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Contestability reconsidered: The meaning of market exit costs
Journal of Economic Behavior & Organization Vol. 34 (1998) 435±443
Contestability reconsidered: The meaning of market exit costs Niko P. Paech* Department of Economics, UniversitaÈt OsnabruÈck, 49069 OsnabruÈck, Germany Received 18 October 1995; received in revised form 14 November 1996
Abstract This paper analyses the main result of the contestable market approach, namely, that potential competition reaches its maximum power if market entry and exit is costless and newcomers can use the hit-and-run strategy. Different time lag structures are considered. Average cost pricing turns out to be no equilibrium if there are no market exit costs. Furthermore, exit costs don't necessarily create a barrier to entry, but may even strengthen the discipline arising from the threat of entry. # 1998 Elsevier Science B.V. JEL classi®cation: D43; L11; L12 Keywords: Potential competition; Hit-and-run entry; Entry and exit costs
1. Introduction The basic idea of the contestable market model by Baumol et al. (1982) is to formulate conditions under which the power of potential competition may be a perfect substitute for price-taking behaviour in oligopolistic or monopolistic markets. Newcomers act like Bertrand competitors, i.e. they undercut the price, capture the whole market, and leave it prior to any price response by incumbents (hit and run). The profitability of entry does not hinge on the result of any post entry game. Instead, it is calculated directly on the basis of the current market price. The adherents of contestability analysis claim an inverse relationship between the profitability of entry and the size of sunk costs, no matter * Corresponding author. Tel.: +49 541 26396; fax: +49 541 969-6142; e-mail: [email protected] 0167-2681/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved PII S 0 1 6 7 - 2 6 8 1 ( 9 7 ) 0 0 0 8 1 - 4
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whether they arise during the entry or exit phase. In their eyes, sunk costs weaken the virtues of potential competition and may form an entry barrier. This paper analyses whether the mere threat of entry may be sufficient to force prices down to average cost. It turns out that market exit costs are a necessary condition for any impact of an entry threat. The following section gives a short description of the contestable market model and emphasizes the role of specific time lags. In Section 3, a separate entry event will be analyzed, taking into account alternative lag structures. Optimal strategies for both potential and established firms conditional on the relevant lag structure will be derived. The last section contains a conclusion. 2. The contestable market approach 2.1. Assumptions and properties Contestable market theory refers to a situation where the impact of potential entry on the price setting behaviour of actual firms is maximal. ``A contestable market is one into which entry is absolutely free, and exit is absolutely costless'' (Baumol, 1982, p. 3). The option to enter and to leave the market costlessly requires that the capital, which has to be invested by an entrant, can be liquidated without any loss or can be completely removed to an alternative use, once the newcomer is forced to leave the market. Otherwise, an entrant would have to incur irreversible costs (sunk costs), which directly reduce the profit he can earn during his stay in the market. The benchmark case of perfect contestability may be represented by the following assumptions: Assumption 1.
Newcomers enter the market as Bertrand competitors.
Assumption 2.
A sustainable industry configuration exists.
Assumption 3.
Price adjustments by established firms are delayed.
Assumption 4.
Incumbents face an entry threat any moment in time.
Assumption 5. Every player knows the demand conditions and the payoff function of all other players (complete information). Assumption 6.
There are no market entry or exit costs (sunk costs).
