Effective algorithms for homogeneous utility functions

Under the assumption of (positive) homogeneity (PH in the sequel) of the corresponding utility functions, we construct polynomial time algorithms for the weak separability, the collective consumption behavior and some related problems. These problems are known to be at least $NP$-hard if the homogeneity assumption is dropped. Keywords: the utility function, the economic indices theory, the collective axiom of revealed preference, the weak separability property, the class of the differential form of the demand.