Models of CompetitionPart III: Imperfect CompetitionAgenda:

1. First let’s review…

2. 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

First let’s review….

What is the profit maximizing condition for perfect competitors?

What is the profit maximizing condition for a monopolist?

What is the equilibrium price and quantity, aggregate producer and consumer surplus for a perfectly competitive firm? (hint: area of triangles!)

What is the equilibrium price and quantity, producer and consumer surplus and dead weight loss for a monopoly? (hint: draw the graph!)

MR = MC

MR = MCIf supply and demand are:P = 100 + Q and P = 1000 – 2Q

100 + Q = 1000 – 2QQ = 300P = $400

CS = ½ (600 * 300) = $90,000PS = ½ (300 * 300) = $45,000

100 + Q = 1000 - 4QQ = 180 P = $640

CS = ½ (360 * 180) = $32,400PS = (360 * 180) + ½ (180*180)= $81,000DW = ½ (360 * 120) = $21,600

Perfect Competition

MonopolyOligopolyMonopolistic Competition

A Continuum of Competition….

Key questions:1.Is there meaningful product differentiation?2.Are there significant barriers to entry or exit?

Model Assumptions LimitationsMonopolistic Competition

Differentiated Products are imperfect substitutesNO barriers to entry

Firms act independently, do NOT respond to other firms

Oligopoly Products are close substitutesHIGH 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 choosePRICE

Price = MC same as perfect competition

Game Theory! Firms strategically anticipate and respond to other firms’ actions

Few Nash equilibria, context specific implications

Models of imperfect competition

Monopolistic Competition: The Chamberlin Model

Monopolistic Competition in the History of Economic Thoughthttp://ccso.eldoc.ub.rug.nl/FILES/root/2002/200215/200215.pdf

Edward Chamberlin Joan Robinson

Key features: Many firms Free entry and exit Symmetry – what’s good for one is

good for the others equallyX Differentiated products make

imperfect substitutes

A matter of degree….

Monopolistic Competition: The Short Run

Joan RobinsonShort Run

Market demand curve

Firm demand curve

Entry of close substitutes

Is this firm making a producer surplus?

Is this firm making a profit?

What will happen in the long run?

P2

Q2

Which is more ELASTIC?

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?

Monopolistic Competition: Long-run Implications

REVIEW: What is Allocative Efficiency in a Perfectly Competitive Market?

Perfect Competition Monopolistic Competition

Avinash Dixit Joseph Stiglitz

The value of diversity!

5 75

Oligopoly: The Cournot Model

Antoine Augustin Cournot (1801-1877)

Few firms (test yourself: why?)Firms choose quantity at the same time and then the market sets priceProducts must be relatively close substitutes.

KEY: Each firm takes the other’s quantity as GIVEN, which reduces the demand available to them!See P&R p. 459

Oligopoly: The Cournot Model

Antoine Augustin Cournot (1801-1877)

A firm’s RESPONSE FUNCTION expresses its Quantity in terms of the other firm’s Quantity

P a bQ

Recall the general linear demand function:

1 2P a b Q Q

* 21

* 12

2

2

a bQQ

ba bQ

Qb

Response functions with MC = 0

Equilibrium is whenQ1 = 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/100FIRM #1 marginal revenue: 65-2Q1/100 –Q2/100FIRM #2 marginal revenue: 65-2Q2/100 –Q1/100

FIRM total cost: C(q) = 722 + q2/200FRIM marginal cost: MC(q) = 2q/200 = q/100NOTE q = Q1 or Q2 depending on which firm you’re thinking about!

1. 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

2. 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)/3Q1 = 1,606

3. What is the equilibrium price and quantity for the market?

Q = 3,212 P = $32.88

TEST YOURSELF!

Compare the equilibrium price, quantity, profit, producer and consumer surplus for the perfectly competitive, monopoly and Cournot Duopoly

markets!

Oligopoly: The Stackelberg Model

Heinrich Freiherr von Stackelberg 1905 - 1946

Firm #1 (leader) knows that firm #2 (follower) will take firm #1’s quantity as given following the Cournout model…

1 2

11

11

1 1

1

2

22

2

2

P a b Q Q

a bQa b Q

b

a bQa bQ

bQ a bQa

a bQP

Demand Function

Substitute firm #2’s response function assuming MC = 0

Firm #1 Demand Function

What is Firm #1’s Marginal Revenue Function?

1

1

22 2

2

a bQMR

aMR bQ

Oligopoly: The Stackelberg Model Continued

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

What is on the X and Y axis?What kind of functions are graphed?

How is Stackelberg different from Cournot?

First Mover Advantage!!

Oligopoly: The Bertrand ModelFirms choose price and the market sets quantityEach firm takes the other’s price as given

Joseph Louis François Bertrand (1822 – 1900)

LowerPrice

SamePrice

HigherPrice

LowerPrice

HigherPrice

SamePrice

Firm #1Firm #2

all

half

half

nothing nothing nothing

half half

all all

half

half

all

all

all

nothing

nothing

nothing

Price set at MCSame as

perfect competition!

CollusionCartelsDynamic games

A Framework for thinking about problemsFrom Basar & Olsder Dynamic Noncooperative Game Theory (1999) p. 2

One decision maker Many decision makers

One decision(a series of

independent decisions)

Static

Multiple related decisionsDynamic

Mathematical programming,

Static optimization

Optimal control theory, Dynamic

optimization

Static Game Theory

Dynamic or differential game

theory

Applications of game theory:Economics, politics, war, infectious disease, engineering, artificial intelligence, portfolio management, product development

Oligopoly GameRules of the game:1. Pick a red or a black card and put it against your chest so no one can see it.2. I’ll pair you randomly with another player.3. 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)

4. We’ll play 5 rounds – the first two with random partners and the last three with the same partner.

5. Highest earners get .5 bonus point (another .5 for the next game…)

Black RedBlack (3,3) (0,5)Red (5,0) (2,2)

Column Player

Row Player

8

High Gains from Cooperation

Black RedBlack (8,8) (0,10)Red (10,0) (2,2)

Column Player

Row Player

(row, column)

The Prisoner’s Dilemma

http://en.wikipedia.org/wiki/John_Forbes_Nash,_Jr.

High Gains from Cooperation

Black RedBlack (8,8) (0,10)Red (10,0) (2,2)

Column Player

Row Player

Von Neumann & Morgenstern

Dominant Strategy: You do better no matter what your opponent does.

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.

Maxmin:Pick the best of the worst-case scenariosRow: 10 or 2 > 8 or 0

Column: 10 or 2 > 8 or 0

Standardized Product, High Barriers → Monopoly, Oligopoly

Diversified Product, Low Barriers → Monopolistic Competition

Standardized Product, Low Barriers → Perfect Competition

Diversified Product, High Barriers → Monopoly, Oligopoly