Consider the market for paper. Let market demand be given by inverse demand function P d (Q) = 60 Q, where Q is tons of paper demanded at price P (Q). There are 20 paper mills supplying the market. Each acting as a price taker. Eac paper mill has a cost function C(Q) = 10Q2 , where Q is one ton of paper produced. When a mill produces paper it also causes pollution down river. A mill does not face any liability due to this pollution but it has been estimated that the external cost associated with its production is EC(Q) = 10Q2 . 1. What is a mill's optimal level of paper production at given price P, Q (P)? 2. Determine market supply of paper and find the market equilibrium. What is the market equilibrium price and quantity? 3. What is the socially efficient level of paper production, Qef f icient, that is the level of market production and consumption that maximizes total surplus? 4. Calculate the deadweight loss in the market equilibrium. Comment on the reason for the existence of the deadweight loss. 5. Suppose the 20 firms are merged into a single firm that acts as a monopolist. The monopolist's cost function is C m(Q) = 20C(Q/20). Determine the monopoly outcome for the paper market. Determine total surplus. Compare the outcome with the competitive market equilibrium and that of the socially efficient output level. Compare and contrast with the usual intution that a monopoly will reduce total surplus relative the perfectly competitive equilibrium outcome.