Applying these assumptions, Baumol et al. (1982, 1983, 1986) claim that a perfectly contestable market can be in equilibrium only if it is resistant to hit-and-run entry. Using the hit-and-run strategy, potential competitors enter the market as a Bertrand competitor and depart prior to any reaction by the established firms. In contrast to a widely used assumption in post entry analysis, newcomer firms do not expect oligopolistic interactions but assume the price to remain unchanged. The most important property of a perfectly contestable market is that potential competitors exercise discipline over the incumbents to the extent that only prices are
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viable which imply zero profits. With at least two operating firms a perfectly contestable market equilibrium yields first-best Pareto optimality, that is, price simultaneously equals marginal cost and minimum average cost. If costs are subadditive, i.e. the industry is a natural monopoly, the equilibrium will be characterized by Ramsey-optimal pricing. Baumol et al. (1982) establish the power of potential competition by means of a simple argument: If the price exceeds average cost or if production is inefficient the market must be out of equilibrium because a profitable entry option exists. 2.2. Sunk costs and time lags Irreversible costs are important to contestability analysis for two reasons: In the absence of sunk costs there will be no room for commitments or other kinds of strategic behaviour by established firms; and apart from such strategic considerations, sunk costs also directly impair the profitability of hit-and-run entry. To simplify matters, we will consider the single product case with a market demand function for a homogeneous good X(p), X0 (p) < 0. There is an incumbent (denoted by i) and an entrant (denoted by j). It will be assumed that the established firm and the potential competitor have access to the same technology, reflected in identical cost functions C(x) including a variable and a fixed component. The latter, which is denoted by F, may be partially sunk. A newcomer who enters the market at, say, time 0 expects that he will be driven out by an aggressive price response at a later time, say R. His payoff function is Z R 1 ÿ eÿrR ÿ s F eÿrR ; p ÿ xj ÿ C xj eÿrt dt ÿ s F eÿrR p ÿ xj ÿ C xj Vj r 0 (1) where p denotes the prevailing market price, xj the newcomer's output and r the discount rate. s denotes a share of the fixed cost which is lost when the newcomer leaves the market. Undercutting the market price by and retiring at time R characterizes the hit-and-run strategy. Under the simplifying assumption ! 0, the highest entry preventing price is p
C xj r s F eÿrR : xj xj 1 ÿ eÿrR
(2)
In the extreme case s 0 this price coincides with average cost, and obviously, as s ! 0, the entry preventing price converges towards average cost. Baumol et al. (1983, p. 494), therefore, conclude, ``where there are almost no sunk costs, markets are almost perfectly contestable.'' But this assertion has to be qualified because, even in the limiting case s 0 and R > 0, a unique statement on the effectiveness of potential competition is not possible. In this case, the entry preventing price equals average cost, but the question still remains whether it would be optimal for established firms to actually charge it. To decide that question, one would first have to investigate whether p AC corresponds to a Nash equilibrium of the entry game, i.e. whether the profit resulting from any strategy p > AC is less than the damage caused by new entry.1 1
AC denotes average cost.
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Under the assumption of absolute costless market exit, the mere existence of an entry lag, however small, contradicts the optimality of a sustainable price.2 If retirement from the market involves a time lag, too, that would induce exit costs because of temporarily uncovered fixed costs. Thus, hit-and-run entry would create a loss to established firms. Yet newcomers and, consequently, the profitability of market entry would be affected by such exit costs as well. It is this ambiguity which this paper is concerned with. 3. A model of hit-and-run entry with time lags In order to stick to the main features of the contestable market approach, namely a situation where strategic behaviour is irrelevant, we will retain Assumptions 1 to 5 and consider the structure of one entry process in isolation, starting at t 0. The time of the earliest possible entry of a newcomer firm is denoted as t0 and the earliest possible exit for both the entrant and the incumbent as tE. The incumbent can respond to the entry at the earliest at tR.3 The existence of a reaction lag (contract period), that is tR > t0, in connection with the absence of any entry and exit costs ensures the feasibility of hit-and-run entry. If the market price is above average cost and a new firm enters as a Bertrand competitor, the existence of a sustainable configuration will imply the displacement of the incumbent at t0, because no residual demand will remain to ensure the survival of the established firm.4 But this would not be the end of the story. Since the (delayed) price response by the incumbent can be regarded as its re-entry, the newcomer would be forced to exit on his part in tR. Otherwise there would be a contradiction within the Bertrand framework. An entry lag would correspond to t0 > 0. Instead of applying the original sunk-cost approach, we allow for an exit lag which is an alternative representation of imperfect contestability. Obviously, every exit lag is equivalent to a certain amount of sunk costs, and vice versa.5 It is assumed that the exit lag, which is reflected by tE > t0, results from technological or institutional reasons, i.e. is exogenous. Thus, if there are market exit costs, they may reduce the payoff associated with hit-and-run entry, but they do not offer the possibility of strategic commitment. The beginning, t0, and the length of an exit lag are the same for both the monopolist and the newcomer.6 2 Incumbent firms could charge a price p > AC during the entry lag, leaving the market without incurring any loss at the moment when entry takes place. See Schwartz and Reynolds (1983). 3 t0, tE and tR are points in time. 4 Because the entrant faces no disadvantage vis-aÁ-vis the incumbent with respect to the available production techniques he is able to replicate the incumbent's output. Thus, firm j only needs to undercut the prevailing price by an arbitrarily small amount. 5 For example, Spence (1983, p. 986) associates sunk costs with ``the period for which a new entrant's costs are sunk, after the investment is costlessly.'' This analogy is also emphasized by Schwartz (1986). 6 A realistic example may be the period of notice for rented capital, employment contracts, or the average time spent on selling production capital or equipment. This means, t0 is the earliest moment in time to both enter the market and to take precautions to ensure reversibility of all investments at the earliest time (i.e. tE). For the monopolist, the necessity of liquidating capital goods or terminating hire and employment contracts only arises in the case of entry. But this may occur at the earliest in t0. Accordingly, t0 marks the beginning of the exit lag for both the newcomer and the incumbent.
