This paper is devoted to the estimation of the power of nonparametric tests of the consistency of observed data on consumption and prices with one of the two axioms. These are Generalized Axiom of Revealed Preference (GARP) and Homogeneous Axiom of Revealed Preference (HARP). Our approach differs from existing ones in both the way of estimating the power of the tests and the alternative hypothesis. We show that the power of HARP test is very close to one, while that for GARP test is less and in many cases much less than one. We also study the applicability of these tests to forecasting.