1

Entry Games in Exogenous Sunk Costs Industries (Sutton, Chapter 2)

Structure-Conduct-Performance Paradigm: Models one-way chain of causation Concentration to Performance, treating Conduct as a ‘Black Box’ New Industrial Economics:

1) Explicitly models Conduct 2) Allows for market structure to be

Endogenous What determines market structure? Sutton (1991) – predictions that generalise across a broad range of industries “Benchmark”: Traditional Limit Theorem which ⇒

0, →∞→ ionConcentratmEquilibriuTheMSAsσ

2

Thus, ⎟⎠⎞

⎜⎝⎛=σ

MSfC4 in a negative way Traditional Limit Theorem holds in Perfectly Competitive Framework, & thus assumes

1) no strategic interaction

2) only exogenous barriers to entry

4C

σMS

3

Entry: Exogenous Sunk Costs

Two stage game

The Entry Decision is a Backward Induction Procedure

Modelling the P(N) function, Stage 2: The P(N) function links price cost margins to a given N P, for any given N, depends on how one models competition (or the ‘intensity of competition’) We modelled this in the earlier lectures for Homogenous Bertrand and Cournot (see lecture on static oligopoly), for Joint Maximising (see early part of lecture on dynamic oligopoly), and for Bertrand Horizontal Product Differentiation (see Salop 1979 circular road model in horizontal product differentiation model)

Stage 1 Long Run

Stage 2 Short Run

Entry σ

P(N)

4

Modelling Entry, Stage 1:

Enter with exogenous sunk cost σ

Entry occurs as long as the expost entry profit > sunk costs of entry

Last firm enters where expost entry profit = σ

5

Bertrand Homogenous Competition with Exogenous Sunk Costs

Stage 2:

Modelling Bertrand Homogenous Good Competition: Result P = MC for N ≥ 2 (see lecture on static oligopoly for more detail…. )

N = 1 ⇒ Pm ⇒ πm N > 1 ⇒ P = MC ⇒ π = σ

Stage 1:

First Firm enters, so long as πm > 0

Second Firm?

Expost entry π = 0 (when N = 2), thus < σ

Therefore, a second firm will not enter

Equilibrium number of firms under Homogenous Bertrand: N* = 1

6

Cournot Homogenous Competition with Exogenous Sunk Costs

Stage 2

2*

2*

2*

*

2

1

1..1

.)(

1.1.,

1,

0

0

0

)(

NSso

NN

cSc

NNcqcPand

NN

cS

NPS

NQqTherefore

NNcPThus

cNPP

cQ

SNQP

cqPqP

q

cqqP

NQqorfirmsidenticalNqqQ

QSPor

PSQLet

i

ii

i

ii

i

i

iii

i

N

iii

=

−

⎭⎬⎫

⎩⎨⎧ −

−=−=

−===

⎭⎬⎫

⎩⎨⎧

−=

=−−=

=−⎟⎟⎠

⎞⎜⎜⎝

⎛ −+=

=−∂∂

+=∂∂

−=

===

⎟⎟⎠

⎞⎜⎜⎝

⎛==

∑=

π

π

π

π

P falls with the number of firms in the industry, but at a decreasing rate

Profits rise with the size of the market, and fall with the number of firms in the industry

7

Stage 1:

σ

σπσπ

SN

orNS

ii

=

=−==

*

2)0(

The equilibrium number of firms increases with the level of S/σ, but at a decreasing rate….

Concentration = 1/N

The equilibrium concentration is inversely related to market size S relative to sunk costs σ.

8

Summary of Short Run relationship Price cost mark-ups and the number of firms in the market, i.e. the P(N) function, for homogenous goods

P

N

MC

pmonop

1

Homogenous Bertrand

Homogenous Cournot

Joint Maximising

2

P, for any given N, depends on the ‘intensity of competition’ Bertrand is most intense, while Joint maximising least intense

9

Summary of Long Run relationship between market concentration (1/N) and market size S relative to exogenous sunk costs σ, for Homogenous Goods

• For a given S/σ, the equilibrium level of concentration increases with the intensity of competition

• For a given intensity of competition, the equilibrium level of concentration falls with an increase in Market Size relative to sunk costs

σS

NC 1=

1 Bertrand (t0 = 0)

Cournot

Joint Maximising

10

Bertrand Competition for Horizontally Differentiated Products with Exogenous

Sunk Costs Salop (1979) Circular Road Model How does horizontal product differentiation affect the P(N) function? How can we endogenise N?

