Using a mixed market model for analyzing imperfectly competitive econo
mies, we maximize the oligopolists' Welfare Function, given individual
rationality and feasibility constraints. We prove that solutions belo
ng to the core for a large class of economies. This class includes, in
particular, every monopoly having a single type of small traders. Not
e that all such solutions yield the large trader, utility-wise, strict
ly more than at any monopoly solution, where the monopolist plays stra
tegically, and the ocean of small traders act as being as price-takers
.