Effective algorithms for homogeneous utility functions

TL;DR

This paper develops polynomial time algorithms for certain economic problems assuming positive homogeneity of utility functions, addressing issues that are NP-hard without this assumption.

Contribution

It introduces efficient algorithms for weak separability and collective consumption problems under homogeneity, which are otherwise computationally hard.

Findings

Algorithms operate in polynomial time under homogeneity

Addresses NP-hard problems by leveraging positive homogeneity

Enhances computational methods in economic utility analysis

Abstract

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.