Download Practice Problem Answers

Practice Problem Answers
Chapter 15
6. An individual’s demand for physician office visits per year is Q = 10 – (1/20)P, where P
is the price of an office visit. The marginal cost of producing an office visit is $120.
a. If individuals pay full price for obtaining medical services, how many office visits
will they make per year?
The solution to this question can be determined by setting the marginal benefit of a
physician office visit equal to the marginal cost. To find the marginal benefit of a physician
office visit, invert the demand function so that it is expressed in terms of price, or the
dollar amount a patient is willing to pay: Q = 10 – 0.05P yields P = 200 – 20Q. Setting
demand equal to supply, or marginal cost, yields 200 – 20Q = 120; 20Q = 80. The patient
will visit the doctor 4 times a year.
b. If individuals must pay only a $20 copayment for each office visit, how many office
visits will they make per year?
When the price is only $20, the quantity demanded is 10 – 0.05(20) = 10 – 1 = 9.
c. What is the deadweight loss to society associated with not charging individuals for
the full cost of their health care?
The deadweight loss triangle is bounded by a quantity difference of 5 (9 – 4) and a
dollar difference of 100. The formula for the area of a triangle is ½ (base × height) = ½
(100 × 5) = $250, represented graphically,
12. Given that subsidized health care leads to increased health care usage, is this necessarily
due to moral hazard? Explain.
Part of the increase in usage may be due to moral hazard, but some of it is probably due
to the income effect. Subsidized health care increases a person’s real income and would increase
expenditure on health care even in the absence of moral hazard. Some people may
have sincerely needed the care without the insurance; with it they can finally afford to obtain
the care they need. Insurance also reduces the price of health care relative to other goods and
services, so people may purchase more units of covered health care and fewer units of uncovered
substitutes, such as nontraditional providers and over-the-counter remedies. This
substitution is the moral hazard aspect of purchasing more covered care, while the income
effect is an increase in usage that should not be characterized as moral hazard.
Chapter 16
2. Explain why takeup rates—the fraction of eligible individuals who enroll in the program—
are so much higher for Medicare than for Medicaid.
While Medicaid coverage is considerably more generous than Medicare coverage, there
are several reasons that takeup rates are modest for Medicaid and nearly universal for
Medicare. First, Medicaid is considered a welfare program designed to help the needy, so
there is a stigma attached to it. Medicare is universal, so there is no such stigma. Second,
while Medicaid offers generous benefits to enrollees, it has relatively low doctor reimbursement
rates, so many doctors do not take Medicaid patients. People who wish to choose their
doctor and be ensured of easy access to care may prefer not to go on Medicaid. These problems
are much less severe with Medicare. Finally, once a person is eligible for Medicare, he
or she is eligible forever. In contrast, eligibility for Medicaid can be transitory, and some individuals
who know they are likely to lose their eligibility shortly—say, when they find a
new job—may not find it worth the hassle of signing up.
10. The fact that such a large fraction of U.S. health care costs is spent on people in their
last six months of life has led many people to call the American health care system
“wasteful.” Why might this be an overgeneralization?
The argument implicit in saying that spending on the last six months wasteful is simple:
it seems silly to spend huge sums of money on people who are dying anyway. However, it is
crucial to note that doctors may not have known that the patients were dying when they
treated them—they may not, in fact, be throwing money at a “sinking ship.” An example is
useful. Suppose that there is only one type of care ever needed: a $10,000 treatment for people
with potentially fatal diseases that could kill them within 6 months. Suppose that this
treatment has a 50% success rate: half of those who are treated live and half die. In this example,
a full 50% of all medical costs are spent on treatment for people who die within the
next 6 months. This is clearly not wasteful: the treatment had a 50% success rate, and the appearance
of “waste” comes from focusing only on the unsuccessful treatments. Of course unsuccessful
treatments look wasteful—but nobody knows in advance which will be
successful, so the treatment itself is not.
Chapter 8
Advanced Questions
10. The city of Gruberville is considering whether to build a new public swimming pool.
This pool would have a capacity of 800 swimmers per day, and the proposed admission
fee is $6 per swimmer per day. The estimated cost of the swimming pool, averaged
over the life of the pool, is $4 per swimmer per day.
Gruberville has hired you to assess this project. Fortunately, the neighboring identical
town of Figlionia already has a pool, and the town has randomly varied the price
of that pool to find how price affects usage. The results from their study follow:
a. If the swimming pool is built as planned, what would be the net benefit per day
from the swimming pool? What is the consumer surplus for swimmers?
At an admission fee of $6, the city earns a profit of $2 per swimmer per day, or a total
of $1,600 per day. Consumer surplus can be determined from the demand function. With
every $2 increase in price, quantity demanded falls by 300. If you assume a linear demand
function, quantity demanded will be zero at an admission price of $11.33. The triangle of
consumer surplus is bounded by the quantity of 800 and the vertical distance of $11.33 –
$6 = $5.33.
Consumer surplus = ½ (800 × 5.33) = $2,132. Total surplus ($1,600 + $2,132) is
$3,732 per day.
b. Given this information, is an 800-swimmer pool the optimally sized pool for Gruberville
to build? Explain.
If you assume that the cost per swimmer does not vary with the size of the pool, then
this is not the optimal pool size. Optimality occurs where marginal cost equals marginal
benefit. Since marginal cost is $4, the pool should set a price of $4 to swim. Then the
marginal benefit to additional swimmers will be exactly $4 (the last swimmer was just
willing to pay to get in). There will be 1,100 swimmers at this price, so the optimum pool
size is thus 1,100. The town earns no profits on the pool, but the consumer surplus now
becomes ½ (1,100 × 7.33) = $4,031.50 per day.