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From the prospect of a potential competitor an exit lag only matters if tE > tR. Then, the newcomer loses all demand to the monopolist in tR, but cannot resell production capital or terminate contracts before tE. Consequently, he bears exit costs R t because of uncovered fixed costs during the time interval [tR, tE]. They amount to tRE F eÿrt dt. If tE tR, the entrant can leave the market prior to any aggressive reaction by the incumbent. Losses due to temporary uncovered fixed costs do not accrue. Thus, exit costs for an entrant only arise during the interval [tR, max{tE, tR}]. The incumbent's exit lag is bounded by tR, because at this time the newcomer retreats, and the whole demand falls back to the monopolist. The established firm has to bear losses due to uncovered fixed costs only during the period [t0, min{tE, tR}]. If tR > tE, the newcomer would delay his exit until tR to exhaust the contract period that protects him from price responses. Therefore, the incumbents's profit over [tE, tR] is 0 since he has to bear no additional costs while he is unable to drive out the entrant. Summing up thus far, two different lag structures may appear: 0 t0 < tR < tE
or 0 t0 tE tR
with
t0 < tR
In t 0, the incumbent has to choose one of the strategies p AC or, p > AC. The first strategy is sufficient to deter entry, for it constitutes a sustainable equilibrium which does not offer any profitable entry option. With p > AC, hit-and-run entry might be possible. In t0 the newcomer chooses between enter or not enter. The beforementioned time lags imply sequential moves. Obviously, an extensive game structure is appropriate to model the entry situation (Fig. 1). The strategy combination (p AC, enter) will not be taken into account, because enter is dominated by not enter as long as the monopolist plays p AC.
Fig. 1. An extensive entry game to model hit-and-run behaviour.
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The following payoff functions have to be specified: Z t0 Z ÿrt pe dt ÿ Vi p > AC; enter Z Vj p > AC; enter
t0 tR
t0
peÿrt dt ÿ Z
Vi p > AC; not enter
tR
t0
Z
min tE ;tR
t0 max tE ;tR
tR
F eÿrt dt
(3)
F eÿrt dt
(4)
peÿrt dt
(5)
(p) denotes the profit stream which is identical for both the incumbent and the newcomer since we assume ! 0. In order to establish (p AC, not enter) as an unique equilibrium of the entry game, it has to be shown that, first, hit-and-run attacks are profitable if the incumbent plays p > AC and, second, the incumbent would suffers a loss. Bearing (4) in mind, the first condition implies Z max tE ;tR Z tR peÿrt dt > F eÿrt dt for p > AC (6) t0
tR
and, using (3), the second condition becomes Z t0 Z min tE ;tR peÿrt dt < F eÿrt dt t0
t0
for
p > AC:
(7)
These inequalities can be expressed as a two-sided condition on (p)/F:7 eÿrtR ÿ eÿr maxftE ;tR g p eÿrt0 ÿ eÿr minftE ;tR g < < eÿrt0 ÿ eÿrtR 1 ÿ eÿrt0 F
for
p > AC
(8)
In the absence of an entry lag, every positive exit lag makes (7) to hold. However, if the exit lag is zero, every arbitrarily small entry lag would prevent (p AC, not enter) from being optimal. It turns out, therefore, that under the hit-and-run hypothesis potential competition requires a sufficient exit lag to be effective. However, the consequences of an exit lag are ambiguous, because in view of (6) it may also impair the profitability of hit-and-run entry. Accordingly, the next two sections will focus on the consequences of exit lags of different lengths, or more precisely, on the two cases tE tR and tE > tR. 3.1. The case tE tR If tE tR, the second integral in (4) vanishes. The existence of an exit lag does not affect the entrant since he may leave the market prior to any price response. If the established firm chooses p > AC, hit-and-run entry will be profitable, i.e. Z tR peÿrt dt > 0: (9) Vj p > AC; enter t0
7
This was pointed out by an anonymous referee.
