We report a generalization of recent results on the existence of marginal cost pricing equilibria (MCPE) in economies with an increasing returns to scale industry. Our result makes no ad hoc assumptions which force the equilibrium to be on the efficiency frontier of the aggregate production possibility set. We also present an additional condition under which our MCPE are productivity efficient in the aggregate.
We prove the existence of approximate equilibria in exchange economies, giving bounds on the excess demand in terms of the number of traders and norms of the endowments, but independent of the preferences.