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ECON 325 – Industrial Organization and Public Policy
How to read an article
Here is a list of some of the questions you might think about as you read a scholarly article in economics. Many of these are obvious and don’t generally require written answers. This exercise will give you a list of things to think about for your article summaries and prepare you to read and digest scholarly articles on your own. Knowing what questions to ask and how to ask them when you read should help you in all of your classes, as you’ll be able to get through a large amount of material efficiently AND effectively.
We will work on this exercise in class, and you’ll be writing answers to the questions listed. When you are working on your own, you may choose to follow this exact process and write out your answers, or you may simply think about (refer to) these questions before or as you are reading.
As with a summary of this article (which we’ll work on tomorrow), your goal here will be to produce answers in your own words that are as accurate and jargon-free as possible.
1. Consider the article “Do Firms Maximize? Evidence from Professional Football” Based on just the title, what do you expect Prof. Romer will be trying to do? What question will he be trying to answer, and how do you predict he’ll do this?
2. What knowledge do you bring to this paper? For example, how much do you know about professional football? About other sports? What classes have you had (in economics or elsewhere) that might relate in some way to this article?
3. Next, read the article summary. How does this change your answer to question 1? Based on just the summary, see if you can come up with a list of three Econ-related questions that the article will likely NOT be able to answer.
4. Look at the acknowledgements at the bottom of the page. Who does the author thank? Do you know anything about these people (it’s ok if you don’t, but always a good idea to look, as this can give you a clue about how this paper will be situated in the literature)? Are there earlier versions of the paper listed? What can you glean about the paper’s purpose from them?
5. Scroll through the paper quickly. This should take no more than 3 minutes, for the entire paper. You are looking to see how the paper is organized, and whether the project appears to be mainly theoretical or empirical. Once you’ve done this, write down your very initial impressions – is the paper mainly theoretical or empirical? What makes you think this? How do your observations (including the titles given for the section headings) make you want to revise the predictions you made in question 1?
6. Read the paper’s conclusion. What results does the paper claim? How does the paper show them? Does the author point out shortcomings or weaknesses? If so, how does the author resolve them (or what does the author suggest could be done to resolve them)?
7. Look carefully at the bibliography. What other papers are cited? Is there an author you’ve seen elsewhere? To what literature (or literatures) does it appear this paper is contributing? Based on the titles and authors, are there articles you’d be interested in exploring further?
8. Finally, read the entire paper, taking notes at the end of each section. As you read, notice what you don’t understand and see if you can explain (in simple English) what the author is trying to do. Mathematical analysis can be hard to get through, but remember that the equations are shorthand language used to express economic ideas. You should be able to find a sentence or two near each equation that explains the economic ideas being conveyed.
Response Paper Guidelines
Your summary will first state the article’s main points and how they are made. That is, does
the article use a model only or is data analysis also done. Regarding the model, what sort of
assumptions are made? How are the main points demostrated? Once you’ve given the main points
and the results, you should discuss what the paper has included, and what it has left out. Does
it apply broadly, or only to a single industry or firm? Does it appear to have a solid grounding
in existing literature? Does it tend to support or refute existing literature? Does it seem to give
a good fit to the real world, or are the results so theoretical as to be practically useless? At the
opposite end of the spectrum, is the paper so lacking in a theoretical foundation that its results
are impossible to generalize? Points are awarded for a clear and concise summary of the article’s
main points. If a person who has not read the article can understand its main points from the first
paragraph of your summary, then you’ve probably done a good job.
Next, you need to consider how the model works (if the paper includes one), and how it could
be extended and supported or refuted. To do this, you must first figure out what the paper shows,
and how it does that. If there is a model, your summary should include a description of what it
does, but should not include every single step of the algebra/calculus used to do so. If there is not
a model, your paper should suggest what sort of model would be most e↵ective in illustrating the
paper’s points. Your summary should describe the model in plain English, not in “mathese”. To
consider how the model could be extended, ask yourself if the assumptions the paper makes are
reasonable. If not, how would you change them (and why)? What happens when you change the
assumptions? Do the model’s results change dramatically? Would you need an entirely di↵erent
model to illustrate the paper’s main point? In this part of your summary, you are demonstrating
that you have read and understood either the model used in the paper, or one that you could
use to illustrate the paper’s main points. You also demonstrate here your skill at picking a paper
apart and considering its main results. Points are awarded for extensions that are creative and
well-thought out and supported. Few points are awarded for extensions that are obvious or not
well-explained and supported.
Your summary will be one to two (single-spaced) pages, and is likely to involve a fair bit of
work. Summaries started the day before they are due will almost certainly receive poor grades.
Summaries that say little more than “I liked the article, and don’t think it can be extended or
improved” will not earn passing grades. EVERY article can be improved and extended, and your
job is to figure out how best to do that. Believe it or not, the best summaries will involve a fair bit
of criticism – it is through this sort of critique that work gets stronger and knowledge is advanced.
