Endogenous Fixed Costs, Integer Effects, and
Corporate Performance
by
Stephen Brammer
University of Bath School of Management
Working Paper Series
2000.04
University of Bath School of Management
Working Paper Series
University of Bath School of Management
Claverton Down
Bath
BA2 7AY
United Kingdom
Tel: +44 1225 826742
Fax: +44 1225 826473
http://www.bath.ac.uk/management
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Endogenous Fixed Costs, Integer Effects, and Corporate
Performance
by
Stephen Brammer
Abstract
An important strand of recent theoretical literature generates robust predictions concerning equilibrium
market structure from models involving zero-profit free-entry conditions. A significant implication of
this modelling approach is that if firms are identical and the number of firms is taken to be a continuous
variable, industry equilibrium involves all incumbents making no excess returns. However, since real
market structures consist of whole number, or integer, values of the number of incumbents, such
models generally predict that indivisibilities in the number of firms are the only source of excess rates
of return in an industry. We generate a number of theoretical propositions concerning the way the
range of per firm excess returns varies with market size and the nature of prevailing fixed expenditures.
The key results relate to upper and lower bounds to the excess profits that firms may earn because of
indivisibilities in firm numbers. We show that where only exogenous fixed costs are important the
potential for such effects to lead to significant excess returns exists only in small markets. Where firms
make significant endogenous investments in order to enhance their products this simple relationship
breaks down. Specifically it is possible that significant excess returns exist even in very large markets
as a direct consequence of integer effects. We argue that this result has important consequences for
corporate strategic decision making.
JEL Classification: L10, L19, L130, L110
Key Words:
Corporate profitability
Address for Correspondence:
Stephen Brammer
School of Management
University of Bath
Claverton Down
Bath BA2 7AY
England
E-mail: [email protected]
3
1. Preamble
There is a long history in Industrial Organisation economics of viewing excess
industry profits as a disequilibrium phenomenon. Since the work of Mason (1930) and
Bain (1956) a considerable amount of research has been done into what particular
elements of industry structure systematically contribute to the earning of above
normal returns. The broad consensus is that both the economies of scale associated
with very heavily capital-intensive production and product related expenditures such
as advertising and R&D contribute to both important barriers to entry to markets and
to the existence of both concentrated market structures.1 Within this schema the latter
provide the opportunity for softening of competitive pressures and the former protect
the excess returns from outside competition. The aim of this paper is to highlight an
alternative interpretation of the cross-section correlation between industry
performance and the key variables traditionally associated with entry barriers. The
broad thrust of our argument is that both significant plant setup costs and costs of
product enhancement may contribute to the existence of persistently high industry
performance in equilibrium.
An important strand of recent theoretical literature generates robust predictions
concerning equilibrium market structure from models involving zero-profit free-entry
conditions.2 Two elements of this theoretical literature are particularly pertinent to the
following discussion. Firstly, the use of a zero-profit free entry condition to drive
market equilibrium determines that industry excess returns may only occur as the
result of either disequilibrium or indivisibilities in the number of incumbent firms.
Secondly, recent theoretical work has highlighted the potential for product enhancing
firm specific expenditures such as advertising or research and development to have
significant implications for the evolution of market structure. Specifically, this work
has highlighted an important mechanism whereby in some markets firms face greater
incentives to improve their products in larger markets (and hence devote greater
resources to doing so). In what follows this mechanism, sunk (or fixed) cost
escalation, is shown to have important implications for the potential for firms to earn
excess returns. The implications of these important theoretical innovations for the
1
See for example Strickland & Weiss (1976), Martin (1979), Comanor and Wilson (1967) and Collins
and Preston (1960)
4
performance of industries and firms have yet to be systematically explored. The
current effort seeks to partially address this agenda.
In addition to these theoretical reasons for investigation of the performance analogue
of this structural work, the significant level of empirical support received3 for the
predictions of these frameworks establishes a good prima facie case for believing that
exploring the performance dual of the existing structural work may lead to an
important new empirical contribution.
2
3
See, for example, Sutton (1991, 1998)
See Sutton (1991, 1998), Robinson and Chiang (1997), Symeonidis (1999) and Matraves (1999)
5
2. Introduction
Where firms are identical using a zero-profit free entry condition to describe
equilibrium market structure entails characterising the nature of industry structure that
derives from firms entering a market until further entry would lead all firms in the
industry to make losses. As discussed above, a significant implication of this
modelling approach is that if the number of firms is taken to be a continuous variable,
industry equilibrium involves all incumbents making no excess returns. However,
since real market structures consist of whole number, or integer, values of the number
of incumbents, such models generally predict that indivisibilities in the number of
firms are the only source of excess rates of return in an industry. Where the size of a
market is greater than that sufficient to lead to the entry of the current number of
firms, but smaller than that necessary to induce further entry, incumbents each earn
profits greater than those necessary to cover any fixed costs of entry. Put differently,
markets that have more than enough "room" for the current number of incumbents
allow those firms to earn positive net profits.
The idea that entry acts to erode the potential for incumbents to earn excess returns
has a long history in economics. However, developing that logic to provide a pivotal
role for integer effects has not formed a significant part of efforts to account for interindustry performance differences. Part of the reason for this might be the presumption
that such effects are typically “small”.
The content of this paper consists of the derivation of two results with respect to the
magnitude of excess profits that incumbent firms may make because of the
indivisibility of firms. We show that the magnitude of per firm excess profits within
free entry games is sensitive to the size of the market and the nature of fixed costs.
Our framework, in common with others in the recent literature, involves a key
distinction between markets where the fixed costs firm incur may be reasonably be
though of as being exogenous, and those where firms make additional product
enhancing expenditures the levels of which are chiefly a function of the size of the
market. Following Schmallensee (1992) we refer to the former type of market as the
“Type One” market, and the latter as the “Type Two” market.
6
3. Theory
It is useful to develop the theory in a number of stages. Firstly we explore how per
firm excess profits vary as the size of the market varies in two illustrative examples.
These examples are due to Sutton (1991) and provide a clear description of the
fundamental difference between type 1 and type 2 markets. Subsequently we discuss
the robustness of the insights these examples highlight.
3.1
An example of a Type 1 market: A homogeneous product Cournot
model
Firms take part in a two-stage game. Firms first decide whether or not to enter the
market, incurring an exogenous fixed cRVWRI LIWKH\GR6XEVHTXHQWO\WKHHQWUDQWV
compete by selecting their levels of output taking those of their (N -1) rivals as given.
The N entrants are assumed to face the following isoelastic demand curve
X = S/P ,
(1)
where X is total number of units sold, P is market price and S is the total value of
sales in the market4. S may be thought of as adequately capturing the size of the
market because it is independent of market price in the form expressed in equation 1.
The gross (final stage) profits of an individual entrant are given by
G
i

