5. Suppose that the inverse demand curve for paper is P = 200 i Q, the market private cost (i.e., the unregulated competitive market supply) is MPC = 80 + Q, and the marginal social harm from pollution (gunk) associated with paper production is MGC = Q, so the marginal cost is MSC = MPC + MGC. (30 pts.) a. What is the unregulated market equilibrium? (5 pts.) b. What is the social optimum? (5 pts.) c. What specic tax per unit of output or gunk results in the social optimum? (5 pts.) d. What is the unregulated monopoly equilibrium level of production? (5 pts.) e. Is there a need to regulate this market (monopoly)? If so, what would be the resulting regulated equilibrium? If there is no need to regulate this market, explain your answer by providing a graph. (10 pts.)