American University, Economics 101: Problem Set 5 Analysis

This economics assignment provides solutions to a problem set covering key microeconomic concepts. Problem 1 analyzes a monopoly market, examining profit maximization, consumer surplus, deadweight loss, and price discrimination strategies. Problem 2 explores a duopoly market scenario using game theory, focusing on advertising decisions, dominant strategies, and Nash equilibrium. Problem 3 delves into pollution control, evaluating different government policies such as emission standards, Pigouvian taxes, and tradable emissions permits. The solutions include detailed calculations, explanations, and graphical analysis to illustrate economic principles and market outcomes.

Instructions:
1. All of your answers will be typed directly into this file. FOLLOW THE
INSTRUCTIONS IN EACH QUESTION REGARDING HOW TO RECORD
YOUR ANSWER.
2. For all typed answers, USE EITHER THE “ARIAL” OR “HELVETICA” FONT
(OR A SIMILAR FONT IF YOU DON’T HAVE THOSE)
3. For questions asking you to “explain your answer”, you must provide an explanation of
your answer to be eligible for full credit.
4. To prepare your file for submission, follow the directions in the description of the
assignment on Blackboard
5. Please name the file that you will submit to Blackboard as follows:
[Family Name]_[First Name]_PS5.pdf
So, for example, a submission from Joe Smith would be named: Smith_Joe_PS5.pdf
PROBLEM 1 (20 POINTS)
Suppose the market for diamonds is controlled by a single monopoly producer, Diamond Corp.
Diamond Corp has constant marginal costs of production, and no fixed costs. Figure 1 on p. 6
depicts the demand for diamonds, the marginal revenue curve for Diamond Corp when charges the
same price for all units sold, and Diamond Corp’s costs of production.
a. If Diamond Corp wants to maximize profit, how many diamonds will it produce and what
price will it charge? [TYPE YOUR ANSWER BELOW]
To maximize profit, Diamond Corp will produce 7 units of diamonds and charge
$650 per diamond.
b. Calculate the amount of Consumer Surplus, Profit and Deadweight generated if Diamond
Corp chooses the quantity and price you found in part (a). [TYPE YOUR ANSWER
BELOW]
Consumer surplus is $1225. Profit is $2450. Deadweight generated is $1225.
c. The CEO of Diamond Corp. hires a market research firm to learn more about the
characteristics of consumers in the market for diamonds. The report concludes that, among
the people who demand diamonds and are willing to pay for them, 7 people have a
willingness to pay $650 or more per diamond, 5 people have a willingness to pay between
$400 and $649.99 per diamond, and the rest of the people have a willingness to pay of less
than $400.
The marketing firm also provides one more important piece of information: the 5 people
who have a willingness to pay between $400 and $649.99 are all senior citizens (i.e. they
are 65 years of age or older).
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How could the CEO of Diamond Corp. use this information to increase Diamond Corp.’s
profits above the level you calculated in part (b)? [TYPE YOUR ANSWER BELOW]
The CEO of Diamond Corp using this information would use strategy of first
degree price discrimination for all the consumers which is based on willingness to
pay.
d. If the CEO of Diamond Corp. followed the strategy you describe in your answer to part
(c), how much total profit will Diamond Corp earn? How much total Consumer Surplus
will there be? How much Deadweight Loss? [TYPE YOUR ANSWER BELOW]
By using the strategy, Diamond Corp makes profit of $4900. There are no
Consumer Surplus and no Deadweight Loss.
e. Suppose that, instead of being able to choose whatever price it wanted, Diamond Corp
were required by the government to sell its diamonds at marginal cost. (That is, suppose
that Diamond Corp must set Price = Marginal Cost.) How many units would be sold? At
what price? [TYPE YOUR ANSWER BELOW]
At Price = Marginal Cost, Diamond Corp would have sold 14 units at price $300
per diamond.
f. Calculate the amount of Consumer Surplus, Profit and Deadweight Loss generated when
Diamond Corp is required to sell its diamonds at marginal cost. [TYPE YOUR
ANSWER BELOW]
At Price = Marginal Cost, Consumer Surplus is $4900. However, Diamond Corp
would make zero economic profit and there will be no Deadweight Loss.
PROBLEM 2
Amy, a student at American University, developed an app last year that allows American
University students to stream premium TV and movie content at discounted rates. For several
months hers was the only app that provided this service, but then another student, Beatriz,
developed a rival app that was capable of providing exactly the same service. Currently, the
market for these discounted streaming services is a duopoly, with only Amy and Beatriz as
producers. Because she was first in the market, Amy has a slightly higher share of the market, but
Beatriz is slowly gaining on her.
