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”:
which 
As
MS

Traditional Limit Theorem
 , The Equilibrium Concentration  0
1
Thus,
 MS 
C4  f 

  
in a negative way
C4
MS

Traditional Limit Theorem holds in Perfectly
Competitive Framework, & thus assumes
1) no strategic interaction
2) only exogenous barriers to entry
2
Entry: Exogenous Sunk Costs
Two stage game
Stage 1
Long Run
Entry

Stage 2
Short Run
P(N)
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)
3
Modelling Entry, Stage 1:
Enter with exogenous sunk cost 
Entry occurs as long as the expost entry profit
> sunk costs of entry
Last firm enters where expost entry profit = 
4
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
N > 1  P = MC
 m
 =
Stage 1:
First Firm enters, so long as m > 0
Second Firm?
Expost entry  = 0 (when N = 2), thus < 
Therefore, a second firm will not enter
Equilibrium number of firms
Homogenous Bertrand: N* = 1
under
5
Cournot Homogenous Competition with
Exogenous Sunk Costs
Stage 2

S

 or P  Q

S
P
Q 
Let




N
Q 
q
 Nqi
i
(identical firms ) or qi 
i 1
Q
N
 i  P qi  cqi
 i
P
 P  qi
c 0
qi
qi
 P
P
c 0
N
 N 
P*  c 

 N  1
qi* 
Therefore ,
so

c 0


Q
N
Thus,
and
S

 Q2

 P
Q
S 1
S N 1

.

.
N
P N
c
N2
 i*  ( P  c ) qi  
c.

 i* 
N
 S N 1
 c .
.
N 1
c
N2

S
N2
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
6
Stage 1:
i 
N* 
S
N
2

(or  i    0)
S

The equilibrium number of firms increases
with the level of S/, but at a decreasing
rate….
Concentration = 1/N
The equilibrium concentration is inversely
related to market size S relative to sunk costs
.
7
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
pmonop
Joint Maximising
Homogenous
Cournot
Homogenous
Bertrand
MC
1
2
N
P, for any given N, depends on the ‘intensity
of competition’
Bertrand is most intense, while Joint
maximising least intense
8
Summary of Long Run relationship between
market concentration (1/N) and market size
S relative to exogenous sunk costs , for
Homogenous Goods
C
1
N
Bertrand (t0 = 0)
1
Cournot
Joint Maximising
S

 For a given S/, 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
9
Bertrand Competition for Horizontally
Differentiated Products with Exogenous
Sunk Costs
(*see Salop 1979 circular road model – include as
part of this lecture)
Stage 2:
(Assume N firms located symmetrically about a
circle of circumference, distance between sellers is
1/N, zero cost):
P
t
N
Result is
, where t is the (exogenous) per
unit cost of distance travelled.
Thus, as t  0
 p  MC
while as N 
 p  MC
i.e. P falls with the number of firms in the industry, but
at a decreasing rate
10
Stage 1:
i  t
s

2
N
Thus, solving for equilibrium number of firms:
N* 
t
s

The equilibrium number of firms increases
with the level t, but at a decreasing rate….
The equilibrium number of firms increases
with the level of S/, but at a decreasing
rate….
Equilibrium concentration is inversely related
to market size S relative to sunk costs 
11
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
t2 > t1 > t0
pmonop
Differentiated
Bertrand: t2
Differentiated
Bertrand: t1
MC
Homogenous
Bertrand: t0= 0
1
2
N
P, for any given N, depends on the ‘intensity
of competition’
Product Differentiation Relaxes the intensity
of price competition
12
Summary of Long Run relationship between
market concentration (1/N) and market size
S relative to exogenous sunk costs , for
Horizontally Differentiated Goods
C
1
N
Homogenous
Bertrand (t0 = 0)
1
t2 > t1 > t0
Differentiated
Bertrand (t1)
Differentiated
Bertrand (t2)
S

Greater product differentiation induces more
entry (so less concentration) for any given s/
 For a given S/, 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
13
Exogenous Sunk Costs
Traditional Limit Theorem:
(–)
 MS 
C 

  
New Game Theoretic Modelling:
(–)
(+)
 MS

C 
, I
 

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……
14
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
15
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
16
Theory to Empirics (figure 6.1): Exogenous
influences that shift the functional relationship
include:
Change in
Technology
S/ 
Decline in
Demand
Equilibrium
Structure
Geographical
Segmentation;
lower transport
costs
Toughness
of Price
Competition
Competition
Policy Regime
17
Cases:
Salt: highly concentrated in all countries (tough
competition policy indicates tough price
competition)
Sugar: concentration reflects
competition policy
US:
strict policy
Europe: relaxed
Japan:
relaxed pre-1914
nature
of
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
18
US SALT – key dates
 Early 1800s – increase p competition and
lower t costs
 Attempts to collude to artificially maintain
higher p - kept breaking down….
 1817 West Virginia
 1876 Michigan Salt Association
 1890 Sherman Act
 1899 National Salt Company
 1914 – tight countrywide coordination
 1922 – FTC investigation
 1914-1950s: stability – consolidations
/mergers / acquisitions resulting in high level
concentration at national and regional levels
19
UK SALT – key dates
1880s:
 increase in 
 decrease in demand (i) lower exports as
production abroad expands (ii) chemical
industry replace salt with brine as key input
 sparked off intense price competition
 predict : high concentration
 1882 – coordination attemp = ‘pooling’
 1888 – salt union
 1905 – defects
 postwar years – 1950s - consolidations
/mergers / acquisitions resulting in high level
concentration
 stability – top 2 firms have >95% of market
20
US SUGAR
 Strict Competition Policy
 Advances in Technology reduce 
 Increase in demand
 1830’s-1870’s
 Regional versus National concentration
levels
 Some regional monopolies – but lower
concentration at national level
CONTINENTAL EUROPE – FRANCE,
GERMANY AND ITALY
 Regulated Quota System in EC (based on
production levels pre-1968)
 Market structure is ‘frozen’ at 1968 levels
JAPAN
 Pre-war – relaxed competition policy –
increase demand – cartel
 Interwar years – tough price competition cartel collapse
 Post-war – governmental policies
21
A Test of the Theory?
 Product Homogeneity…….
 What factors determine Intensity of
Competition? Can firms manipulate these?
 Barriers to Entry – can firms manipulate
these?
22