Suppose that Anu’s utility function is given by U = √10W, where W represents annual income...

Suppose that Anu’s utility function is given by U = √10W, where W represents annual income in thousands of dollars. Suppose that Anu is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. a. Should she take the new job? b. Assume Anu takes the new job. Would she be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she be willing to pay for that insurance?

Solutions

Expert Solution

If income is $40 K, utility is given by

U(40000)=(10*40)^1/2=20

If income is $44 K, utility is given by

U(44000)=(10*44)^1/2=20.9762

Probability that income is $44K =p=0.40

If income is $33 K, utility is given by

U(33000)=(10*33)^1/2=18.1659

Probability that income is $33K =1-p=1-0.40=0.60

Expected utility=p*U(44000)+(1-p)*U(33000)=0.40*20.9762+0.60*18.1659=19.2900

Utility in case of sure income of $40K =20 (we have calculated above)

We can see that expected utility is lower. Anu should not take the new job.

Variable part of income=44000-33000=11000

She may buy insurance $11000 such that expected utility is same as utility in case of sure income of $40K. Let she is willing to pay a sum of $X K for this purpose.

Expected utility if she buys insurance=U(44000-1000X)=[10(44-X)]^1/2

Which should be equal to U(40000) i..e

[10(44-X)]^1/2=20

10(44-X)=400

44-X=40

X=4

She should be winning to pay a maximum of $4000 for this insurance.

Rahul Sunny answered 1 year ago

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