The probability of getting sick is 0.05-0.03x and the expenditure is 200 if being sick. Moreover, health condition x depends on effort. The relation between effort and x is x = x0 exp(e-0.5). XO is a random variable that follows uniform distribution U[0,1] and e is the effort level that can take three values: 0, 0.3 and 0.5. The private cost of effort is c(e) = 10e^2. 1. Please provide the range of XO that will optimally pay effort 0, 0.3, and 0.5 respectively when they correctly calculate their probability of being sick. 2. If we consider an insurance policy that covers the loss in full, and the premium is 6.5. Assume x0 = 0.8. (a) If buyers are risk neutral, will they purchase the policy? Given the optimal decision of whether or not to purchase the policy, what is the resulting probability of getting sick, and what is the expected medical expenditure (before insurer reimburses, if any)? (b) Is the insurer's profit positive, negative, or zero? Does there exist a premium level that satisfies the following two conditions: (1) the buyers are willing to purchase the insurance; (i) the insurer earns a nonnegative profit? Explain. (c) What contractual changes will you make to let a market exist such that the two conditions hold?

The probability of getting sick is 0.05-0.03x and the expenditure is 200 if being sick. Moreover, health condition x depends on effort. The relation between effort and x is x = x0 exp(e-0.5). XO is a random variable that follows uniform distribution U[0,1] and e is the effort level that can take three values: 0, 0.3 and 0.5. The private cost of effort is c(e) = 10e^2. 1. Please provide the range of XO that will optimally pay effort 0, 0.3, and 0.5 respectively when they correctly calculate their probability of being sick. 2. If we consider an insurance policy that covers the loss in full, and the premium is 6.5. Assume x0 = 0.8. (a) If buyers are risk neutral, will they purchase the policy? Given the optimal decision of whether or not to purchase the policy, what is the resulting probability of getting sick, and what is the expected medical expenditure (before insurer reimburses, if any)? (b) Is the insurer's profit positive, negative, or zero? Does there exist a premium level that satisfies the following two conditions: (1) the buyers are willing to purchase the insurance; (i) the insurer earns a nonnegative profit? Explain. (c) What contractual changes will you make to let a market exist such that the two conditions hold?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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