1. There are two types of drivers on the road today. Speedy Racers have a 5% chance of causing an accident per year, while those Low Riders have a 1% chance of causing an accident per year. There are the same number of Speed Racers as there are Low Riders. The cost of an accident is $12,000.
a. Suppose an insurance company knows with certainty each driver's type. What premium would the insurance company charge each type of driver?
b. Now suppose that there is asymmetric information, so the insurance company does not know with certainty each driver's type. Would insurance be sold if
i. drivers self-reported their types to the insurance companies?
ii. no information at all is known about individual driver types?
If you are uncertain whether insurance would be sold, explain why.
2. Your utility function is U = log(3C) where C is the amount of consumption that you have in any given period. Your income is $60,000 per year and there is a 4% change that you will be involved in a bad accident that will cost you $40,000 next year.
a. What is your expected utility? Include a sketch in your answer.
b. Calculate an actuarially fair insurance premium. What would be your expected utility if your purchased the actuarially fair premium?
c. What is the most that you would be willing to pay for insurance, given your utility function?
3. A middle-income worker will retire in January 2014. In the year prior to retirement, her gross monthly earnings are $4,500. Her Social Security pension benefit is $1,500 per month. Prior to retirement, she was subject to total taxes on her labor earnings amounting to 20 percent.
a. Calculate her gross and net-of-tax replacement rates following retirement.
b. Suppose the cash value of Medicare subsidies that she expects to receive during retirement amount to $4,000 per year. Recalculate the replacement rates including Medicare.
4. Using the bend points in Figure 13-1 of our text, calculate the Primary Insurance Amount and Gross Replacement Rates for the following workers/families at age 67 (spouse, if any, is also 67):
a. Unmarried worker with AIME = $2300.00
b. Married worker (non-working spouse) with AIME = $2300.00.
c. Non-working widow of worker with AIME = $2300.00
d. Married worker with AIME of $2300.00 with working spouse. Spouse's AIME is $1,500.00
e. What extra Social Security benefits did the spouse in "d" above earn by working?
f. Divorced (former) spouse of deceased worker with AIME = $2,300. They had been been married 15 years.
5. We are going to use the Social Security Administration's benefit calculator to estimate SS benefits for various individuals. Go to https://www.ssa.gov/planners/benefitcalculators.htm. We will use the "Quick" calculator.
a. Estimate the benefits in today's dollars for a worker born 1/1/91 whose earnings in the current year are $35,000. Do not specify a retirement age, and use today's dollars. What monthly benefit is available for this worker at his/her normal retirement age? Early retirement age?
b. Estimate the benefits in today's dollars for a worker born 1/1/91 whose earnings in the current year are $60,000. What monthly benefit is available for this worker at his/her normal retirement age? Early retirement age?
c. Estimate the benefits in today's dollars for a worker born 1/1/60 whose earnings in the current year are $260,000. What would the spouse receive upon the worker's death if the spouse is not yet of retirement age but is caring for a child? Upon retirement age? What is the family maximum?