1. Models of Competition Part III: Imperfect Competition
Agenda:
First let’s review…
A continuum of competition: two key questions
3. Models of Imperfect Competition
A. Monopolistic Competition
B. Cournot Oligopoly
C. Stackelberg Oligopoly
D. Bertrand Oligopoly
4. Game theory

2. First let’s review….
What is the profit maximizing condition for perfect competitors?
MR = MC
What is the profit maximizing condition for a monopolist?
MR = MC
If supply and demand are:
P = Q and P = 1000 – 2Q
What is the equilibrium price and quantity, aggregate producer and consumer surplus for a perfectly competitive firm? (hint: area of triangles!)
100 + Q = 1000 – 2Q
Q = 300
P = $400
CS = ½ (600 * 300) = $90,000
PS = ½ (300 * 300) = $45,000
What is the equilibrium price and quantity, producer and consumer surplus and dead weight loss for a monopoly? (hint: draw the graph!)
100 + Q = Q
Q = 180
P = $640
CS = ½ (360 * 180) = $32,400
PS = (360 * 180) + ½ (180*180)= $81,000
DW = ½ (360 * 120) = $21,600

3. Monopolistic Competition
A Continuum of Competition….
Perfect Competition
Monopolistic Competition
Oligopoly
Monopoly
Causes of monopoly:
Economies of scale (production technology – go back to gnomes), regulation (we don’t want everyone tearing up the roads to lay gas pipe, we want to know who to go to when something blows up)
Network externalities, Location (also a form of product differentiation)
Patents
Of the four assumptions underlying perfect competition, really only two are important: product differentiation and barriers to entry/exit. Pricing power comes from these (assumption #2) and we never have perfect information (transactions costs)
Key questions:
Is there meaningful product differentiation?
Are there significant barriers to entry or exit?

4. 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)
Cournot
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
Game Theory!
Firms strategically anticipate and respond to other firms’ actions
Few Nash equilibria, context specific implications

5. Monopolistic Competition: The Chamberlin Model
Key features:
Many firms
Free entry and exit
Symmetry – what’s good for one is good for the others equally
X Differentiated products make imperfect substitutes
Edward Chamberlin
Joan Robinson
Chamberlin, E.H. (1933) The Theory of Monopolistic Competition: A Re-orientation of the Theory of Value. Harvard University Press, Cambridge MA.
Robinson, J. (1933) The Economics of Imperfect Competition, MacMillian, London.
Poor Joan was British and a woman and the paper was written in 1933, so as Americans we only refer to the “Chamberlin” model
Friedman argued that Chamberlin model added nothing to the model of perfect competition (1953) “The methodology of positive economics,” in Essays in Positive Economics, Chicago: Chicago University Press.
Dixit and Stiglitz (1977) “Monopolisitc competition and optimum product diversity” American Economic Review, 67:297 – 308
Symmetry is necessary to make the math models work, not for the intuition, so we won’t focus on that.
A matter of degree….
Monopolistic Competition in the History of Economic Thought

6. Monopolistic Competition: The Short Run
Joan Robinson
Market demand curve
Which is more ELASTIC?
Firm demand curve P2
Firm demand is more elastic because customers can easily switch to competitors – but if you need (want) a shirt you ultimately get one so market demand is less elastic Q2
Entry of close substitutes
Is this firm making a producer surplus?
Is this firm making a profit?
What will happen in the long run?

7. Monopolistic Competition: Long-run Implications
REVIEW: What is Allocative Efficiency?
Is there any producer surplus in the long run?
Is there any economic profit in the long run?
Is there allocative efficiency in the long run?

8. What is Allocative Efficiency in a Perfectly Competitive Market?
REVIEW:
What is Allocative Efficiency in a Perfectly Competitive Market?
What can make the supply curve slope up in the long-run?
Is there producer surplus in the long run?
Is there consumer surplus in the long run?
See P&R p. 455 for a graphical comparison of long-run equilibrium in perfect and monopolistic competition

9. Monopolistic Competition
Perfect Competition
Monopolistic Competition
The value of
diversity!
Avinash Dixit
Joseph Stiglitz

10. Antoine Augustin Cournot
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. 5 75
Antoine Augustin Cournot
( )
KEY: Each firm takes the other’s quantity as GIVEN, which reduces the demand available to them!
See P&R p. 459

11. Antoine Augustin Cournot
Oligopoly: The Cournot Model
A firm’s RESPONSE FUNCTION expresses its Quantity in terms of the other firm’s Quantity
Antoine Augustin Cournot
( )
Recall the general linear demand function:
Response functions with MC = 0
Equilibrium is when
Q1 = Q2
See P&R p. 461 for a numerical derivation which requires some calculus to get the marginal revenue.

