2 (10 points) Harris United Insurance Company ("Hunco") offers multiple medical insurance plans. Sophisticated mar- ket research has concluded that there are 2 types of customers, "High" and "Low" risk (H&L). There are equal numbers of each type of customer. Demand curves of individual customers, as a function of the number of doctor visits per year, are: High: QH=25-PH + PH = 100 4QH Low: QL10- PL PL = 100 - 10QL MRH = 100 - 8QH MRL = 100 - 20QL Assume the marginal cost of providing each doctor visit is $20. Ignore fixed costs. (a) (5 points) If Hunco can segment the market, it will sell different insurance plans in different seg- ments, and charge its customers differently. What are the optimal 2-part pricing schemes for each segment? (Hint: Note that 2-part pricing schemes involves an up-front fee (the annual amount you pay for the insurance plan), and the copayment (a constant fee that you pay on the spot each time you go to your doctor). Help Hunco figure out the optimal up-front fee and copayment for each type of customer.) (b) (2 points) If Hunco must use the same 2-part pricing scheme for all customers (i.e. cannot segment customers), which of the two schemes in part (a) would be most profitable? Briefly explain. (c) (3 points) Suppose Hunco offered customers two plans, both of which were 2-part pricing schemes you figured out in part (a). Customers would choose their preferred pricing plan. Will it be successful for Hunco to have customers self-select into the most profitable insurance plan, without exactly knowing which type each customer is? Briefly explain