Continuous Choice Functions and the Strong Axiom of Revealed Preference.

In this note, it is shown that a result due to Uzawa showing that the weak axiom of revealed preference together with a regularity condition implies the strong axiom of revealed preference can be derived from the regularity condition alone, if the choice function is continuous in prices and in income. The observation that the weak axiom of revealed preference is not needed suggests that this regularity condition is remarkably strong. The main result of the paper is quite general in the sense that the only additional assumption on the choice function is that the whole budget be spent.