Models of Competition
Part IIIa: Cournot Oligopoly
Agenda:
1. A continuum of competition: two key questions
2. Models of Imperfect Competition – Overview
3. Cournot – Choose quantity
A. Marginal revenue function
B. Response function
C. Equilibrium condition
D. Competing garden gnomes
A Continuum of Competition….
Perfect
Competition
Monopolistic
Competition
Oligopoly
Monopoly
Key questions:
1. Is there meaningful product differentiation?
2. Are there significant barriers to entry or exit?
Models of imperfect competition
Model
Assumptions
Limitations
Monopolistic
Competition
Differentiated Products are
imperfect substitutes
NO barriers to entry
Firms act independently, do NOT
respond to other firms
Oligopoly
Products are close substitutes
HIGH barriers to entry
(including economies of scale)
Firms take other firms’
QUANTITY as given
Firms produce equal quantities
Stackelberg
2nd mover can NOT respond
to 1st mover
1st mover advantage. 1st mover
produces same quantity as
monopolist.
Bertrand
Firms simultaneously choose
PRICE
Price = MC same as perfect
competition
Firms strategically anticipate
and respond to other firms’
actions
Few Nash equilibria, context
specific implications
Cournot
Game Theory!
Oligopoly: The Cournot Model
Few firms (test yourself: why?)
Firms choose quantity at the same time and then the
market sets price
Products must be relatively close substitutes.
Antoine Augustin Cournot
(1801-1877)
KEY: Each firm takes the
other’s quantity as GIVEN,
which reduces the demand
available to them!
See P&R p. 459
5
75
Oligopoly: The Cournot Model
A firm’s RESPONSE FUNCTION expresses its
Quantity in terms of the other firm’s Quantity
P  a  bQ
P  a  b Q1  Q2 
Recall the general linear demand function:
Antoine Augustin Cournot
(1801-1877)
MRQ1  a  2bQ1  bQ2
Response functions with MC = 0
a  bQ2
Q 
2b
a  bQ1
*
Q2 
2b
*
1
Equilibrium is when
Q1 = Q2
Example: Garden Gnomes…AGAIN!
Another firm manages to come up with different technology that also
makes Garden Gnomes absorb CO2 and combat global warming.
They have a patent too, and conveniently the same cost structure as
you. So now the market is a duopoly. (Round Q to nearest whole #)
Market demand: QD = 6500 -100P or P = 65 – Q/100
FIRM total cost:
C(q) = 722 + q2/200
FRIM marginal cost:
MC(q) = 2q/200 = q/100
NOTE q = Q1 or Q2 depending on which firm you’re thinking about!
1. What is the Marginal Revenue for Firm #1?
2. What is the response function for Q1 (an expression for Q1 in terms of Q2)?
HINT: remember, if in doubt try MR = MC!
3. How much does Q1 produce? HINT: remember there is symmetry in the
response functions since both firms have the same cost structure.
4. What is the equilibrium price and quantity for the market?
TEST YOURSELF!
Compare the equilibrium price, quantity, profit,
producer and consumer surplus for the perfectly
competitive, monopoly and Cournot Duopoly
markets!
Market demand: QD = 6500 -100P or P = 65 – Q/100
FIRM total cost:
C(q) = 722 + q2/200
FRIM marginal cost: MC(q) = 2q/200 = q/100
Model
Price
Quantity
Perfect Competition
$5
6,000
Monopoly
$43.33
2,167
Cournot Oligopoly
$32.48
3,252