The employer offers one insurance contract to all employees, and charges them an initial premium at time 𝑇 = 1 equal to

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The employer offers one insurance contract to all employees, andcharges them an initial premium at time 𝑇 = 1 equal to 𝑃 = 10.After 𝑇 = 1, for all subsequent periods the employer chargesemployees a premium that equals the average cost of the people whobuy insurance in the previous year. Think about the graphicalframework for adverse selection we studied in Class 6. Assume thatconsumer demand is characterized by:𝑃 = 25 ― 0.8 𝑄and assume that marginal and average cost are characterizedby:𝑀𝐶 = 25 ― 1.2 𝑄𝐴𝐶 = 25 ― 0.6 𝑄Suppose that there are 20 consumers, and that demand exceedsmarginal cost there, so that:𝑄𝑚𝑎𝑥 = 20(If you like, imagine Q indexing thousands of consumers.)
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The Employer Offers One Insurance Contract To All Employees And Charges Them An Initial Premium At Time T 1 Equal To 1 (121.44 KiB) Viewed 10 times

The Employer Offers One Insurance Contract To All Employees And Charges Them An Initial Premium At Time T 1 Equal To 2 (53.24 KiB) Viewed 10 times

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 T≥ 2 will be messy decimals. I would use a spreadsheet, and then at the end, round answers to the nearest hundredth.) P Q MC AC T=1 10.00 Welfare loss AWelfare loss T=2 T=1 T=3 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? T=2 T=4 T=3 T=5 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.