A stuntman's probability of becoming disabled is equal to 0.4. If he becomes disabled, then earnings will be equal to 100. If he is not disabled, his earnings will be equal to 200. Assume the individual has utility equal to U = ln Y, where Y is earnings.

a. Assuming that the person cannot purchase insurance, write down the expression for this person's expected utility.

b. Now assume that the person can purchase insurance at a price of $qper dollar of insurance. Write down the expression for expected utility assuming that this person purchases $X of insurance.

c. Solve for this person's optimal level of insurance (i.e., solve for X) assuming that q = 0.5.

d. Does the individual fully insure? Why?