Econ 344
Problem Set #3
Assigned:Tu. Oct. 4, 2007
Due:Th. Oct. 11, 2006
Corresponding Chapters: Rosen Ch9-Ch10
Part I Multiple Choices (2*9=18 points)
1.When people behave in ways that involve increased risk because they have insurance, this is known as
a)adverse selection.
b)moral hazard.
c)asymmetric information.
d)a HMO.
b
2Health care markets may be inefficient because of
a)poor information.
b)adverse selection.
c)moral hazard.
d)all of the above.
e)none of the above.
d
3An actuarially fair return means
a)returns on investments are indexed to the stock market.
b)returns on investments have to be positive.
c)benefits received, on average, would be equal to the premiums paid.
d)premiums for insurance are generally paid by the government.
e)none of the above.
c
4When the average buyer of an insurance policy is likely to have higher risk than others in his class, this is known as
a)adverse selection.
b)moral hazard.
c)asymmetric information.
d)a HMO.
e)none of the above.
A
5.Asymmetric information generally implies
a)information between parties is not equal.
b)all parties are fully informed.
c)information is costless.
d)information is too costly to transmit.
e)a and c.
a
6.A pay-as-you-go system means
a)you pay for your dinner as you go to the table to eat.
b)current working citizens pay for current retired citizens.
c)there is no need for taxes since current workers pay for current retirees.
d)retirees are paid from accounts that have accumulated with interest over their working lives.
e)all of the above.
b
- Which of the following is NOT one of the three forms or moral hazard related to health insurance (HI)?
- With HI, people are less likely to try their best to live a healthy life style.
- People tend to over-consume health care services if they have HI.
- Those who think they have a higher risk of getting cancer are more likely to buy HI.
- If people know that they will have access to health care even if they do not have HI, they will not buy HI.
c---is adverse selection
. 8. The Earned Income Tax Credit (EITC)
a)provides more income to those people on welfare.
b)is a tax on low income workers.
c)provides additional tax credits to low income workers.
d)is a tax break for the wealthiest Americans.
e)was eliminated by the Bush administration.
c
9.Which is the largest cash transfer program for the poor?
a)TANF
b)Medicare
c)SSI
d)Medicaid
e)Section 8
a
True/False/Uncertain----explain (2*3=6pts.)
10.Under federal tax law, employerprovided health insurance is not subject to axation.
T
11.Having a Social Security program makes people less inclined to save for their own retirement. U
12.One reason for the recent increases in health care costs is the aging of the American population.
T
III. Open questions
- (20 points) Purpose—understand how cost sharing may alleviate moral hazard problem.
Anna’s demand each year for visit to doctors is given by: Q = 10 - .05P, where Q is the number of visits, and P is the price Anna pays for a visit.
- (5 points) How many visits would Anna take if P=$80 and she is not insured?
Q=10-.05*80=6.
- (7 points) How many visits would Anna take if P=$80 but she is insured with a co-insurance payment of 25%? Suppose P=$80 is also the true social cost of visits to doctors, what is the social welfare loss from this co-insurance program for Anna?
The price Anna pays is: .25*80=20
Q=10-.05*20=9.
Welfare loss=.5*(9-6)*(80-20)=90
- (7 points) Please draw Anna’s demand curve and show the visits she takes and the price she pays in part a. and b. Please also indicate the welfare loss in b.
d (6 points) Will a co-pay of $20 per visit improve social welfare relative to the co-insurance policy in part b.? Why and by how much, if any?
A co-pay (or co-payment) is a fixed dollar amount the patient must pay per unit of health care provided. In this question, a co-pay of $20 per visit happens to equal the co-insurance payment of 25% (80*25%=20). Thus, here a co-pay of $20 per visit will not improve social welfare relative to the co-insurance policy in part b.
2. Social Security Reform (16 pts.)
a) What is the difference between pay as you go and fully funded social security systems? What is the reason Social security may be in trouble?
Pay-as-you-go system---current workers supporting current retirees
Fully funded---tax current workers and invest for their retirement
SS trouble is demographics are pushing system toward insolvency
b) Name at least three incremental reform proposals
-raise payroll taxes
Expand taxable wages
Raise retirement age
Lower benefits
c.Name at least two fundamental reform proposals and briefly discuss the problems associated with each.
Invest the trust fund into stock market
privatization
d) Do you think making social security voluntary will work? explain
.
unlikely
3. Expected utility of insurance (20 pts)
Johnny is considering whether to buy health insurance His utility is given by U(I)= √I where I is his yearly income equal to $25,000. However there is a 5% chance that he’ll fall sick with a avian flu virus which will cost him $5000.
- what is his expected utility of not buying any insurance?
EU = .05* √(25000-5000) + .95 √(250000) = 157.28
b. what is the actuarially fair premium for the health insurance in this case?
.05(5000) + .95(0) =250
c. Assuming that the premium is actuarially fair, what is th expected utility associated with buying full insurance (ie insuring all $5,000 of potential loss)? What is the expected utility associated with insuring only half of the loss ($2500)? Is Johnny going to choose full insurance or partial insurance?
Full Ins .05 *√(20000-250+5000) +.95 √(25000-250) =157.32
Partial .05 * √(20000-125 +2500) + .95 (25000-125) = 157.31
Full insurance is preferred.
4. 20 pts) Ch8 #1, p188.
In California, a welfare recipient can earn $225 per month without having her benefits reduced. Beyond $225 benefits are reduced by 50 cents for every dollar of earnings. Consider Elizabeth, a resident of California, a resident of California, who can earn $10 per hour. If she does not work she is eligible for welfare benefits of $645.
- If she works 10 hours, how much are her earnings; how much is her welfare benefit; and how much is her income?
- After Elizabeth works a certain number of hours, she does not receive any benefits at all. What is that number of hours?
- Use your answer to parts a and b to plot her budget constraint.
- Sketch a set of indifference curves consistent with Elizabeth’s participating in the labor market.
a.Note that the figure below shows the correct shape of the budget constraint, but the numbers themselves are outdated. With a wage rate of $10 per hour, Elizabeth earns $100. Because the deduction in California is $225, none of her earnings are counted against the $645 welfare benefit. Thus, her total income is $745 (=$100+$645).
- The actual welfare benefits collected by a person equals B=G-t(Earnings-D), where B=actual benefits, G=welfare grant, t=tax rate on earned income, and D=standard deduction. Thus, (Earnings-D) is the net earnings that are taxed away in the form of reduced benefits. When benefits equal zero (B=0), the expression becomes 0=G-t(Earnings-D), which collapses to: Earnings=G/t+D. This is known as the “breakeven formula.” In the California context here, the expression becomes Earnings=$645/0.5 + 225, or Earnings=$1,515. With a wage rate of $10 per hour, this corresponds to 151.5 hours of work per month.
- The diagram shows the correct shape of the budget constraint, but the “577” figure should be replaced with “645” and the “9” hours should be replaced with “22.5”.
- The diagram above shows one possibility – in this case, Elizabeth is both working and on welfare – but she collects a reduced welfare benefit in this case.