  N 
=  P  q i  − c i q i .

 

  i=1 
∑
(2)
4
Note that this demand function has the property that if a monopolist has a positive marginal
cost the monopoly price goes to infinity. We abstract from this possibility in the text that
follows. The reader should add the following caveat to the end of results that follow: "Unless
the market is monopolised in which case the monopolist sets some high, but finite level of
price."
7
Differentiation of the final stage profits of firm i with respect to qi and solution for qi
yields firm i’s reaction function. Assuming firms are symmetric, whereupon x i = x for
all i yields the Cournot equilibrium where market price is given by equation 3 below.
1 

P = c1 +

N −1

(3)
Each firm has equilibrium output of
q=
S N -1
•
,
c N2
(4)
and hence final stage profits of
G
i
= (P − c)q =
S
N2
.
(5)
Given the way in its final stage profits vary with the number of rivals it faces a firm
will choose to enter if its profits net of the fixed cost of entry are positive, i.e. a firm
will enter if
S
(k + 1) 2
− >0,
(6)
where k is the number of rivals that enter the market. Put differently, a firm will
choose to enter if it expects to make sufficient profits cover the fixed costs of entry,
i.e. when
S
(k + 1) 2
> .
(7)
If the number of firms were a continuous variable, entry would continue until all the
firms made zero net profits. Setting the final stage profits of a representative firm (as
8
given in (5) above) equal to the fixed cost of entry and solving for N provides the
equilibrium number of entrants as
N=
S
.
(8)
If N were discontinuous, and specifically so that only an integer number of firms
could enter at the second stage of the game, then the equilibrium number of firms
would be the integer component of the left hand side of equation 8.
We can now turn to the key issue of what bounds the entry decision rule described
above places upon the levels of excess profits earned by incumbents. Clearly the
lower bound on gross profits earned by each incumbent is the value of the exogenous
setup cost since if these weren’t at least covered then the firm would not have chosen
to enter. The upper bound to the profits that can be earned is given by the profits made
by each of the k rivals that currently occupy the market that a potential entrant faces
its entry decision over. Rearrangement of the decision rule described above in
equation 7 in equality form yields an expression for the magnitude of the profits
earned by each of the k current incumbents as a function of k aQG DV
2
S
1 
= σ  + 1 .
2
k
k

