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11 Chapter Monopolistic Competition and Oligopoly (Appendix)
Chapter 11 Monopolistic Competition and Oligopoly (Appendix)
APPENDIX QUESTIONS
1.Is the game shown by Figure 11.3 in the chapter (not this appendix) a zero-sum game or is it a
positive-sum game? How can you tell? Are there dominant strategies in this game? If so, what are
they? What cell represents a Nash equilibrium and why? Explain why it is so difficult for Uptown
and RareAir to achieve and maintain a more favorable cell than the Nash equilibrium in this
single-period pricing game. LO8
Answer: This is a positive-sum game since the sum of the payoffs for each firm is
positive. Yes, the dominant strategy is for both firms to use a low price strategy. This
strategy will provide the highest payoff regardless of what the other firm does. The Nash
equilibrium is for both firms to play the low price strategy (low-low cell) since neither
firm has an incentive to deviate from this strategy given the strategy of the competing
firm.
The more favorable outcome would be for both firms to collude and use the high price
strategy. Both firms would earn a profit of $12 rather than $8 in this case. The problem is
that both firms have an incentive to deviate from this strategy given that the other firm is
playing the high price strategy. By pricing low, given the other firm is pricing high,
profits increase to $15 (rather than $12 through cooperation).
2.Refer to the payoff matrix in question 8 at the end of this chapter. First, assume this is a onetime game. Explain how the $60/$57 outcome might be achieved through a credible threat. Next,
assume this is a repeated game (rather than a one-time game) and that the interaction between the
two firms occurs indefinitely. Why might collusion with a credible threat not be necessary to
achieve the $60/$57 outcome? LO8
Answer: Either firm could threaten to flood the market to induce the other firm to choose
the $40 pricing strategy. This threat is likely to be credible since both firms benefit from
the $40 pricing strategy. In a repeated game setting this threat may not be necessary since
the present value of cooperation may exceed the one-time gains from deviating from the
$40-$40 pricing strategy. Thus, each firm may have incentive not to deviate from the
$40-$40 strategy out of fear of lower profits in the future.
11A-1
Chapter 11 Monopolistic Competition and Oligopoly (Appendix)
3. Refer to the payoff matrix below. LO8
Assuming this is a sequential game with no collusion, what is the outcome if Firm A moves first
to build a new type of commercial aircraft? Explain why first-mover strategies in the real-world
are only as good as the profit projections on which they are based. How could a supposed win
from moving first turn out to be a big loss, whereas the loss of being preempted turn out to be a
blessing in disguise?
Answer: The dominant strategy for firm B is to build. The payoff from this buildstrategy is greater than the alternative not to build, regardless of what firm A does. Since
firm A will recognize this strategy, they will choose not to build, thus minimizing their
losses. Thus, even as a first mover firm A will choose not to build.
A win for firm B may not materialize if the projections about profits are incorrect. For
example, if there is a global downturn that reduces the demand for aircraft and firm B has
already built the aircraft, then this may result in a loss for firm B.
4. ADVANCED ANALYSISSuppose you are playing a game in which you and one other
person each picks a number between 1 and 100, with the person closest to some randomly
selected number between 1 and 100 winning the jackpot. (Ask your instructor to fund the
jackpot.) Your opponent picks first. What number do you expect her to choose? Why? What
number would you then pick? Why are the two numbers so close? How might this example relate
to why Home Depot and Lowes, Walgreens and Rite-Aid, McDonalds and Burger King, Borders
and Barnes & Noble, and other major pairs of rivals locate so close to each other in many welldefined geographical markets that are large enough for both firms to be profitable? LO8
Answer: As the first player it is optimal to choose 50. The reasoning is that your
opponent could choose a number that significantly reduces your chances of winning if
you didnt choose 50. For example, if you choose 1, the next player could choose 2.
Thus, the only way you win is if the number 1 is drawn. How about picking 25? Your
opponent would pick 26. Thus you only have a 25% chance of winning. How about 49?
The same logic applies.
The logic applies to companies that market similar (identical products). All of these
companies choose a central location to maximize their share of costumers, assuming
consumers base their behavior on distance alone. But even if this isnt a valid assumption
the theory still applies for a homogeneous population.
