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., nonfixed 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 nontransitive 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 satisfies the weak axiom, can we find a (non necessarily transitive) preference that generates it? To answer this first question, we give a proof using the separating hyperplane theorem. With the help of this result, we identify a class of nontransitive preferences which generate continuous demand functions, and within which any demand function satisfying the weak axiom can be rationalized.
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Date of creation:  01 Jan 2000 
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Handle:  RePEc:oxf:wpaper:2000w12 
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