Suppose there is a 50-50 chance that an individual with logarithmic utility from wealth and with a current wealth of $20,000 will suffer a loss of $10,000 from a car accident. Insurance is competitively provided at actuarially fair rates.

a. Compute the outcome if the individual buys full insurance.

b. Compute the outcome if the individual buys only partial insurance covering half the loss. Show that the outcome in part (a) is preferred.

c. Now suppose that individuals who buy the partial rather than the full insurance policy take more care when driving, reducing the damage from loss from $10,000 to $7,000. What would be the actuarially fair price of the partial policy? Does the individual now prefer the full or the partial policy?