I will grade your papers for both grammar and content, looking to see that your ideas are well
thought out and presented, and that you understand the article you summarize. If your summary
does not demonstrate that you have figured out the model presented, you will not get full credit.
If your summary does not extend the paper in some way, you will not get full credit.
4
ECON 325 – Industrial Organization and Public Policy
How to summarize an article
Group Exercise
1. Consider the article “Do Firms Maximize? Evidence from Professional Football” In two or three sentences, describe the article’s main point. What is it that Prof. Romer is setting out to do in this study? There are two problems you need to confront when you do this – the first is figuring out what to say, and the second is figuring out how to say it. Your goal here is to produce a short paragraph in your own words that is as accurate and jargon-free as possible.
2. Next, exchange your response with your two group mates, and come up with a consensus summary of the article’s main point.
3. Your next step is (as a group) to write a page or so describing how Prof. Romer goes about answering the question he has set out to answer. Your job here will be to describe the techniques he used, including the problems he encountered and how he resolves them. Hint #1: Remember who your audience is – you’re writing this summary to refer to later so that you don’t have to re-read the entire article when you want to describe what it says in your paper. Hint #2: Prof. Romer probably used techniques and tools with which you are not familiar. In writing your description of his techniques, you will have to do the best you can, and figure out what else you’d need to know to understand the techniques completely.
4. Finally, you need to point out shortcomings of Prof. Romer’s work (every published paper has shortcomings) and describe how the work could be extended. If you look carefully, you will see that Prof. Romer admits (and tries to overcome) some of the shortcomings of his research. How well has he done at this? What additional problems do you see in this article, and how would you fix them? As a group, talk about the shortcomings you noticed, and how you might extend the research on this question.
5. Come up with a short (one to three sentence) conclusion for your summary.
Due Jan 17
Your article summary will be one to two pages long (single-spaced), and may involve a fair bit of mathematical analysis. You will give the article’s main points (in plain English), and demonstrate that you understand (and can replicate) the theory used to make these points. Notice that this does not mean you simply reproduce the article in different words. The successful summary will demonstrate an understanding of the article, including its strengths and weaknesses, and will point out sources that extend the work. There are two objectives of this exercise. First, useful summaries are designed to allow you to quickly recall an article’s main point. This will enable you to consider several articles at the same time, and should help you compare and contrast various points of view in the literature. Summaries provide an important first step in entering the (generally interesting) conversation that takes place in scholarly journals.
Second, useful summaries allow you to develop your own intellectual confidence, curiosity and courage. In order to succinctly state an article’s main point, you will need to understand both what the article accomplishes and where it falls short. Every piece of writing is incomplete in some way, and the successful summary will note the ways the article could be extended or changed to address different questions. In order to complete this part of your summary, you will need the confidence to think that your questions about what the article is missing are important, the curiosity to search for other sources that address your questions, and the courage to explain your questions clearly and succinctly and point to these sources. I will grade your papers for both grammar and content, looking to see that your ideas are well thought out and presented (eg that they demonstrate intellectual courage), and that you have related the material from the article to what we’ve been learning in class (eg that your summary demonstrate intellectual confidence and curiosity). The goal is for you to be able to refer back to the summary to figure out what the article is about and some related questions the article does not consider. Thus, while I am grading, I will be thinking about whether or not I am able to understand the article’s main point based only on what you’ve written. You will lose credit if I am forced to turn to the article to make sense of your summary. I will also be looking to see that you’ve come up with questions the article doesn’t address, and found a couple of sources that might be useful in thinking about these questions. Finally, when the article contains a theoretical model, you will lose credit if your summary does not demonstrate that you have figured out how it works.
A Sequential Entry Model with Strategic Use of Excess Capacity
Author(s): Brad Barham and Roger Ware
Source: The Canadian Journal of Economics / Revue canadienne d’Economique, Vol. 26, No.
2 (May, 1993), pp. 286-298
Published by: Wiley on behalf of the Canadian Economics Association
Stable URL: http://www.jstor.org/stable/135908
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A sequential entry model with strategic use
of excess capacity
B R A D B A R H A M University of Wisconsin, Madison
ROGER WARE Queen’s University
Abstract. A model of sequential entry with Leontief costs is studied in which demand is
iso-elastic. Some or all firms may hold excess capacity in the perfect equilibrium to the
entry game. Firms with a first-mover advantage trade off the positioning value of a large
investment in capacity, leading to a large market share, against the possible costs of bearing
the burden of entry deterrence through holding excess capacity in equilibrium.
Un modele d’entree sequentielle avec utilisation strategique de la capacite excedentaire.