(9)
There are two important features of this upper bound to the excess profits that may be
earned by incumbent firms. Firstly, a firm’s ability to earn super-normal profits is a
simple decreasing function of the number of rivals it faces in its market. Secondly, the
level of excess profits made by each incumbent is a mark-up on the level of the
exogenous setup cost made upon entry which itself depends upon the number of rivals
faced. Specifically, a monopolist can earn gross profits four times greater than those
necessary to cover its cost of entry without attracting entry, conversely, where the
number of firms is arbitrarily large each firm may only earn profits sufficient to
covers the cost of entry and any excess profits attract new firms into the market. The
bounds to the gross profits that individual firms may earn are shown in figure 1
9
below. Changes in the value of the setup cost lead to vertical shifts in the upper bound
to gross profits.
Figure 1: The range of gross profits per firm in a homogeneous product Cournot model
Gross Profit
per firm
( Πi )
G
∞
1
Number of
rivals (k)
The next step is to consider the relationship between the range of excess returns
earned by incumbents and the size of the market. Since k= N-1 it follows from
equation 8 that the number of rivals faced by potential entrants is given by
k=
S
−1
.
(10)
Equation 10 states that the number of rivals faced by potential entrants is a simple
monotonically increasing function of the size of the market relative to the exogenous
setup cost. Substitution of the right hand side of equation 10 into the right hand side
of equation 9 yields


G
Π i = σ 1 +


2


1 
 .
S
− 1 

(11)
10
From equation 11 it follows that the upper bound to the level of integer profits that the
k incumbents may earn is a decreasing function of the size of the market. Hence in
larger markets firms are able to make smaller levels of excess returns without
attracting further entry than in smaller markets.
Since the net returns firms earn from their activities are difficult to measure
empirically, economists have tended to try to provide an explanation of the gross
profitability of firms. In addition, a rough price-cost margin has been traditionally
employed as a useful description of the existence of market power. For these reasons
there is some value in reframing the analysis above in terms of gross industry
margins. Our first observation concerns the relationship between the minimal level of
industry margins and the size of the market. Note that this relationship concerns the
margins earned by incumbents when N is continuous and each firm makes zero net
profit.
Substitution of equation 8 above into equation 3 yields the following
description of the relationship between market price and the size of the market:



P = c1 +




1 
.
S
− 1 
σ

(12)
From equation 12 it follows that as S becomes arbitrarily large market price converges
upon marginal cost. Hence in very large markets the minimal level of unit margins
converges upon zero.
Turning to the upper bound to margins that coincides to that earned by incumbents
when market size is marginally smaller than that necessary to induce further entry, it
is important to note that in a simple Cournot world price is a simple decreasing
function of the number of incumbents. Further, the maximal extent of integer profits is
the level of profits earned by incumbents when the actual number of incumbents for a
given size of market is one less than that consistent with the free-entry zero net profit
condition.
11
From this it follows that the level of market price consistent with this maximal integer
effect is given by
1 

