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

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).

The deductible from part a) is

Deductible	Premium
0	7050
500	7020
1000	6990
2000	6935

a. (4 marks) What would be the premium charged for each of the 4 different deductible offerings?

b. (4 marks) Calculate the utilities that would be earned by the high risk and the low risk insureds for each of the 4 contracts.

c. (1 mark) What contract would the low risks prefer?

d. (1 mark) What contract would the high risks prefer?

e. (2 marks) 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?

f. (5 marks) 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.

g. (2 mark) Would low risk insured prefer a separating contract, a pooled insurance contract or no insurance? Provide support for your answer.