(1) Suppose that there are two consumers. The first consumer has a demand function 91 = 12 - 3p and the second consumer has a demand function 92 = 12 - 2p. Suppose that the monopolist has a constant marginal cost c and cannot distinguish the consumers. The monopolist would like to design the optimal two-part tariff scheme (p, E), where P is the per unit price and E is the "entry fee". The monopolist needs to consider two alternatives. In alternative 1, the monopolist excludes consumer 1: (p, E) is such that consumer 1 finds it too exensive to pay the entry fee. This case is similar to the example we covered in class. In alternative 2, the monopolist sets (p, E) such that both consumers participate. (a) Assume c = 1. What is the optimal two part tariff for the monopolist? Is p = c? How much does each consumer purchase? What is the monopolist's profit? (b) Now assume that c = 2. What is the optimal two part tariff for the monopolist? How much does each consumer purchase? What is the monopolist's profit? Note: For simplicity, we assume that there are only two consumers in the market, but you may interpret this as a market populated by many consumers, where half of them have the first demand function and the other half the second demand function.