P = c1 +
.
N −2

(13)
Equation 13 indicates that the level of price consistent with maximal integer effects
converges upon marginal cost as the number of incumbents becomes very large. Since
a monotonically increasing relationship between the number of incumbents an S
pertains within this model, it follows that this maximal level of price converges on
marginal cost in very large markets. Subtracting equation 3 (the minimal price) from
equation 13 (the maximal price) gives
c
,
(N − 2)(N − 1)
(14)
which is clearly decreasing in N for all N>2. Hence the maximal level of the market
price lies above the price consistent with zero-profit making free entry but the extent
to which it is decreasing in the number of incumbents and hence, for reasons identical
to those discussed above, the size of the market. This result is diagrammatically
illustrated in figure 3 overleaf.
12
Figure 2: The range of gross profit margins in a homogeneous product Cournot model as Market Size
varies
Gross
Industry
Margin
Maximal
Margin
Minimal
Margin
Market
Size (S)
13
3.2
An example of a type 2 market: A Cournot model with perceived quality
We now turn our attention to a different type of market. Following from the
discussion above, the difference between markets of different "types" relates to the
nature of fixed expenditures firms can make. In a type two market firms can raise the
quality of their product by incurring only or mainly extra fixed costs. The key
mechanism that operates in such a model is that firms have greater incentives to
improve their products in larger markets since additional fixed expenditures can be
recouped over a larger sales volume. This "escalation" of fixed costs will be shown to
imply two important results. Firstly, we will show that the total magnitude of industry
integer profits increases throughout the range of market size where escalation of fixed
expenditures occurs. Secondly, we highlight the possibility of a non-monotonic
relationship between the equilibrium number of firms and the size of the market.
In what follow it is convenient to separate the theoretical discussion into two parts.
Firstly we tackle the issue of how industry total integer profits vary with market size
in a type 2 world. Subsequently, we address the issue of how the equilibrium number
of firms varies with market size. From these discussions we provide a characterisation
of the range of possible outcomes.
Identical consumers are assumed to face the choice of whether to buy a unit of a
differentiated product, x, or a unit of an undifferentiated alternative, z. They do so in
the standard utility maximising manner. Their Cobb-Douglas utility function is:
U = (ux ) z 1−δ
δ
(12)
If firms offered uniform product quality this would yield the following inverse
demand function
P=
S
,
Q
(13)
14
where S is total expenditure by consumers on differentiated products and Q is the total
output of the N firms in the market. Note that equation 13 is identical to the inverse
demand function facing firms in the simple Cournot example outlined in section 2.1
above. However, if firms offer different levels of product quality, then the level of
demand for each firm’s product depends upon its quality relative to the alternatives on
offer. If N -1 firms offer a common level of vertical product quality u , then the
inverse demand function facing a deviant firm offering a level of product quality
of u ≠ u is
P=
S
,
u
Q +  q
u
(14)
where Q equals the aggregate output of the N -1 non-deviant firms, q is the output of
the deviant firm, u is the level of product quality offered by the deviant and u is the
level of product quality offered by the non-deviants. Using equation 14 we can, as in
the simple example above, generate profit functions for the deviant and the N -1 nondeviant firms. Partial differentiation with respect to their own output yields first order
conditions which, in turn provide the equilibrium output level for the deviant firm of
( )
(15)
( )
(16)


u
q u u = (N − 1) − (N − 2 ) q
u


and a price of
1 
u
P u u = c +
.
 u N − 1
The non-deviant firms each produce an output of
q=
( )
[( )
u u (N − 1)
S
⋅
c u u (N − 1) + 1 2
]
(17)
15
at a price of


1
P = c 1 +
.
u u N − 1

( )
(18)
Using equations 15 and 16 we can then derive the final stage profits of the deviant
firm as a function of the level of product quality it provides as


1
Π G u u = S 1 −
1
u

+
 u N − 1
( )
2


 .


