ECONOMICS 3200M Lecture 8 February 3, 2005

1
ECONOMICS 3200MLecture 8February 3, 2005
2
Oligopoly

• Cournot competition
• Duopoly case
• Homogeneous products, single instrument Qi
  (quantity produced by each firm)
• Demand function P(Q) 1 Q 1- Q1 Q2
• Ci (Qi) Ci Qi (constant returns), where C1 ? C2
• Firm 1
• Max ?1 (Q1, Q2) Q1 (1- Q1 Q2) C1 Q1
• d ?1 /d Q1 1- 2 Q1 - Q2 - C1 0
• Reaction function for firm 1 Q1 1- Q2 - C1/2
  R1 (Q2)
• Strategic substitutes since d Q1/d Q2 lt 0
• Reaction function for firm 2 Q2 1- Q1 C2/2
  R2 (Q1)

3
Oligopoly

• Cournot competition
• Nash equilibrium solve by equating reaction
  functions
• R1 (Q2) R2 (Q1)
• Q1 1 C2 2C1 /3
• Q2 1 C1 2C2 /3
• P 1 C1 C2 /3
• ?1 1 C2 2C1 2/9
• ?2 1 C1 2C2 2/9
• If C1 lt C2 ? ?1 gt ?2
• With symmetric costs and N firms Ci C
• Qi 1 - C/(N1)
• P 1 NC/(N1)
• As N increases, Qi decreases, P decreases
  towards C and the profit for each firm decreases
  towards 0

4
Q1
Q2 R2 (Q1, C2)
1
Q1 R1 (Q2, C1)
Q2
5
Oligopoly

• In monopoly (if no X-inefficiency), Bertrand
  competition and perfect competition models,
  production occurs at lowest cost
• Higher cost producer cannot survive
• With Cournot competition, higher cost producer
  can survive

6
Oligopoly

• Stackelberg competition
• Firm 1 is the leader and firm 2 is the follower
  why?
• Firm 1 knows firm 2s reaction function assume
  same demand and cost conditions as in Cournot
  example
• Firm 1
• Max ?1 (Q1, Q2) Q1 (1- Q1 Q2) C1 Q1
• Q2 1- Q1 C2/2 R2 (Q1)
• ?Max ?1 (Q1) Q1 (1- Q1 C2)/2 C1 Q1
• d ?1 /d Q1 0.5- Q1 0.5C2 - C1 0
• Q1 1 C2 2C1 /2 gt Q1 (Cournot) 1 C2
  2C1 /3
• Q1 (follower) lt Q2 (Cournot)
• Leader has higher profits than in Cournot game
  Firm 1 a leader most likely because it ahs lower
  costs

7
Q1
Q2 R2 (Q1, C2)
S
N
Q1 R1 (Q2, C1)
Q2
8
Oligopoly

• Equilibrium prices (highest to lowest)
• Monopoly/Infinite period repeated duopoly
• Cournot duopoly
• Stackelberg duopoly
• Competition/Bertrand duopoly/Single game duopoly
• Extensions
• (1) Bertrand with sunk costs, firm 1 incumbent,
  firm 2 potential entrant
• Unless potential entrant has a cost advantage,
  firms 2 anticipates that incumbent will lower
  price to eliminate economic profits (firm 1 will
  ignore its sunk costs in setting price in
  response to entry P lt AC where AC includes sunk
  costs), so firm 2 will not invest ex ante in what
  will become sunk costs ex post because it will
  not be able to earn competitive return on
  investment
• First mover advantage with sunk costs

9
Oligopoly

• Extensions
• (2) Stackelberg with capacity constrain for
  leader
• If leader (firm 1) does not have capacity to
  produce Q1 1 C2 2C1/2, firm 1 will
  produce up to its capacity
• Resulting equilibrium pt. 2 in following

10
Q1
Q2 R2 (Q1, C2)
S
SQ1
2
2Q1
N
NQ1
Q1 R1 (Q2, C1)
Q2
11
Oligopoly

• Extensions
• (3) Repeated game Bertrand
• Cooperation with PPM , and monopoly profits
  shared
• Competition shifts away from prices to other
  strategies involving instruments that cannot be
  easily detected or imitated
• Research
• Marketing, sales

12
Monopolistic Competition

• Product differentiation
• Product consists of bundle of characteristics
  quality,location, colour, time of availability,
  etc.
• Computers, laptops, clothing, air travel, MBA
  programs
• Firms have some degree of market power
• Standard model
• Free entry may drive profits to 0, at least for
  marginal firms in market
• Definition of industry/market?
• Critical value for cross-price elasticity of
  demand?

13
Monopolistic Competition

• Location model example of differentiation
• Different locations represent different varieties
  of a product
• Varieties differentiated by geographic location
  or other characteristics
• Consumers have preferred location/characteristics
  for a product
• For given price, utility maximized at preferred
  location
• Utility declines as actual product location
  differs (moves farther away) from preferred
  location
• To make problem manageable, focus on one
  characteristic

14
Monopolistic Competition

• Vertical differentiation model characteristic
  quality
• Quality (S) S? 0, 1
• Consumers agree over most preferred mix of
  characteristics and over preference ordering S1
  gt S2 implies that quality S1 exceeds quality S2
  and higher quality preferred over lower quality
• Consumers have perfect information regarding
  quality
• Value (utility U) to consumer U ?S P
• Model
• Consumer buys if U gt 0 ? ?S gt P
• Does not buy if U ? 0 ? ?S ? P
• Distribution of tastes (? ) across all consumers
  F(?), where F(?min) 0 and F(?max) 1
• F(?0) proportion of all consumers with taste
  parameter ? ? 0, ?0

15
Monopolistic Competition

• Case 1
• 2 products with qualities S1 gt S2 and P1 gt P2
• Assume
• S1/P1 gt S2/P2 ? ? S1/P1 gt ? S2/P2
• Consumers will prefer the higher quality product
  if
• ? S1 P1 gt ? S2 P2 and
• ? S1 P1 gt 0
• Since ? S1/P1 gt ? S2/P2 then
• ? S1/P1 1 gt ? S2/P2 1
• P1? S1 P1 gt P2? S2 P2
• Since P1 gt P2 , consumers prefer higher quality
  product
• Product differentiation, but only high quality
  variety of product is produced and sold