Public–private collusion

We study collusion between a public firm and a private firm facing linear demand and quadratic costs. We characterize the collusive outcome that results from Nash bargaining and compare it to the non-cooperative outcome. If the public firm’s taste for consumer surplus is mild, both firms reduce output (as in a private duopoly). If it is intermediate, while the public firm reduces output, the private firm expands output to such an extent that total output increases. If it is strong, the private firm’s output expansion does not compensate for the public firm’s output contraction, and thus total output decreases. We also characterize collusion sustainability, and assess the impact of relative bargaining power, degree of cost convexity, public firm’s taste for total surplus, and cost asymmetry. We conclude that, by reducing the productive inefficiency that is caused by the public firm being more expansionary, collusion may lead to higher profits and consumer surplus.