John is deciding whether to exert effort (e = 1) to avoid an accident at work or not exert any effort (e = 0). If e1, the probability of an accident is 0.5. If e = 0, the probability of an accident is 1. John's income without the accident is $100. In case of an accident, medical expenses will be $64. John utility of income is VI. The cost of effort, C(e), is 0 if effort is e = 0 and 1 if effort is e = 1. John's utility function is u(I, e) = √-C(e). (a) What are the expected utility values that John would face when he exerts effort and when he does not exert effort? Based on your calculations, should he exert effort? Briefly explain the intuition behind his decision in one or two sentences. Now suppose there is a risk neutral insurance company. Suppose the insurance company cannot monitor whether John exerts effort or not. The insurance company considers two plan contracts. • Contract Plan A: о Premium: p = $36. ○ • Payout in the event of accident: d = $64 Contract Plan B: Premium: p $19. Payout in the event of accident: d = $32 (b) For each plan contract, calculate John's final income in the event of no accident and in the event of an accident occurs. It might be useful to list them in a table like this: Plan Contract Ino accident Iaccident A B Which contract that provide consumption smoothing across two possible states of the world. In other words, which contract provides the best overall insurance to John? (c) For each of these contracts, determine which of the two effort levels, e = 0 or e = 1, would be expected utility maximizing for John if he decides to enroll in the plan contract. Assume that, if both effort levels yield the same expected utility, John will opt into effort level e = 1. Briefly
John is deciding whether to exert effort (e = 1) to avoid an accident at work or not exert any effort (e = 0). If e1, the probability of an accident is 0.5. If e = 0, the probability of an accident is 1. John's income without the accident is $100. In case of an accident, medical expenses will be $64. John utility of income is VI. The cost of effort, C(e), is 0 if effort is e = 0 and 1 if effort is e = 1. John's utility function is u(I, e) = √-C(e). (a) What are the expected utility values that John would face when he exerts effort and when he does not exert effort? Based on your calculations, should he exert effort? Briefly explain the intuition behind his decision in one or two sentences. Now suppose there is a risk neutral insurance company. Suppose the insurance company cannot monitor whether John exerts effort or not. The insurance company considers two plan contracts. • Contract Plan A: о Premium: p = $36. ○ • Payout in the event of accident: d = $64 Contract Plan B: Premium: p $19. Payout in the event of accident: d = $32 (b) For each plan contract, calculate John's final income in the event of no accident and in the event of an accident occurs. It might be useful to list them in a table like this: Plan Contract Ino accident Iaccident A B Which contract that provide consumption smoothing across two possible states of the world. In other words, which contract provides the best overall insurance to John? (c) For each of these contracts, determine which of the two effort levels, e = 0 or e = 1, would be expected utility maximizing for John if he decides to enroll in the plan contract. Assume that, if both effort levels yield the same expected utility, John will opt into effort level e = 1. Briefly
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:John is deciding whether to exert effort (e = 1) to avoid an accident at work or not exert any effort (e =
0). If e = 1, the probability of an accident is 0.5. If e = 0, the probability of an accident is 1. John's
income without the accident is $100. In case of an accident, medical expenses will be $64. John utility of
income is VI. The cost of effort, C(e), is 0 if effort is e = 0 and 1 if effort is e =
is u(1, e) = VI – C(e).
1. John's utility function
(a) What are the expected utility values that John would face when he exerts effort and when he
does not exert effort? Based on your calculations, should he exert effort? Briefly explain the
intuition behind his decision in one or two sentences.
Now suppose there is a risk neutral insurance company. Suppose the insurance company cannot
monitor whether John exerts effort or not. The insurance company considers two plan contracts.
Contract Plan A:
Premium: p = $36.
Payout in the event of accident: d = $64
Contract Plan B:
Premium: p = $19.
Payout in the event of accident: d = $32
(b) For each plan contract, calculate John's final income in the event of no accident and in the event
of an accident occurs. It might be useful to list them in a table like this:
Plan Contract
Ino accident
Iaccident
А
В
Which contract that provide consumption smoothing across two possible states of the world. In
other words, which contract provides the best overall insurance to John?
(c) For each of these contracts, determine which of the two effort levels, e = 0 or e = 1, would be
expected utility maximizing for John if he decides to enroll in the plan contract. Assume that, if
both effort levels yield the same expected utility, John will opt into effort level e = 1. Briefly
relate vour answer to the concept of moral hazard.
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