1
Chapter 1 Exercises
3. (엑셀 이용 권장 Spreadsheet recommended) Your county is considering building a public
swimming pool. Analysts have estimated the present values of the following effects over the
expected useful life of the pool:
PV
(million dollars)
State grant:
Construction and maintenance costs:
Personnel costs:
Revenue from county residents:
Revenue from non-residents:
Use value benefit to county residents:
Use value benefit to non-residents:
Scrap value:
2.2
12.5
8.2
8.6
2.2
16.6
3.1
0.8
The state grant is only available for this purpose. Also, the construction and
maintenance will have to be done by an out-of-county firm.
a. Assuming national-level standing, what are the social net benefits of the project?
b. Assuming county-level standing, what are the social net benefits of the project?
c. How would a guardian in the county budget office calculate net benefits?
d. How would a spender in the county recreation department calculate net benefits?
Social CBA
National Standing
-0.2
Social CBA
County Standing
1.1
County
Guardians
-6.9
County
Spenders
8.9
2
Chapter 2 Exercises
2. Let’s explore the concept of willingness to pay with a thought experiment. Imagine a
specific sporting, entertainment, or cultural event that you would very much like to
attend-perhaps a World Cup match, the seventh game of the World Series, a Garth Brooks
concert, or Kathleen Battle performance.
a. What is the most you would be willing to pay for a ticket to the event?
b. Imagine that you won a ticket to the event in a lottery. What is the minimum
amount of money that you would be willing to accept to give up the ticket?
c. Imagine that you had an income 50 percent higher than it is now, but that you
didn’t win a ticket to the event. What is the most you would be willing to pay for a
ticket?
d. Do you know anyone who would sufficiently dislike the event that they would not
use a free ticket unless they were paid to do so?
e. Do your answers suggest any possible generalizations about willingness to pay?
2.a. Students’ answers will vary (they should be > or = 0).
2.b. Most people would be willing to pay less to obtain something than the amount of
compensation they would require to give the same thing up willingly if they already owned it. This
difference has been frequently observed and economists refer to it as "the difference between
willingness to pay and willingness to accept." Though some of the difference may be attributable
to the lower wealth level of the individual in the first case than in the second case, it almost
certainly also reflects the way people perceive gains and losses.
4. Three mutually exclusive projects are being considered for a remote river valley: Project
R, a recreational facility, has estimated benefits of $10 million and costs of $8 million;
project F, a forest preserve with some recreational facilities, has estimated benefits of $13
million and costs of $10 million; project W, a wilderness area with restricted public access,
has estimated benefits of $5 million and costs of $1 million. In addition, a road could be built
for a cost of $4 million that would increase the benefits of project R by $8 million, increase
the benefits of project F by $5 million, and reduce the benefits of project W by $1 million.
Even in the absence of any of the other projects, the road has estimated benefits of $2
million.
a. Calculate the benefit-cost ratio and net benefits for each possible alternative to the
status quo. Note that there are seven possible alternatives to the status quo: R, F, and
W, both with and without the road, and the road alone.
b. If only one of the seven alternatives can be selected, which should be selected
according to the CBA decision rule?
4.a. The seven possible alternatives to the status quo have the following costs (millions), benefits
(millions), benefit/cost ratios, and net benefits (millions):
Alternative
B
C
B/C Ratio
NB
3
Project R without road
Project R with road
Project F without road
Project F with road
Project W without road
Project W with road
Road alone
$10
18
13
18
5
4
2
$8
12
10
14
1
5
4
1.25
1.50
1.30
1.38
5.00
0.80
0.50
$2
6
3
4
4
-1
-2
4.b. Even though Project W without the road has the largest benefit/cost ratio, Project R
with the road offers the largest net benefits among the possible projects and therefore would be
selected by the CBA decision rule.
