Industrial Organization or Imperfect Competition Entry deterrence II

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Industrial Organization or Imperfect
Competition Entry deterrence II

• Univ. Prof. dr. Maarten Janssen
• University of Vienna
• Summer semester 2008
• Week 9 (May 19, 20)

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Stackelberg with Entry Cost Leader
Q2
r1
Stackelberg Equilibrium
r2
Q1S
Q1
Optimal output
3
Stackelberg with Low Entry Cost Leader
Q2
r1
Stackelberg Equilibrium
r2
Q1S
Q1
Entry deterrence is not optimal (accommodated
entry)
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Stackelberg with High Entry Cost Leader
Q2
r1
Stackelberg Equilibrium
r2
Q1S
Q1
Monopoly Output is enough for entry deterrence
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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
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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

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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)

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Entry Deterrence under Cournot

• 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

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Credibility and Predation

• Take a simple example
• two companies incumbent and entrant
• Entrant makes its decision first
• enter or stay out of incumbents market
• Incumbent then chooses
• accommodate or fight
• Game tree is as follows

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The Example
What if entrant decides to Enter?
Fight is eliminated
Incumbent is better to Accommodate
(0,0)
(0,0)
Fight
Fight
(2,2)
Accommodate
Enter, Accommodate is the unique subgame perfect
equilibrium forthis game
Enter
M2
Enter
(2,2)
Newvel
Entrant will choose to Enter since Incumbent will
Accommodate
N1
Stay Out
(1,5)
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The Chain-Store Paradox

• What if incumbent competes in more than one
  market or with more than one rival?
• threatening one may affect the others
• But Seltens Chain-Store Paradox arises
• 20 markets established sequentially
• will incumbent fight in the first few as a
  means to prevent entry in later ones?
• No this is the paradox
• Suppose incumbent fights in the first 19
  markets, will it fight in the 20th?

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Entry Deterrence how to make the threat credible?

• An example
• P 120 - Q 120 - (q1 q2)
• marginal cost of production 60 for both
• cost of each unit of capacity is 30
• firms also have fixed costs of f
• incumbent chooses capacity K1 in stage 1
• entrant chooses capacity and output in stage 2 at
  moment firms compete in quantities.

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Core idea

• By moving your cost to an earlier moment, you
  effectively lower marginal costs when you compete
• More aggressive competitor
• Higher profits

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The Example (cont.)
By installing capacity of K1 , marginal cost up
to K1 is 30, not 60. So, best response function
up to K1 is shifted out.
q2
90
60
kink in best response function. NOTE The
incumbent will never let installed capacity stay
idle it can credibly commit to produce at least
K1 in the production stage
R1
30
R2
q1
60
30
45
K1
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Some of the relevant math

• Standard profit function for firm 1 is p P(Q)q1
  c(q1) (120-Q)q1 - 60q1 (60-Q)q1
• Standard reaction function q1 30 ½ q2
• Installing capacity changes consideration for any
  q1 up to K1 to p P(Q)q1 c(q1) (120-Q)q1
  - 30q1 30K1 (90-Q)q1 30K1
• New reaction function q1 45 ½ q2 for q1
  K1
• K1 does not effect the marginal consideration

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The Example (cont.)
Installing capacity below the Cournot output
level is ineffective.
q2
90
60
R1
30
R2
q1
60
30
45
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The Example (cont.)
Can the incumbent let installed capacity
rationally stay idle?
q2
90
60
R1
30
R2
q1
60
30
45
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So, in equilibrium firm 1 will produce up to
capacity. How much capacity to install?
q2
90
If f 0 p P(Q)K1 c(K1) (120-K1-30-
½K1)K1 - 60K1 (30-½K1)K1 Effectively, firm 1
is a Stackelberg leader and rationally installs
the monopoly output
60
R1
30
R2
q1
60
30
45
K1
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Thus, similar reasoning as Stackelberg

• If there is a fixed cost of production (entry),
  then it may be rational to install more capacity
  than the monopoly output in order to deter entry
• If there is an entry cost of 200 in this example,
  then installing 32 units of capacity is enough to
  deter entry
• At K1 32, optimal reaction (if positive) is 14,
  total output would be 46, per unit profit 14 and
  operating profits are 14.14 196

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The Example (cont.)
q2
90
R1
Effectively this commits the incumbent to q1
32. The entrants best response to q1 32 is q2
14. So, operating profit does not cover the
entrants 200 overhead.
60
30
S
15
R2
R2
q1
60
30
32
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Conclusion

• Entry deterrence can take the form of installing
  a large capacity (that is fully used in
  equilibrium)
• Analyzed in context of Stackelberg or Cournot
  model
• Effectively, yeilds same type of considerations
  and results
• Without fixed cost, Cournot reduces to
  Stackelberg if one party can move its capacity
  choice to an earlier moment
• With fixed cost, it can lead to entry deterrence
  behavior like in Stacklberg with fixed cost of
  entry