Both Amy and Beatriz are now considering spending money on advertising for their app, to try to
gain more market share and increase their sales. Advertising in this market can be very effective.
If only Amy advertises (and Beatriz does not), Amy will earn $8,000 per month in profits and
Beatriz will earn only $500. If only Beatriz advertises (but Amy does not), Beatriz will earn
$6,000 and Amy will earn $1,000. If both of them advertise, Amy’s monthly profits will be
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$5,000 and Beatriz’s will be $3,000. If neither of them advertise, Amy’s profits will be $7,000 and
Beatriz’s will be $4,000.
a. The figure below is a payoff matrix that summarizes the payoffs to Amy and Beatriz (in
terms of monthly profits) that will result from their decision to advertise or not to
advertise, depending on what the other player has chosen. Payoffs to Beatriz belong in the
(white) upper-right portion of each square, and payoffs to Amy belong in the (shaded)
lower-left portion. Based on the information provided above, fill in the empty rectangles in
the payoff matrix. [TO ENTER AN ANSWER INTO A RECTANGLE, CLICK
ANYWHERE IN THE RECTANGLE AND THEN TYPE YOUR ANSWER]
BEATRIZ
b. What is the definition of a “dominant strategy”? [TYPE YOUR ANSWER BELOW]
In game theory, dominant strategy can be defined as the strategy which is better
than all the available strategy option for a given player as it gives the highest
payoff no matter what strategy is taken by the opponent.
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AMY
Don’t
Advertise Advertise
Don’t
Advertise
Advertise
8000
123$800$80
00$$
$7000
$8000
$500
$4000 $6000
$1000
$3000
$5000

c. Does Amy have a dominant strategy? If so, what is it? Does Beatriz have a dominant
strategy? If so, what is it? For full credit you must explain your answer. (That is, if you
think a player does not have a dominant strategy, explain why. If you think a player does
have a dominant strategy, explain how you know that strategy is dominant.) [TYPE
YOUR ANSWER BELOW]
Yes, Amy have dominant strategy. Dominant strategy for Amy is to advertise. By
looking at the payoff matrix, it can be seen that if Beatriz choose don’t advertise then
choosing advertise would pay Amy more than choosing don’t advertise since $8000 is
greater than $7000. Again, if Beatriz choose advertise then also choosing advertise
would pay Amy more than choosing don’t advertise, since $5000 is greater than $1000.
Thus, advertise is dominant strategy for Amy because it gives highest payoff irrespective
of strategy choice of Beatriz. On the other hand, if Amy choose to advertise the Beatriz
would choose advertise because advertise pay more than don’t advertise since $3000 is
greater than $500. Similarly, if Amy choose don’t advertise then Beatriz would choose
advertise because it gives more pay than don’t advertise since $6000 is greater than
$4000. Therefore, Beatriz chooses to advertise irrespective of what Amy does because
choosing to advertise gives the highest payoff. Therefore, dominant strategy for Beatriz is
to advertise.
d. Is there a Nash Equilibrium of the game depicted in the payoff matrix above? If not, how do
you know. If there is a Nash Equilibrium, what is it and how do you know it’s a Nash
Equilibrium? [TYPE YOUR ANSWER BELOW]
Yes, there is a Nash Equilibrium in the above payoff matrix. The Nash Equilibrium
in the payoff matrix is given by Amy’s Advertise choice and Beatriz’s Advertise choice
($5000, $3000). Given the choice of Amy as advertise, Beatriz cannot gain from any
choices other than advertise because by choosing other available choices Beatriz would
be worse off. Similarly, in the case of Amy any choice of strategy other advertise would
make her worse given the choice of Beatriz as advertise. Advertise/Advertise ($5000,
$3000) is the only Nash Equilibrium in the above payoff matrix.
PROBLEM 3
In the island nation of Belair there are two fossil fuel power plants that provide all the nation’s
electricity. One plant is owned by Aircorp and the other is owned by Belcorp. The Aircorp plant is
older and operates with less efficient equipment than the Belcorp plant. Both plants produce
pollution as a by-product of their production of electricity. (That is, they produce pollution at zero
cost.)
Figure 2 (on p. 6) depicts the Marginal Benefit of Pollution for each of the two plants – that is, the
curves reflect the cost of cleaning up 1 unit of pollution at various levels of pollution emission for
each plant. Table 1 (on p. 7) contains the data used to generate the graph.
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a. If there is no government regulation of pollution, how many units of pollution will
Aircorp emit? How many units of pollution will Belcorp emit? Explain your answers.
