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Questions on Oligopoly
Questions with Solutions Provided:
1. An industry consists of two firms, each of which have variable costs of $10 per unit
but no fixed costs. The industry demand curve is P = 70 - Q.
a) Solve for the Cournot equilibrium. In doing so, derive the reaction function of each
firm (call Q1 and Q2 the output of each firm). Solve for each firm's output, the market
price, and each firm's profits.
b) Graph the reaction functions of each firm.
c) Now suppose that firm 1 is a Stackelberg leader while firm 2 is a follower. Assume,
as usual, that the follower behaves like a Cournot duopolist (that is, assumes that the
leader's output is fixed). How will each firm behave (in terms of reaction functions)?
What will each firm produce, what will the price be, and what profits will each firm
earn?
d) What will happen if this market is "contestable"? What conditions are necessary for
contestability to be a real possibility?
e) Compare the Cournot and Stackelberg outcomes with the outcomes if the firms
collude and split the market, and with the outcome if the firms compete as price takers
and split the market. Compare the four outcomes in terms of price, output, and each
firm's profits. On a graph of the demand curve, show price and output for each
outcome. Draw the industry's marginal cost curve. Compute the efficiency loss relative
to competition for the other three outcomes.
Solutions to Above Questions:
1a) P = 70 - Q1 - Q2
Thus for the first firm, MR1 = (70-Q2) - 2Q1 = MC = 10 so the first firm's reaction
function is Q1 = 30 - 0.5Q2
Similarly, for the second firm, MR2 = (70-Q1) - 2Q2 = MC = 10 so the second firm's
reaction function is Q2 = 30 - 0.5Q1
Solving the two reaction functions simultaneously, Q1 = 30 - .5(30-.5Q1)
or Q1 = 15 + .25Q1 or .75Q1 = 15 or Q1 = 20
From the second firm's reaction function, Q2 = 20
From demand, P = 30
Each firm's profits are π1 = π2 = Qi(P-AC) = 20(30-10) = 400
b)
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Quantity
produced
by Firm 2
60
Reaction
function of
Firm 1- R1(Q2)
30
Reaction
function of
Firm 2- R2(Q1)
20
0
20
30
60
Quantity
produced
by Firm 1
c) Firm 2 continues to react according to Q2 = 30 - 0.5Q1
Firm 1, the Stackelberg leader, takes this reaction function as a given.
Thus firm 1 knows that if he produces Q1, firm 2 will react accordingly and the price
will be P = 70 - Q1 - (30-.5Q1) = 40 - 0.5Q1. This is, therefore, the demand function for the
output of the Stackelberg leader.
Thus, MR1 = 40 - Q1 = MC = 10, so Q1 = 30 and, from #2's reaction function, Q2 = 15.
Therefore, since output is 45 units, P = 70 – 45 = 25, π1 = Q1(P-AC) = 30(15) = 450, π2 =
Q2(P-AC) = 225
d) A market is contestable if potential competitors can enter and exit without incurring
sunk (irretrievable) costs. If the market is contestable, then any potential competitor
will be willing to enter if there are positive profits. Thus, the price of incumbent firms is
driven down to AC, so P = 10, QT = 60.
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e) Under collusion, MRT = 70-2QT
MR=MC=10, so QT = 30, P = 40,
Thus Q1=Q2=15, π1=π2=450
From the graph at right,
P
i) Competition has P = 10, Q = 60,
CS = 1800, DWL = 0
ii) Cournot has P = 30, Q = 40, CS = 800
Since πT = 800, DWL = 200
iii) Stackelberg has P = 25, Q = 45,
CS = 1012.5
Since πT = 675, DWL = 112.5
iv) Collusion has P = 40, Q = 30,
CS = 450
Since πT = 900, DWL = 450
70
40
30
25
10
0
MC = AC
30
40
45
60
70
P
Questions with No Solutions Provided:
2. Assume that industry demand is P = 1000 – Q and that there are three firms in an
industry who all adopt Cournot-type assumptions. In other words, each of the firms
assumes that the other firms will keep their output constant at its current level so
that this firm can profit maximize with the residual demand. Each one of these firms
has marginal costs which are constant at MC = 100. The sum of the output of the
three firms makes up total quantity produced, so q1 = q2 = q3. In this industry, what
will be the equation of the reaction function of Firm #1?
