Problem 1: Pure Public Good. Carol and Maggie live in a town with a population of two. The air in town is very polluted, and a traveling salesman comes through town selling air purifying devices. Carol and Maggie each have private marginal benefit curves that depend on the total number of units Q purchased. These are given by: pC = 48 2Q pM = 24 Q The salesman has horizontal supply (constant marginal cost) given by S = SM C = 12. 1. First, consider a private competitive market. a) Imagine that Carol is alone. What quantity does Carol buy? b) Imagine that Maggie is alone. What quantity does Maggie buy? c) When they are together, what quantity does Carol buy? What quantity does Maggie buy? What is the total quantity (Qc) purchased? 2. Next, consider the socially optimal outcome. a) Find the joint demand / SM B curve. b) What is the socially optimal quantity (Q?)? 3. Dissatisfied with the level of private provision (Qc), the government purchases two units. Carol and Maggie are free to purchase additional units if they find it privately optimal to do so. a) What quantity does Carol buy, and why? b) What quantity does Maggie buy, and why? 4. Finally, suppose the government knows both individual demand curves and implements Lindahl pricing to reach the socially optimal level Q?. a) How much will the government charge Carol for each unit? b) How much will the government charge Maggie for each unit? c) Is this sufficient to fund Q? units?