Insurance plan death spiral. A large employer provides insurance to employees and charges them any premium...

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Insurance plan death spiral. A large employer provides insurance to employees and charges them any premium it chooses. However, the employer must try to cover the expected medical expenditures of those who it insures. The employer offers one insurance contract to all employees, and charges them an initial premium at time T = 1 equal to P = 10. After T = 1, for all subsequent periods the employer charges employees a premium that equals the average cost of the people who buy insurance in the previous year. Think about the graphical framework for adverse selection we studied in Class 6. Assume that consumer demand is characterized by: P=25-0.8Q and assume that marginal and average cost are characterized by: MC = 25-1.2Q AC = 25 - 0.6 Q Suppose that there are 20 consumers, and that demand exceeds marginal cost there, so that: emax =20 (If you like, imagine Q indexing thousands of consumers.) a) [3 points] With the initial price P = 10, what is the initial quantity of insurance sold to employees? What are the average and marginal costs at that quantity? Show your work. b) [8 points: 0.5 each for 16 new numbers] Under the assumption that the employee sets the price in each year equal to last year's average cost, use a spreadsheet to work through what P, Q, AC, and MC are for years T = 1, 2, 3, 4, and 5. (I have filled in the first entry in the first column, which is the price in part (a). Your other answers for T2 will be messy decimals. I would use a spreadsheet, and then at the end, round answers to the nearest hundredth.) MC AC T=1 T=2 10.00 T=3 T=4 T=5 Recall that the welfare loss in a given year is the area below the demand curve and above the marginal cost curve, measured over the slice extending from the equilibrium quantity Q to Qmax- When these "curves" are linear, it is the area of a trapezoid, which you can calculate as the average willingness to pay (the average of the two levels on the demand curve) minus the average marginal cost, times Qmax - Q. Note that Qmax = 20. c) [6 points: 5 numbers and 1 statement] Compute the welfare loss from adverse selection in the market for each year. Is this welfare loss increasing or decreasing over time? Welfare loss AWelfare loss T=1 T=2 T=3 T=4 T=5 d) [2 points] Assume that after T = 5, the employer realizes that adverse selection is creating a death spiral for the plan and decides to mandate that all employees buy insurance. However, its mandate is only partially effective, so that the top 90% of people in terms of value of insurance actually buy, and the bottom 10% in terms of value find a way to avoid the mandate (despite the fact that their social value from insurance is positive). What is the welfare impact of the mandate moving from T = 5 to T = 6? Report a number as well as a sign. Insurance plan death spiral. A large employer provides insurance to employees and charges them any premium it chooses. However, the employer must try to cover the expected medical expenditures of those who it insures. The employer offers one insurance contract to all employees, and charges them an initial premium at time T = 1 equal to P = 10. After T = 1, for all subsequent periods the employer charges employees a premium that equals the average cost of the people who buy insurance in the previous year. Think about the graphical framework for adverse selection we studied in Class 6. Assume that consumer demand is characterized by: P=25-0.8Q and assume that marginal and average cost are characterized by: MC = 25-1.2Q AC = 25 - 0.6 Q Suppose that there are 20 consumers, and that demand exceeds marginal cost there, so that: emax =20 (If you like, imagine Q indexing thousands of consumers.) a) [3 points] With the initial price P = 10, what is the initial quantity of insurance sold to employees? What are the average and marginal costs at that quantity? Show your work. b) [8 points: 0.5 each for 16 new numbers] Under the assumption that the employee sets the price in each year equal to last year's average cost, use a spreadsheet to work through what P, Q, AC, and MC are for years T = 1, 2, 3, 4, and 5. (I have filled in the first entry in the first column, which is the price in part (a). Your other answers for T2 will be messy decimals. I would use a spreadsheet, and then at the end, round answers to the nearest hundredth.) MC AC T=1 T=2 10.00 T=3 T=4 T=5 Recall that the welfare loss in a given year is the area below the demand curve and above the marginal cost curve, measured over the slice extending from the equilibrium quantity Q to Qmax- When these "curves" are linear, it is the area of a trapezoid, which you can calculate as the average willingness to pay (the average of the two levels on the demand curve) minus the average marginal cost, times Qmax - Q. Note that Qmax = 20. c) [6 points: 5 numbers and 1 statement] Compute the welfare loss from adverse selection in the market for each year. Is this welfare loss increasing or decreasing over time? Welfare loss AWelfare loss T=1 T=2 T=3 T=4 T=5 d) [2 points] Assume that after T = 5, the employer realizes that adverse selection is creating a death spiral for the plan and decides to mandate that all employees buy insurance. However, its mandate is only partially effective, so that the top 90% of people in terms of value of insurance actually buy, and the bottom 10% in terms of value find a way to avoid the mandate (despite the fact that their social value from insurance is positive). What is the welfare impact of the mandate moving from T = 5 to T = 6? Report a number as well as a sign.