Les auteurs etudient un modele d’entree sequentielle dans le cas oiu les cofuts sont ‘a la
Lontieff et la demande iso-elastique. On postule qu’une ou plusieurs firms ont une capacite
excedentaire en equilibre parfait au debut du jeu. Les firmes qui ont l’avantage de faire
le premier mouvement etablissent une relation d’ equivalence entre la mise en place d’un
investissement important en capacite accrue ouvrant la porte ‘a une plus grande part de
marche et la possibilite de devoir assumer les cou’ts inherents au travail de prevention de
nouvelles entrees via une capacite excedentaire en equilibre.
I. INTRODUCTION
In a recent article, Bulow, Geanakoplos, and Klemperer (1985) (BGK) demon-
strated using a two-firm, two-stage game that excess capacity can serve as a cred-
ible entry-deterring strategy when demand is iso-elastic. Their result is in sharp
contrast to the majority of capital commitment models of entry deterrence (Dixit
1980; Eaton and Lipsey 1981; Eaton and Ware 1987; Gilbert 1986; Spulber 1981;
and Ware 1984, in that in entry-deterrence equilibrium the BGK incumbent holds
excess capacity which is idle and would be utilized to expand output only in the
event of entry. In many respects the BGK results are also more consistent with
empirical evidence on the strategic use of excess capacity by multiple incumbents,
reported for some industries by Esposito and Esposito (1974), Cossuta and Grillo
(1986), Masson and Shannan (1982), and Rosenbaum (1989).
Canadian Journal of Economics Revue canadienne d’Economique, XXVI, No. 2
May mai 1993. Printed in Canada Imprime au Canada
0008-4085 / 93 I 286-98 $1.50 ? Canadian Economics Association
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Sequential entry model 287
In this paper we present a sequential entry model of investment’ with the BGK
framework of iso-elastic demand. Our purpose is to investigate the way in which
excess capacity is used as strategic instrument in a framework of multiple incumbent
firms. Broadly speaking, two forces govern the equilibrium level of investment of
a typical firm in a sequential entry framework. First, investment has a positioning
component: it may give the firm some strategic advantage over its rival firms in the
market. Second, each firm’s investment contributes to entry deterrence: it creates
strategic barriers to the profitable entry of firms.
In contrast to the two-firm game, investment in entry deterrence has a public
good aspect in a multiple firm framework. Each firm’s investment in entry deter-
rence will benefit all incumbent firms, but the costs must be incurred privately. Two
features of this non-cooperative nature of investment in entry deterrence that have
been discussed in other work are delegation and underinvestment (see Gilbert and
Vives 1986; McLean and Riordan 1989; Schwartz and Baumann 1988; Tirole 1988;
Waldman 1987, 1988). Delegation refers to the incentive of early entrants in the se-
quence of investment not to do their full share of entry deterrence in the knowledge
that later entrants will be forced to pick up the slack, because these later entrants
have a strong incentive to deter further entry. Underinvestment may occur when
this process of coordination breaks down, in a classic prisoner’s dilemma fashion.
As a result, the collective entry deterrence efforts of the incumbent firms, acting
individually and non-cooperatively, amount to less than a jointly optimal amount
of investment, judged by a standard of optimal cooperative entry deterrence by the
incubent firms.
With a neoclassical production technology, strategic competition in capacity may
be interpreted in terms of excess capacity. Excess capacity must be defined as in-
vestment that exceeds the cost-minimizing level, given output. Brander and Spencer
(1983), Reynolds (1986), and Schwartz and Baumann (1988) all have provided re-
sults in this framework, the last in a sequential entry model. With our framework
of Leontief costs, excess capacity is literally unused or idle and is motivated solely
by strategic behaviour towards entry; with variable proportions technologies, ‘ex-
cess’ capacity is used strategically towards both other incumbents and potential
entrants. Thus, the phenomena of delegation, positioning, and underinvestment are
more sharply defined in our framework. We extend the BGK analysis to a full
sequential entry model with multiple incumbent firms. We demonstrate the exis-
tence of equilibria in which some or all producing firms hold excess capacity as an
instrument of entry deterrence. Delegation also occurs with early entrants, forcing
later movers to incur a greater than equal share of excess capacity costs. Investment
has a positioning value as well as making a contribution to entry deterrence. Thus,
in some cases positioning opportunities outweigh delegation opportunities, and the
earlier entrant holds all of the entry deterring capacity. Underinvestment remains a
theoretical possibility in the model but under quite restrictive conditions.
1 The sequential entry methodology permits the number of firms and their size distribution to
be determined endogenously as part of the equilibrium (see, e.g., Eaton and Ware 1987). This
methodology is further described in the following section.
