2. The economics of risk aversion

Valerie is a martial arts expert who chose a career as a stunt double in action movies. If she remains healthy and is able to work in enough movies, she earns an annual income of $1,000,000. However, the nature of Valerie's work is very risky. She can work with bumps and bruises, but a serious injury puts her out of work. In the event of a serious injury, Valerie's annual income falls to $600,000.

Suppose there is a 75% chance that she will suffer a serious injury.

For Valerie, the annual expected value oflostincome due to injuries is.

The following table shows Valerie's total utility at various levels of income.

IncomeTotal Utility(Dollars)(Utils)600,00080700,000280800,000440900,0005601,000,0006601,100,000740

When Valerie's income rises from $600,000 to $700,000, her additional, or marginal, utility from the $100,000 increase isutils, and when her income rises from $900,000 to $1,000,000, her additional, or marginal, utility isutils.

Valerie's utility function exhibits diminishing marginal utility. That is, when Valerie's income is relatively low ($600,000), every additional dollar of income adds more to utility than when her income is relatively high ($900,000).

Suppose Valerie has an opportunity to insure against the risk of serious injury. For a premium of $300,000 per year, an insurance firm offers to pay Valerie the full $400,000 she stands to lose in the event of a serious injury.

This is an example of a better-than-fair/Unfair/Fairinsurance policy.

Fill in the following table to determine whether Valerie should accept the offer.

Income in Different States of the World

Expected IncomeExpected Utility(Dollars)(Dollars)(Dollars)(Utils)No InjuriesSerious Injury0.25 probability0.75 probabilityWithout insuranceWith insurance

Assuming Valerie wants to maximize her expected utility, she should accept the insurance company's offer.