Question

Assume that Wonku drives a car carrying a market value of $10,000. The only other asset he owns is the $3,000 in his checking account. Thus, he has a total initial wealth of $13,000. If he drives carefully, he incurs a cost of $3,000.

Assume he faces the following loss distributions when he drives with or without care.

Drives with care		Drives without care
Probability	Loss	Probability	Loss
0.25	10000	0.75	10000
0.75	0		0

Now, when he has an accident, his car is a total loss. Wonku’s problem has four parts: whether to drive with or without care, when i) he has no insurance; and ii) when he has insurance. Assume that the insurance company has a premium of $2875. Will Wonku switch to driving without care after purchasing insurance? At what level of premiums will Wonku become indifferent between driving with or without care? Assume Wonku’s utility of wealth is given by U(W) = 20 + .

(PLEASE TYPED NOT HANDWRITTEN!)

Answer 1

Explanation:-

Drives with care	Drives without care
Probability loss	probability loss
0.25 10,000	0.75 10,000
0.75 0	0.25 0
E(loss)=0.2510,000=2500	E(loss)=0.7510,000=7500

Wokus intial wealth i.e W=13,000

cost of driver with care =3000

1. If wonkus has insurance ,

W = 10,125 (13,000-2875)

Under drive with care ,

E(W) =10,125-3000

=7,125

Under drive without care,

E(W) = 10,125

from the above, it is clearly that wonkus prefers to drive without car.

2. If wonkus doesnot have insurance

Under drive with care,

E(W) = 13,000-3000-2500

=7500

   Under drive without care,

E(W) = 13,000-7500

= 5500

Clearly wonkus prefers to drive with care.

If you have any dought about thus answer dont give dislike ,tell us your dought in the comment then i can explain, Please rate me by giving me a like or thumb because it motivates me to do more work,Thank you.