(19)
Equation 19 describes some interesting results. Firstly note that it indicates how the
incentive to deviate from offering a common level of product quality varies with the
size of the market. Clearly, the profit earned by a deviant firm is increasing in the size
of the market, a feature we will return to. Second, the deviant’s profit increases as the
extent to which the level of product quality it offers is raised above that commonly
available. Thirdly, equation 19 illustrates the impact of changes in market structure,
reflected in changes in N, on the gross profits of an incumbent. Ceteris paribus, rises
in N lead to falls in the gross profits of incumbents.
Further, note that if firms are ex post identical, equation 19 reduces to
G
=
S
,
N2
(20)
which is identical to the gross profits earned by each firm in the simple Cournot case
discussed above.
Equipped with the knowledge of the particular way in which its profits depend upon
the level of product quality it offers relative to rivals, the firm is now in a position to
decide what level of quality to offer. Sutton (1991) develops his example by assuming
16
the function describing the fixed cost of achieving increases in vertical product quality
takes the following specific form5:
A(u i ) =
(
)
a γ
ui − 1
γ
(21)
A (ui) is the fixed cost involved in producing a product with vertical quality of ui. The
parameter a may be interpreted as the cost of delivering an advertising message aimed
DWLQFUHDVLQJSHUFHLYHGTXDOLW\ LVDVVXPHGWRWDNHDYDOXHRIJUHDter than 1 and may
be interpreted as the rate of (diminishing) returns to those messages.
:H FRPELQH $ X ZLWK WKH H[RJHQRXV VHWXS FRVW WRDUULYHDWDQH[SUHVVLRQWKDW
describes total fixed outlays, F (u).
F (u ) = A(u ) + σ =
(
)
a γ
ui − 1 + σ
γ
(22)
Each firm seeks to maximise its profits by selecting an appropriate level of product
quality given its cost function. The profit of the deviant net of all fixed costs is:
ΠN


1
≡ Π G − F (u ) = S 1 −
u
1

+
 u N − 1
2


a γ
 − u −1 −σ
γ


(
)
(23)
In general, a firm will find it optimal to deviate from the symmetric configuration if
δΠ G
δu
≥
u = u =1
δF
δu
(24)
u =1
Equation 24 states that a firm will only find it optimal to deviate from a situation in
which no advertising occurs if the rise in its gross profits from deviation are greater
than or equal to the increase in its fixed costs it incurs by doing so. Given that
Providing that γ > 1, this function exhibits diminishing returns. This is one of the established
empirical "stylized facts" concerning advertising expenditures, see Clarke (1976).
5
17
deviation is profitable, the deviant then chooses the level of u such that its profits are
maximised. In this example, partially differentiating equation 23 with respect to u
yields the following first order condition:
(
G


1
1 −
u
1

+
 u N − 1
)
− F (u )
= −2Su
2
X
u 2
 1
+  u

 N-1 u 





+ au
−1
=0
(25)
Simplification, and substitution of the assumption that ex post all firms will offer a
common level of product quality allows the simplification of equation 25 to
2S
(N - 1)2
N3
= au .
(26)
Equation 26 describes the choice of product quality offered, and hence an implicit
level of fixed expenditures made, by a representative firm as a function of the number
of entrants at stage one of the game. Let the value of F (u) implicitly defined in
equation 26 be denoted F*.
As in the homogeneous product case above, entry occurs until further entry is
unprofitable. Hence a potential entrant will enter if
S
> F*
(k + 1) 2
.
(27)
Under symmetry and continuous N, this means that entry will occur until N satisfies
the following equality
S
N2
= F ∗ (N; S)
(28)
whereupon each firm will earn profits just sufficient to cover its total fixed outlays.
18
Rearrangement of equation 28 yields
N=
S
F*
.
(29)
Equation 29 describes the equilibrium relationship between the number of firms and
market size relative to total fixed expenditures.
Having established the fundamentals of the model we are now in a position to
consider the upper and lower bounds to the levels of gross profits that incumbents
may earn. Let us firstly consider the properties of the lower bound to gross profits. By
analogous reasoning to that employed in the homogeneous product case, it follows
straightforwardly from the decision rule described by equation 27 above that the
lower bound to firm gross profits is the level of total fixed expenditures. However, in
a type 2 world there are two components to total fixed expenditures those being the
exogenous cost of building a plant and the endogenously determined cost of product
improvement. The first of these remains independent of the size of the market,
however since the incentives to improve products are sensitive to market size the
magnitude of the latter depends upon the size of the market.
To see how endogenous fixed costs vary with market size we first substitute the right
hand side of equation 29 into equation 26 yielding
2S
S 
 - 1
F 
3
S2
2
= au
.
(30)
 
