  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.