two stage game

Stage 1 Stage 2Entry

Sunk cost σ

NE Prices

(given N)

11

Stage 2:

1. N Sellers are located symmetrically around the circle

2. Circumference is normalised to = 1

3. Distance between each seller is thus 1/N

Given number of firms N, find NE in prices

12

Representative Selleri profit function, where TC = 0:

sales = 2d

indifferent consumer:

p + td = ⎯p + t[1/N – d]

so Ntppd 12

_

+−

=

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+==

tpp

Npdp

_12.π

⎯p ⎯p

p

← d → ← d →← 1/N – d → ← 1/N – d→

Selleri

13

seller maximises it’s profit by choosing p, given ⎯p,

01_

=−−

+=∂∂

tp

tpp

Npπ

S.N.E. ⇒ p = ⎯p

⇒ Ntpi =

*

as t → 0 ⇒ p → MC

as N→ ∞ ⇒ p → MC

Equilibrium profits solve as:

ppwhereeiN

dxi === ..12

sizemarketisswhereNsdsxi == 2

2.Nst

Ns

Ntxp iii ===π

14

Summary of Short Run relationship Price cost mark-ups and the number of firms in the market, i.e. the P(N) function, for Horizontally Differentiated goods

p

N

MC

pmonop

1

Homogenous Bertrand: t0= 0

Differentiated Bertrand: t1

Differentiated Bertrand: t2

t2 > t1 > t0

2

P, for any given N, depends on the ‘intensity of competition’ Product Differentiation Relaxes the intensity of price competition

15

Recall, the P(N) function that links price cost margins to a given N P, for any given N, depends on the ‘intensity of competition’ (Bertrand is most intense) Horizontal Product Differentiation relaxes the intensity of competition

16

Stage 1: Enter with sunk cost σ? Last firm enters where expost entry profit = σ

σπ == 2Nsti

Thus, solving for equilibrium number of firms:

σstN =*

17

Summary of Long Run relationship between market concentration (1/N) and market size S relative to exogenous sunk costs σ, for Horizontally Differentiated Goods Greater product differentiation induces more entry (so less concentration) for any given s/σ

• For a given S/σ, the equilibrium level of concentration increases with the intensity of competition

• For a given intensity of competition, the equilibrium level of concentration falls with an increase in Market Size relative to sunk costs

σS

NC 1=

1 Homogenous Bertrand (t0 = 0)

Differentiated Bertrand (t1)

Differentiated Bertrand (t2)

t2 > t1 > t0

18

Exogenous Sunk Costs

Traditional Limit Theorem:

⎟⎠⎞

⎜⎝⎛=σ

MSC

New Game Theoretic Modelling:

⎟⎠⎞

⎜⎝⎛= IMSC ,σ

Note that only a Lower Bound to the equilibrium level of concentration is predicted by the theory.

Concentration may be above the predicted lower bound – depending on the specifics of the industry e.g first mover advantage……

( – )

( – ) (+)

19

Note that while in the short-run, an industry may fall below the lower bound to concentration, this is not possible in the long run.

For any given market size relative to sunk costs, if concentration is below the predicted lower bound this implies that there are too many firms in the industry. Prices are not high enough to sustain a normal rate of return on sunk costs incurred. This results in the forced exit of firms, or mergers/acquisitions – thereby reducing N and increasing concentration levels back up to (or above) the predicted lower bound

20

The Salt and Sugar Case Studies (Sutton, Chapter 6)

Objective: examine the long run evolution of market structure for the salt and sugar industries using theoretical framework above. Both Salt and Sugar industries were initially highly fragmented. Today they are highly concentrated.

Theoretical Predictions: market will become more concentrated where there is (i) a decrease in market size relative to sunk costs or (ii) an increase in the intensity of competition

21

Theory to Empirics (figure 6.1): Exogenous influences that shift the functional relationship include:

Change in Technology S/ σ

Decline in Demand

Geographical Segmentation; lower transport costs

Competition Policy Regime

Toughness of Price Competition

Equilibrium Structure

22

Cases: Salt: highly concentrated in all countries (tough competition policy indicates tough price competition) Sugar: concentration reflects nature of competition policy US: strict policy Europe: relaxed Japan: relaxed pre-1914 Salt and Sugar: • homogenous good, tough price competition • Theory predicts a concentrated structure • Intense price competition resulted in

attempts to collude • Price coordination in fragmented and

homogenous good industry is hard to maintain

• Concentrated structure emerged as a result of firm exit/mergers/acquisitions