Stan is a martial arts expert who chose a career as a stunt double in action mov

Question

Stan is a martial arts expert who chose a career as a stunt double in action movies. If he remains healthy and is able to work in enough movies, he earns an annual income of $1,000,000. However, the nature of Stan's work is very risky. He can work with bumps and bruises, but a serious injury puts him out of work. In the event of a serious injury, Stan's annual income falls to $600,000. Suppose there is a 25% chance that he will suffer a serious injury For Stan, the annual expected value of lost income due to injuries is The following table shows Stan's total utility at various levels of income. Income Total Utility 600,000 700,000 800,000 900,000 1,000,000 1,100,000 (Utils) 300 500 650 750 820 870 When Stan's income rises from $600,000 to $700,000, his additional, or marginal, utility from the $100,000 increase is utils, and when his income rises from $900,000 to $1,000,000, his additional, or marginal, utility is utils

Explanation / Answer

Solution:-

Stan’s earns $1,000,000 with no injury i.e. no loss and with injury the loss is $400,000. Risk of injury having probability of 0.25

Expected value of Loss= 0.25 × (0) + 0.25 × (400,000) = 100,000

When Stan’s income increases from 600,000 to 700,000 then his additional utility for 100,000 increase is 500-300=200 units. When his income increases from 900,000 to 1,000,000 the additional utility will be 820-750=70 units.

Stan’s utility shows Diminishing Marginal Utility. For higher income, each dollar adds less utility than that of lower income such as $600,000.

Income without insurance when no injuries $1,000,000 & when injuries $600,000

Expected Income=0.25(1000000) + 0.75(600000) =$700000

Expected utility=500

Income with insurance when no injuries $1, 000000-$100,000=$900,000 & with injuries (600,000-100,000+400,000=$9, 00,000)

Expected income is $9, 00,000

Expected Utility =750 Utility (from table provided)

She would accept the insurance company's offer.

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