rationing depends negatively on the buyer-seller ratio and positively on the concavity of the buyer's utility function …

We show that an agent maximizing some utility function on a discrete (as opposed to continuous) consumption space will … continuous quantities. An application of Afriat's Theorem then guarantees that there is a strictly increasing utility function on …

symmetry if the latter is generated by a field. Moreover, solving the PDEs yields the functional form for utility equivalent to …, multivariate separability, and homogeneity, including the cases of Cobb-Douglas and CES utility. …