Suppose Hannah is strictly risk averse with a utility function u over monetary amounts (y):

u(y)=y

Hannah is facing a risky situation: Either nothing happens to her wealth of $576 with probability 3/4 or she losses everything (so ends up with $0) with probability 1/4.

a) What is the expected payoff that Hannah is facing? Provide the numerical value.

b)What is Hannah's expected utility in this gamble? Provide the numerical value.

c) What is Hannah's certainty equivalent for the gamble? Provide the numerical value.

d) Suppose Hannah can purchase insurance for 25 cents per dollar of coverage to insure herself against the bad outcome in the gamble. Check all correct statements.

1) 25 cents per dollar of coverage is not the actuarially fair premium.

2) The probability of the bad state is the same as the insurance premium per dollar of coverage.

3) Hannah would never buy insurance at such a premium.

4) The insurance premium of 25 cents per dollar of coverage is actuarially fair.

e)Suppose Hannah purchases full coverage (i.e. $576 worth of coverage) from the insurance company. Check all correct statements.

1) With full coverage Hannah faces the same amount of money in both states of the world.

2) With full coverage Hannah would be worse off than without insurance.

3) Hannah would pay the insurance company $144.

4) Hannah would pay the insurance company $576.

5) Hannah would pay the insurance company $432.

f) What is the optimal amount of coverage that Hannah will purchase at a premium of 25 cents per dollar of coverage? Provide the numerical value.

g)What is Hannah's expected utility if she purchases full coverage at 25 cents per dollar of coverage? Use two decimals in your numerical answer.

h)Suppose the insurance premium per dollar of coverage is no longer 25 cents, but 50 cents. Check all the correct statements.

a) Hannah would still purchase full coverage.

b)Hannah would purchase less than full coverage.

c)Hannah is better off choosing a coverage of $500 than full coverage.

d)Hannah is better off purchasing no insurance than full coverage.

e)Hannah is better off choosing a coverage of $500 than $300.

f)Hannah is better off choosing a coverage of $300 than no insurance.

g)Hannah is better off choosing a coverage of $500 than no insurance.

i)Suppose we depict Hannah's insurance problem in the state-contingent space with the payoffs in the good state of the world on the horizontal axis. Check all the statements that are true.

a) Hannah's indifference curves in the state-contingent space have a slope with an absolute value of 3 at the 45 degree line.

b) With an insurance premium of 50 cents per dollar of coverage Hannah's budget constraint has a slope with an absolute value of 1/2.

c) With an insurance premium of 50 cents per dollar of coverage Hannah's budget constraint has a slope with an absolute value of 1.

d) With an insurance premium of 25 cents per dollar of coverage Hannah's budget constraint has a slope with an absolute value of 1/3.

e) With an insurance premium of 25 cents per dollar of coverage Hannah's budget constraint has a slope with an absolute value of 3.

f) Hannah's indifference curve is always tangent to her budget constraint.