A Geometric Measure for the Violation of Utility Maximization

Revealed Preference methods offer a nonparametric test for whether a set of observations on a consumer can be rationalized by a utility function. If a consumer is inconsistent with the Generalized Axiom of Revealed Preference, having an idea of how severe this violation of utility maximization is can be useful. One widely used measure is the Afriat efficiency index. We propose a new measure based on the extent to which the upper bound of the indifference surface of a decision intersects the budget on which the decision was made. The measure is intuively appealing and has some attractive advantages over the Afriat efficiency index. As a cutoff-rule evaluated by Monte Carlo experiments the new measure performs very well compared to the Afriat efficiency index. The results suggest that the new measure is better suited to capture small deviations from utility maximation.