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Entry can only be deterred by exercising strategy p AC. Thus, if the incumbent plays p > AC, the monopoly price would be a dominant strategy, since smaller prices above average cost do not affect the optimality of hit-and-run entry. The optimal strategy of the incumbent, therefore, depends on the sign of Z t0 Z tE pM eÿrt dt ÿ F eÿrt dt; (10) Vi p pM ; enter t0
t0
M
where p denotes the monopoly price. As regards the various cases conforming with the constellation tE t0 0, it is easy to see that in general only a sufficiently long exit lag may prevent the incumbent from monopoly pricing. However, the case tE t0 0 calls for a more detailed explanation. At first glance, it would appear that the incumbent is indifferent to p AC and p pM, as Vi(p AC, not enter) Vi(p pM, enter) 0. Both strategy combinations form a Nash equilibrium.8 It can be argued, however, that (p pM, enter) is the preferred solution since it complies with Selten's (1975) `trembling-hand' criterion.9 If the monopolist plays p AC, he is sure of getting 0, whereas if he chose the monopoly price, instead, he would keep the chance of exploiting the possibility that the newcomer will stay out by mistake, without taking any risk of a lower payoff than 0. 3.2. The case tE > tR In this situation, the upper limit of the second integral in (4) is given by tE. The monopolist is now able to deter entry by means of a price, ^p, which meets the restriction Z tR Z tE p; enter ^ peÿrt dt ÿ F eÿrt dt 0: (11) Vj p ^ t0
tR
In the case of p^ pM this constraint would not be binding since firm i possesses a safe monopoly position. On the other hand, the constraint is binding if AC < ^p < pM , but it would still be possible to discourage entry by setting a price above average cost. However, the optimality of whether or not to deter entry now depends on which of the two payoffs Z tR p; not enter ^peÿrt dt (12) Vi p ^ t0
and Vi p pM ; enter
8
Z
t0 t0
pM eÿrt dt ÿ
Z
tR t0
F eÿrt dt:
(13)
Since none of them rests on an incredible threat, both equilibria are also subgame perfect. The basic idea of this concept is that there always exists a small probability that a player will take a choice by `mistake'. Consequently, every pure strategy of the game is chosen with a positive probability, even if it can be reached only after a deviation from equilibrium. An equilibrium is `perfect', if each player's equilibrium strategy is optimal against both the equilibrium strategies of his opponents, and some slight perturbations. Note that this criterion is an appropriate refinement even under perfect information. 9
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is larger. In the absence of an entry lag the incumbent will always play p ^p, whereas for p pM to be optimal, a sufficiently long entry lag is necessary. 4. Summary and conclusion The preceding analysis suggests that a market into which entry is absolutely free and exit is absolutely costless cannot be perfectly contestable. The possibility to leave a market absolutely costlessly and without any delay strengthens the strategical position of hit-and-run entrants, because they need not fear retaliatory price responses if they enter to exploit transient profit options. At the same time, the established firm is protected against losses from hit-and-run attacks as well since it can leave the market on the same terms. Without an exit lag, the incumbent sets the price pM to exploit any entry lag. If this motivates a hit-and-run attack he will leave the market costlessly in t0 and will come back in tR. No oligopolistic interaction will occur, because the entrant exits prior to a reaction by the established firm. The same holds in the absence of an entry lag since the incumbent, still charging pM, will maintain the chance to profit from the non-appearance of any newcomer without taking a risk. In the extreme case tR tE > t0, average cost pricing may appear as an equilibrium. Given the main assumptions of contestability theory, the power of potential competition reaches its theoretical maximum only if market exit costs are sufficiently high. This contradicts the assertion of Baumol, Panzar and Willig that potential competition which appears as hitand-run entry, will force market price down to average cost where there are no sunk costs. Although the exit lag approach is equivalent to a certain amount of sunk costs, the constellation tR tE > t0 involves an important feature, which cannot be represented by the sunk cost approach. If the monopolist loses the whole demand to an entrant which