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288 Brad Barham and Roger Ware
II. THE STRUCTURE OF THE SEQUENTIAL ENTRY MODEL
1. Costs
All firms possess identical Leontief cost functions C(xi, ki) = f + c(aki + (1 -a)xi),
where xi _ ki, xi is quantity produced and ki capacity installed by firm i. a is a
parameter that captures the proportion of unit production costs that are sunk before
production takes place. The (flow) value of fixed costs is denoted by f, and c is
a constant. Leontief costs are assumed in order to keep the focus of attention on
excess capacity which is literally unused.
2. Demand
It is common in models based on a Cournot equilibrium to assume the Hahn-
Novshek condition: that each firm’s marginal revenue is decreasing in the output of
rival firms.2 In symbols, p’ = xip” < 0, where p(.) is the inverse demand function. Generally, this condition serves the purpose of ensuring the existence of a Cournot equilibrium. However, in capacity commitment models it also guarantees that it
would never pay any firm to hold excess capacity as a barrier to entry. The reason
is that, for any given capacity, new entry would lower the marginal revenue of all
incumbent firms, and hence any capacity unused in the pre-entry equilibrium would
certainly be unused in the post-entry game. While the Hahn-Novshek restriction has
convenient analytical properties, it removes from consideration the particular focus
of this paper, the possibility of sequential equilibrium involving excess capacity
used as a weapon to deter entry.
We work with a family of demand functions, constant elasticity, that do not
satisfy the Hahn-Novshek condition. Over some range of quantities, each firm’s
marginal revenue is increasing in market output. This raises the possibility that
excess capacity might be held as a barrier to entry, because the incumbent can
credibly threaten to increase oputput after entry. BGK first demonstrated this point
through an example in their 1985 paper using the inverse demand function
P =AX-. (1)
Figure 1 depicts a firm i’s reaction function given an investment in capacity ki,
and our demand and cost assumptions. Note how the reaction function is positively
sloped over some range of output of a rival firm or entrant, denoted as xj. It is
firm i’s credible potential for expanding output along the positively sloped portion
of its reaction function that makes it possible for excess capacity to be held in a
deterrence equilibrium. The entrant’s reaction function is also shown in the figure.
Given the investment of ki by firm i, suppose the entrant were to choose a capacity
corresponding to point B, its best output response to an incumbent’s output of
xi = ki. Absent entry, firm i would produce a monopoly quantity at point A.
Entry raises its marginal revenue, and induces it to expand output to point B. If
2 The first comprehensive discussion of this issue, so far as we are aware, is by Carl Shapiro in his
excellent survey of oligopoly theory, Shapiro (1989).
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Sequential entry model 289
firm is
variable cost
reaction function
x.
=~~~~~~~~~~ k
g/ ~~cost reactionfucin,
FIGURE 1 Reaction functions for constant elasticity demand
the entrant’s profits at point B are non-positive, entry will be deterred, and the
incumbent will hold excess capacity in equilibrium.3
3. Sequential entry framework
The sequential entry framework assumes the existence of a large but finite number
of firms, more than could profitably enter the industry, each in sequence making
an investment choice with identical technologies. These investments must be sunk,
otherwise they would have no strategic value. The initial sequence or identity of the
firms is arbitrary. Each firm makes its choice knowing the choices of its predecessors
and with complete information about the structure of the game. A choice of zero
in capacity is effectively a choice not to enter. A market equilibrium (Cournot in
this paper) is then realized in the final stage, conditioned on the sequence of sunk
investments, and so involving only those firms with positive capacities. Therefore,
in the sequential entry equilibrium, the number of firms and their size distribution
are determined endogenously.
3 This brief description of the workings of the model ignores for the sake of simple exposition, the
possibility that the entrant’s best choice will not be at B, given ki. In fact, in the case illustrated,
the entrant would choose a capacity level less than that at B, so that both incumbent and entrant
would produce less in the post-entry equilibrium. Capacity ki would then not necessarily be
sufficient to deter entry and, in any case, would be an excessive investment, since not all of it
would be utilized even after entry.
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290 Brad Barham and Roger Ware
III. PROPERTIES OF THE PERFECT NASH EQUILIBRIUM
Eaton and Ware (1987, prop. 4) showed that, in a sequential entry model with
Leontief costs, and where demand satisfies the Hahn-Novshek condition, firms do
not hold excess capacity in equilibrium. In the model we study here, firms can hold
excess capacity in equilibrium; hence, entry deterrence involves a real cost to any
such firm. As such, that firm would like to delegate the task of entry deterrence,
possibly even to an entrant it could deter, at some cost. This cost incentive to
delegate makes determining specific equilibria more difficult but also provides a
rich range for exploring positioning versus delegation possibilities.
Eaton and Ware also introduced a useful distinction between blockaded and
strategic equilibria to sequential entry games. A blockaded equilibrium for n firms
is one in which the n-producing firms make their capacity choices independently
of the possibility of further entry.4 In a strategic equilibrium the incumbents have
to invest strategically in order to deter further entry. The following property is
immediate.
