Download - Catalyst

Econ 200 Homework 5
Due Monday, March 17th
1. There is a plastic company outside of town that discharges toxic chemicals into the groundwater as part of its
production process. The estimated health damages from the chemicals are $40 per ton of plastic produced. Below is
the company's marginal cost schedule. If the price of plastic is $160/ton, what is the socially efficient number of tons
that should be produced? Will the private market lead to this quantity? If not, explain one way to make sure this is the
quantity produced.
Quantity
(tons)
1
2
3
4
5
6
7
8
9
Private
marginal cost
100
110
120
130
140
150
160
170
180
Externality
40
40
40
40
40
40
40
40
40
Social marginal
cost
140
150
160
170
180
190
200
210
220
When the pollution externality is considered, the efficient quantity of plastic is 3 tons, since that is where the social cost
is equal to the price. In a private market 7 tons of plastic will be produced, since the plastic company does not include
the externality when calculating their private costs.
One way to ensure 3 tons of plastic is produced would be to institute a $40/ton tax on the toxic chemicals. Then the
company would have to pay for the damages imposed by its production, thus considering the cost of the pollution in its
private costs. Another option would be cap the amount the company could emit to the amount they pollute when
producing 3 tons of plastic. Another option would be to clearly establish who was liable for the pollution and try to
reduce transaction costs so the town and plastic company could negotiate to the efficient quantity.
2. We talked about 3 main market-based methods of cost-effectively getting to the socially efficient level of pollution
when there are externalities: taxes, cap-and-trade and assigning liability for pollution (i.e. Coase Theorem).
a). Why do you suppose that no one has suggested reducing carbon emissions by making polluting companies
liable for all of their emissions?
There are countless emitters of carbon, and everyone is affected by global warming, so the transactions costs associated
with negotiating would be too large for this to be effective.
b). Explain 2 differences between using a carbon tax and using a cap-and-trade system to control carbon
emissions.
Both a carbon tax and cap-and-trade could reduce pollution at the same cost to society. We talked about 2 main
differences between the policies, though. First, the two solutions will lead to different outcomes if the cost of cleaning
up carbon is different than expected. A cap-and-trade system guarantees a certain level of carbon emissions (the cap, or
number of permits), while the cost of cleaning up carbon (i.e. the cost of permits) can increase (decrease) if it is more
expensive (cheaper) to clean up carbon than expected. A tax guarantees that the cost to companies (the tax) will remain
constant, while the amount of carbon emitted can increase (decrease) if it is more expensive (cheaper) to clean up
carbon than expected. Another difference has to do with who gains and loses under the policy. A tax generates
revenue, which can be used for activities such as decreasing income taxes, sending rebates to consumers who will have
to buy more expensive goods, or invest in new green technology. The same is true of a cap-and-trade if permits are
auctioned off. However, if permits are given away,then the firms that are given the permits will be the ones to benefit
from putting a price on carbon.
3. Are the following statements true or false? Explain.
a). The benefits of corrective taxes as a way to reduce pollution have to be weighed against the deadweight loss
that these taxes create.
False. Corrective taxes eliminate the inefficiency created by externalities, and thus reduce deadweight loss instead of
creating it.
b). When deciding whether to levy a corrective tax on consumers or producers, the government should be
careful to levy the tax on the side of the market generating the externality.
False. Just like other taxes, the share of a tax burden paid by consumers and producers depends solely on the relative
elasticities of demand and supply. If demand for a product is relatively more inelastic than supply, consumers will pay a
greater share of the tax even if producers are generating the externality.
4. Some child immunizations such as the immunizations against Polio and Hepatitis B are required before children can
attend school. Given that children get some benefit from avoiding these diseases, why do you suppose schools have to
mandate these immunizations instead of relying on parents to voluntarily immunize their children?
There is a positive externality associated with immunizing children. Immunized children are less likely to spread diseases
and there is a public health benefit from decreasing the potentials of epidemics. Since parents only consider the private
benefit to their children when deciding whether to immunize, not enough immunizations would be purchased
voluntarily (i.e. in a free market). To make sure the efficient level of immunization happens, schools require students to
be immunized.
5. Greater consumption of alcohol leads to more car accidents, and thus imposes costs on people who do not drink and
drive.
a. Show on a graph of the alcohol market: the private market equilibrium, any externalities associated with
alcohol, and the socially efficient market equilibrium.
b). On your graph show the deadweight loss associated with the private market equilibrium (hint: deadweight loss
would occur because some units of alcohol are consumed for which the social cost exceeds the social value).
