Models of Competition Part III: Imperfect Competition Agenda: 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
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Models of Competition Part III: Imperfect Competition Agenda: 1.First let’s review… 2.A continuum of competition: two key questions 3. Models of Imperfect.
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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
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 #)
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…)
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