Department of Agricultural and Resource Economics
University of California at Berkeley
EEP1/ECON3
P. Berck
Introduction to Environmental Economics and Policy
Problem Set 4, 2009
(Luosha, Du and Koichiro Ito)
Chapter 5. Q1 [total 2 points, 0.5 point each part]
1.
While price is a very effective way of allocating goods, governments sometimes like to keep the price of
a good low for political reasons. Suppose, using Figure 5.3, that the Tunisian government decided to provide 36
cubic meters of water, but only charge 0.18 dinars per cubic meter.
(a) What is total willingness to pay?
Total willingness to pay is area1+area2+area3 when the Tunisian government decided to provide 36 cubic
meters of water (see the figure below).
(b) What is consumer surplus in this case? Remember that consumer surplus is the area under the demand
curve, but above the price paid, between the vertical axis and the quantity consumed.
Since the government only charges 0.18 dinars per cubic meter, the consumer surplus is area1+area2.
(c) If the government sells the water at the market-clearing price of 0.28 dinars per cubic meter, what is the
consumer surplus?
Now, the price increases to the market-clearing price (0.28 dinars per cubic meter), the consumer surplus is
just area 1.
(d) What happens to the difference in consumer surplus between these cases? Does it vanish?
The consumer surplus decreases as the price per cubic meter increases from 0.18 dinars to 0.28 dinars.
The consumer surplus does vanish by area 2.
0.28
1
o
r
m
2
u
l
a
1
3
Chapter 6 Q2 [7 points in total]
2. The following table gives information on visitors to Jellybear Park
City of Origin
Alabaster
Beautiful
Cornucopia
Delight
Population
1000
3000
5000
7000
Distance
1
3
5
7
A researcher keeps careful track of visitors to Jellybear and learns that there is a total of 3,750 visits to the
park. The only cost of traveling to the park is is mileage, at $1/mile. The researcher estimates the relationship
between costs and number of visits per capita (per person) to be Visits/Capita= 1 - 0.15 * Cost.
(a) [1 point] Add columns to this table identifying total costs of a visit from each place, visits per capita from
each town, and the total number of visits from each town (that is, the visits/capita multiplied by the population).
City of Origin
Alabaster
Beautiful
Cornucopia
Delight
Population
1,000
3,000
5,000
7,000
Distance
1
3
5
7
Total costs of a visit
1*$1/mile= $1
$3
$5
$7
Visits/capita
= 1-0.15*1=0.85
0.55
0.25
0 (cause it is
negative, -0.05)
Total # of visits
0.85*1,000=850
1,650
1,250
0
(b) [0.5 point] Why doesn’t the researcher observe anyone coming from Delight to Jellybear?
Delight is too far away, which leads to a higher travel cost and then results in a negative visits/capita
(based on the formula provided above). So, nobody from Delight wants to go to Jellybear.
(c) [0.5 point] If getting to the park is the only cost associated with a visit (that is, there is no admission price),
how many people in total visit Jellybear? Start a table with one column of admission price (in this case, $0) and
total visits.
Admission price
Total visits
0
3,750 (the sum of visits from Alabaster, Beautiful, Cornucopia and Delight)
(d) [2 points] Because of management costs, park managers are considering charging for admission to
Jellybear. They are considering prices ranging from $1/visit to $5/visit. For each whole dollar value between
$1 and $5 per visit, figure out (i) the new cost of visiting for each town, (ii) the new number of visits/capita
from each town, (iii) the new number of visits from each town, and (iv) the total visits (remember that negative
visits do not exist; they count as zero).
