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Principles of Microeconomics
Spring, 2001
Dr. Kathryn Wilson
Due: Thursday, April 26
Homework 6 – Answer Key
1. There is a country with the following income distribution:
% of Population
% of Income
bottom 20%
5
lower middle 20%
10
middle 20%
15
upper middle 20%
25
top 20%
45
a. Draw the Lorenz Curve for the country.
Cumulative % of Income
Lorenz Curve
100
80
60
40
20
0
0
20
40
60
80
100
Cumulative % of Families
b. What would happen to the Lorenz Curve if the government imposed a progressive tax? What would
happen to the gini coefficient for the country if the government imposed a progressive tax? Explain.
A progressive tax taxes higher income people at a higher percent than lower income people. The
result is that after-tax income is more evenly distributed, resulting in a Lorenz curve that is closer
to the perfect equality line. This results in a smaller gini coefficient for the country since income is
more evenly distributed in society if there is a progressive tax.
c. Describe the three theories of how income should be distributed and what each theory implies about
how the government should use taxes and transfer programs.
Perfect equality suggests that everyone should have the same amount of income. This would imply
a very progressive tax system and a lot of transfer programs. The government would collect tax
money from the rich and give it to the poor until everyone had exactly the same amount of money.
An income distribution that is based on productivity or marginal revenue product implies that
people should be paid based on what they produce. In this case, the tax system should be the same
flat rate for all people (or no taxes at all) and there would be no transfer program. Each person
would have money based on what his or her job earns.
It is harder to say the implications of the Rawlsian theory. Rawls says that each of us “knows”
what the “right” distribution should look like but that we are biased by where we think we will be
on the income distribution. Government would use the appropriate level of progressivity in taxes
and redistribute money with transfers to get this “right” distribution.
2. Describe two things you found interesting or surprising about what we covered on poverty.
Answers to this question will vary.
3. We said that national defense is an example of a public good. Describe how national defense (such as
an anti-missile system) is nonrivalrous and nonexcludable.
In order to be nonrivalrous, it must be the case that national defense of one person is not
diminished if the defense is provided to another person. In the case of an anti-missile system, the
level of defense is the same no matter how many people are in the region being protected.
Therefore, it is nonrivalrous. In order to be nonexcludable it must be impossible or prohibitively
costly to keep someone from receiving the product if it is produced. If we build an anti-missile
system, the system must protect everyone in the area – it is not like the system can allow missile’s
that will hit Kathy Wilson but not allow missiles that will hit others. If anti-missile protection is
provided, it is provided to everyone in the area. Therefore, it is nonexcludable. Since national
defense meets both the criteria of nonrivalrous and nonexcludable, it is a public good.
4. a. In your own words, briefly describe what we mean by each of these. (I do not want you to write the
definition but rather explain it in your own words.)
i. Rational Absenteeism
This is the idea that the costs of voting might be greater than the benefits of voting so it is
rational for a person to decide not to vote. The benefits to voting are the utility a person
gets from fulfilling a civic duty, while the costs include both time and effort of going to the
polling place. Economists think that for many individuals the personal benefits do not
outweigh the personal costs of voting so it may be rational to choose not to vote.
ii. Rational Ignorance
Similar to rational absenteeism, rational ignorance involves weighing benefits and costs.
Individuals must consider the benefits of being well informed of political issues compared to
the time and energy (and perhaps monetary) costs of being well informed. If the personal
benefits do not outweigh the costs, it is rational for an individual to decide to NOT be well
informed on political issues.
iii. Special Interest Groups
These are groups of people who share a common cause. If benefits go to just a few
individuals (the special interest group) and the costs of a program are spread out over
many, many individuals, a special interest group may be able to lobby to get what is in their
best interest even if it is not what is best for society. Since the costs are spread out over so
many people, those who bear the cost don’t have the same incentive to lobby as the few who
get a large benefit.
b. What do you think these three things imply about our ability as a nation to provide the efficient level
of public goods?
This actually provides a pretty grim picture of our ability to provide the efficient level of public
goods. Most people will do not vote in elections, and those who do vote probably aren’t well
informed. Therefore, we may not vote into office people who will provide the level of the public
good that is consistent with the preferences of the population. To make matters worse, special
interest groups may be able to lobby to get their interests passed even if it is to the detriment of
most of society.
5. Your next-door neighbor likes to throw loud parties during the week and it interferes with your ability
to study and to get a good night sleep.
a. How is this an example of an externality?
An externality is when the benefits or costs of an activity affect not only the person who buys the product but
also affect a third party. When your neighbor has parties, it has a negative effect on you and thus is an
externality.
b. If the city of Kent were to take the advice of Coase, what would they do to solve the problem?