EQUILIBRIUM PROPERTY 1. Blockaded equilibria never involve excess capacity. Strategic
equilibria may or may not involve excess capacity.
The intuition of this result is clear from the fact that excess capacity is held
only to make the threat of expanding output credible in the event of entry. Since
blockaded equilibria effectively contain no threat of entry, incumbent firms have
no reason to hold excess capacity.
We are particularly interested in perfect equilibria that do involve excess ca-
pacity. Since this unused capacity will be used only after entry, any firm holding
it must satisfy the increasing marginal revenue condition; that is, at the equilib-
rium capacities and quantities that firm’s marginal revenue must be increasing in
industry output. By differentiating marginal revenue, we see that the increasing
marginal revenue condition requires that
/n
Xi (>X ) Ex . (2)
j=1
From equation (2) we derive
EQUILIBRIUM PROPERTY 2. A necessary condition for equilibria with multiple in-
cumbents holding excess capacity is that market demand satisfy the inequalities
1/(m – 1) > e ? 1/n, where m < n is the number of incumbents holding excess
4 More formally, in a blockaded equilibrium the solution to a game with n firms imposed exoge-
nously is identical to the equilibrium in which the number of firms is determined as part of the
solution.
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Sequential entry model 291
capacity in equilibrium. Note that for m ? 2, this inequality requires demand to
be inelastic.
Proof: Let M be the set of firms holding excess capacity in equilibrium. Then from
(2) above, there must hold m inequalities of the form
Xi> E>xj iEM.
hL4i
Summing, we have
Zxi > E(m- 1)xi + EM xj
iEM iEM jfM
or
(1-E(m-1)) xi > EmExj.
iEM ioM
For the left-hand side to be positive, we require E < l/(m - 1), which proves the
first part of the inequality. To show the second part, note that the basic first-order
condition for a (capacity unconstrained) Cournot equilibrium can be written
P – C'(xi) Si
P E
where C'(xl) is marginal cost of the firm i, and si is firm i’s equilibrium market
share. A solution to the set of first-order conditions requires that si/E < 1 or
E > si. This is equivalent to requiring that each firm perceive demand to be elastic
in equilibrium. If all firms are unconstrained, equilibrium is symmetric, si = l/n,
and the inequality is established. Suppose that some firms are constrained. Since
these must be the smallest firms, for the firms holding excess capacity, si > l/n
and the inequality still provides a lower bound on E. QED
Having established these preliminary results, we are ready to investigate further
the properties of equilibria involving excess capacity. In the ensuing analysis we
work with an explicit parameterization of the model, involving inelastic demand, in
order to illustrate the factors determining equilibrium where multiple incumbents
can potentially hold excess capacity. In particular we show, both diagrammatically
and by numerical simulation, how delegation gives way to a positioning advantage
for firm 1, as fixed costs are increased and the limit output falls.
The basic parameters of the simulation are: A = 1000.0, c = 10.0. We adopt
an elasticity value of 0.6 as convenient; it allows two firms to produce in Cournot
equilibrium, but equilibria display clear patterns of delegation and positioning. Our
derivation of equilibrium is constructive: first we check that at least two firms
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292 Brad Barham and Roger Ware
firm 2’s variable cost
reaction function
kI+ k2+ k3
= LO + k3(LO)
k+k3
k +k2=LO(f)
1 2 ~ ~ E
firm l’s
variable cost
k i ‘\\\ reaction function
k~~~~~ k2 . …. k2
FIGURE 2 Construction of the perfect equilibnum with two incumbent firms (model parameters:
e = 0.6; a = 0.4; A = 1000.0; c = 10.0)
are needed to deter further entry. We must also check that two firms can credibly
produce sufficient output (after entry) that a third firm can be deterred.
Figure 2 depicts the variable cost reaction functions for firms 1 and 2, that is,
the solution to the equation
MRi(xi, xj) = (1 – a)c.
Recall that a is the production costs that must be sunk in the form of capacity
investment. The procedure for solving for a particular perfect equilibrium to the
model can now be described. The limit output (Lo) is derived as a function off, the
fixed costs of entry. Note that limit output must be defined a bit more carefully than
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Sequential entry model 293
in models which satisfy the Hahn-Novshek condition; limit output is the output that,
if credibly produced by the incumbents after entry, would just drive the entrant’s
profits to zero. In computing the limit output, we also obtain the potential entrant’s
most efficient output level, conditioned on the limit output, k3*(LO). In figure 2 the
sum of these is drawn in as the equation
k1 + k2 + k3 = LO(f) + k(LO), (4)
where firm 3’s output is shown in the figure added to that of firm 1. A dashed line
is also drawn representing the limit output itself, that is, the equation
k1 + k2 = LO(f). (5)
Given the locaiton of the limit output line in figure 2, an entry-deterring equilibrium
will involve excess capacity, because this dashed line passes to the right of the
intersection point of the two reaction functions (point C in the figure). Total output
corresponding to C is the most that two firms can produce without additional entry.
