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 0.1, and no loss with probability 0.9. 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

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 0.1, and no loss with probability 0.9. 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

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter19: The Problem Of Adverse Selection

Section: Chapter Questions

Problem 7MC

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Suppose that left-handed people are more prone to injury than right-handed people. Lefties have an 80 percent chance of suffering an injury leading to a $1,000 loss (in terms of medical expenses and the monetary equivalent of pain and suffering) but righties have only a 20 percent chance of suffering such an injury. The population contains equal numbers of lefties and righties. Individuals all have logarithmic utility-of-wealth functions and initial wealth of $10,000. Assume perfectly competitive insurance market and find (i) the first best and (ii) the second-best contracts.
Draw a graph with utility on the Y axis and income on the X axis for a risk averse person. Label the following points on the Y axis The expected value of utility while uninsured The expected value of utility with actuarially fair, full insurance The expected value of utility with actuarially far, partial insurance
Explain how risk aversion makes a market for insurance possible
Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = square root x . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain
. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) √x . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.
You are a risk-averse investor with a CRRA utility function. You are faced with the decision to invest your total wealth W of £1,000,000 into a riskless asset which generates a return of 5% or into a risky asset which either generates a return of 20% or a loss of −4% with equal probability. Find the optimal investment allocation with a coefficient of relative risk aversion η=2, and comment on your results.
Show that an agent with utility function u(x) = log x is more risk aversethan an agent with utility function ˜u(x) = √x.
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?
Indicate whether the statement is true or false, and justify your answer.Risk-averse individuals have a concave value function for prospective gains and a convex value function for prospective losses.
Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematically
If a risk‐neutral individual owns a home worth $200,000 and there is a three percent chance the home will be destroyed by fire in the next year, then we know that:a) He is willing to pay much more than $6,000 for full cover.b) He is willing to pay much less than $6,000 for full cover.c) He is willing to pay at most $6,000 for full cover.d) None of the above are correct.e) All of the above are correct.
Which of the following statements is FALSE regarding the concept of "adverse selection"? Multiple Choice Adverse selection describes a situation where an individual's demand for insurance is positively correlated with the individual's risk of loss. Adverse selection occurs when someone increases their exposure to risk when insured. This can happen, for example, when a person takes more risks because someone else bears the cost of those risks. The relationship between smoking status and mortality provides a good illustration for adverse selection, especially in the case in which a life insurance company did not vary its premiums according to smoking status of its customers. To counter the effects of adverse selection, insurers may offer premiums that are proportional to a customer's risk.