The monopolist of a good faces two groups of consumers. Each consumer in Group A has an inverse demand function given by P = 10 - Q. Each consumer in Group B has an inverse demand function given by P = 12 - Q. There are 100 consumers in each group. Marginal cost is 2 per unit for all units. You may assume that arbitrage is not possible. (a) Suppose that the firm engages in third degree price discrimination. Calculate the profit maximizing prices and the associated output and profit per consumer, and show your work. In which market is price higher? Explain. (b) Next, suppose that the firm wishes to use two part tariffs to engage in first degree price discrimination. What are the profit maximizing two-part tariffs to charge to each group? Explain and show your work. (c) Now, suppose that while the monopolist knows that the two groups exist, and that there equal numbers in each group, it does not know whether an individual consumer is in group A or group B. It plans to implement a form of second degree price discrimination by setting a single two part tariff. Will the optimal two-part tariff be either of those identified in (b), or something else? Explain. NOTE: you do not need to solve for the optimal two part tariff to answer this question. You may assume that units of the good are perfectly divisible if necessary. (d) Finally, continue to suppose that the monopolist cannot identify the group of an individual consumer, and suppose that the monopolist attempts to engage second degree price discrimination by offering the following pricing blocks: Block A: Receive 8 units of the good for a total price of $48. Block B: Receive 10 units of the good for a total price of $52. Given these two bundles, will all consumers choose to purchase, and will they separate themselves into their groups by the bundles they choose? Explain. Can this be the profit maximizing pair of bundles? Explain.