Stable solutions vs. multiplicative utility solutions for the assignment problem

The purpose of this note is (1) to illustrate that a utility maximization approach is not necessarily a stable solution for a matching assignment problem (2) to compare stable solutions with utility maximization solutions that are derived from a two attribute, multiplicative, utility function. It is demonstrated for an example, generated and studied by McVitie and Wilson (1971), that the utility maximization solutions do not seem, on a numerical basis, to perform worse than the stable solutions. Some policy implications are suggested based on this partial evidence.