ECON-115 Industrial Organization – Second Midterm Key 2k14
Name ____________________
Part I: Matching. Match the terms on the left with the definitions on the right (1/2 point each)
1 First mover
K a. Takes place under the Cournot Model, when response
advantage
functions are downward sloping
2 Sequential games
E b. No firm wants to change its current strategy given that no
other firm changes its current strategy
3 Prisoner’s Dilemma D c. It provides a firm’s profit maximizing choices, given the
other firm’s choice of output
4 Limit pricing
I d. An example where two dominant strategies do not lead to
the optimal outcome for the players
5 Reaction function
C e. One player moves; the second player follows
6 Productive capacity L f. Their presence radically alters the outcome of Bertrand
style competition.
7 Strategy
J g. The strategy that’s never chosen
8 Nash equilibrium
B h. Debunks the idea that incumbent firms should fight
competitors to “scare off” future competition
9 Aggressive
A i. A way to deter a rival’s entry by keeping prices low
response
10 Capacity
F j. In game theory, it’s a plan of action
constraints
11 Dominated strategy G k. One possible outcome of Stackelberg competition
12 Chain-store
H l. Installing it prior to production may deter a rival’s entry
paradox
into a market, especially if it’s costly to do
Part II: Multiple Choice. For questions 13-34, circle the best answer. (1/2 point each)
13. A critical assumption of game theory is:
a. People like to compete
b. Firm’s strategies are unpredictable
c. Players act rationally
d. None of the above
14. A dominant strategy is one that is:
a. Most effective
b. Always chosen by a player
c. Very profitable
d. Ensures market domination by one firm
For questions 15, 16 and 17, use the following pay-off matrix. Firm 1’s options are “Top” and
“Bottom” and its pay-offs are the values on the left side of each box. Firm 2’s options are “Left”
and “Right” and its pay-offs are the values on the right-hand side of each box.
FIRM II
FIRM I
Left
Top 3, 2
Bottom 2, 5
15. Does Firm 1 have a dominant strategy?
a. Yes, Top
b. Yes, Bottom
c. No dominant strategy
d. Not enough information to determine this
16. Does Firm 2 have a dominant strategy?
a. Yes, Left
b. Yes, Right
c. No dominant strategy
d. Not enough information to determine this
17. What is the Nash Equilibrium in this example?
a. Top, Left
b. Top, Right
c. Bottom, Left
d. Bottom, Right
18. A critical assumption of the Cournot Model of Duopoly is:
a. Firms cooperate
b. Firms practice product differentiation
c. The firms are focused on pricing
d. Firms produce identical products
19. Under Cournot, a “reaction function” for each firm is:
a. Its profit maximizing function
b. Dependent on the other firm’s output
c. Similar to the cost function
d. a & b
20. In the Cournot Model, the Nash equilibrium occurs where:
a. Price = marginal cost
b. The intersection of the reaction functions
c. Firm 1’s output > Firm 2’s
d. None of the above
Right
5, -2
6, 4
21. From a welfare perspective, the Cournot Model predicts that in a market with two identical
firms and products, the outcome in terms of overall market price and aggregate quantity is:
a. Superior to a monopoly but less good than under perfect competition
b. Equal to the monopoly outcome
c. Similar to a perfectly competitive market
d. The outcome varies depending on the product.
22. Assume a market demand function, P = A – BQ, and all firms’ per unit costs = c. A Cournot
Model for N identical firms ultimately yields the following price function: P = (A + Nc)/(N + 1).
If we rewrite this as P = A/(N + 1) + Nc/(N + 1), what does this tell us?
a. As the number of firms grows, price tends to increase
b. As the number of firms grows, aggregate output remains constant
c. As the number of firms grows, price tends to the competitive outcome (P = c)
d. b & c
23. Bertrand’s Duopoly Model differs from Cournot’s in one significant respect:
a. Firms compete on price
b. Firms compete on cost reduction
c. Firms compete on quantity
d. Both models are very similar
24. In its most basic form (two firms, identical cost structures and products, no capacity
constraints), the Bertrand Model predicts price ultimately will:
a. Equal cost
b. Equal price under a monopoly
c. Pmonopoly > Pbertrand > Pcournot
d. Pmonopoly > Pbertrand > Pcompetitive
For questions 25 – 26, use the following information:
Two identical movie theaters show the same film on the same night with each theater’s fixed
marginal cost for presenting the film = 5/person. The demand function for watching the film is Q
= 550 – 10P. Each theater’s capacity is 225.
25. What is the quantity demanded if the theaters set price = cost?
a. 100
b. 550
c. 500
d. 1050
26. Given the capacity constraints the theaters face, the Bertrand Model points to the following
more likely outcome.
a. Aggregate attendance 225; Price = 32.50
b. Aggregate attendance is between 225 and 450; Price cannot be determined.
c. Aggregate attendance 450; Price = 10
d. Aggregate attendance 450; Price = 12
27. In applying Bertrand competition to product differentiation (using the Hotelling spatial
model), it can be determined that for two firms, profits for each = Nt/2, where N is the total
number of consumers and t is the value consumers put on getting their own preferred variety of
product. The implication is:
a. The more value consumers place on their preferred products, the more profits firms
earn.
b. The more value consumers place on their preferred products; the less profits firms earn.
c. The value consumers place on their preferred products does not affect profits.
d. The question is meaningless because all firms maximize profits at MC = MR.
28. One major difference between Cournot and Bertrand competitions is how they respond to
changes in their competitors’ costs. Cournot competitors respond “aggressively” while Bertrand
competitors respond “passively.” In practical terms, if a firm’s costs rise, the second firm:
a. Decreases quantity under Cournot and increases price under Bertrand.
b. Increases quantity under Cournot and decreases price under Bertrand.
c. Increases quantity under Cournot and increases price under Bertrand.
d. Decreases quantity under Cournot and decreases price under Bertrand.
