Health Economics
14th Edition
ISBN: 9781137029966
Author: Jay Bhattacharya
Publisher: SPRINGER NATURE CUSTOMER SERVICE
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Question
Chapter 7, Problem 10AP
(a)
To determine
Determine the Utility function (U-I).
(b)
To determine
Describe the relationship between risk aversion and
(c)
To determine
Determine whether the given statement is true or false.
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Anita bought a new scooter for $500. She is deciding whether she should insureher scooter against theft. She has recently read in the news that one out of 10 scooters arestolen in her town. She can buy scooter theft insurance at the price of 12 cents per $1 ofinsurance. How much insurance will Anita buy if her utility function is U(C) = 2C + 100?
Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U’ > 0) and convex (U” > 0).
Draw a utility function in U - I space that fits this description.
Explain the connection between U” and risk aversion.
True or false: this individual prefers no insurance to an actuarially fair, full contract. Be sure to explain your answer.
. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000.
a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.
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- Suppose a company offers a standard insurance contract with a premium (r) of $2,000 and a payout (q) of $10,000. Suppose that Adelia earns a healthy state income of $70,000, a sick state income of $50,000, and has a 20% chance of becoming ill. For Adelia, this insurance contract would be: A. actuarially fair and partial B. actuarially fair and full C. actuarially unfair and full D. actuarially unfair and partialarrow_forward5) A person with a current wealth of $100,000 who faces the prospect of 25 percent chance of losing his or her $20,000 automobile through theft during the next year. Suppose this person's utility function is U(Y) = InY. a). If this person takes no action, what is the expected utility? b). What is the actuarially fair premium? What is his expected utility if he purchase this insurance. c). Suppose that now the insurance company provides a new type of insurance. This insurance costs $4900 and requires the individual to incur the first $1000 of the loss from theft would yield. That is expected utility of this new insurance? Will the person choose the insurance in b) or c)?arrow_forwardTess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function c. Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. 1. Suppose the actuarially fair premium charge is 2600, Calculate Tess’ expected utility with full insurance if she is charged the premium. Round to two decimal places. 2. What is the premium that private insurance companies will charge for full insurance? Round to two decimal places. 3.Assume the social welfare function is the sum of the Tess’ and Lex’s utility functions. Select the correct statement regarding the explanation for what has happened in the private market and the role of social insurance. a.Adverse section has lead to market failure. The government could improve social welfare by…arrow_forward
- Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 Suppose that insurance companies do not know specific probabilities of adverse events for Tess or Lex, but do know the average probability of an adverse event. If they assumed that both Tess and Lex purchase full insurance, what is the actuarially fair premium charged? Round to two decimal placesarrow_forwardConsider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U’ > 0) and convex (U’’ > 0). a) Draw a utility function in U - I space that fits this description. b) Explain the connection between U’’ and risk aversion.arrow_forwardIn the summer of 1984, Nicholai opened a small art gallery in the West Village and amassed a collection worth $2,60,000. An insurance company figured there was a 5% chance the collection would be destroyed and worth $0. Nicholai has utility u(x) = x0.5. If Nicholai purchases full insurance at a fair price, his expected utility would be ___. while if he declines the insurance he would face an expected utility of а. 1,487.5; 1,531.8 b. 1,487.5; 1,444.9 с. 1,571.6;B 1,531.8 d. 1,571.6; 1,444.9arrow_forward
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