The Evolution of Welfare Economics

Equilibrium is attained when the existing contracts can neither be varied without recontract with the consent of the existing parties, nor by contract within the field of competition. The advantage of this general method is that it is applicable to the particular cases of imperfect competition, where the conceptions of demand and supply are no longer appropriate.

This is the idea of the core of an economy, which is an even stronger welfare criterion than is Pareto optimality. This idea is finally definitively developed in the Debreu Scarf (1963) Limit Theorem and subsequent work by Israel Aumann, Werner Hildenbrand, Bob Anderson and others. The idea is that Edgeworth's ideas of contract define a bargaining situation which is modeled as a cooperative game. A solution, core allocations converge to the set of competitive allocations and the number of traders grows.