Tricks for maximizing collective utility functions

This paper compares different centralized collective models for maximizing the utility of a household from the point of view of the single members that compose it. We describe the collective maximization program as a vector optimization problem and analyze the household welfare and Pareto specification as special scalar cases. The comparisons of these programs reveals interesting relationships among the Lagrangian multiplier and the sharing rule parameters. We also generalize a multiobjective dual problem that leads to the characterization of the individual shares of total income. Hence, we have a measure of the distribution of wealth inside the household.