The Optimal Antitrust Policies for Vertical Price Restraints in a Non-Green Supply Chain

This paper studies the optimal antitrust policies for vertical price restraints in an infinitely-lived non-green supply chain channel that emits air pollution during production. The channel involves a supplier and a retailer that can either engage in sequential (Stackelberg) price competition where the supplier moves first or engage in vertical price coordination where they choose the retail price to maximize their joint profits and choose the wholesale price using the generalized Nash bargaining. We first consider the absence of an antitrust authority and characterize a necessary and sufficient condition for the stability of coordination, which we call internal stability. Then, we characterize the socially optimal antitrust policies. The policies we consider involve the costly auditing of the channel to detect coordination at a fixed probability in each period and a penalty fee charged to the channel members in case coordination is detected. When coordination is internally unstable, it is socially optimal to prevent its formation if the relative abatement cost of collusive emissions is sufficiently large or if the minimum cost of auditing is sufficiently small. In the case where coordination is internally stable, destabilization is also an option for the antitrust authority. In this case, our necessary and sufficient conditions characterizing the optimal antitrust decisions imply that it is socially optimal to destabilize (allow) the vertical price coordination of the channel if both the minimum cost of auditing and the relative abatement cost of collusive emissions are sufficiently small (large) and to prevent it otherwise.