When the admission fee is $1:
City of Origin Population Distance Total costs of a visit
Visits/capita
Total # of visits
(travel costs+admission) =1-0.15*cost
Alabaster
1,000
1
1*$1/mile+1=2
0.7
700
Beautiful
3,000
3
3*$1/mile+1=4
0.4
1,200
Cornucopia
5,000
5
5*$1/mile+1=6
0.1
500
Delight
7,000
7
7*$1/mile+1=8
0
0
Total visits
2,400
When the admission fee is $2:
City of Origin Population Distance
Alabaster
Beautiful
Cornucopia
Delight
1,000
3,000
5,000
7,000
1
3
5
7
When the admission fee is $3:
City of Origin Population Distance
Alabaster
Beautiful
Cornucopia
Delight
1,000
3,000
5,000
7,000
1
3
5
7
When the admission fee is $4:
City of Origin Population Distance
Alabaster
Beautiful
Cornucopia
Delight
1,000
3,000
5,000
7,000
1
3
5
7
When the admission fee is $5:
City of Origin Population Distance
Alabaster
Beautiful
Cornucopia
Delight
1,000
3,000
5,000
7,000
1
3
5
7
Total costs of a visit
(travel costs+admission)
1*$1/mile+2=3
3*$1/mile+2=5
5*$1/mile+2=7
7*$1/mile+2=9
Visits/capita
=1-0.15*cost
0.55
0.25
0
0
Total visits
Total # of visits
Total costs of a visit
(travel costs+admission)
1*$1/mile+3=4
3*$1/mile+3=6
5*$1/mile+3=7
7*$1/mile+3=10
Visits/capita
=1-0.15*cost
0.4
0.1
0
0
Total visits
Total # of visits
Total costs of a visit
(travel costs+admission)
1*$1/mile+4=5
3*$1/mile+4=7
5*$1/mile+4=9
7*$1/mile+4=11
Visits/capita
=1-0.15*cost
0.25
0
0
0
Total visits
Total # of visits
Total costs of a visit
(travel costs+admission)
1*$1/mile+5=6
3*$1/mile+5=8
5*$1/mile+5=10
7*$1/mile+5=12
Visits/capita
=1-0.15*cost
0.1
0
0
0
Total visits
Total # of visits
550
750
0
0
1,300
400
300
0
0
700
250
0
0
0
250
100
0
0
0
100
(e) [1 point] Put the information on admission price and total visits in the table from (c). This table shows the
relationship between admission price and total number of visits. What is it?
Admission price
Total visits
0
3,750
$1
2,400
$2
1,300
$3
7,00
$4
250
$5
100
(f) [1 point] Estimate the consumer surplus associated with visiting Jellybear Park when the admission fee is
$0. (It will be an approximate value, since the relationship in (e) is not a straight line.)
Admission
price
5
4
3
2
1
0
100
250
700
1,300
2,400
3,750
Total visits
Based on the information obtained from part e), we can trace out the demand curve for total visits of
Jellybear park as a function of the price of admission fee, see the figure above (note: the figure is not drawn to
scale). So, when the admission fee is $0, consumers capture all the benefits. Therefore, consumer surplus is the
whole gray shaded area.
(g) [1 point] What method have you used to estimate the value of visits t
Travel Cost Method
Chapter 7 Q3 [4 points in total]
3. In the Argo Dam study, about 62% of the survey population preferred to take down the dam, while 31%
preferred to keep it, and 7% expressed no preference. For those who preferred keeping the dam, the estimated
willingness to pay to keep it was $161/adult; those who wanted the dam removed would pay an estimated
$135/adult to have it taken down. Ann Arbor has about 96,000 people.
(a) [1 point] Democracy is based on each person having one vote. If there were a vote in Ann Arbor on dam
removal, what is the likely outcome, if a representative fraction of the population votes?
The likely outcome is NO DAM because 62% of the survey population represents the majority (let’s assume
the survey population is representative to the whole population).
(b) [1 point] If willingness to pay is a measure of how strongly people care about an issue, which group felt
more strongly about whether to remove Argo Dam, those who wanted to keep the dam or those who wanted to
remove it? Who would be more likely to show up to vote?
If willingness to pay is a measure, those who wanted to keep the dam felt more strongly about whether to
remove Argo Dam because the estimated willingness to pay to keep it (per adult) is greater than the estimated
willingness to pay to remove it (per adult). And those who wanted to keep the dam would be more likely to show
up to vote.
(c) [2 points] Use the above values to estimate whether the aggregate willingness to pay for keeping the dam
was larger or smaller than the aggregate willingness to pay for removing the dam. Would this calculation
produce a recommendation different than the outcomes in (a) or (b)? If so, what are some advantages and
disadvantages of a decision based on (i) seeking high voter turnout from a representative share of the population,
(ii) those who feel most passionate encouraging those who think like them to vote, or (iii) having the city
council decide based on an analysis of whether net benefits are larger for keeping or removing the dam?
