Download Introduction Cournot Competition

University of Hong Kong
ECON6021 Microeconomic Analysis
Oligopoly
Introduction
Three models of oligopoly.
 Cournot competition
 Bertrand competition
 Stackelberg competition
Cournot
Competition
An industry is characterized as Cournot
oligopoly if
1. There are few firms in the market
serving many consumers.
2. The firms produce either differentiated
or homogeneous products.
3. Each firm believes rivals will hold their
output constant if it changes its output.
4. Barriers to entry exist.
Reaction Functions and
Equilibrium.
 further simplification: duopoly – 2 firms
only
 reaction function defines the
profit-maximizing level of output for a
firm for given output levels of the other
firm.
Q 1  r 1 Q 2 .
and
Q 2  r 2 Q 1 .
 Point E thus corresponds to the Cournot
equilibrium– where neither firm has a
unilateral incentive to change its output
 If the (inverse) demand in a
homogeneous-product Cournot duopoly is
P  a  bQ 1  Q 2 ,
where a and b are positive constants, then
the marginal revenues of firms 1 and 2 are
MR 1 Q 1 , Q 2   a  bQ 2  2bQ 1
MR 2 Q 1 , Q 2   a  bQ 1  2bQ 2
 Assume that total cost functions
C 1 Q 1   c 1 Q 1 and C 2 Q 2   c 2 Q 2 .
 Equating MRMC, we have
a  bQ 2  2bQ 1  c 1
for firm 1, and
a  bQ 1  2bQ 2  c 2
for firm 2.
 Their reaction functions are
Q 1  r 1 Q 2   a  c 1  1 Q 2
2
2b
for firm 1, and
Q 2  r 2 Q 1   a  c 2  1 Q 1
2
2b
Isoprofit Curves.
 How to graphically determine the firm’s
profits.
Four aspects of the figure are important to
understand.
1. Every point on a given isoprofit curve
for firm 1 yields firm 1 the same level
of profits.
2. Isoprofit curves that lie closer to firm l’s
monopoly output (Q M
1 ) are associated
with higher profits for that firm.
3. The isoprofit curves for firm 1 reach
their peak where they intersect firm l’s
reaction function.
4. The isoprofit curves do not intersect
one another.
Changes in Marginal
Costs.
 What happens if there is a decline in firm
2’s marginal cost?
Collusion
 Whenever a market is dominated by only a
few firms, firms can benefit at the expense
of consumers by ”agreeing” to restrict
output or, equivalently, charge higher
prices. Such an act by firms is known as
collusion.
Stackelberg
Oligopoly
An industry is characterized as a
Stackelberg oligopoly if:
1. There are few firms in the market
serving many consumers.
2. The firms produce either differentiated
or homogeneous products.
3. A single firm (the leader) selects an
output before all other firms choose
their outputs.
4. All other firms (the followers) take as
given the output of the leader and
choose outputs that maximize profits
given the leader’s output.
5. Barriers to entry exist.
Model
 Two firms–Firm 1 is the leader with a
“first-mover” advantage, and Firm 2 is the
follower, who maximizes profit given the
output produced by the leader.
 same cost functions, and demand function
as in Cournot model
 Follower’s reaction function:
Q 2  r 2 Q 1   a  c 2  1 Q 1 ,
2
2b
which is simply the follower’s Cournot
reaction function.
 After taking into account the follower’s
response, the leader’s profits are

a  c2  1 Q
2 1
2b
 The leader chooses Q 1 to maximize
 1 Q 1 .
 It is straightforward to show that the
leader’s output is
Q 1  a  c 2  2c 1 .
2b
 1 Q 1  
a  b Q1 
Bertrand Oligopoly
An industry is characterized as a Bertrand
oligopoly if:
1. There are few firms in the market
serving many consumers.
2. The firms produce identical products
as a constant marginal cost.
3. Firms engage in price competition and
react optimally to prices charged by
competitors.
4. Consumers have perfect information
and there are no transaction costs.
Q1  c
5. Barriers to entry exist.
Model
 Consider a Bertrand duopoly, and both
firms have the same marginal cost.
 Price war – Both firms charge a price
equal to marginal cost: P 1  P 2  MC!
Conclusions
 Three models of oligopoly have been
introduced.
 Interdependence of choices are
emphasized.
 Collusion improves firms’ collective
profits (at the expense of consumers)