In the equilibrium firm 1 delegates as much excess capacity to firm 2 as possible:
the limit to this delegation is found where firm 2’s variable cost reaction function
cuts line (4) above, that is, point E in the figure. The equilibrium capacity choice
for firm 1 is the point vertically below point E on line (5), so that between them
firms 1 and 2 have total capacity equal to the limit output. The choice for firm 1
also involves excess capacity in entry deterring duopoly equilibrium – this can be
verified in the figure because firm l’s capacity choice lies above point C.
Why is firm 1 unable to delegate still more excess capacity to firm 2? Consider a
small reduction in firm l’s capacity choice. Even if firm 2 were to increase its own
capacity choice by an equal amount, the additional capacity commitment would not
be credible, since it would not be used in the event of entry. Thus a minimum of
k* is required in order for entry deterrence to be feasible.
As we increase the value off, the limit output decreases, and both limit output
lines (4) and (5) in the figure shift to the left. The equilibrium is constructed in
exactly the same way, with the equilibrium point in the figure shifting down firm
2’s variable cost reaction function towards point C. As f is increased, firm l’s
excess capacity decreases faster than that of firm 2, until a value, f2, is reached
such that firm 1 holds no excess capacity at all in equilibrium. For even larger
values f, the equilibrium is constructed in the same way, except that now firm 1
will be capacity contrained in equilibrium; firm l’s equilibrium output is less than
the Cournot duopoly output (point C) in this region.
Note that for all f-values in a neighbourhood greater than f2, firm 1 produces
less output in equilibrium than firm 2. Firm 1 may still be more profitable, because
it does not have to bear the cost of excess capacity. At some value, f3, the profits
of firms 1 and 2 in equilibrium will be the same, even though the equilibrium is
asymmetric. For still larger values off, firm 1 will force a switching of roles. Firm
1 will prefer to hold the excess capacity and be the larger firm in equilibrium, while
firm 2 chooses just enough capacity to make up the limit output, and is capacity
constrained in equilibrium. In figure 2 the equilibrium is constructed after this
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294 Brad Barham and Roger Ware
< = delegation phase | positioning phase i
Cournot quantity
(variable cost)
j__ _ _ _ _ _ _ _ _ _ j_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ I fi x e d
f f2 f3 f4 costs
equilibrium capacity for firm 1 eqilibrinum excess capacity for firm 1
, equilibrium capacity for firm 2 equilibrium excess capacity for firm 2
FIGURE 3 An illustration of excess capacity and the phases of equilibrium as fixed costs are varied
switch point by using firm l’s variable cost reaction function in exactly the same
way as firm 2’s was used in the first phase of equilibria, switching the entrant’s
capacity (and output) choice, k3, to the k2 axis, so that the whole construction is
reversed;
Figure 3, drawn to illustrate the results of our simulations, shows how the equi-
libria depend on f, the fixed costs of entry, in terms of quantities and excess
capacity. The phases of delegation and positioning are clearly identified as func-
tions of f. We define the range fi < f < f3 as the delegation phase and the phase f3 < f < f4 as the positioning phase, where fi to f4 are defined, as follows, for a given value of a.
fi = the smallest value of fixed costs such that two firms are still able to deter
further entry.
f2 = the value of fixed costs at which firm 1 no longer holds excess capacity in
equilibrium.
f3 = the largest value of fixed costs such that firm 2 is larger in equilibrium – that
is, for f-values above f3, firm 1 prefers the positioning advantage of being
the large firm, as opposed to the advantage of delegating the costs of excess
capacity to firm 2.
f4 = the value of fixed costs such that a single firm can deter entry and the equi-
librium becomes a strategic monopoly.