6. Because of a recent wave of jewellery store robberies, a city increases police surveillance
of jewellery stores. The increased surveillance costs the city an extra $500,000 per year, but
as a result, the amount of jewellery that is stolen falls. Specifically, without the increase in
surveillance, jewellery with a retail value of $1 million would have been stolen. This stolen
jewellery would have been fenced by the jewellery thieves for $600,000. What is the net
social benefit resulting from the police surveillance program?
6. As a result of the increase in surveillance, the jewellery stores (or their insurance companies)
receive benefits of $1,000,000, taxpayers incur costs of $500,000, and the jewellery robbers incur
costs of $600,000.
The answer to this question depends on whether the jewellery robbers are given standing.
After all, they are (unfortunately) part of society.
If the robbers are given standing, society suffers a $100,000 net loss:
$1,000,000 - $500,000 - $600,000 = -$100,000.
If the robbers are not given standing, which would appear to be the more appropriate
approach, society enjoys a $500,000 net benefit from the surveillance project:
$1,000,000 - $500,000 = $500,000.
7. (엑셀 이용 권장 spreadsheet recommended.) Excessive and improper use of antibiotics is
contributing to the resistance of many diseases to existing antibiotics. Consider a regulatory
program in the United States that would monitor antibiotic prescribing by physicians.
Analysts estimate the direct costs of enforcement to be $40 million, the time costs to doctors
and health professionals to be $220 million, and the convenience costs to patients to be $180
million (all annually). The annual benefits of the program are estimated to be $350 million
in avoided resistance costs in the United States, $70 million in health benefits in the United
States from better compliance with prescriptions, and $280 million in avoided resistance
costs in the rest of the world. Does the program have positive net benefits from the national
perspective? If not, what fraction of benefits accruing in the rest of the world would have to
be counted for the program to have positive net benefits?
4
Millions of
Dollars
Regulatory program to monitor
antibiotic prescribing by U.S.
physicians to reduce the
spread of resistant strains
Regulatory enforcement
Time cost to doctors
Convenience cost to patients
Total U.S. Costs
40
220
180
440
Avoided U.S. resistance costs
Better drug compliance
Total U.S. Benefits
350
70
420
Avoided non-U.S. resistance costs
Fraction counted as U.S. Benefits
280
0
U.S. Net Benefits
-20
To determine what fraction of benefits to non-U.S. resistance costs would have to be included in
the CBA to show zero benefits can be determined by changing the value of cell C13 until U.S. Net
Benefits rise to zero. Any larger fraction will then yield positive net benefits. The net benefits are
about $20,000 when the fraction equals .0715. This might be a good time to talk to students about
rounding –here, $20,000 should be rounded to zero.
Chapter 3 Exercises
3. 엑셀에 익숙하지 않은 학생은 함께 올리는 엑셀 파일을 활용하여 직접 해 보기 바랍니다.
This is the first significant spreadsheet exercise. It is intended to make clear the meaning
of compensating variation and its relationship to the change in consumer surplus measured under
the Marshallian demand schedule.
The provided spreadsheet shows the compensating variation, change in consumer surplus, and
equivalent variation for a change in price from $0.20 to $.40. The numbers shown are as follows:
Compensating variation:
-$41.42
Change in consumer surplus:
-$38.04
Equivalent variation:
-$29.29
Note that the compensating variation and equivalent variation bracket the change in consumer
surplus. Also note that the discrepancy between these money metrics and the change in consumer
surplus is quite large. This results because the good makes up such a large fraction of the
consumer’s expenditure so that the income effect that puts a wedge between the money metrics is
very large.
