Industrial production of goods causes pollution that damages the environment. Suppose the marginal social cost of pollution can be represented by the function MSC = 2T, where T represents tons of pollution. Suppose the marginal social benefit of pollution can be represented by the function MSB = 1,000 - 2T.

1. In an unregulated market, how many tons of pollution will be emitted?
2. Solve for the socially optimal amount of pollution.
3. What level of Pigouvian tax will reduce pollution to the optimal level?