Let’s first calculate the aggregate willingness to pay for each group. The aggregate willingness to pay for
“keep it” is $161*96,000*31%=$4,791,360. The aggregate willingness to pay for “remove it” is
$135*96,000*62%=$8,035,200. If the decision is made based on the aggregate willingness to pay, the likely
outcome would be “NO DAM” since $8,035,200 is greater than $4,791,360, which is consistent with the
recommendation from (a) but contradict with the likely outcome from (b).
If the decision is made based on (i) seeking high voter turnout from a representative share of the
population, the advantage is that it follows the majority’s votes and it is democratic. The disadvantage is that it
doesn’t take people’s preferences into account (how strongly people feel about the project). If the decision is
made based on (ii) people’s passion (in our case, people’s willingness to pay to support their decision), the
advantage is that it takes preferences into account but it ignores the majority rule. If the decision is made based
on (iii) the net benefits (in our case, it is the aggregate willingness to pay), the advantage is that it considers
both the majority rule and people’s preference. However, in practical, it is hard to collect information on
people’s willingness to pay from every single individual.
Chapter 8 Q2 [8 points in total]
2. Automakers can produce cars using machinery and labor. In particular, 50 cars can be produced using the
following combinations of machinery and labor:
Machinery
Labor
5
2
4
3
3
5
(a) [1 point] If you were to graph these points on a figure with Machinery on the horizontal axis and Labor on
the vertical axis, what would you be graphing? In other words, what do these different combinations of inputs
represent?
The line illustrated on the left panel is the isoquant
labor
curve for car production, every point on the curve
5
represents different input bundles that would yield a
production of 50 cars.
3
2
3
4
5
machine
(b) [1 point] Suppose machinery costs $30/machine, while labor costs $40/worker. How much would each of
these combinations cost? Perform a similar calculation if machinery costs $50 and labor $40; and if machinery
costs $70 and labor $40.
Machinery
Labor
$30/machine&
$50/machine &
$70/machine & $40
$ 40/worker
$40/workers
labor
5
2
30*5+40*2=230
50*5+40*2=330
70*5+40*2=430
4
3
30*4+40*3=240
50*4+40*3=320
70*4+40*3=400
3
5
30*3+40*5=290
50*3+40*5=350
70*3+40*5=410
(c) [1 point] What is the lowest-cost combination of machinery and labor when the price of machinery is $30
and the price of labor is $40? When machinery costs $50 and labor costs $40? When machinery costs $70 and
labor costs $40?
The lowest-cost combinations of machinery and labor are marked in red in last part for each pair of cost
combinations.
(d) [1 point] As the price of machinery rises relative to the price of labor, what happens to the relative amounts
of machinery and labor that minimize cost?
If the price of machinery increases relative to the price of labor, car producers will use more labors and
reduce the usage of machinery to minimize the cost.
(e) [1 point] As the price of machinery increases, while the price of labor stays constant, what happens to the
minimum possible total cost of producing 50 cars?
If the price of machinery increases but the price of labor stays constant, the minimum possible total cost of
producing 50 cars will increase.
Suppose that the use of machinery causes pollution, while the use of labor does not. Machinery costs
$30/machine if environmental costs are not considered, but each machine causes $20/machine of environmental
damage.
(f) [1 point] If the environmental damage from machinery use is not included in the cost of productionin other words, if the damage is an externality from the automakers’ point of view- -, what input combination
would they use, and what would be their costs?
If the environmental damage is not taken into account, the cost of machinery is $30 and the cost of
labor remains at $40. Based on the observations from part (b), 5 machinery and 2 labors will be the lowest-cost
combination of inputs, the total cost is $230.
(g) [1 point] If automakers had to pay for the damages associated with machine use, what input
combination would they use, and what would be their costs?
If automakers have to pay for the environmental damage, the cost of machinery will increase to $50
($30+$20) and the cost of labor remains at $40. Based on the table drawn in part b), now we move from the
third column to the fourth column. The lowest-cost combination of inputs is 4 machinery and 3 labors, leading
to a cost of $320.
(h) [1 point] If the government instead used a standard to limit machine use to 4 machines, what input
combination would automakers use, and what would be their costs?
Automakers will use 4 machinery and 3 labors. Since there is no price change in this case, machinery
costs $30/machine and labor costs $40/worker. Therefore, total costs is 4*30+3*40 = $240.