Irreducibility, Resource Relatedness and Survival in Equilibrium with Individual Non-convexities

Standard results in general equilibrium theory, such as existence and the second efficiency and core equivalence theorems, are most easily proved for compensated equilibria. A new condition establishes that, even with individual non-convexities, in compensated equilibrium any agent with a cheaper feasible net trade is also in uncompensated equilibrium. Some generalizations of McKenzie’s irreducibility assumption are then presented. They imply that (almost) no agent is at a cheapest point, so the easier and more general results for compensated equilibria become true for uncompensated equilibria. Survival of all consumers in uncompensated equilibrium also depends on satisfying an additional assumption that is similar to irreducibility.