The Economics of Risk Aversion 1. The economics of risk aversion Aa Aa Juanita i

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The Economics of Risk Aversion

1. The economics of risk aversion Aa Aa Juanita 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 $800,000. However, the nature of Juanita'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, Juanita's annual income falls to $400,000 Suppose there is a 75% chance that she will suffer a serious injury For Juanita, the annual expected value of lost income due to injuries is The following table shows Juanita's total utility at various levels of income Income Total Utility 400,000 500,000 600,000 700,000 800,000 900,000 (Utils) 3,700 5,000 6,000 6,700 7,200 7,600 When Juanita's income rises from $400,000 to $500,000, her additional, or marginal, utility from the $100,000 increase is utility is utils, and when her income rises from $700,000 to $800,000, her additional, or marginal, utils marginal utility. That is, when Juanita's income is relatively high Juanita's utility function exhibits ($900,000), every additional dollar of income adds ($600,000) to utility than when her income is relatively low

Explanation / Answer

For Juanita, the annual expected value of lost income due to injuries is = 75% x (800000 - 400000) = $300000

When Juanita's income rises from $400000 to $500000, her additional utility from the $100000 increase is = 5000 - 3700 = 1300 utils, and when her income rises from $700000 to $800000, her additional utility is = 7200 - 6700 = 500 utils.

Juanita's utility function exhibits diminishing marginal utility. That is, when Juanita's income is relatively high, every additional dollar of income adds less to utility than when her income is relatively low.

Premium = $300000

This is an example of actuarially fair insurance policy.

Expected utility without insurance = 7200 x 0.25 + 3700 x 0.75

She would accept the insurance company's offer.

Income ($) No injuries Serious injury Expected income ($) Expected utility (utils) Without Insurance 800000 400000 500000 4575 With insurance 500000 500000 500000 5000

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