Competition/Monopoly/Bertrand Oligopoly/Cournot Oligopoly/Stackelberg Oligopoly
General assumptions:
All firms produce and sell the identical product
Industry (inverse) demand curve: P = a - bQ
The AC of any firm includes a "normal" profit return on invested capital (so  refers to
"excess" profits)
$
a
D
Slope = b/2
Slope = b
MR
(a+c)/2
(a+2c)/3
LRMC = LRAC
c
0
(a-c)/2b 2(a-c)/3b
(a-c)/b
a/b
Q
A. Competitive industry:
Extra assumptions:
"Many" firms
Every firm, actual and potential, is identical and has a U-shape AC curve with minimum
point at a AC of "c"
Implication:
Industry LR competitive supply curve is horizontal, at c
Outcome:
P=c
Q = (a-c)/b
=0
B. Monopoly:
Extra assumptions:
Single firm
Firm has LRMC = LRAC = c
Implication:
 = QP - Qc = Q(a-bQ) - Qc
Maximizing outcome:
d/dQ = a - 2bQ – c = 0
Q = (a-c)/2b
P = (a+c)/2
 = (a-c)2/4b
C. Bertrand Oligopoly:
Extra assumptions:
n firms (2 or more)
Each firm has LRMC = LRAC = c
Each firm chooses price as its competitive vehicle, myopically assumes that other firms will
not respond by adjusting their prices
Outcome:
Identical to competitve outcome, regardless of n
D. Cournot Oligopoly:
Extra assumptions:
n firms (2 or more)
Each firm has LRMC = LRAC = c
Each firm chooses quantity as its competitive vehicle and myopically assumes that other
firms will not respond by adjusting their quantities
Maximizing outcome (for two identical firms: 1,2):
1 = Pq1 - cq1 = (a-bQ)q1 - cq1 = (a-b[q1+q2])q1 - cq1
d1/dq1 = a - 2bq1 -bq2 - c = 0
q1 = (a-c-bq2)/2b
q1
(a-c)/b
Firm 2’s reaction function
(a-c)/2b
Firm 1’s reaction function
(a-c)/3b
Similarly, q2 = (a-c-bq1)/2b
q1 = q2 = (a-c)/3b
0
Q = q1 + q2 = 2(a-c)/3b
P = a - bQ = (a+2c)/3
1 = Pq1 - cq1 = (a-c)2/9b
 = 1 + 2 = 2(a-c)2/9b
These results generalize, for n firms, to:
Q = n(a-c)/(n+1)b
P = (a+nc)/(n+1)
 = n(a-c)2/(n+1)2b
As n gets large:
Q
(a-c)/b (the competitive quantity)
P
c (the competitive price)

0
(a-c)/3b
(a-c)/2b
(a-c)/b
q2
E. Stackelberg-Cournot Oligopoly:
Extra assumptions:
One firm (e.g., firm 1) understands the reaction function(s) of the other firm(s) and takes
them into account in making its own choice of output:
Outcome (for two firms: 1,2):
1 = Pq1 - cq1 = (a-bQ)q1 - cq1 = (a-b[q1+q2])q1 - cq1
But q2 = (a-c-bq1)/2b
By substitution, 1 = (a-b[q1+{a-c-bq1}/2b])q1 - cq1
d1/dq1 = …. = 0
q1 = (a-c)/2b
q2 = (a-c)/4b
Q = q1 + q2 = 3(a-c)/4b
P = a – bQ = (a + 3c)/4
1 = Pq1 – cq1 = (a-c)2/8b
2 = Pq2 – cq2 = (a-c)2/16b
 = 1 + 2 = 3(a-c)2/16b