Question

1. Suppose Bob has income of $18,000. There is a 20% chance that Bob will get...

1. Suppose Bob has income of $18,000. There is a 20% chance that Bob will get sick and have to spend $10,000 of his income on a treatment. Suppose Bob’s income-utility relationship is given by:   

Where I is Bob’s income.

U(I) = square root I

Complete the table below to find Bob’s total certain utility for various levels of wealth, along his marginal utility associated with increases in his wealth.

Wealth

Certain Utility

Marginal Utility = change in utility per extra $2,000

0

0.0

2000

44.7

22.36

4000

63.2

9.26

6000

77.5

8000

89.4

10000

100

12000

109.5

14000

118.3

16000

126.5

18000

134.2

20000

141.42

22000

148.3

a. What is Bob’s expected income, given that he faces a chance of illness? What is the actuarially fair premium for Bob’s circumstance?

b. How happy is Bob if he doesn’t buy any insurance? (Hint: expected utility!) Compare this to how happy Bob is if he can buy insurance at the actuarially fair premium.

Homework Answers

Answer #1

a. Bob's income=$18,000

probablity of illness=0.2

probablity of being healthy=0.8

expenses during illness=$10,000

Bob's expected income=0.2*($18,000-$10,000)+0.8*($18,000)

= 0.2*$8,000+0.8*$18,000

= $1,600+$14,400

=$16,000

Acturially fair premium=0.2*$10,000=$2,000

b. Bob's expected utility with insurance=0.2 sqrt18000-2000 +0.8sqrt18000

=0.2* sqrt16000 + 0.8sqrt18000

=0.2*126.5+0.8*134.2=132.66

Bob's expected utility with no insurance=0.2*sqrt8000 + 0.8sqrt18000

=0.2*89.4+0.8*134.2

=125.24

As Bob's expected utility is more when he takes insurance of fair premium so, he should take insurance policy.

thanx

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
6. Suppose Bob has an income of $500, the price of a bike bell is $2,...
6. Suppose Bob has an income of $500, the price of a bike bell is $2, and the price of bike light is $100. Which of the following bundles is in Bob’s opportunity set? A) 50 bike bells, five bike lights B) 200 bike bells, two bike lights C) 100 bike bells, one bike lights D) 150 bike bells, three bike lights 7. Suppose Bob and Rob consume e-bikes and scooters. Bob and Rob face the same prices and both...
Suppose that an economist has a utility function U = (Income)0.25. Her income is $65K a...
Suppose that an economist has a utility function U = (Income)0.25. Her income is $65K a year, but there is a 10 percent chance of becoming ill and making only $57K. (a) What is her expected utility if she does not have insurance? (b) What is the actuarially fair insurance premium? (c) How much is she willing to pay for insurance?
Suppose that Elizabeth has a utility function U= (or U=W^(1/3) ) where W is her wealth...
Suppose that Elizabeth has a utility function U= (or U=W^(1/3) ) where W is her wealth and U is the utility that she gains from wealth. Her initial wealth is $1000 and she faces a 25% probability of illness. If the illness happens, it would cost her $875 to cure it. What is Elizabeth’s marginal utility when she is well? And when she is sick? Is she risk-averse or risk-loving? What is her expected wealth with no insurance? What is...
8. Suppose Bob consumes e-bikes and scooters. If Bob’s income and prices of both goods increase...
8. Suppose Bob consumes e-bikes and scooters. If Bob’s income and prices of both goods increase by the same percentage, A) Bob will buy more of both goods. B) Bob will buy more of both goods if they are both normal goods. C) Bob will buy less of both goods if they are both inferior goods. D) Bob’s utility maximizing bundle stays the same. 9. Suppose Bob spends his entire income on e-bikes and scooters. Every month he spends half...
Suppose that your utility function is U = √ I where I is the amount of...
Suppose that your utility function is U = √ I where I is the amount of income you make per month. Suppose that you typically make $8,100 per month, but there is a 5 percent chance that, in the next month, you will get sick and lose $3,200 in income. (a) What is your expected utility if you do not have health insurance to protect against this adverse event? [1 mark] (b) Suppose you can buy insurance that will fully...
4) Jack’s income is $16,900. There is a 30% chance Jack will get sick during the...
4) Jack’s income is $16,900. There is a 30% chance Jack will get sick during the next year. If Jack gets sick, he will incur a loss of $4,800. His utility function is U(I)=I0.5 (that is, utility equals the square root of Income). (4 pts) a) What is Jack’s expected income? b) What is Jack’s expected loss? c) What is Jack’s expected utility? d) What is the maximum amount of money Jack is willing to pay for insurance? What is...
1. Suppose that John has an income of $50,000 when healthy. If he falls sick, he...
1. Suppose that John has an income of $50,000 when healthy. If he falls sick, he has to pay $10,000 to cover his medical bills. There is a 40% probability that John will become sick. a. Calculate John’s expected income E (I). b. Suppose that John’s utility function is: U(I) = ln (I). Calculate John’s expected utility of income E (U(I)). c. Calculate the utility of John’s expected income U (E (I)). Compare this value to your answer in (b)....
Bob, age 60 and single, has recently retired from IBM. He has $690,000 available in his...
Bob, age 60 and single, has recently retired from IBM. He has $690,000 available in his 401(k) fund and he is thinking of using that money to open a used car business that will be located at 210 Ocean View Drive in Pensacola, Florida. Bob has estimated that the business might make $300,000 in taxable income.  Bob’s personal wealth including investments in land, stocks, and bonds is about $14,000,000. He reported an interest income of $20,000 and dividend income of $6,000...
What role could the governance of ethics have played if it had been in existence in...
What role could the governance of ethics have played if it had been in existence in the organization? Assess the leadership of Enron from an ethical perspective. THE FALL OF ENRON: A STAKEHOLDER FAILURE Once upon a time, there was a gleaming headquarters office tower in Houston, with a giant tilted "£"' in front, slowly revolving in the Texas sun. The Enron Corporation, which once ranked among the top Fortune 500 companies, collapsed in 2001 under a mountain of debt...
Discuss ethical issues that can be identified in this case and the mode of managing ethics...
Discuss ethical issues that can be identified in this case and the mode of managing ethics Enron finds itself in this case. How would you describe the ethical culture and levels of trust at Enron? Provide reasons for your assessment. THE FALL OF ENRON: A STAKEHOLDER FAILURE Once upon a time, there was a gleaming headquarters office tower in Houston, with a giant tilted "£"' in front, slowly revolving in the Texas sun. The Enron Corporation, which once ranked among...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT