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Industrial Organization or Imperfect Competition

Entry deterrence I

Univ. Prof. dr. Maarten JanssenUniversity of ViennaSummer semester 2012Week 6 (April 26)

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Definition of entry deterrence Incumbent’s 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

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Capacity Expansion and Entry Deterrence Central point: For predation to be successful

—and therefore rational—the 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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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

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Demand and Residual Demand

Market demand P(Q)=P(q1,Q-i=0)

q1

P(q1)

P(q1, Q-i =10)

P(q1, Q–i =20)

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Cournot Reaction Functions Firm 1’s 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 1’s product ( reaction functions are downward sloping).

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Cournot Model

The problem Max{(P(qi+Q-i) qi – C(qi)}defines de best-response (or reaction) function of firm i to a conjecture Q-i as follows:

P’(qi+Q-i)qi + P(qi+Q-i) – C’(qi) = 0

Q-i

qiqiM

qj

r1

qi*(qj)

Firm i’s reaction Function

Q-i=0

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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

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Cournot Equilibrium

q2

q1q1

M=30

r1

r2

q2M=30 Cournot equilibrium

q1* maximizes firm 1’s

profits, given that firm 2 produces q2

*

q2* maximizes firm 2’s

profits, given firm 1’s output q1

*

No firm wants to change its output, given the rival’s

Beliefs are consistent: each firm “thinks” rivals will stick to their current output, and they do so!

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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 firm’s

individual market share and monopoly power.

i

ij ji

iiij ji s

qqP

qMCqqP

)(

)()(

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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)/P, 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)

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Different concentration measures C4 is sum of four largest market shares

Can’t 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

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“Justifying” HHI

2

)(

)()(i

ij ji

iiiij ji s

qqP

qMCsqqP

i

ij ji

iiij ji s

qqP

qMCqqP

)(

)()(

HHI

qqP

cqqP

ij ji

ij ji

)(

)(

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Changes in marginal costs

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Another look at Cournot decisions

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

A

B CIncreasing Profits for

Firm 1

D

Q1Q1

M

r1

Q2

16

Q2

Q1Q1

M

r1

Q2*

Q1*

Firm 1’s Profits

Firm 2’s Profits

r2

Q2M Cournot Equilibrium

Profits at Cournot equilibrium

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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

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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 scale and firms are not capacity constrained

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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 leader’s output.

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Stackelberg Equilibrium

Q1S

Q2S

Follower’s Profits Decline

Leader’s Profits Rise

Stackelberg Equilibrium

r2

Q1Q1

M

r1

Q2*

Q1*

Q2

Cournot Equilibrium

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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

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Stackelberg Mathematics I

Qp Linear Demand and No production cost

Stackelberg Follower’s Profit

FF qQ)(

Stackelberg Follower’s Reaction Curve:

LF qq 21

2

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Stackelberg Mathematics II

LLL

LL

qqq

qQ

])[(

)(

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2

Stackelberg Leader’s Profit

LL

L qq

)2

( Or,

Optimal Output Leader:

2Lq

Is credibility used somewhere?

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Stackelberg with Fixed Entry Cost: Follower

Q1

Q2

Follower’s Profits are High

Follower’s Profits are Low

With Entry Cost: follower’s profits in the market can be too low to recover entry cost

Reaction Curve with Entry cost

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Follower’s decision with entry cost fStackelberg Follower’s Profit (with α=β=1)

fqQ FF )1(

Stackelberg Follower’s Reaction Curve:

If πF ≥0, i.e., if (1-qL)2/4 ≥ f or qL ≤ 1 - 2√fqF = (1-qL)/2

Otherwise qF = 0

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Stackelberg with Entry Cost: Leader

Q1

r1

r2

Q2

Q1S

Stackelberg Equilibrium

Optimal output

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Stackelberg with Low Entry Cost: Leader

Q1

r1

r2

Q2

Q1S

Stackelberg Equilibrium

Entry deterrence is not optimal (accommodated entry)

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Stackelberg with High Entry Cost: Leader

Q1

r1

r2

Q2

Q1S

Stackelberg Equilibrium

Monopoly Output is enough for entry deterrence

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When do the different cases occur? Leader’s profit of entry accommodation is 1/8 (as p =

¼ and its output is ½); follower’s profit is 1/16 – f. Leader’s profit of entry deterrence is 2√f(1-2√f) (as p

= 2√f and [total] output is 1- 2√f); choosing minimal output level to deter

Entry deterrence profitable if 2√f(1-2√f) > 1/8, i.e., iff √f > ¼(1- ½√2) 0 < √f < ¼(1- ½√2) is too costly ¼(1- ½√2) < √f < ¼ entry deterrence in proper sense (distort

output decisions compared to monopoly decision) √f > 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 1-2√f; price is 2√f Thus, TS is higher under entry deterrence if f < 1/32 Entry deterrence is individually optimal for incumbent

and takes place if (1- ½√2)2/16 < f < 1/32 Thus, entry deterrence is sometimes optimal from a

TS point of view (entry can be excessive)