12. 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 = P or P = 65 – Q/100
FIRM #1 marginal revenue: 65-2Q1/100 –Q2/100
FIRM #2 marginal revenue: 65-2Q2/100 –Q1/100
FIRM total cost: C(q) = q2/200
FRIM marginal cost: MC(q) = 2q/200 = q/100
NOTE q = Q1 or Q2 depending on which firm you’re thinking about!
What is the response function for Q1 (an expression for Q1 in terms of Q2)?
HINT: remember, if in doubt try MR = MC!
Q1 = 2167 –Q2/3
How much does Q1 produce?
HINT: remember there is symmetry in the response
functions since both firms have the same cost structure.
Q1 = 2500 –(2500-Q1/3)/3
Q1 = 1,606
What is the equilibrium price and quantity for the market?
Q = 3,212 P = $32.88

13. TEST YOURSELF!
Compare the equilibrium price, quantity, profit, producer and consumer surplus for the perfectly competitive, monopoly and Cournot Duopoly markets!

14. Oligopoly: The Stackelberg Model
Firm #1 (leader) knows that firm #2 (follower) will take firm #1’s quantity as given following the Cournout model…
Demand Function
Heinrich Freiherr von Stackelberg
Substitute firm #2’s response function assuming MC = 0
What is Firm #1’s
Marginal Revenue Function?
Firm #1
Demand Function

15. Oligopoly: The Stackelberg Model Continued
What is on the X and Y axis?
What kind of functions are graphed?
First mover produces the same quantity as a pure monopolist
Cournot equilibrium
As long as second mover doesn’t respond and push the equilibrium to Cournot
How is Stackelberg different from Cournot?
First Mover Advantage!!

16. Joseph Louis François Bertrand
Oligopoly: The Bertrand Model
Firms choose price and the market sets quantity
Each firm takes the other’s price as given
Firm #1
Lower
Price
Same
Price
Higher
Price
Joseph Louis François Bertrand 
(1822 – 1900)
Firm #2
Lower
Price
all
half
nothing
all
all
all
all
half
nothing
Same
Price
Price set at MC
Same as
perfect competition!
half
half
half
Higher
Price
all
half
nothing
nothing
nothing
nothing
Collusion
Cartels
Dynamic games

17. A Framework for thinking about problems
From Basar & Olsder Dynamic Noncooperative Game Theory (1999) p. 2
One decision maker
Many decision makers
One decision
(a series of independent decisions)
Static
Mathematical programming,
Static optimization
Static Game Theory
Multiple related decisions
Dynamic
Optimal control theory, Dynamic
optimization
Dynamic or differential game theory
Game theory – I know that you know, and will respond, and you know that I know and will respond…
Applications of game theory:
Economics, politics, war, infectious disease, engineering, artificial intelligence, portfolio management, product development

18. Oligopoly Game 8 Rules of the game:
Pick a red or a black card and put it against your chest so no one can see it.
I’ll pair you randomly with another player.
Show each other your cards and compute your pay-off
Play red card: you get 2 (cut your price)
Play black card: your opponent gets 3 (keep your price the same)
We’ll play 5 rounds – the first two with random partners and the last three with the same partner.
Highest earners get .5 bonus point (another .5 for the next game…) 8
(row, column)
You do not need to assume anything about the other player or take any of his or her actions as given. Both actions contribute to the outcome.

19. The Prisoner’s Dilemma
Dominant Strategy:
You do better no matter what your opponent does.
Von Neumann & Morgenstern
Maxmin:
Pick the best of the worst-case scenarios
Row: 10 or 2 > 8 or 0
Column: 10 or 2 > 8 or 0
Nash is a professor at Princeton. Nobel in page dissertation leading to “The Nash Equilibrium”
Von Neumann, J., and O. Morgenstern Theory of Games and Economic Behavior 3rd. Ed. Princeton, NJ: Princeton University Press
All dominant strategies are Nash, but not all Nash are dominant strategies
Nash Equilibrium:
No player has an incentive to change strategies. Often one player has a dominant strategy, and the other chooses a dominant strategy given their opponent’s dominant strategy.

20. Standardized Product, Low Barriers → Perfect Competition
Standardized Product, High Barriers → Monopoly, Oligopoly
Diversified Product, Low Barriers → Monopolistic Competition
Diversified Product, High Barriers → Monopoly, Oligopoly