Question

16.Suppose the utility function of Nathasha was given U(I)=(ROOT10I). Where' I' represents annual income (in $1,000).
(1)Explain whether she is risk-preferred, risk-neutral, or hedging.
(2) Let's say she has a current income of $40,000 (I=40) and is sure to make the same income next year. She has a new job. New jobs have a 0.6 chance of earning $44,000 and a 0.4 chance of earning $33,000. Should she take this job?
(3) In (2) will she try to insure against the uncertain income of the new job? If she were insured, how much would she pay (hint: how much is the risk premium)?

Answer 1

Economics

16.Suppose the utility function of Nathasha was given U(I)=(ROOT10I). Where' I' represents annual income (in $1,000).
(1)Explain whether she is risk-preferred, risk-neutral, or hedging.
(2) Let's say she has a current income of $40,000 (I=40) and is sure to make the same income next year. She has a new job. New jobs have a 0.6 chance of earning $44,000 and a 0.4 chance of earning $33,000. Should she take this job?
(3) In (2) will she try to insure against the uncertain income of the new job? If she were insured, how much would she pay (hint: how much is the risk premium)?

Ans 1)

U = Utility Function

I = Annual Function

Function

U (I) = (ROOT10I)

Ans 1) Annual Income = $1000

Utility (I)= root 10i

Value of root 10= 3.162

U (i)= 3.162 *1000

       = $3162

It means utlility of $ 1000 of her income is $ 3162 in actual. So it means she is risk prererred.

(2) Let's say she has a current income of $40,000 (I=40) and is sure to make the same income next year. She has a new job. New jobs have a 0.6 chance of earning $44,000 and a 0.4 chance of earning $33,000. Should she take this job?

Ans 2) If her income increased to $40,000 then below will be the new utlility

Case a) when Annual Income = $40000

Utility (I)= root 10i

Value of root 10= 3.162

U (i)= 3.162 *40000

       = $126,480

It means utlility of $ 40,000 is $ 126,480

Case b) when Annual Income= $44,000

Value of root 10= 3.162

U (i)= 3.162 *44000

       = $139,128

It means utlility of $ 44,000 is $ 139,128

Case c) when Annual Income= $33,000

Value of root 10= 3.162

U (i)= 3.162 *33000

       = $104,346

Above analysis show the utility as more than $100,000 so its better to take the change where possibility of getting the job is 0.6% as if she did not get it there is nothing to loose.

(3) In (2) will she try to insure against the uncertain income of the new job? If she were insured, how much would she pay (hint: how much is the risk premium)?

Ans 3- Generally insurance does not cover against definite uncertainty but with exception this risk can covered. The premium calculation is bit of complex. I will explain below

Current Income- $40,000

New income and chance of getting it – 0.6 and $44,000

New income and change of getting it- 0.4 and $33,000

So change of getting the new job is 60% and not getting it is 40% so the difference 20% so the premium to be charged is 20% of 40,000, premium payable is $8000 every year.