Price Regulation in Oligopolistic Markets

We consider price regulation in oligopolistic markets when firms are quantity setters. We consider a market for a homogeneous good with a demand function of special form (-linearity), constant returns to scale, and identical firms. Marginal costs can take two values only: low or high. Values of all parameters except the marginal costs are known to the regulator. Assuming that the regulator is risk-neutral and maximizes expected social welfare (defined as the sum of consumer surplus and profits), we characterize the optimal policy and show how this policy depends on the basic parameters of demand and costs.