A number of paper companies dump sewage into a local river as a byproduct of production. The resulting environmental damage incurs a social cost of 60 cents per ream of paper that is produced. Suppose marginal cost function for the paper companies is given by MC = .01Q, while the demand curve for paper is given by Q = 1200 - 200P.

a. Solve for the social marginal cost function (that is, the function that takes into account the private marginal cost of production and the social cost of the externality).

b. What are the total costs of production (including the cost due to environmental damage) at the unregulated equilibrium quantity of 400?

c. What size tax would induce the firms to cut back to the socially optimal quantity of 360?