We provide two new, simple proofs of Afriat’s celebrated theorem stating that a finite set of price-quantity observations is consistent with utility maximization if, and only if, the observations satisfy a variation of the Strong Axiom of Revealed Preference known as the Generalized Axiom of...

Lowe and Hurter introduced the "generalized market area problem" of simultaneously determining production levels and distribution patterns at n plants to satisfy demand distributed over a subset of R^k. Here we give simpler proofs and extensions of their results. We also show how the problem can...