 F
SincHDDQG DUHDVVXPHGWREHFRQVWDQWVWKHOHYHORISURGXFWTXDOLW\WKDWILUPVRIIHU
in equilibrium will be increasing (decreasing) in S according to whether the partial
derivative of the left-hand side of equation 30 with respect to S is positive (negative).
19
That partial derivative is
2 (S − F)2
S
F
F
,
(31)
and is clearly positive for all S > F. Hence firms offer higher quality products in larger
markets. Combining this insight and equation 22 above indicates that as firms offer
increasingly high quality products in larger markets they each incur higher fixed costs
of doing so. Since the lower bound to the gross profits earned by each incumbent are
given by total fixed costs, it follows from this that the lower bound to gross profits is
increasing in the size of the market.
The next step is to consider the nature of the relationship between the upper bound to
gross profits earned by incumbents and the size of the market. As in the simple
homogeneous product example, this upper bound follows directly from the entry
decision rule as described by equation 27. Rearrangement of equation 27 in equality
form yields the gross profits of each of the k incumbents as
2
S
1

= F * 1 +  .
2
k
k

(32)
From equation 32 it follows that as in the simple homogeneous product case the upper
bound to the relationship between the gross profits earned by each incumbent is a
simple mark-up over total fixed costs incurred which is decreasing in the number of
rivals each firm faces. However, because in a type two world the relationship between
the number of incumbents and the size of the market is potentially complex the shape
of this upper bound in S space is potentially similarly complex. As Sutton (1991)
observes, this relationship is potentially very complex in type two markets and is
particularly sensitive to the prevailing nature of fixed costs, especially the
interrelationship between the exogenous and endogenous components of total fixed
expenditures. For our purposes it suffices to give a characterisation of this
relationship.
20
Sutton identifies a robust property of the relationship between S and N. That property
is that, in contrast to the type one case above, the number of incumbents does not tend
to an arbitrarily large number as the size of the market becomes very large. However,
beyond this the precise nature of this relationship between S and N is highly sensitive
to parameterisation. There are three qualitative characterisations of the relationship
between S and N.
Figure two: The qualitative nature of the relationship between N and S in the example type two market
Number
of firms
Low
N*
Intermediate
High
Market Size
The first involves a simple tendency of N to rise to a finite value as S becomes very
large. Broadly, such a relationship is likely to be observed in type two markets where
exogenous component of fixed costs is significant. Intuitively, such markets share the
monotonicity of the relationship between S and N with the type one markets that they
are so similar to. As market size rises from low levels, advertising is initially nonoptimal. The market resembles a type one market and hence increases in S yield entry.
21
Note, however that the increase in N for any given increase in S is less than in similar
markets where the exogenous cost of setup is smaller. At some critical level of the
size of the market it becomes optimal for incumbents to improve their products.
Further increases in the size of the market increase the incentive to improve their
products and they increase their fixed expenditures on product improvement. These
increases in the total fixed costs firms incur act to offset partially, but not completely
for all non-infinite S, the tendency for rises in S to yield entry.
The second case involves a "small" exogenous fixed cost of entry. At levels of S
where advertising is non-optimal expansions in the size of the market lead to rapidly
rising numbers of incumbents. Once advertising becomes optimal the increases in
fixed expenditures lead to a shakeout where some of the incumbents exit the market
until N converges upon its limiting value. This case introduces the possibility of a
non-monotonic relationship between N and S. The final case involves a critical level
of the exogenous setup cost such that at the level of S where product improvement
becomes profitable N has exactly reached its limiting value whereupon further rises in
S lead to increasingly high quality products but neither entry nor exit.
Hence there are two circumstances under which the maximal level of per firm integer
profits are increasing in S. If N is non-increasing in S then it follows from our
discussion above that the maximal level of per firm excess returns is increasing in S.
Alternatively, it could be that although N is increasing in S, the magnitude of maximal
integer profits increases in S more quickly than does the number of incumbents and
hence maximal per firm excess returns rise as S rises.
The qualitative properties of the upper and lower bounds to the relationship between
the gross profit earned by each incumbent and the size of the market are summarised
in figure 4 below. There are several important differences between this figure and the
