Complete solution of the integrability problem for homothetic demand functions

For any Walrasian demand function, the Strong Axiom implies (and is implied by) rationalizability by a complete preorder. However, these equivalent conditions do not ensure the existence of a continuous utility function or complete preorder giving raise to the primitive demand. We here propose a self‐contained proof of a related fact: if the demand is homothetic and continuous, the Strong Axiom characterizes the existence of a continuous and homogeneous of degree one subjective utility function (or a continuous and homothetic complete preorder) representing the demand. Our contruction depends upon standard tools and overturns the need for ad‐hoc axioms that were used in prior published literature on the topic.