Question

Suppose that pollution in a neighborhood comes from two factories, with marginal benefit curves given by MB1 = 12 – P1 and MB2 = 8 – P2. The level of pollution in the neighborhood is given by P = P1 + P2. The government wants to limit pollution by instituting a pollution-rights market. The government’s desired level of P is 10, so it prints 10 pollution rights and offers them for sale to the firms. Find the equilibrium selling price of a pollution right, as well as the allocation of rights (and hence pollution levels) across the two factories.