Industrial Organization I

1
Industrial Organization I

• Homogeneous Product Oligopoly (II)

2
Bertrand Price competition

• Bertrand (1883) Who sets prices if not the
  firms?
• Bertrand conjecture is similar to Cournots
  rivals price is taken as given (or fixed)
• Consumers have perfect information
• Firms have identical costs
• Goods are homogeneous
• No transportation costs
• No capacity constraints

3
Bertrand example
p1
Joint Profit Maximization p1p25x10-5x335
10
MC13
p2
10
MC23

• Assumptions
• 2 firms, MC1MC2
• Unit demand, 10 consumers, each willing to pay a
  max of 10
• Lowest p captures the whole market, if tie, they
  split the market

4
Bertrand Example
Joint Profit maximization p1p25x10-5x335 (not
an equilibrium)
p1
10
Equilibrium p1p20
8
p19x10-9x363 p20 (not an equilibrium)
MC13
45o
p2
10
MC23
9

• Strategies price3,10
• Profit
• (pi-3)x10 if piltpj
• (pi-3)x5 if pipj
• 0 if pigtpj
• Equilibrium No incentive to change strategies

5
Bertrand More formally
Why? A deviation must not be profitable pigtc
means zero profit piltc means negative profit
6
Bertrand Paradox

• The perfectly competitive solution is found even
  in a highly concentrated market (2 firms)
• It is hard to believe that firms in highly
  concentrated industries will not earn above
  normal profits
• Solutions of the paradox
• Capacity constraints
• Geographic differentiation (transportation costs)
• Consumers have imperfect information
• Product differentiation
• Repetitive interaction

7
Capacity Constraints

• Suppose that k17 and k23
• What is the equilibrium?

8
So far

• Quantity setting firms (Cournot)
• Price setting firms (Bertrand)
• Conjecture or belief rivals action is taken as
  given
• Bertrand, Cournot and Collusion can be nested
  in a more general model

9
General Conjectural Variation Model

• 2 firms

Conjecture
Conjectural Variation
Equivalent, but literature confusion
2 firms
10
Conjectural Variations N-firm case

• More generally, for the N-firm case, Bertrand
  conjecture is
• Intuition to keep price constant (i.e. pmc),
  firm 2 must exactly offset the output change by
  firm 1
• The collusion conjectural variation is

11
N-firm Collusion and Bertrand

• Symmetric case q1q2q3

N
CV in monopoly
Conjecture In N-firm Bertrand Case
12
Conjectural variation Elasticity
13
Conjectural variation Perceived MR
MR

• Oligopolist equates perceived MR with MC
• Why Perceived MR depends on conjecture about
  how firm 2 will react to a change in firm 1s
  output

14
Conjectural variation Perceived MR
p(Q)
p(Q)
Perceived MR of oligopolist
Q
Weighted MR between monopolists MR and PCs MR
15
Criticisms of CV models

• Conjectures are arbitrary
• Certain values do not correspond to any
  theoretical model
• Interpretation of CV models are implausible
• Conjecture is a dynamic concept, but it is
  employed in a static (one-shot) framework
• Firms do not adjust and may continue to use
  false conjectures
• Firms maximize PV of profits choice of
  quantity/price today may not only affect todays
  profits (this is a more general criticism)

16
Popularity of CV Models

• is known as conduct parameter
• Why Estimate of or as an index of market
  power for the industry
• Given criticism of conjectural variations, is
  not referred as CV in empirical analysis. Rather
  index of market power

17
Sequential Moves

• 2-stage game
• Stage 1 leader (firm 1) chooses quantity
  produced
• Stage 2 follower (firm 2) chooses quantity
• Quantity is strategic variable, but with
  differentiated products Stackelberg price also
  exists

Firm 1 (Leader)
q1
Firm 2 (Follower)
What is the solution concept?
q2
18
Stackelberg Game
First Stage
Firm 2s reaction function R2(q1) (nothing new
here)

• Second Stage
• Firm 1 anticipates the reaction of firm 2 to q1
  and will choose the optimal quantity accordingly.
• Alternatively, firm 1 maximizes profit subject
  to firm 2s reaction

19
Stackelberg Game
20
Stackelberg Game

• Equilibrium under Stackelberg leadership is more
  competitive
• Leader can profit at the expense of rival first
  mover advantage

21
Stackelberg
p(Q)
p(Q)
MR(Q)
Effective demand for Leader p(q1R2(q1))
MR of leader
c
Q
22
R1(q2)
q2
Firm 1s Isoprofit curves
K1
K2
K3
R2(q1)
K4
Cournot Equilibrium
KS
q1

• Firm 1 moves first
• Has to choose quantity on firm 2s reaction
  curve (because this is what 1 expects 2 will do)
• It chooses the q2 that gives the maximum
  isoprofit curve possible

23
Stackelberg model

• Firm 2 does no longer choose quantity on own
  reaction curve
• This makes shape of effective demand different
  than in Cournot case
• First mover does not always have an advantage
• Stackelberg with differentiated products gives
  second mover and advantage
• Some entry games produce an advantage for the
  entering firm.