2. (30 points) President Obama hired you as a consultant (because he thinks your previous

work with Janet Yellen was simply outstanding). But this time, he wants you to collect the

data from 1999-2012 and plot the following figures (x-axis time, y-axis the variable of

interest). To get full credit for your work (and you want to be cited by President Obama),

add on each graph your last name (example, YourLastName, 2015).

– Health Insurance Historical Tables:

– http://www2.census.gov/programs-surveys/demo/tables/health-insurance/

time-series/hib/hihistt1b.xls

(a) Plot the fraction of people who are covered by any type of insurance over this

period (x-axis years, y-axis the covered rate). Do you see any trend over time?

(b) Plot the fraction of people who are covered by any type of insurance by race

over this period (x-axis years, y-axis the covered rate) on the same graph. Which racial

or ethnic group has seen the largest increase in its rate of healthy insurance coverage

from this period?

(c) Now, President Obama would like to know whether this increase is largely coming from

increases in the rate of government-provided insurance, employer-provided insurance,

or privately purchased insurance? Plot a figure using the data here to support your

answer (you decide what information to plot in this figure to best support your case).

3. (10 point each) Problems from Chapter 17, Questions 15 and 17. Hint: for question 17, the

utility function is U(F,X) = 1/3ln(F)+2/3ln(X). The corresponding marginal utilities are

MU F = 1/3(1/F) and MU X = 2/3(1/X), respectively.

4. (10 points) There are two types of drivers on the road today. Speed Racers (The Clash fans)

have a 5% chance of causing an accident per year, while Low Riders (Lana del Rey fans)

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 drivers type. What premium

would the insurance company charge each type of driver?

Copyright c ?2017 Daolu Cai 1 Public Finance

Copyright c ?2017 Daolu Cai

(b) Now suppose that there is asymmetric information so that the insurance company does

not know with certainty the drivers type. Would insurance be sold if

i. drivers self-reported their types to the insurance company?

ii. no information at all is known about individual drivers types?

5. (10 points ) Rose’s preference is represented by the utility function U = ln(2C) where C is

the amount of consumption she has in any given period. Her income is 40,000 dollars per

year and there is a 2% chance that she will be involved in a catastrophic accident that will

cost her 30,000 dollars next year.

(a) What is her expected utility?

(b) Calculate an actuarially fair insurance premium. What would her expected utility be

was she to purchase the actuarially fair insurance premium?

(c) What is the most that she would be willing to pay for insurance, given her utility

function?

6. (20 points) Chimnesia has two equally sized groups of people: smokers and nonsmokers.

Both types of people have utility U = ln(C), where C is the amount of consumption that

people have in any period. So long as they are healthy, individuals will consume their entire

income of 15,000. If they need medical attention (and have no insurance), they will have to

spend 10,000 to get healthy again, leaving them with only 5,000 to consume. Smokers have

a 12% chance of requiring major medical attention, while non- smokers have a 2% chance.

Insurance companies in Chimnesia can sell two types of policy. The low deductible (L-)

policy covers all medical costs above 3,000, while the high deductible (H-) policy only covers

medical costs above 8,000.

(a) What is the actuarially fair premium for each type of policy and for each group?

(b) If insurance companies can tell who is a smoker and who is a nonsmoker and charges

the actuarially fair premiums for each policy and group, show that both groups will

purchase the L-policy.

(c) Suppose that smoking status represents asymmetric information: each individual knows

whether or not they are a smoker, but the insurance company doesn’t. Explain why

it is impossible, at any prices, for both groups to purchase L-policies in this setting.

Which groups, if any, do you expect to buy L-policies, and at what price?

(d) Suppose that smoking status represents asymmetric information: each individual knows

whether or not they are a smoker, but the insurance company doesn’t. Show that it is

possible for both groups to purchase insurance, with one group buying L-policies and

one group buying H-policies.