Real income growth and revealed preference inconsistency

Abstract

If a smooth demand function violates the strong axiom of revealed preference, the income and prices can follow a cycle and returm to their starting values even though real income is always rising. We show how real income growth along the "worst" revealed preference cycle depends on the range of price variation and on violations of the Slutsky conditions. We relate this result to proposed reforms of the consumer price index and use it to justify a new index of local demand inconsistency. We also use the Slutsky matrix to determine an upper bound on the number of observations required to detect revealed preference inconsistency.