Consider a worker, Janice, who has the option to purchase DI (disability insurance) on the private market. Janice becomes disabled with probability q=0.01. She can purchase DI by paying the premium p. If the Janice is disabled, she will earn no income. But if she is insured, she will receive a total payment of $15,000 from the insurance company (her consumption will be $15,000). If the Janice is not disabled, she earns an income of $20,000. She has utility: U = 3C where C is the amount of consumption. Determine the actuarially fair insurance premium, p*. Write down the expected utility function for Janice if she purchases insurance at the actuarially fair price.
Consider a worker, Janice, who has the option to purchase DI (disability insurance) on the private market. Janice becomes disabled with probability q=0.01. She can purchase DI by paying the premium p. If the Janice is disabled, she will earn no income. But if she is insured, she will receive a total payment of $15,000 from the insurance company (her consumption will be $15,000). If the Janice is not disabled, she earns an income of $20,000. She has utility: U = 3C where C is the amount of consumption. Determine the actuarially fair insurance premium, p*. Write down the expected utility function for Janice if she purchases insurance at the actuarially fair price.
Chapter5: Gross Income: Exclusions
Section: Chapter Questions
Problem 12DQ
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Transcribed Image Text:Consider a worker, Janice, who has the option to purchase DI (disability insurance) on the private
market. Janice becomes disabled with probability q = 0.01. She can purchase DI by paying the premium
р.
If the Janice is disabled, she will earn no income. But if she is insured, she will receive a total payment of
$15,000 from the insurance company (her consumption will be $15,000).
If the Janice is not disabled, she earns an income of $20,000.
She has utility: U = 3C3 where C is the amount of consumption.
Determine the actuarially fair insurance premium, p".
Write down the expected utility function for Janice if she purchases insurance at the actuarially
fair price.
Will Janice choose to purchase this disability insurance? Explain.
What is the most she would be willing to pay for DI insurance?
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