Industrial Organization or Imperfect Competition Entry deterrence I

1
Industrial Organization or Imperfect
Competition Entry deterrence I

• Univ. Prof. dr. Maarten Janssen
• University of Vienna
• Summer semester 2008
• Week 7 (May 5, 6)

2
Definition of entry deterrence

• Incumbents choice of business strategy such that
  it can only be rationalized in face of threat of
  entry
• Two different mechanisms often contemplated
• Building up capacity
• Studied in both Cournot and Stackelberg context
• Choice of prices to signal (low) cost structure
• Context of game with asymmetric information
• First, discuss briefly Cournot and Stackelberg
  models
• Then extensions to entry deterrence
• Later, pricing choices

3
Capacity Expansion and Entry Deterrence

• Central point For predation to be successfuland
  therefore rationalthe incumbent must somehow
  convince the entrant that the market environment
  after the entrant comes in will not be a
  profitable one. How this credibility?
• One possibility install capacity
• Installed capacity is a commitment to a minimum
  level of output

4
Cournot Model

• 2 (or more) firms
• Market demand is P(Q)
• Firm i cost is C(q)
• Firm i acts in the belief that all other firms
  will put some amount Q-i in the market.
• Then firm i maximizes profits obtained from
  serving residual demand P P(Q) - Q-i

5
Demand and Residual Demand
6
Cournot Reaction Functions

• Firm 1s reaction (or best-response) function is
  a schedule summarizing the quantity q1 firm 1
  should produce in order to maximize its profits
  for each quantity Q-i produced by all other
  firms.
• Since the products are (perfect) substitutes, an
  increase in competitors output leads to a
  decrease in the profit-maximizing amount of firm
  1s product (? reaction functions are downward
  sloping).

7
Cournot Model

• The problem Max(P(qiQ-i) qi C(qi)
• defines de best-response (or reaction) function
  of firm i to a conjecture Q-i as follows
• P(qiQ-i)qi P(qiQ-i) C(qi) 0

qj
Q-i0
8
Cournot Equilibrium

• Situation where each firm produces the output
  that maximizes its profits, given the the output
  of rival firms
• Conjectures about what the others produce are
  correct.
• No firm can gain by unilaterally changing its own
  output

9
Cournot Equilibrium

• q1 maximizes firm 1s profits, given that firm 2
  produces q2
• q2 maximizes firm 2s profits, given firm 1s
  output q1
• No firm wants to change its output, given the
  rivals
• Beliefs are consistent each firm thinks rivals
  will stick to their current output, and they do
  so!

10
Properties of Cournot equilibrium

• The pricing rule of a Cournot oligopolist
  satisifes
• Cournot oligopolists exercise market power
• Cournot mark-ups are lower than monopoly markups
• Market power is limited by the elasticity of
  demand
• More efficient firms will have a larger market
  share.
• The more firms, the lower will be each firms
  individual market share and monopoly power.

11
Concentration measures

• Different industries have very different
  structures and also different behaviours
• SCP paradigm
• Structure (cost, entry conditions, number of
  firms)
• Conduct (prices, product differentiation,
  advertising,etc.)
• Performance (Lerner index (P-MC)/MC, profit,
  welfare, etc.)
• Concentration measures try to provide indication
  of conduct and/or performance on the basis of
  structural features
• Preference for one number representation
• Use this for regression analysis (e.g. Lerner
  index on concentration measure)

12
Different concentration measures

• C4 is sum of four largest market shares
• Cant be used in highly concentrated sectors such
  as in mobile telephony
• No difference between four firms with 25 market
  share and monopolist
• Why 4?
• Market shares of 5th, 6th etc. largest firm has
  no effect
• HHI uses all information sum of all squared
  market shares
• Larger market shares get more weight

13
Justifying HHI
14
Changes in marginal costs
15
Another look at Cournot decisions

• Firm 1s Isoprofit Curve combinations of outputs
  of the two firms that yield firm 1 the same level
  of profit