29. Unlike simultaneous games, a sequential game creates an advantage to:
a. The first mover
b. The second mover
c. The first or second mover [Check answer]
d. Neither player
30. The Stackelberg Duopoly Model is similar to the Cournot Model in that:
a. Both are price based.
b. Both are sequential games.
c. Both are quantity based.
d. Neither confers a first mover advantage.
31. In the Stackelberg Duopoly Model, the first mover produces output (q) at:
a. The competitive level
b. The monopoly level
c. At a level similar to Cournot
d. All of the above are possible
32. Why are consumers better off when one firm enjoys a first mover advantage (Stackelberg), as
compared to a Cournot situation when neither firm enjoys an advantage?
a. Superior product quality
b. Better customer service
c. Great product differentiation
d. More quantity produced and lower prices
33. Under Stackelberg competition, but where firms compete on price, the advantage will be
conferred on the ________ and the prices will ultimately set ______
a. First mover, at marginal cost
b. Second mover, where MR = MC
c. Neither party, at marginal cost
d. Neither party, where MR = MC
34. In discussing the evolution of markers, which fact about the entry of new competitors is true?
a. Entry is common
b. The survival rate for entrants is low
c. Entrants are small
d. All of the above
35. Both forms of predatory behavior – predatory pricing and limit pricing – enable monopolists
to retain control of markets. However, legal action almost always focuses on predatory pricing.
Why?
a. Most regulators are unfamiliar with limit pricing.
b. Limit pricing sounds benign, where predatory pricing sounds menacing.
c. A limit pricing strategy is more difficult to maintain.
d. Predatory pricing has an identifiable victim.
36. During its first 50 years of existence, Alcoa exercised a virtual monopoly over the aluminum
ingot market. What happened to prices of aluminum (per lb.) during this time?
a. Rose slowly with inflation
b. Fall dramatically
c. Stayed nearly constant
d. Fell but only after government intervention
PART III. Problems. Solve the following problems. Please show your work. (5 points each)
31. A regulated monopoly faces the following demand for its product, P = 56 – 2Q, and has a
marginal cost of MC = 20. Q is the quantity sold and P is the price.
a. Under regulation, the firm must set P = MC. Find the regulated price and quantity in this
market.
56 – 2Q = 20
2Q = 36
Q = 18
P = 20
b. Suppose the firm is allowed to set prices at its profit-maximizing level. What is equilibrium
price and quantity for its product now? Use marginal revenue (MR) = 56 – 4Q to solve the
problem.
56 – 4Q = 20
36 = 4Q
Q=9
P = 56 – 2(9) = 38
c. Now, imagine there are two identical firms, selling the same product and with the same MC =
20. The resulting market price is P = 56 – 2*(q1+q2). Use this information to find the Cournot
solution to both firms’ profit maximizing output and price.
(A – C)/3B
(56 – 20)/3(1) = 12
q1 = q2 = 6
Qtotal = 12
P = 56 – 2(12) = 32
d. Comparing prices set at marginal cost (a.), prices set at the profit maximizing level (b.) and
prices set by profit maximizing oligopolies (c.), where are the prices highest? Lowest? How does
the oligopoly prices in c. compare to the other two?
Prices are highest at profit maximization (38)
Prices are lowest at marginal cost (20)
Oligopoly is between the two 20 < 32 < 38
32. A market demand function is P = 100 – Q. MC = 40. There are two firms, one a “leader”
(Firm 1) and the second a “follower” (Firm 2). Firm 1 will select its output, q1; Firm 2, observing
Firm 1’s choice of q1, will then select its own output, q2. Both firms have 0 fixed costs and a
constant marginal cost of 40 per unit produced.
a. Derive the follower firm – Firm 2’s – best response function. Do so by determining Firm 2’s
marginal revenue function and equating it to marginal cost.
P = 100 – q1 – q2
P(q2) = 100q2 – q1q2 – q22
P’(q2) = 100 – q1 – 2q2 = 40
60 – q1 = 2q2
q2 = 30 – q1/2
b. Firm 1 – the leader – makes its optimal choice of output knowing Firm 2’s best response
function. Use Firm 2’s best response function (determined in (a.), to calculate Firm 1’s profit
maximizing output, q1*. Do so by determining Firm 1’s demand and marginal revenue (MR)
functions and then by equating MR to marginal cost.
P = 100 – q1 – 30 + q1/2
P = 70 – q1/2
Pq1 = 70q1 – q12/2
Pq1’ = 70 – 2q1/2 = 40
q1 = 30
c. Use your answers to calculate Firm 2’s output, q2*. Then calculate:
q2 = 30 – 15 = 15
1) Overall quantity sold (Q) = 15 + 30 = 45
2) Market price (P) = 100 – 45 = 55
3) Profit to Firm 1 (leader) = (55 – 40)(30) = 450
4. Profit to Firm 2 (follower) = (55-40)(15) = 225
d. Use the original demand equation (P = 100 – Q) to calculate the monopoly price (at the point
where MR = MC) and quantity produced under monopoly. Use this result to answer the
following questions.
100Q – Q2 = 100 – 2Q = 40
2Q = 60
Q = 30
1) The monopoly quantity is equal to what other quantity is the problem?
Equal to 30 which is q1 (Firm 1)
2) Given your answer in 1), is the consumer better off under a monopoly or Stackelberg
oligopoly? Please justify your answer in terms of quantities and prices.
Better off under Stackelberg because more Quantity is produced at lower prices
(q1 = 30, P = 70) Stackelberg
(q2 = 15, P = 85) Monopoly
Profit for firm 1 > Profit for firm 2
450 > 225