1. Economics 202: Intermediate Microeconomic Theory
Finish Chapter 15

2. Oligopoly with Fixed Number of Firms
Reaction Functions
P = a - bQ, MC = c, Q = q1 + q2
Profits for firm 1?
(q1) = Pq1 - cq1 = (a-bq1-bq2) q1 - cq1
Max   MR = MC  a -2bq1-bq2= c
Solving for q1  q1= (a-c-bq2)/2b
This is firm 1’s “Reaction Function”
Cournot Duopoly
Firm 2 output
(a-c)/b •
(a-c)/2b
q2*
Firm 2 has same solution
Which pair of quantities is Nash equilibrium?
q1*
(a-c)/2b
(a-c)/b
Solve the two reaction functions
q1* = (a-c)/3b = q2*
Market Price = a/3 + 2c/3 < Monopoly Price
Firm 1 output
Cournot model says total output is greater than monopoly, Price and total profits lower

3. Models of Oligopoly Augustin (Augie) Cournot model Cournot Example
Each firm assumes its rival does not change output
Qmonopoly < Qcournot < Qcompetitive, thus Pmono > Pcournot > Pcomp
Cournot Example
A local carrot monopolist can produce at constant marginal cost of $5. The firm faces a market demand curve given by P = 53 - Q.
Find profit-maximizing price, output, profit and resulting DWL.
Suppose a second firm, with same cost structure, enters the market. Assuming the firms are Cournot duopolists, find each firm’s reaction function.
What are the Cournot equilibrium, market price, and profits of each firm?

4. Models of Oligopoly Augustin (Augie) Cournot model Cournot Example
Each firm assumes its rival does not change output
Qmonopoly < Qcournot < Qcompetitive, thus Pmono > Pcournot > Pcomp
Cournot Example
A local carrot monopolist can produce at constant marginal cost of $5. The firm faces a market demand curve given by P = 53 - Q.
Find profit-maximizing price, output, profit and resulting DWL.
Suppose a second firm, with same cost structure, enters the market. Assuming the firms are Cournot duopolists, find each firm’s reaction function.
What are the Cournot equilibrium, market price, and profits of each firm?

5. Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand
Dominant Firm (or Price Leadership) model
Cooperative (cartel) model

6. Models of Oligopoly Heinrich von (Hank) Stackelberg model
Continue our previous example
Is it advantageous to go first?
How much will each firm produce now?
Assume firm 1 acts first (the “Stackelberg leader”) and firm 2 is a “naive Cournot follower”
Yes, it is advantageous to move first ( 1 = 22 ). Why?
Fait accompli. Your output is large regardless of what rival does.

7. Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand
Dominant Firm (or Price Leadership) model
Cooperative (cartel) model

8. Models of Oligopoly Joe Bertrand Model
Each firm assumes its rival does not change price
Two catalog firms announce their prices when they send out fall edition
Customers buy from lower-priced seller
Low-priced seller supplies whole market
With P>MC, under-cutting is profitable
Equilibrium is same as competitive market, P = MC
Price
Criticisms
Key assumptions: firms take their rivals’ output (or price) as given
These are clearly wrong as the market is adjusting toward equilibrium
monopoly
(a+c)/2
cournot c
bertrand 1 2 3 4 5
# firms

9. Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand
Dominant Firm (or Price Leadership) model
Cooperative (cartel) model

10. Models of Oligopoly Dominant Firm model (aka, Price Leadership model)
Here the leader assumes its rivals behave as competitors in choosing qi
Price ($/unit)
How much can dominant firm sell?
Sfringe
Now dominant firm sets MR = MC P1
At Pdom, competitive rivals produce Qfringe
MCdomin
Pdom
Qdom + comp < Q comp + comp
MCdom P2
Pdom > MCdom & Pdom = MCfringe
Dmkt
MRdomin
Qdom
Qfringe
Qd+c
Qc+c
Output

11. Price Leadership Model of Oligopoly
Application: pharmaceutical industry
Patent on drug X expires  copycats
Pbrand-name drug ?
Pbrand-name drug falls
Brand-name manufacturers often then engage in 3rd-degree price discrimination
PHMO/Hosp < Plocal pharmacy
Why?
But there are drawbacks to this market segmentation strategy
Pharmacies have sued brand-name manufacturers to give them same low price
Price ($/unit)
Sfringe
S’fringe
MCdomin
Pdom
P’dom
Dmkt
MRdomin
Q’dom
Qdom
Qfringe
Qd+c
Output

12. OPEC and CIPEC
OPEC is the Organization of Petroleum Exporting Countries
CIPEC is the French acronym for Int’l Council of Copper Exporting Countries
Why has OPEC been successful in raising its price, but CIPEC has not?
OPEC cartel as a dominant firm
Price
Oil Market
Snon-opec
How much can dominant firm sell? P1
Now dominant firm sets MR = MC
At Popec, rivals produce Qfringe
Qopec + comp < Q comp + comp
Popec
Popec >> Pcomp
Inelastic Snon-opec & inelastic Dmkt  inelastic Dopec  Popec >> Pcomp
Price controls on gas in 1970s actually reinforced OPEC’s strategy!!
Encouraged domestic consumption
Discouraged domestic production
Pcomp
MCopec P2
Dmkt
MRopec
Qopec
Qtotal
Qfringe
Output
Qc+c

13. OPEC and CIPEC CIPEC (Chile, Peru, Zambia, Zaire)
MCCIPEC is not much less than MCnon-cipec
Why has OPEC been successful in raising its price, but CIPEC has not?
CIPEC cartel as a dominant firm
Price
Copper Market
How much can dominant firm sell?
Now dominant firm sets MR = MC
Snon-cipec
At Pcipec, rivals produce Qfringe
Pcipec not much above Pcomp P1
MCcipec
Why can’t CIPEC increase
copper prices much?
D for copper is more elastic
(aluminum is a good substitute)
Comp’ve supply more elastic than for oil (if P rises, simply go to scrap heap)
Successful cartel needs relatively inelastic D & inelastic Snon-cartel. Not easy
Pcipec
Pcomp P2
Dmkt
MRcipec
Qcipec
Qtotal
Qfringe
Output
Qc+c

14. Price Leadership Model of Oligopoly Example
Assume an industry has two firms and market demand is given by P = 100 – 2Q where Q = qA + qB
The firms have the following cost functions
TCA = qA TCB = 3qB2
Let A be the price leader (dominant firm), and firm B the competitive fringe firm, the follower
Calculate A and B

15. Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand
Dominant Firm (or Price Leadership) model
Cooperative (cartel) model

16. Cartel Model of Oligopoly
Banned by antitrust laws in the US, but not in many other countries
Firms attempt to coordinate price and output decisions to earn monopoly 
MC1 = MC2 = … = MCN = MR
Why do cartels fail? caviar cartel story
(1) incentive to cheat (2) heterogeneous cost structures/size/output (3) econ >0  entry
Output
Price
Dmkt S P1 Q
Market
Firm d AC MC
dcartel
mrcartel
q*cartel P2
MRmkt
Nq*cartel d’
q*cheater