Table 1 reports the critical values, fi to f4, for our simulation model and shows
the capacities, quantities, and profits computed for one set of these f-values and
three values of a. The comparative statics with respect to a, the capacity cost
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Sequential entry model 295
TABLE 1
Simulation results
(i) critical values forf
a fi f2 f3 f4
0.2 29.0 36.4 37.0 124.0
0.4 18.0 24.1 26.4 112.0
0.6 6.3 11.2 16.0 98.0
(ii) some illustrative equilibria in a -f space (note: profit figures shown are gross of fixed costs, f)
a f = 29.0 36.4 37.0
ki = 3.772 k2 = 3.772 ki = 3.092 k2 = 3.772 ki = 3.023 k2 = 3.772
0.2 xl = 3.092 X2 = 3.092 xl = 3.092 X2 = 3.092 xl = 3.023 X2 = 3.057
rl = 116.13 7r2 = 116.13 i1 _ 117.53 ir2 = 116.13 iri = 119.00 ir2 = 119.00
kl = 4.414 k2 = 3.150 kl 4.337 k2 = 2.510 ki = 4.330 k2 = 2.465
0.4 xl = 3.383 x2 = 3.150 xl = 2.938 x2 = 2.510 xl = 2.903 X2 = 2.465
irl = 110.22 7r2 = 106.48 i1 = 139.20 7r2 = 123.71 i1rl = 141.66 7i2 = 125.15
kl = 5.074 k2 = 2.490 kl 4.902 k2 = 1.945 kl = 4.889 k2 = 1.906
0.6 xi = 3.135 X2 = 2.490 xl = 2.581 X2 = 1.945 xl = 2.539 x2 = 1.906
i1rl = 133.23 72 = 115.07 ml =168.68 ir2 = 137.60 i1rl = 171.80 ir2 = 139.58
coefficient, are less clear cut than they are forf. First, as the sunk capacity cost
proportion of production costs rises, so does the cost of holding excess capacity
in order to deter entry. This increases the pay-off to delegation of entry deterrence
by firms moving early in the sequence. At the same time, however, increasing
a increases the positioning advantage of these same firms, thereby creating more
strategic opportunity to be large, and raising the opportunity cost of delegating entry
deterrence (if it involves holding excess capacity) to later entrants. And, thirdly,
an effect that is peculiar to models exhibiting excess capacity in equilibrium: the
larger is a, ceteris paribus, the larger will be equilibrium output which implies
lower industry profits with inelastic market demand. The outcome of these trade-
offs can be determined by simulation only in specific cases. Note how the profits
of firm 1 fall as the degree of sunkness increases between 0.2 and 0.4 for fixed
costs equal to 29.0 but rise in the other cases of increasing sunkness of capacity
investments.
Our analysis of the properties of perfect equilibria in the model may be sum-
marized as- follows.
EQUILIBRIUM PROPERTY 3: Perfect equilibria may have all producing firms (firms
holding positive capacity) holding excess capacity, or some subset of the industry
only holding excess capacity. Firms holding excess capacity in a perfect equilibrium
may come at the beginning or the end of the sequence of entering firms.
It is instructive at this point to relate our results on delegation of entry de-
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296 Brad Barham and Roger Ware
terrence and positioning to those of McLean and Riodan (1989) (hereafter MR
and Schwartz and Baumann (1988) (hereafter SB). In MR firms make a binary
choice of technology, one choice being less profitable but more effective in deter-
ring further entry. Because the choice is discrete and is defined only in an abstract
sense of profitability, an analogy to our concept of positioning cannot be directly
found within MR’s framework. Thus, firms in our model face a richer trade-off
than they do in MR, because they make direct capacity and quantity choices from
a continuous strategy set. Nevertheless, any delegation equilibrium in our model
(corresponding to the region indicated in figure 3), must satisfy MR’s criteria for
a delegation equilibrium in which the first firm is able to exploit its first-mover
advantage and delegate entry deterring responsibility only when it knows that the
second firm will find it more profitable to deter than to allow further entry (see
7-9). Moreover, the equilibria to our model in the positioning region are analo-
gous to MR’s discussion of partial entry deterrence, in which the ‘entry deterring’
technology is more profitable than the ‘normal’ technology (see 15-16). Under this
assumption MR find that the first firm in the investment sequence will choose the
entry deterring technology, which is similar to our result that the first firm holds
excess capacity to obtain a positioning advantage in equilibrium.
SB study sequential entry with a neoclassical technology in which investment
in capacity lowers marginal costs in the production stage. Because of the ‘smooth’
technology for input substitution, excess capacity can only be defined indirectly
as the ratio of actual equilibrium capital, to the cost minimizing capital given
equilibrium output choices. Nevertheless, SB’s simulation results show striking
similarities to the properties of our model. For a given equilibrium number of
firms, at high levels of fixed cost the first mover exploits his positioning advantage
at the cost of a greater share of the costs of entry deterrence (revealed in SB by a
lower capacity ‘utilization’ rate). At lower levels of fixed costs, delegation becomes
more attractive to the first mover, and the second firm bears a disproportionate cost
of entry deterrence. Because of the smooth technology, in SB the transition between
these two regions is gradual, whereas in our model, as illustrated in figure 3, it
is sharp and discontinuous. In SB ‘excess capacity’ serves two strategic goals: to
deter entry, and to gain a strategic advantage over incumbent rivals. Equilibrium
property 1 of our model demonstrates that excess capacity will never be carried
for the latter purpose, so that its sole rationale is to deter entry.
