Duality of welfare and profit maximization

Abstract

Many economists are aware that the conditions for the efficiency and monopolization in a partial equilibrium framework are the extremes of the Ramsey-Boiteux formula when the Lagrange multiplier for the budget varies. We formalize the duality existing between the welfarist and monopolist constrained maximization programs by proving the following 'folk theorem': max Welfare s.t. profit ≥ fixed cost ⇔ max Profit s.t. output ≥ minimum