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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 Accessed: 12-12-2017 16:05 UTC

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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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