equivalent for they type one example above. Firstly, there is an upward sloping lower
bound to the gross profits earned by incumbents since the total fixed costs incurred by
incumbents is increasing for at least some range of the size of the market. Secondly,
the gross profits earned by each firm do not tend towards this lower bound in contrast
to the homogeneous case discussed above. Instead, because the number of incumbents
remains strictly finite independent of the size of the market firms are able to earn
22
positive excess returns because of integer effects for all ranges of the size of the
market. Thirdly, the slope and character of the upper bound to the size of gross profits
that incumbents can make is potentially non-monotonic and isn’t even necessarily
downward sloping. The intuition is as follows. In a type two market a given rise in
the size of the market can induce incumbents to increase their spending on product
improvement to such an extent that some incumbents find it optimal to exit from the
market. As this happens the potential for integer effects to exist is enhanced for two
reasons. Firstly, higher fixed costs mean that a potential entrant has a larger hurdle to
overcome and this requires a larger pool of profits to entice entry to occur. Secondly,
fewer incumbents means that the larger pool of residual demand is spread over fewer
firms and hence each firm has a larger share of those excess returns.
Figure 4: The range of gross profits per firm in a Cournot model with perceived product quality
Gross Profit
per firm
( Πi )
G
ΠG
i at NLIMIT
$X
Market Size
∞
Turning to the nature of the relationship between unit margins and the size of the
market in a type two world it is first important to note that if firms are ex post
identical then the uniform market price reduces to that given in equation 3 above.
Hence if firms offer identical products prices and hence margins depend only upon the
number of incumbents. It is immediate from this and the earlier discussion of the
relationship between N and S where products can be improved that gross unit margins
23
do not converge upon zero in very large markets but remain strictly positive
independent of the size of the market. Furthermore, because of the rich range of
possible relationships between N and S it is possible that maximal unit margins may
be increasing in the size of the market.
4. Discussion
The two examples above highlight an interesting dichotomy in the performance-size
relationship between markets of different types. Broadly speaking, the results indicate
that significant excess returns due to integer effects may only be a small market
phenomenon in type 1 markets. Conversely, in type 2 markets escalation of productenhancing expenditures leads to the potential of such excess profits to be earned even
in very large markets. Viewed from the perspective of an individual firm, the results
imply that a firm engaged in production in a type 1 market may only earn significant
excess profits if the market is small. In type 2 markets however, firms can earn
significant excess returns in any size of market.
These results are suggestive of valuable hypotheses with respect not only to the
determinants of industry performance but also to the determinants of corporate
performance. Do firms that occupy large type 2 markets typically outperform those in
equivalently large type 1 markets?
From an anti-trust perspective the results discussed above imply some novel
prescriptions. Firstly, note that within the example above to the extent that
concentration is a function of only firm numbers rather than size inequalities between
them the results predict a positive concentration-profits relationship. However, firms
earn significant excess returns in markets with fixed costs not because they are
successful in colluding with each other but because of the associated integer effects.
Hence excess returns under such circumstances represent no cause for concern for
anti-trust bodies. The theory above suggests that such profits may be particularly
important where significant product enhancement has taken place.
At this point it is important to raise a caveat with respect to the results illustrated
above. That caveat relates to the generality of the results. As described above the
24
results are derived from consideration of two carefully chosen examples. If the results
are to be useful, particularly in inter-industry and inter-firm empirical contexts then
they need to hold more widely than in the examples discussed above. Certainly,
Sutton (1991) shows the relationship discussed above with respect to the relationship
between the number of incumbents and the size of the market to be unusually robust.
Given that, the key relationship of concern for our result is that between unit margins
and the number of incumbents. In the models above there is a monotonically
decreasing relationship between margins and N. This result holds generally across
variants of the Cournot model and also across many variants of the Bertrand model
hence it seems intuitively reasonable to view the result as fairly robust to variations in
the intensity of price competition forms are assumed to face. In addition, strategic
