Little Bo Peep owns property worth $325,000, which is subject to wind damage. He has no other wealth. The probability of wind damage is 5%, and the amount of damage from windstorm is $130,000. Little Bo Peep’s utility function is the square root utility function: U(w) = sqrt(w)

a. The insurance company offers the menu of contracts below. Are they priced at their actuarially fair value? If not, what is the loading on the contracts?

Deductible	Premium
0	7050
500	7020
1000	6990
2000	6935

b.  Suppose insurance were compulsory. Which contract would Little Bo Peep choose?

c.  If insurance were not compulsory, would she purchase insurance? Why or why not?

d.  What is the maximum amount that Little Bo Peep is willing to pay for full insurance? What is her risk premium?

Consider now a population of 2 types of individuals with square root utility function as defined above:

Group	Prob. of loss	Initial wealth	Size of loss	Proportion of the Population
Low Risk	0.04	325,000	130,000	90%
High Risk	0.08	325,000	130,000	10%

Suppose insurance was compulsory – that is both low risk and high risk insureds had to purchase insurance. Insurers offer a menu of pooling contracts with the same deductibles as in part a), but do not charge any loadings (insurance is priced at its actuarially fair value).

e.  What would be the premium charged for each of the 4 different deductible offerings?

f.  Calculate the utilities that would be earned by the high risk and the low risk insureds for each of the 4 contracts.

g. What contract would the low risks prefer?

h. What contract would the high risks prefer?

i.  If insurance were not compulsory and insurers could not differentiate between risk types, would insurers offer these pooling contracts in equilibrium? If not, what contract(s) would they offer?

j.  If the insurer wanted to offer 2 contracts that would cause the insureds to signal their risk types, what are the two contracts that could exist in equilibrium? Assume that insurers do not charge any loadings.

k.  Would low risk insured prefer a separating contract, a pooled insurance contract or no insurance? Provide support for your answer.

Answer rating: 100% (QA)

a No the contracts are not priced at their actuarially fair value The loading on the contracts is calculated as follows Deductible Premium Loading 0 7... View the full answer