Coase thinks we should assign property rights – he says the problem is that no one has legal property rights
to the loudness of the air. If we assign property rights to you, you can force your neighbor to pay you every
time he throws a party. If we assign property rights to your neighbor, you will have to pay him to NOT to
throw a party. It doesn’t matter who we assign property rights to – either you or your neighbor – either way
we will get the efficient amount of partying to the point where the marginal benefit to society of the last party
equals the marginal cost to society (including the cost to you in terms of less studying and sleep).
c. If the city of Kent were to take the advice of Pigou, what would they do to solve the problem?
Pigou would put a tax on partying (or noise). Every time your neighbor throws a party, he would have to pay
the government a tax. If the tax is set equal to how much you are harmed by the party (the marginal external
cost), your neighbor will choose the efficient amount of partying. Note, though, he is not choosing the
efficient level because he cares about you – rather, since he pays a tax equal to how much you are harmed,
when he considers the tax he is essentially considering the marginal external cost.
d. How could the city of Kent use regulation to solve the problem?
In fact, the city of Kent does use regulation to solve the problem by having a noise ordinance. It is
illegal to make too much noise during certain times. If you violate this, you can be fined or
arrested. Notice that from an efficiency point of view, this might be too strict of a law. There may
be parties where the marginal benefit to your neighbor of partying is greater than the marginal cost
the party is imposing on you – in which case, we do want your neighbor to throw the party. The
noise ordinance makes even these “socially efficient” parties illegal.
e. Do we (society) want there to be zero amount of partying? What is the efficient amount (I am looking
for a formula, not an actual number).
No. It is not the case that we want no partying. Rather, we want a level of partying where the marginal
benefit of the party equals the marginal cost of the party. The marginal benefit includes the utility your
neighbor and his friends get from the partying while the marginal costs include the actual costs of the party
(such as food and drinks) PLUS the marginal cost you incur through less studying and sleep. As long as the
marginal benefits to society of the party outweigh the marginal costs to society of the party, we want for the
party to happen (it is socially efficient for the party to happen). It is just the parties where the marginal
benefits are less than the marginal costs that we want eliminated.
6. The following are the costs for pollution abatement for four firms (pollution abatement just means
getting rid of pollution).
Firm 1
Firm 2
Firm 3
Firm 4
1st ton of pollution
$200
$400
$600
$800
2nd ton of pollution
$300
$500
$800
$1000
a. The government determines that we must eliminate 4 tons of pollution in total. To accomplish this,
they pass a law that every firm must eliminate 1 ton of pollution. What is the cost of the pollution
abatement program? $200 + $400 + $600 + $800 = $2,000 (each firm eliminates 1 ton of pollution)
b. Instead of regulating each firm must eliminate pollution, the Government issues 4 “permits to pollute 1
ton”. Each firm is given one of the permits, but they are allowed to trade the permits. We still will end
up with 4 tons of pollution, but who will do the pollution? (who will buy/sell the permits) What will be
the cost of the pollution abatement program?
Firms that can eliminate pollution cheaply will want to sell their permits (and eliminate the
pollution) as long as the price they can sell the permit for is more than the cost of eliminating the
second unit of pollution. Firms that cannot eliminate pollution cheaply will want to buy a permit so
that they don’t have to eliminate any pollution. (Remember, you can only pollute as many tons as
you have permits). Firm 1 has a very low cost of eliminating pollution; if they sold their permit,
they would only have to pay $300 to eliminate the 2nd ton of pollution. Firm 4 has a very high cost
of eliminating pollution; if they bought a permit, they would not have to eliminate the first ton of
pollution (which costs them $800). Firm 4 is willing to pay up to $800 for a permit (the cost of
eliminating the 1st ton of pollution) and firm 1 is willing to accept anything over $300 to sell their
permit (the cost of eliminating the 2nd ton of pollution). So, firm 1 will sell a permit to firm 4 for a
price of between $300 and $800. Similarly, firm 2 will sell a permit to firm 3 for a price between
$500 and $600. In the end, firms 1 and 2 have to each eliminate 2 tons of pollution and firms 3 and
4 don’t have to eliminate any. The cost of eliminating pollution is $200+$300+$400+$500=$1400,
much lower than in part a (even though we are still eliminating 4 tons of pollution). In other words,
by using tradable permits, 4 tons of pollution were eliminated for $600 less than if the government
used regulation and made each firm reduce 1 ton of pollution.
c. Describe the benefits of the government to using tradable permits as a way to control pollution. What
are the drawbacks or potential problems with using tradable permits?
The benefit is that the cost of eliminating pollution is much lower because those firms that can
eliminate pollution most cheaply are the firms that are eliminating the pollution. We did not have
time to talk about the drawbacks of using tradable permits.
7. Pick out a newspaper article and analyze/explain it based on the information you have learned this
semester. For example, you might use supply and demand to explain what is happening or you might use
what we learned in market structure, etc. Basically, I want you to pick any article you would like and
show how your understanding of the article now is better than what it would have been before you took a
class on Principles of Microeconomics.
Answers will vary.