asymmetries such as first mover advantages should not alter the result since it relates
to the entry of the marginal firm. Having sequential rather than simultaneous entry
decisions would reduce the equilibrium number of firms but the marginal entry
decision still relates to fixed cost recovery. Hence, in a type one market the number of
incumbents would still converge upon infinity in a very large market and hence the
spirit of the result would still hold.
5. Conclusion
In the analysis above we present an alternative interpretation of the long-standing
positive correlation between industry performance and key variables traditionally
interpreted as barriers to entry. Put crudely, we have argued that rather than protecting
profits earned from collusion from competitive pressures external to the industry such
expenditure may be a more direct source of excess returns. The entry decision made
by firms relates to fixed cost recovery. Broadly speaking, the pool of excess profits
made in the industry is a function of the magnitude of the fixed cost of entry made by
the marginal entrant. The excess profit per firm is a function of the size of the fixed
cost and the number of incumbents that it is shared among.
In a type one market the fixed cost of entry is independent of the size of the market.
As the market expands a firm external to the industry will eventually conjecture that it
can recover its fixed costs if it enters and will do so. This cycle of market size
expanding until another firm enters whereupon the net profits of the incumbents are
25
driven back to zero continues across the entire range of the size of the market. Firms
earn lower integer returns in larger markets because the pool of integer profits is
spread across a larger number of firms. Type two markets are different in two
important respects. Firstly, the fixed cost faced by a potential entrant is, at least over a
range, increasing in the size of the market. Secondly, one of the impacts of the
escalation of endogenous expenditures is to lead to a potential breakdown of the
monotonically increasing relationship between the number of incumbents and the size
of the market. In combination these features lead to an increase in the pool of integer
profits in a market and a limit to the number of incumbents who share that pool.
Hence it is possible to earn significant integer related excess returns in very large type
2 markets.
Furthermore, the fact that the results highlighted above relate to industries earning
excess returns in equilibrium makes them particularly interesting from the corporate
strategic viewpoint. This is because is excess returns due to barred entry cannot be
earned forever, eventually the barriers will be overcome and industry profitability
returned to "normal" levels.6 Where excess returns are an equilibrium phenomenon
they may be earned indefinitely.
6
This is a significant empirical phenomenon. For example, significant entry barriers protected the
profitability of the Wrapped Impulse Ice Cream market, the Feminine Hygiene products market and the
Condom market, however each of these markets have had significant recent entry and performance has
been correspondingly reduced.
26
References
Bain, J.S., (1956) "Barriers to New Competition" Cambridge, MA. Harvard
University Press.
Clarke, D.G., (1976) "Econometric Measurement of the Duration of Advertising
Effect on Sales", Journal of Marketing Research, Vol.13 pp.345-57.
Collins, N.R. and Preston, L.E., (1960) Review of Economics and Statistics Vol.25
Pp. 271-286
Comanor, W.S. and Wilson, T.A. (1967) "Advertising, Market Structure and
Performance." Review of Economics and Statistics, 49 (4), pp.423-40
Martin, S. (1979) "Advertising, Concentration and Profitability: The Simultaneity
Problem." Bell Journal of Economics, 10(2), pp.639-47
Matraves, C. (1999) "Market Structure, R&D and Advertising in the Pharmaceutical
Industry" Journal of Industrial Economics vol. XLVII. No.2. pp.169-194.
Porter, M.E. (1980) "Competitive Strategy - Techniques for analysing industries and
competitors" New York: The Free Press, Macmillan.
Porter, M.E. (1985) "Competitive Advantage - Creating and sustaining superior
performance" New York: The Free Press, Macmillan.
Robinson, W.T. & Chiang, J. (1996) "Are Sutton’s Predictions Robust?: Empirical
Evidence into Advertising, R&D, and Concentration" Journal of Industrial
Economics vol.XLIV. No.4. pp.389-408.
Schmalensee, R., (1989) "Inter-Industry Differences of Structure and Performance"
in Richard Schmalensee and Robert Willig (Eds.) Handbook of Industrial
Organisation, Amsterdam: North Holland.
27
Schmalensee, R., (1992) "Sunk Costs and Market Structure: A Review Article."
Journal of Industrial Economics, Vol. XL (2)
Strickland, A.D. and Weiss, L.W. (1976) "Advertising, Concentration and Price-cost
Margins" Journal of Political Economy, vol.84, pp1109-1121.
Sutton, J. (1991) "Sunk costs and Market Structure." Cambridge, MA: MIT Press.
Sutton, J. (1998) "Technology and Market Structure: Theory and History",
Cambridge, MA: MIT Press.
Symeonidis, G. (1999) "Price Competition, Non-Price Competition and Market
Structure: Theory and Evidence from the UK."
Tirole, Jean. (1988) "The Theory of Industrial Organisation" MIT Press
28