Finally, we considered the possibility of underinvestment in entry deterrence
occurring in perfect equilibria to our model. If, as in MR, underinvestment is said
to occur among firms 1,… ,j when, as a group, these firms could have invested
more in entry deterrence and yielded each individual firm a higher pay-off, then
underinvestment can occur only if demand is inelastic. This follows logically from
both the property that when demand is elastic only one firm can credibly invest
in excess capacity as well as the principle that free-rider problems associated with
underinvestment can arise only if it is necessary for two or more firms to coordinate
entry-deterring behaviour (see Waldman 1991 or MR). Consider the behaviour of
the firms that cannot credibly invest in excess capacity. As in Eaton and Ware
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Sequential entry model 297
(1987), they will invest in capacity up to the maximum output level they can obtain
in the Cournot output stage of the game. Only firm l’s decision involves a choice
concerning entry deterrence, and thus the potential for free riding is eliminated.
Though we have not generated an example, underinvestment cannot be ruled
out in the case where demand is inelastic. Moreover, if it occurs, underinvestment
is most likely ceteris paribus when demand is not strongly inelastic, capacity costs
are high, and/or fixed costs are low; that is, when the decline in revenues resulting
from entry are most likely to be outweighed by the gains in capacity savings.
IV. CONCLUSIONS
Although there has been a proliferation of models of strategic entry deterrence, very
few of these have shed any light on the phenomenon of excess capacity that is held
as an instrument of entry deterrence. In this paper, working in a sequential entry
framework, with constant elasticity demand and Leontief costs, we have shown that
equilibria can occur in which some or all of the producing firms hold idle capacity
as an instrument of entry deterrence. These equilibria all fall within the category
described by Eaton and Ware (1987) as strategic equilibria. Moreover, for excess
capacity to be a credible entry deterrent, the marginal revenue of the firm holding
the excess capacity must be increasing in the output of an entrant. The implied
relationship between firm outputs in equilibrium and elasticities is discussed in the
paper.
The fact that entry deterrence through holding excess capacity involves a real cost
to the firm allows us to examine the sharing of the entry deterrence burden between
incumbent firms in a non-cooperative framework. Moreover, since investment in
capacity conveys a positioning advantage, giving early movers a larger market share,
we are able to examine how this trade-off between positioning and delegation works
out in equilibrium. To summarize what turns out to be a fairly complex interaction,
the first firm will delegate excess capacity where feasible, unless it is able to deter
entry with a large market share, keeping subsequent entrants small. In the latter
case, the first firm will be forced to hold any excess capacity required to deter
further entry. Even when this configuration is feasible, the first firm may be willing
to give up its dominant position if the excess capacity required is too costly.
It is clear that the model is not very restrictive in its predictions. The first
step towards empirical clarification of the strategic excess capacity notion should
probably be to test the demand side of the model, that is, the assumption of convex
demand. We note that we were only able to obtain equilibria in which multiple
firms hold excess capacity in equilibrium, where market demand is inelastic. If
these demand configurations were to be rejected by the data, then the search for
an empirically plausible model of strategic excess capacity would have to shift to
a different class of model (see, e.g., Dixon 1985, Masson and Shannon 1982, and
Rosenbaum 1989 on price-setting games).
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298 Brad Barham and Roger Ware
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- Contents
- Issue Table of Contents
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Canadian Journal of Economics, Vol. 26, No. 2, May, 1993
Front Matter
The Anticipated Sectoral Adjustment to the Canada – United States Free Trade Agreement: An Event Study Analysis [pp. 253 – 271]
Some Empirical Support for the Heckscher-Ohlin Model of Production [pp. 272 – 285]
A Sequential Entry Model with Strategic Use of Excess Capacity [pp. 286 – 298]
Armington Models and Terms-of-Trade Effects: Some Econometric Evidence for North America [pp. 299 – 316]
Factor Ownership, Taxes, and Specialization [pp. 317 – 336]
Bilingualism and Network Externalities [pp. 337 – 345]
Comparing Environmental Markets with Standards [pp. 346 – 354]
Pollution Taxes, Subsidies, and Rent Seeking [pp. 355 – 365]
Regional Employment Subsidies and Migration [pp. 366 – 379]
A New Model of the Gold Standard [pp. 380 – 391]
Time-Varying Technological Uncertainty and Asset Prices [pp. 392 – 415]
Stabilization of the Canadian Dollar: 1975-1986 [pp. 416 – 446]
A Welfare Comparison between VERS and Tariffs under the GATT [pp. 447 – 456]
International Migration, Increasing Returns, and Real Wages [pp. 457 – 468]
On Directions of Commodity Tax Reform in the Presence of a Given Non-Linear Income Tax Schedule [pp. 469 – 480]
Content Protection, Urban Unemployment and Welfare [pp. 481 – 492]
Reviews of Books
untitled [pp. 493 – 496]
untitled [pp. 496 – 499]
Obituary: Dr John R. Finlay 1941-1992 [p. 501]
Obituary: Douglas D. Purvis 1947-1993 [pp. 501 – 503]
Back Matter [pp. 500 – 504]