[TYPE YOUR ANSWER BELOW]
Without any government regulation of pollution, Aircorp would emit 100 units of
pollution and Belcorp would emit 100 units of pollution. Both Aircorp and Belcorp faces
zero cost for emitting pollution thus whatever amount of pollution they emit that does not
include in their cost of production or have to pay in any means for polluting. Hence, they
would emit pollutants as long as there is requirement for production of electricity.
b. Suppose the government of Belair decides that it wants to reduce total pollution emissions
to 100 units by prohibiting any company from emitting more than 50 units of pollution.
How many units of pollution will each firm now emit? What will be the Marginal Benefit
of Pollution for each firm at their level of emissions? (Note: you are being asked to provide
4 numbers here: Aircorp emissions; Aircorp Marginal Benefit of
Pollution; Belcorp emissions; Belcorp Marginal Benefit of Pollution) [TYPE YOUR
ANSWER BELOW]
After pollution prohibition rule imposed by the government, both Aircorp and
Belcorp would emit 50 units of pollution each. For Aircorp at 50 units of pollution
emission, Marginal Benefit of Pollution is 150. On the other hand, for Belcorp at 50 units
of pollution emission, Marginal Benefit of Pollution is 50.
c. Suppose that instead of the policy in part (b), the government decides to reduce pollution
using a Pigouvian Tax (i.e. a per-unit emissions tax). Specifically, they impose a tax of $30
per unit of pollution of emission. How many units of pollution will each firm now
emit? What will be the Marginal Benefit of Pollution for each firm at their level of
emissions? [TYPE YOUR ANSWER BELOW]
After government imposes tax of $30 per unit of pollution emission, Aircorp would
emit 90 units of pollution and Belcorp would emit 70 units of pollution. At 90 units of
pollution emission, Aircorp’s Marginal Benefit of pollution is 30. At 70 units of pollution
emission, Belcorp’s Marginal Benefit of pollution is 30.
d. The $30 per-unit emissions tax fails to achieve the government’s goal of 100 total units of
pollution, and the Governor of Belair asks for your help in improving the tax policy. How
much should the per-unit tax be if the government wants to achieve 100 units of
total pollution? How many units of pollution will each firm emit when the tax is at this
level? [TYPE YOUR ANSWER BELOW]
In order to achieve the goal of 100 total units of pollution the government should
impose a tax of $75 per unit of pollution emission. At this level of tax, Belcorp would emit
25 units of pollution and Aircorp would emit 75 units of pollution.
The governor of Belair decides that she wants to pursue pollution reduction using a tradeable
emissions permit program rather than with environmental standards or Pigouvian taxes. She issues
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100 pollution permits (with each allowing the holder of the permit to emit 1 unit of pollution) and
gives 50 permits to Aircorp and 50 permits to Belcorp.
e. Immediately after the permits are given to the two firms (and before any trading occurs),
how many units of pollution will each firm emit? What will be the Marginal Benefit of
Pollution for each firm at their level of emissions? [TYPE YOUR ANSWER BELOW]
After receiving 50 pollution permits each, Aircorp would emit 50 units of pollution
and Belcorp would emit 50 units of pollution. At 50 units of pollution level, Marginal
Benefit of Pollution for Aircorp is 150. . At 50 units of pollution level, Marginal Benefit of
Pollution for Belcorp is 50.
f. How many units of pollution will each firm emit after they have been able to buy and/or
sell as many permits from each other as they want to? What will be the Marginal
Benefit of Pollution for each firm at those levels of emissions? [TYPE YOUR
ANSWER BELOW]
After Aircorp and Belcorp are able to buy permit from each other, Aircorp would emit 75
units of pollution and Belcorp would emit 25 units of pollution. At 75 units of pollution,
Marginal Benefit of Pollution for Aircorp is 75. At 25 units of pollution, Marginal Benefit of
Pollution for Belcorp is 75.
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FIGURE 1. Demand, Marginal Revenue and Costs in the Diamond Market
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FIGURE 2. Marginal Benefit of Pollution for Aircorp and Belcorp
TABLE 1. Marginal Benefit of Pollution for Aircorp and Belcorp
Marginal Benefit of Pollution
Units of
Pollution Belcorp Aircorp
0 100 300
5 95 285
10 90 270
15 85 255
20 80 240
25 75 225
30 70 210
35 65 195
40 60 180
45 55 165
50 50 150
55 45 135
60 40 120
65 35 105
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70 30 90
75 25 75
80 20 60
85 15 45
90 10 30
95 5 15
100 0 0
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