On the Pareto Efficiency of a Socially Optimal Mechanism for Monopoly Regulation

Baron and Myerson (BM) (1982)propose an incentive-compatible, individually rational and ex-ante socially optimal direct-revelation mechanism to regulate a monopolistic firm with unknown costs. We show that their mechanism is not ex-post Pareto dominated by any other feasible direct-revelation mechanism. However, there also exist an uncountable number of feasible direct-revelation mechanisms that are not ex-post Pareto dominated by the BM mechanism. To investigate whether the BM mechanism remains in the set of ex-post undominated mechanisms when the Pareto axiom is slightly weakened, we introduce the epsilon-Pareto dominance. This concept requires the relevant dominance relationships to hold in the support of the regulator's beliefs everywhere but at a set of points of measure epsilon, which can be arbitrarily small. We show that a modification of the BM mechanism which always equates the price to the marginal cost can epsilon-Pareto dominate the BM mechanism at uncountably many regulatory environments, while it is never epsilon-Pareto dominated by the BM mechanism at any regulatory environment.