Solving iterative for a price change from $.20 to $.30 yields the following:
Compensating variation:
-$22.47
5
Change in consumer surplus:
Equivalent variation:
-$21.37
-$18.35
(관련 추가문제)
For the improvement in E we have
U0 = 10.25 + 1000.75 = 32.6228
U1 = 20.25 + 1000.75 = 32.8120
CS is WTP for the improvement, so we need to solve
32.6228 = 2 0.25 + YN0.75
for YN, as follows
32.6228 = 1.1892 + YN0.75
YN0.75 = 31.4336
0.75ln(YN ) = ln(31.4336) = 3.4479
ln(YN ) = 4.5972
YN = 99.2032
Then,
CS=Y0 - YN = 100 - 99.2032 = 0.7968
ES is WTA compensation for foregoing the improvement, so we need to solve
32.8120 = 10.25 + YN0.75
for YN, which gives
YN = 100.7928
so that ES = YN - Y0 = 0.7928.
For the deterioration in E we have
6
U0 = 10.25 + 1000.75 = 32.6228
U1 = 0.50.25 + 1000.75 = 32.4637
CS is WTA compensation for the change, and solving
32.6228 = 0.5 0.25 + YN0.75
for YN = 100.6715 gives CS = YN - Y0 = 100.6715 - 100 = 0.6715.
ES is WTP for the change not to occur, and solving
32.4637 = 10.25 + YN0.75
for YN = 99.3298 gives ES = Y0 - YN = 100 - 99.3298 = 0.6702.
Chapter 4 Exercises
1. Consider a low-wage labor market. Workers in this market are not presently covered by
the minimum wage, but the government is considering implementing such legislation. If
implemented, this law would require employers in the market to pay workers a $5 hourly
wage. Suppose all workers in the market are equally productive, the current market
clearing wage rate is $4 per hour, and that at this market clearing wage there are 600
employed workers. Further suppose that under the minimum wage legislation, only 500
workers would be employed and 300 workers would be unemployed. Finally, assume that
the market demand and supply schedules are linear and that the market reservation wage,
the lowest wage at which any worker in the market would be willing to work, is $1.
Compute the dollar value of the impact of the policy on employers, workers, and society as a
whole.
1. As a consequence of the increase in the wage they must pay, employers lose surplus that
corresponds to the area of a trapezoid resulting from the reduction in the size of the surplus triangle
under the demand curve for labor. The trapezoid, in turn, can be thought of as a rectangle with
sides equal to the wage increase ($5-$4 = $1) and the new employment level (500) and a triangle
with a height equal to the wage increase ($1) and a base equal to the reduction in the number of
workers demanded (600-500=100). Adding these two areas together, we have (1)(500) +
(1)(100)/2 = $550.
The 500 workers who remain employed in the market each gain surplus equal to the $1
increase in the wage that they receive. Hence, their total increase in surplus is ($1)(500) = $500).
The 100 workers who lose their jobs as a result of the minimum wage obviously lose
7
surplus. If these workers are assumed to be equally distributed along the market supply curve
between the market reservation wage of $1 and the market equilibrium wage of $4, their average
loss of surplus can be computed as (.5)($4-$1) = $1.50. Hence, their total loss of surplus is
($1.50)(100) = $150. Alternatively, they can be viewed as losing $4 of earnings for each hour they
are unemployed, but gaining leisure that has an average hourly value to them of $2.50 [= (.5)($1 +
$4)]. Thus, their total loss in surplus is ($4.00-$2.50)(100) = $150, the same amount as computed
above.
Finally, 200 workers are induced by the higher wage to enter the market. However, since
jobs are not available for these persons, they do not work either before or after the minimum wage
is introduced. Hence, they neither gain nor lose surplus.
Therefore, the total impact of the minimum wage on society as a whole equals:
$500 - $150 - $550 = -$200.
3. A country imports 3 billion barrels of crude oil per year and domestically produces
another 3 billion barrels of crude oil per year. The world price of crude oil is $18 per barrel.