16
Profits at Cournot equilibrium
Q2
Firm 2s Profits
r1
Q2M
Q2
Firm 1s Profits
r2
Q1M
Q1
Q1
17
Cournot versus Bertrand I

• Predictions from Cournot and Bertrand homogeneous
  product oligopoly models are strikingly
  different. Which model of competition is
  correct?
• Kreps and Scheinkman model two stages
• firms invest in capacity installation
• then choose prices.
• Solution firms invest exactly the Cournot
  equilibrium quantities. In the second stage they
  price to sell up to capacity.
• We discussed this implicitly when discussing
  capacity constraint Bertrand competition

18
Cournot versus Bertrand II

• Cournot model is more appropriate in environments
  where firms are capacity constrained and
  investments in capacity are slow.
• Bertrand model is more appropriate in situations
  where there are constant returns to scalse and
  firms are not capacity constrained

19
Stackelberg Model

• 2 (or more) firms
• Producing a homogeneous (or differentiated)
  product
• Barriers to entry
• One firm is the leader
• The leader commits to an output before all other
  firms
• Remaining firms are followers.
• They choose their outputs so as to maximize
  profits, given the leaders output.

20
Stackelberg Equilibrium
21
Stackelberg summary

• Stackelberg model illustrates how commitment can
  enhance profits in strategic environments
• Leader produces more than the Cournot equilibrium
  output
• Larger market share, higher profits
• First-mover advantage
• Follower produces less than the Cournot
  equilibrium output
• Smaller market share, lower profits

22
Stackelberg Mathematics I
Linear Demand and No production cost
Stackelberg Followers Profit
Stackelberg Followers Reaction Curve
23
Stackelberg Mathematics II
Stackelberg Leaders Profit
Or,
Optimal Output Leader
Is credibility used somewhere?
24
Stackelberg with Fixed Entry Cost Follower
Q2
Followers Profits are High
Reaction Curve with Entry cost
Followers Profits are Low
Q1
With Entry Cost followers profits in the market
can be too low to recover entry cost
25
Followers decision with entry cost f
Stackelberg Followers Profit (with aß1)
Stackelberg Followers Reaction Curve
If pF 0, i.e., if (1-qL)2/4 f or qL 1 - 2vf
qF (1-qL)/2
Otherwise qF 0
26
Stackelberg with Entry Cost Leader
Q2
r1
Stackelberg Equilibrium
r2
Q1S
Q1
Optimal output
27
Stackelberg with Low Entry Cost Leader
Q2
r1
Stackelberg Equilibrium
r2
Q1S
Q1
Entry deterrence is not optimal (accommodated
entry)
28
Stackelberg with High Entry Cost Leader
Q2
r1
Stackelberg Equilibrium
r2
Q1S
Q1
Monopoly Output is enough for entry deterrence
29
When do the different cases occur?

• Leaders profit of entry accommodation is 1/8 (as
  p ¼ and its output is ½) followers profit is
  1/16 f.
• Leaders profit of entry deterrence is 2vf(1-2vf)
  1/8 (as p 2vf and total output is 1- 2vf)
• choosing minimal output level to deter
• Entry deterrence profitable if 2vf(1-2vf) gt 1/8,
  i.e., iff vf gt ¼(1- ½v2)
• 0 lt vf lt ¼(1- ½v2) is too costly
• ¼(1- ½v2) lt vf lt ¼ entry deterrence in proper
  sense (distort output decisions compared to
  monopoly decision)
• vf gt ¼ monopoly output to deter entry

30
Is entry deterrence in Stackelberg context always
bad?

• Welfare (TS) if entry takes place is ½ - 1/32 f
• Total output is ¾ price is ¼
• Welfare (TS) if entry is deterred is ½ - 2f
• Total output is 1-2vf price is 2vf
• Thus, TS is higher under entry deterrence if
  f lt 1/32
• Entry deterrence is individually optimal for
  incubent and takes place if (1- ½v2)2/16 lt f lt
  1/32
• Thus, entry deterrence is sometimes optimal from
  a TS point of view (entry can be excessive)