means that he is temporarily displaced, he has to bear exit costs. Contrarily, this does not apply to the newcomer since the exit lag does not exceed the reaction lag which just prevents him from a retaliatory price response. Only this unlikely asymmetry, in connection with one further condition, namely, that market exit costs exceed the profit which can be earned by the monopolist during the entry lag, yields a motivation to carry out strategy p AC. However, if the exit lag surpasses the reaction lag, entry deterrence by means of a price above average cost becomes possible. In conclusion, it may be said that within the scope of contestability theory, market exit costs may not only increase the effectiveness of potential competition, but they are even a necessary condition for any impact of an entry threat at all. The inverse relationship between sunk costs and the power of potential competition which has not been challenged up to now, should be reconsidered. Acknowledgements The author gratefully acknowledges helpful comments and suggestions by Michael Braulke, Friedrich Breyer, Udo Broll, JoÈrg Schimmelpfennig, Heinrich Ursprung, and an anonymous referee.
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References Baumol, William J., 1982. An uprising in the theory of industry structure, American Economic Review 72, 1±15. Baumol, William J., Panzar, John C., Willig, Robert D., 1982. Contestable markets and the theory of market structure. Harcourt Brace, San Diego. Baumol, William J., Panzar, John C., and Willig, Robert D., 1983. Contestable markets: An uprising in the theory of industry structure: Reply, American Economic Review 73, 491±496. Baumol, William J., Panzar, John C., Willig, Robert D., 1986. On the theory of contestable markets. In: Stiglitz, Joseph, Frank Mathewson, G. (Eds.), New Developments in the Analysis of Market Structure. MIT Press, Cambridge, p. 339±365. Schwartz, Marius, and Reynolds, Robert J., 1983. Contestable markets: An uprising in the theory of industrial structure: Comment, American Economic Review 73, 488±490. Schwartz, Marius, 1986. The nature and scope of contestability theory. In: Morris, Derek J., Sinclair, P.J., Slater, Martin D., Vickers, John S. (Eds.), Strategic Behavior and Industrial Competition. Oxford University Press, Oxford, p. 37±57. Selten, Reinhard, 1975. Reexamination of the perfectness concept for equilibrium points in extensive games, International Journal of Game Theory 4, 25±55. Spence, A. Michael, 1983. Contestable markets and the theory of industry structure: A review article, Journal of Economic Literature 21, 981±990.
Contestability reconsidered: The meaning of market exit costs Niko P. Paech* Department of Economics, UniversitaÈt OsnabruÈck, 49069 OsnabruÈck, Germany Received 18 October 1995; received in revised form 14 November 1996
Abstract This paper analyses the main result of the contestable market approach, namely, that potential competition reaches its maximum power if market entry and exit is costless and newcomers can use the hit-and-run strategy. Different time lag structures are considered. Average cost pricing turns out to be no equilibrium if there are no market exit costs. Furthermore, exit costs don't necessarily create a barrier to entry, but may even strengthen the discipline arising from the threat of entry. # 1998 Elsevier Science B.V. JEL classi®cation: D43; L11; L12 Keywords: Potential competition; Hit-and-run entry; Entry and exit costs
1. Introduction The basic idea of the contestable market model by Baumol et al. (1982) is to formulate conditions under which the power of potential competition may be a perfect substitute for price-taking behaviour in oligopolistic or monopolistic markets. Newcomers act like Bertrand competitors, i.e. they undercut the price, capture the whole market, and leave it prior to any price response by incumbents (hit and run). The profitability of entry does not hinge on the result of any post entry game. Instead, it is calculated directly on the basis of the current market price. The adherents of contestability analysis claim an inverse relationship between the profitability of entry and the size of sunk costs, no matter * Corresponding author. Tel.: +49 541 26396; fax: +49 541 969-6142; e-mail: [email protected] 0167-2681/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved PII S 0 1 6 7 - 2 6 8 1 ( 9 7 ) 0 0 0 8 1 - 4
