2. The economics of risk aversion Aa Aa Zach 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 Zach\'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, Zach\'s annual income falls to $800,000 Suppose there is a 50% chance that he will suffer a serious injury For Zach, the annual expected value of lost income due to injuries is The following table shows Zach\'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) 2,800 4,200 5,300 6,200 6,900 7,500 When Zach\'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 Zach\'s utility function exhibits ($900,000), every additional dollar of income adds ($600,000) marginal utility. That is, when Zach\'s income is relatively high to utility than when his income is relatively low Suppose Zach has an opportunity to insure against the risk of serious injury. For a premium of $100,000 per year, an insurance firm offers to pay Zach the full $200,000 he stands to lose in the event of a serious injury This is an example of insurance policy
Zach earns $1,000,000 with no injury i.e. no loss and with injury the loss is $200,000. Risk of injury having probability of 0.5
Expected value of Loss= 0.5×(0)+0.5×(200,000)=100,000
When Zach \'s income increases from 600,000 to 700,000 then his additional utility for 100,000 increase is 4200-2800=1400 utils. When his income increases from 900,000 to 1,000,000 the additional utility will be 6900-6200=700 utils.
Xach\' 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 $800,000
Expected Income=0.5(1000000)+0.5(800000)=$900000
Expected utility=6200
Income with insurance when no injuries $1,000000-$100,000=$900,000 & with injuries (800,000-100,000+200,000=$900,000)
Expected income is $900,000
Expected Utility =6200 utils (from table provided)
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