Assuming linear schedules, economists estimate the price elasticity of domestic supply to be
0.25 and the price elasticity of domestic demand to be 0.1 at the current equilibrium.
a. Consider the changes in social surplus that would result from imposition of a $6
per barrel import fee on crude oil that would involve annual administrative costs
of $50 million. Assume that the world price will not change as a result of the
country imposing the import fee, but that the domestic price will increase by $6
per barrel. Also assume that only producers, consumers, and taxpayers within
the country have standing. Determine the quantity consumed, the quantity
produced domestically, and the quantity imported after the imposition of the
import fee. Then estimate the annual social net benefits of the import fee.
b. Economists have estimated that the marginal excess burden of taxation in the
country is 0.25. Re-estimate the social net benefits assuming that 20 percent of
the increase in producer surplus is realized as tax revenue under the existing tax
system. In answering this question, assume that increases in tax revenues less the
cost of administrating the import fee are used to reduce domestic taxes.
c. The reduction in the country’s demand for imports may affect the world price of
crude oil. Assuming that the import fee reduces the world price from $18 to $16
per barrel, and thus, the after-tax domestic price is $16 + $6 = $22 per barrel, a
net increase in domestic price of $4 per barrel, repeat the analysis done in parts a
and b.
3.a. The imposition of the import fee would have the following effect on the domestic
market:
Change in quantity consumed: -.1 = (∆q/∆p)(p/q)
∆q = (-.1)∆p(q/p)
∆q = (-.1)($30)(6 billion)/($90)
∆q = -.2 billion
8
Change in domestic supply: .25 = (∆q/∆p)(p/q)
∆q = (.25)∆p(q/p)
∆q = (.25)($30)(3 billion)/($90)
∆q = .25 billion
Thus, after imposition of the fee, domestic consumption will fall to 5.8 billion barrels per
year, domestic production will rise to 3.25 billion barrels per year, and imports will fall to 2.55
billion barrels per year (5.8 billion - 3.25 billion).
The changes in surplus to producers, consumers, and tax-payers is as follows:
Change in domestic producer surplus:
A. Surplus from additional .25 billion barrels produced
Revenue = (.25 billion)($120) = $30 billion/year
Production costs (area under supply schedule) =
(.5)($120-$90)(.25 billion) + ($90)(.25 billion) = $26.25 billion/year
Net change in surplus from new production =
$30 billion/year-$26.25 billion/year = $3.75 billion/year
B. Surplus from higher prices on original production =
($120-$90)(3 billion) = $90 billion/year
Total change in producer surplus =
$3.75 billion + $90 billion = $93.75 billion/year
Change in consumer surplus:
C. "Deadweight loss" from reduced consumption =
(.5)($120-$90)(.2 billion) = $3 billion/year
D. Additional payments on quantity still consumed =
($120-$90)(5.8 billion) = $174 billion/year
Total change in consumer surplus =
(-$3 billion) + (-$174 billion) = -$177 billion/year
Change in tax revenues:
E. Import fee applied to new import level:
($30)(2.55 billion) = $76.5 billion/year
F. Administrative costs
-$.25 billion/year
Total change in tax revenues =
9
$76.5 billion - $.25 billion = $76.25 billion/year
CBA from country's perspective:
Costs:
Change in consumer surplus
Benefits:
Change in domestic producer surplus
Net gain to tax-payers
Net benefits:
-$177.00 billion/yr
$93.75 billion/yr
$76.25 billion/yr
-$7.00 billion/yr
The import fee would have negative net benefits of $7 billion/year and therefore does not
pass the CBA test.
Notice that over half of the loss in consumer surplus is offset by an increase in producer
surplus. Note also that we can base our decision on only one year if we assume that none of the
parameter values will change over time. If any of the parameters changed over time, then we
would have to extend the analysis to multiple periods. This would be the case, for example, if we
thought that the estimated elasticities were appropriate for the short-run, but not for the longer-run
because producers and consumers would be better able to adjust to higher prices as time passed
because they would have more opportunities to change their capital stocks.