P
Supply
externality
Deadweight loss
Demand: Private marginal
value (i.e. benefits)
Q*
Q
M
Social marginal value
(i.e. benefits) Q
Q
6. Suppose there are four coal-burning plants that each release 50 tons of sulfur dioxide (SO2) into the atmosphere. The
costs to each firm of cleaning up their SO2 emissions are shown below:
Firm
Firm A
Firm B
Firm C
Firm D
Initial pollution (in
tons)
50
50
50
50
Cost of cleaning up 1
ton of SO2
$200
$150
$100
$50
The government has decide that only 100 tons of SO2 can be released into the atmosphere without causing acid rain, so
100 tons needs to be cleaned up.
a). If the government said each firm had to clean up half of its SO2 emissions (so each firm could emit 25 tons),
what would be the cost of cleaning up the 100 tons of SO2?
If each firm had to clean up 25 tons of SO22, then the cost would be 25(200)+25(150)+25(100)+25(50)=$12,500.
b). If the government wanted to set a corrective tax instead, what would be a tax that would lead to only 100
tons of SO2 being emitted? Who would end up cleaning up their SO2 and what would be the cost of cleaning up the 100
tons of SO2?
If the government set a tax between Firm B and Firm C’s cost of cleaning up SO2, the same amount of SO2 could be
cleaned up for a lower cost than above. For example, if the tax was $125, then Firms C and D would be better off
cleaning up their SO2 than paying the tax and Firms A and B would be better off polluting and paying the tax. Thus Firms
C and D would clean up all of their SO2 and the total cost of cleaning up the 100 tons of SO2 would be
50(100)+50(50)=$7500.
c). If the government wanted to set up a cap-and-trade system instead, how many SO2 permits should they
issue? If they auction off the permits, what will the price of permits be? Who would end up cleaning up their SO2 and
what would be the cost of cleaning up the 100 tons of SO2?
The government should issue 100 permits to ensure only 100 tons of carbon is emitted. If the auctioned off the permits,
the price of permits would fall between Firm B and Firm C’s cost of cleaning up SO2. [If the permit price was below $100,
Firms A, B and C would want to buy them and the quantity of permits demanded would be 150, so the price has to
increase. If the price of permits was above $150 then only Firm A would want to buy permits and the quantity of permits
demanded would only be 100 so the price would have to decrease. When the price is between $101 and $149, Firms A
and B would want permits and the quantity of permits demanded would equal the quantity of permits supplied.] With a
permit price between $101 and $149, Firms A and B will buy permits and pollute, while Firms C and D will clean up their
pollution, so the total cost of cleaning up the 100 tons of SO2 would be 50(100)+50(50)=$7500.
d). Would anything change from part c). if the government gave each firm 25 permits instead?
The firms would trade permits until Firms A and B had all the permits. Firms C and D again would be the ones cleaning
up pollution so the cost of cleaning up the pollution will be the same. The only thing that would be different would be
the benefits and costs to the companies. Firms C and D will benefit since they will be able to sell the permits they got for
free at a price higher than the cost of cleaning up their SO2 emissions. Firms A and B will be better off as well, since they
only have to buy half of the permits they use (instead all of them as above). The government brings in no revenue in this
scenario.
6. Timber companies in the U.S. cut down trees both on privately owned land and publically owned land. Will the
amount of trees cut down on each type of land be efficient or not, in the absence of any government regulation? Should
the government regulate logging on public land? Should it regulate logging on private land?
On privately owned land, the amount of logging is likely to be efficient. Loggers have incentives to do the right amount
of logging, because they care that the trees replenish themselves and the forest can be logged in the future. Publicly
owned land, however, is a common resource, and is likely to be overlogged, because loggers won't worry about the
future value of the land.
Because public lands tend to be overlogged, the government can improve things by restricting the quantity of logging to
its efficient level. Selling permits to log, or taxing logging, could be used to reach the appropriate quantity by
internalizing the externality. Such restrictions are unnecessary on privately owned lands, because there is no externality.
