Shalini’s vNM utility for money is u(x) = x1/2, where x is her final wealth level. She currently has $1600 and is uninsured. When she drives her car she faces the following gamble. With 90% probability she will not get into an accident, and with 10% probability she will get into an accident and incur $1500 in auto damages. What is the maximum amount she would be willing to pay for an insurance policy that completely covers any auto damages?

Shalini

The maximum amount that she would be willing to pay for an insurance policy that completely covers any auto damages is:

= $150.

Step-by-step explanation:

Utility for money, u(x) = x1/2

x, her final wealth level = $1,600

Loss from accident

Probability     Loss incurred    Expected Loss

90%                  $0                            $0 (90% * $0)

10%                   $1,500                 $150 (10% * $1,500)

100%                                             $150

b) The amount that Shalini would be willing to pay for an insurance policy for all auto damages is limited to her expected loss from auto damages.  Since she has a 90% chance of not being involved in an accident, her expected loss will be reduced to $150.  This represents 10% of the loss from damages that she would incur if she was involved in an accident, which is 10% probable.