3.b. Assuming 20 percent of producer surplus is collected as taxes, the costs and benefits
are:
Change in consumer surplus:
After tax change in producer surplus:
Net gain to taxpayers
Net gain to taxpayers times METB
Net benefits
-$177.00 billion
$75.00 billion
$95.00 billion
$23.75 billion
$16.75 billion
Not only do tax-payers enjoy reductions in tax payments, but the reduction in tax payments results
in a reduction in deadweight loss. To calculate this latter benefit, we multiply the fiscal change by
the METB. Taking account of the METB in this case makes an important difference: the tax
would not pass the net benefits test if METB is zero (implicitly assumed in part a), but would pass
the net benefits test if the METB is .25.
3.c. The following changes in quantities result:
Change in quantity consumed: -.1 = (∆q/∆p)(p/q)
∆q = (-.1)∆p(q/p)
∆q = (-.1)($20)(6 billion)/($90)
∆q = -.133 billion
Change in domestic supply: .25 = (∆q/∆p)(p/q)
∆q = (.25)∆p(q/p)
10
∆q = (.25)($20)(3 billion)/($90)
∆q = .167 billion
Thus, after the tax, 5.867 billion barrels are consumed, 3.167 billion barrels are domestically
produced, and 2.7 billion barrels are imported.
Consumer surplus loss =
(.5)(.134 billion)($110-$90) + (5.867 billion)($110-$90) = $118.68 billion/year
Producer surplus gain =
(.25 billion)($120) - [(.5)(.25 billion)($120-$90) + (.25 billion)($90)] + (3 billion)(120-$90)
= (.5)(.167 billion)($110-$90) + (3 billion)($110-$90)
= $61.67 billion/year
Net taxpayer gain =
($30)(2.7 billion) - $.25 billion = $80.75 billion/yr.
If the METB is assumed to be zero, then net benefits are $23.74 billion per year.
Assuming that 20 percent of producer surplus is transferred to the government through the existing
tax system and the METB is 0.25, the net social benefits are:
(49.34) + (80.75+12.33) + (0.25)(80.75+12.33) – 118.68 = $47.01 billion/year.
4. (Spreadsheet required) A proposed government project in a rural area with one-hundred
unemployed would require the hiring of 20 workers. The project would offer wages of $12
per hour. Imagine that the reservation wages of the one-hundred unemployed fall between
$2 and $20.
a. Estimate the opportunity cost of the labor required for the project assuming that
the government makes random offers to the 100 unemployed until 20 of them
accept jobs. (First, generate a list of the reservation prices of 100 persons
according to the formula $2+$18u where u is a random variable distributed
uniformly [0,1]. Second, work down the list to identify the first 20 workers with
reservation wages less than $12. Third, sum the reservation wages of these 20
workers to get the opportunity cost of the labor used for the project.)
b. Estimate the opportunity cost of the labor required for the project assuming that
the government can identify and hire the 20 unemployed with the lowest
reservation wages.
c. Repeat part a. 15 times to get a distribution for the opportunity cost and
compute its standard deviation.
4. The purpose of this exercise is to explore the opportunity cost of unemployed labor and
introduce students to the use of random number generators.
4. a. and b. Students should follow the directions on the spreadsheet. The opportunity cost
11
of hiring the 20 workers will be larger in part a (the more realistic scenario) than in part b (an
unrealistic scenario unless some method, such as the demand for bribes, can be used to find those
with the lowest reservation wages).
4.c. Note: Each time the spreadsheet is opened, it will provide a new draw of reservation
wages. To complete this part of the question, the spreadsheet will have to be opened a total of 15
times. Students can keep a record of the opportunity costs in one of the columns, say H, by
entering the amount and saving the spreadsheet before reopening it. The command, DSTDEV can
be used to find the standard deviation. Alternatively, the column can be summed and the sum
divided by 15 to get the mean. A second column equal to the difference between the value and
mean can be added. A third column would give the squares of these differences. Summing this
last column and dividing by 14 yields the standard deviation.