7. Characterize these goods as either public goods, common property goods, private goods or club goods (natural
monopolies):
 Police protection (i.e. a police department): Club good (this is different than national defense b/c police could
theoretically choose who they protect)
 Salmon in the ocean: Common property resource
 Salmon in a private lake: Private good
 Snow plowing city streets: Public good
 Snow plowing individual driveways: Private good
 Wikipedia: Public good (could be club good if they required membership to view)
 A novel about the history of Wikipedia: private good
 The information included in an individual Wikipedia post: public good
Which of these will the private market provide an efficient amount of? When the private market doesn’t provide an
efficient amount, how can we ensure an efficient amount is provided?
A private market will provide an efficient amount of salmon in a lake, snow plowing in individual driveways and novels
about the history of Wikipedia, since these are all private goods (assuming there are no externalities that make the
private market inefficient). Police departments are provided by city governments to ensure the efficient amount of
police protection. The government regulates how many salmon in ocean water can be caught. City street snow plowing
is generally provided by city governments (sometimes homeowner association hire their own private snow plow
services). Wikipedia appeals to user donations. To ensure enough general knowledge is free and available to people, the
government and private foundations give out grants to support such research.
8. Both public goods and common property resources involve externalities.
a). Are the externalities associated with public goods generally positive or negative? Use examples in your
answer. Is the free-market quantity of public goods generally greater or less than the efficient quantity?
The externalities associated with public goods are positive. Because the benefits from the public good received by one
person do not reduce the benefits received by anyone else, the social value of public goods is substantially greater than
the private value. Examples include national defense, knowledge, uncongested non-toll roads, and uncongested parks.
Because public goods are not excludable, consumers will want to free ride off the consumption by others and the freemarket quantity is less than the efficient quantity.
b). Are the externalities associated with and common property resources generally positive or negative? Use
examples in your answer. Is the free-market quantity of and common property resources generally greater or less than
the efficient quantity?
The externalities associated with common resources are generally negative. Because common resources are rival in
consumption but not excludable, the use of the common resources by one person reduces the amount available for
others. Because common resources are not priced, people tend to overuse them  their private cost of using the
resources is less than the social cost. Examples include fish in the ocean, the environment, congested non-toll roads, and
congested parks.
9. If residents in a certain town get street lamps for their downtown area, it will make the area safer and more enjoyable.
Say there are 4 residents whose value of streets lights is as follows:
If the price of street lights is $25, what is the efficient number of street lights to be put in downtown? Is the city likely to
get that many street lamps if it is left to the private market? If not, how can the city ensure that many streetlights are
purchased?
Q
1
2
3
4
5
6
Amy
$10
$9
$8
$7
$6
$5
Beth
$7
$6
$5
$4
$3
$2
Chad
$8
$7
$6
$5
$4
$3
Daniel
$11
$10
$9
$8
$7
$6
Social
benefit
$36
$32
$28
$24
$20
$16
Since street lamps are a public good, the social benefit from having street lamps is equal to the sum of all the citizens’
private benefits. The efficient number of street lamps would be 3, since the social benefit exceeds the cost ($25) for the
first three street lamps only. If it is left to the private market the city is unlikely to get that many street lamps because no
one person would get enough private benefit from a streetlamp to buy one. The streetlamp company couldn’t sell the
right to use the lamps to consumers because the light is non-excludable, so people would just want to free ride off other
people’s purchases. One solution is to have the government tax all citizens to raise revenue to buy the streetlamps. The
city could buy 3 streetlamps if it raised $75 in taxes, so that means taxing each person $18.75, or $6.25 per lamp. The
consumers are generally better off since they value each lamp more than $6 (except Beth for the 2nd and 3rd lamp and
Chad for the 3rd lamp; this is true of taxes, not everyone is always made better off by what government expenditures go
towards).
What if a business opened up downtown that would get a lot of benefit from having a light outside of its door, such that
the business’s willingness to pay for street lamps is:
Q
1
2
3
4
5
Business
$50
$40
$30
$20
$10
Now how many street lamps would a private market yield? Is this efficient or not?
Now a private market would lead to 3 lamps being purchased since the business owner will find it beneficial to buy 3
lamps even if the other citizens free ride off of him. This is not efficient though, because if you add his value to the other
citizens’ value, the benefits of additional street lamps would still be higher than $25. Considering the total social value,
now the efficient number of street lamps is 5. So having 1 person with private benefits higher than the cost meant the
city could use the free market to get some, but not the efficient, number of streetlamps.
Q
1
2
3
4
5
6
Business's Citizens'
value
value
$50
$36
$40
$32
$30
$28
$20
$24
$10
$20
$0
$16
Total
social
value
$86
$72
$58
$44
$30
$16