A) q1 = 1000 - q2
B) q1 = 900 - q2
C) q1 = 450 - q2
D) q1 = 450 - .5q2
E) q1 = 1000 – q3
F) q1 = 900 – q3
G) q1 = 450 – q3
H) q1 = 450 - .5q3
I) q1 = 1000 - q2 - q3
J) q1 = 900 - q2 - q3
K) q1 = 450 - q2 - q3
L) q1 = 450 - .5q2 - q3
M) q1 = 450 - .5q2 - .5q3
N) none of the above
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3-9. An industry consists of two firms, each of which have variable costs of $12 per unit
but no fixed costs. The industry demand curve is P = 216 - 2Q. Questions 3 through 9
concern this industry.
3. If the firms collude and agree to split the total profits in the industry, then the price
that will result is:
A) $0
B) $12
C) $24
D) $28
E) $32
F) $34
G) $36
H) $38
I) $40
J) $45
K) $49
L) $56
M) $63
N) $69
O) $75
P) $80
Q) $88
R) $104
S) $108
T) $114
U) $118
V) $124
W) $148
X) $156
Y) more information is needed to answer
Z) none of the above
4. If the firms compete under the Cournot assumptions (that is, each firm assumes that
the other firm will not change its output), then the price that will result in the Nash
equilibrium is:
A) $0
B) $12
C) $24
D) $28
E) $32
F) $34
G) $36
H) $38
I) $40
J) $45
K) $49
L) $56
M) $63
N) $69
O) $75
P) $80
Q) $88
R) $104
S) $108
T) $114
U) $118
V) $124
W) $148
X) $156
Y) more information is needed to answer
Z) none of the above
5. Now suppose that one firm is a Stackelberg leader while other firm is a follower.
Assume, as usual, that the follower behaves like a Cournot duopolist (that is, assumes
that the leader's output is fixed). Then the price that will result is:
A) $0
B) $12
C) $24
D) $28
E) $32
F) $34
G) $36
H) $38
I) $40
J) $45
K) $49
L) $56
M) $63
N) $69
O) $75
P) $80
Q) $88
R) $104
S) $108
T) $114
U) $118
V) $124
W) $148
X) $156
Y) more information is needed to answer
Z) none of the above
6. Now suppose that the firms compete under the Bertrand assumptions. Then the price
that will result in the Nash equilibrium is:
A) $0
B) $12
C) $24
D) $28
E) $32
F) $34
G) $36
H) $38
I) $40
J) $45
K) $49
L) $56
M) $63
N) $69
O) $75
P) $80
Q) $88
R) $104
S) $108
T) $114
U) $118
V) $124
W) $148
X) $156
Y) more information is needed to answer
Z) none of the above
7. If we move from the Cournot equilibrium obtained in question 4 to the Stackelberg
leader-follower equilibrium obtained in question 5, then the deadweight loss falls by :
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A) $0
G) $100.50
M) $455.75
S) $808.25
Y) $1200.25
B) $5
C) $10
H) $155.25 I) $180.75
N) $505.75 O) $550.25
T) $883.25
U) $900.00
Z) none of the above
D) $20
J) $200.00
P) $605.50
V) $950.50
E) $40
K) $325.75
Q) $650.25
W) $1010.75
F) $50
L) $435.50
R) $750.75
X) $1156.00
8. Now change the problem slightly. The first firm continues to have variable costs of
$12 per unit and no fixed costs, but now the second firm has variable costs of $36 per
unit and no fixed costs. If the firms compete under the Cournot assumptions (that is,
each firm assumes that the other firm will not change its output), then the price that will
result in the Nash equilibrium is:
A) $0
B) $12
C) $24
D) $28
E) $32
F) $34
G) $36
H) $38
I) $40
J) $45
K) $49
L) $56
M) $63
N) $69
O) $75
P) $80
Q) $88
R) $104
S) $108
T) $114
U) $118
V) $124
W) $148
X) $156
Y) more information is needed to answer
Z) none of the above
9. Again, we continue with the cost assumptions outlined in question 8. Now suppose
that the first firm is a Stackelberg leader while second firm is a follower. Assume, as
usual, that the follower behaves like a Cournot duopolist (that is, assumes that the
leader's output is fixed). Then the price that will result is:
A) $0
B) $12
C) $24
D) $28
G) $36
H) $38
I) $40
J) $45
M) $63
N) $69
O) $75
P) $80
S) $108
T) $114
U) $118
V) $124
Y) more information is needed to answer
E) $32
F) $34
K) $49
L) $56
Q) $88
R) $104
W) $148
X) $156
Z) none of the above