Consider the model of competitive insurance. Peter is a risk averse individual with the utility function u(w) = w0.5. His current wealth is $300 and with probability 1/2 he will incur a loss of D = $240, but with probability 1/2 he will incur no loss. Ann has the same utility u(w) = w0.5 and current wealth $300 as Peter, but a different probability of loss: she will incur a loss of D = $240 with probability 0.3, and no loss with probability 0.7. In the separating equilibrium Peter is offered actuarially fair full insurance contract, so his wealth is equal to $180, whether loss happens or not. What amount of insurance (approximately) will Ann be offered an insurance contract with?

Consider the model of competitive insurance. Peter is a risk averse individual with the utility function u(w) = w0.5. His current wealth is $300 and with probability 1/2 he will incur a loss of D = $240, but with probability 1/2 he will incur no loss. Ann has the same utility u(w) = w0.5 and current wealth $300 as Peter, but a different probability of loss: she will incur a loss of D = $240 with probability 0.3, and no loss with probability 0.7. In the separating equilibrium Peter is offered actuarially fair full insurance contract, so his wealth is equal to $180, whether loss happens or not. What amount of insurance (approximately) will Ann be offered an insurance contract with?

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter19: The Basic Tools Of Finance

Section19.2: Managing Risk

Problem 2QQ

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Consider the model of competitive insurance discussed in lectures (Topic 6.7). Peter is a risk averse individual with the utility function u(w) = w0.5. His current wealth is $300 and with probability 1/2 he will incur a loss of D = $240, but with probability 1/2 he will incur no loss. Ann has the same utility u(w) = w0.5 and current wealth $300 as Peter, but a different probability of loss: she will incur a loss of D = $240 with probability 0.3, and no loss with probability 0.7. As we showed in lectures, in the separating equilibrium Peter is offered actuarially fair full insurance contract, so his wealth is equal to $180, whether loss happens or not. Ann will be offered an insurance contract with the amount of insurance (approximately) equal to 0 O 18 38 O 58 O 120 O 240
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