11A-2
Chapter 11 Monopolistic Competition and Oligopoly (Appendix)
APPENDIX PROBLEMS
1. Consider a punishment variation of the twofirm oligopoly situation shown in the figure
below. Suppose that if one firm sets a low price while the other sets a high price, then the firm
setting the high price can fine the firm setting the low price. Suppose that whenever a fine is
imposed, X dollars is taken from the lowprice firm and given to the highprice firm. What is the
smallest amount that fine the X can be such that both firms will want to always set the high price?
LO8
Answer: $3 million and one cent (also accept $3 million as an answer here).
Feedback: Let's look at the following example. Consider a punishment variation of the
twofirm oligopoly situation shown in Figure 11.3 in the chapter (not in this appendix).
Suppose that if one firm sets a low price while the other sets a high price, then the firm
setting the high price can fine the firm setting the low price. Suppose that whenever a fine
is imposed, X dollars is taken from the lowprice firm and given to the highprice firm.
What is the smallest amount that the fine X can be such that both firms will want to
always set the high price?
From the above figure we can see if one firm deviates from the high price while the other
maintains the high price the firm that deviates will earn an extra $3 million in profits (If
the firm continued with the high price it would earn $12 million and if the firm deviates it
will earn $15 million).
Given this potential for additional profit the fine will need to be equal to or greater than
this value. If the fine is set at $3 billion (plus one cent) it is in the firm's interest to
maintain the high price because the fine (penalty) is greater than the gain.
11A-3
Chapter 11 Monopolistic Competition and Oligopoly (Appendix)
2. Consider whether the promises and threats made toward each other by duopolists and
oligopolists are always credible (believable). Look at the figure below. Imagine that the two
firms will play this game twice in sequence and that each firm claims the following policy. Each
says that if both it and the other firm choose the high price in the first game, then it will also
choose the high price in the second game (as a reward to the other firm for cooperating in the first
game). LO8
a) As a first step toward thinking about whether this policy is credible, consider the situation
facing both firms in the second game. If each firm bases its decision on what to do in the second
game entirely on the payouts facing the firms in the second game, which strategy will each firm
choose in the second game?
b) Now move backward in time one step. Imagine that it is the start of the first game and each
firm must decide what to do during the first game. Given your answer to part a, is the publicly
stated policy credible? (Hint: No matter what happens in the first game, what will both firms do
in the second game?)
c) Given your answers to a and b, what strategy will each firm choose in the first game?
Answer: (a) Each firm will choose the low price strategy in the second game.
(b) No..
(c) Each firm will choose the low price strategy in the first game.
Feedback: Let's look at the following example. Consider whether the promises and
threats made toward each other by duopolists and oligopolists are always credible
(believable). Look back at Figure 11.3 in the chapter (not in this appendix). Imagine that
the two firms will play this game twice in sequence and that each firm claims the
following policy. Each says that if both it and the other firm choose the high price in the
first game, then it will also choose the high price in the second game (as a reward to the
other firm for cooperating in the first game).
11A-4
Chapter 11 Monopolistic Competition and Oligopoly (Appendix)
a) As a first step toward thinking about whether this policy is credible, consider the
situation facing both firms in the second game. If each firm bases its decision on what to
do in the second game entirely on the payouts facing the firms in the second game, which
strategy will each firm choose in the second game?
Each firm will choose the low price strategy in the second game. The reason is that there
can be no penalty after this stage of the game because the game ends. Here the low price
strategy strictly dominates the high price strategy for both firms. If Uptown air plays low
they are better off than if they played high regardless of the choice made by RareAir. If
RareAir plays high then Uptown Air receives $15 (which is greater than $12). If RareAir
plays low then Uptown Air receives $8 (which is greater than $6).
The same logic applies to the choice made by RareAir. Thus, the choice is low-low at this
stage of the game.
b) Now move backward in time one step. Imagine that it is the start of the first game and
each firm must decide what to do during the first game. Given your answer to part a, is
the publicly stated policy credible? (Hint: No matter what happens in the first game, what
will both firms do in the second game?)
The policy is not credible because firms will not follow through on promises to play the
high price strategy in the second game. Because both firms will base their decisions in
the second game on the payouts in the second game, they will always choose the low
price strategy in the second game.
c) Given your answers to a and b, what strategy will each firm choose in the first game?
Each firm will choose the low price strategy in the first game. This is because they know
that nothing they do in the first game will affect the decisions that each of them will make
to play the low price strategy in the second game. Thus, they base their decision about
the first game solely on the payouts from the first game. Doing so leads both firms to
choose the low price strategy in the first game.
11A-5