You are a policy advisor responsible for air pollution in a region where there are only two chemical plants run by firm A and firm B. Firm A’s pollution abatement costs are 2x^3 , where x is a unit of pollution. Firm B is newer and has pollution abatement costs of 2x^2. Assume that neither firm is initially abating pollution. The per-unit benefit to a unit of pollution abatement is a constant $600.
1) What is the socially optimal level of pollution abatement? What is the socially optimal allocation of pollution abatement across the two firms?