., non-fixed point theoretic, proof of equilibrium existence when the excess demand function of an economy satisfies the weak axiom? (ii) What conditions are sufficient for a non-transitive preference to generate a continuous demand function? Note that such a demand must satisfy the weak, though not necessarily the strong, axiom. This motivates the next question. (iii) Given a function that satisfy the weak axiom, can we find a preference that generates it?