This paper is devoted to revealed preference theory and its applications to testing economic data for consistency with utility maximization hypothesis, construction of index numbers, and forecasting. The quantitative measures of inconsistency of economic data with utility maximization behavior are also discussed. The structure of the paper is based on comparison between the two tests of revealed preference theory - generalized axiom of revealed preference (GARP) and homothetic axiom of revealed prefernce (HARP). We do this comparison both theoretically and empirically. In particular we assess empirically the power of these tests for consistency with maximization behavior and the size of forecasting sets based on them. For the forecasting problem we show that when using HARP there is an effective way of building the forecasting set since this set is given by the solution of the system of linear inequalities. The paper also touches upon the question of testing a set of Engel curves rather than finite set of observations for consistency with utility maximization behavior and shows that this question has effective solution when we require the rationalizing utility function to be positively homogeneous.