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whether they arise during the entry or exit phase. In their eyes, sunk costs weaken the virtues of potential competition and may form an entry barrier. This paper analyses whether the mere threat of entry may be sufficient to force prices down to average cost. It turns out that market exit costs are a necessary condition for any impact of an entry threat. The following section gives a short description of the contestable market model and emphasizes the role of specific time lags. In Section 3, a separate entry event will be analyzed, taking into account alternative lag structures. Optimal strategies for both potential and established firms conditional on the relevant lag structure will be derived. The last section contains a conclusion. 2. The contestable market approach 2.1. Assumptions and properties Contestable market theory refers to a situation where the impact of potential entry on the price setting behaviour of actual firms is maximal. ``A contestable market is one into which entry is absolutely free, and exit is absolutely costless'' (Baumol, 1982, p. 3). The option to enter and to leave the market costlessly requires that the capital, which has to be invested by an entrant, can be liquidated without any loss or can be completely removed to an alternative use, once the newcomer is forced to leave the market. Otherwise, an entrant would have to incur irreversible costs (sunk costs), which directly reduce the profit he can earn during his stay in the market. The benchmark case of perfect contestability may be represented by the following assumptions: Assumption 1.
Newcomers enter the market as Bertrand competitors.
Assumption 2.
A sustainable industry configuration exists.
Assumption 3.
Price adjustments by established firms are delayed.
Assumption 4.
Incumbents face an entry threat any moment in time.
Assumption 5. Every player knows the demand conditions and the payoff function of all other players (complete information). Assumption 6.
There are no market entry or exit costs (sunk costs).
Applying these assumptions, Baumol et al. (1982, 1983, 1986) claim that a perfectly contestable market can be in equilibrium only if it is resistant to hit-and-run entry. Using the hit-and-run strategy, potential competitors enter the market as a Bertrand competitor and depart prior to any reaction by the established firms. In contrast to a widely used assumption in post entry analysis, newcomer firms do not expect oligopolistic interactions but assume the price to remain unchanged. The most important property of a perfectly contestable market is that potential competitors exercise discipline over the incumbents to the extent that only prices are
N.P. Paech / J. of Economic Behavior & Org. 34 (1998) 435±443
437
viable which imply zero profits. With at least two operating firms a perfectly contestable market equilibrium yields first-best Pareto optimality, that is, price simultaneously equals marginal cost and minimum average cost. If costs are subadditive, i.e. the industry is a natural monopoly, the equilibrium will be characterized by Ramsey-optimal pricing. Baumol et al. (1982) establish the power of potential competition by means of a simple argument: If the price exceeds average cost or if production is inefficient the market must be out of equilibrium because a profitable entry option exists. 2.2. Sunk costs and time lags Irreversible costs are important to contestability analysis for two reasons: In the absence of sunk costs there will be no room for commitments or other kinds of strategic behaviour by established firms; and apart from such strategic considerations, sunk costs also directly impair the profitability of hit-and-run entry. To simplify matters, we will consider the single product case with a market demand function for a homogeneous good X(p), X0 (p) < 0. There is an incumbent (denoted by i) and an entrant (denoted by j). It will be assumed that the established firm and the potential competitor have access to the same technology, reflected in identical cost functions C(x) including a variable and a fixed component. The latter, which is denoted by F, may be partially sunk. A newcomer who enters the market at, say, time 0 expects that he will be driven out by an aggressive price response at a later time, say R. His payoff function is Z R 1 ÿ eÿrR ÿ s F eÿrR ; p ÿ xj ÿ C xj eÿrt dt ÿ s F eÿrR p ÿ xj ÿ C xj Vj r 0 (1) where p denotes the prevailing market price, xj the newcomer's output and r the discount rate. s denotes a share of the fixed cost which is lost when the newcomer leaves the market. Undercutting the market price by and retiring at time R characterizes the hit-and-run strategy. Under the simplifying assumption ! 0, the highest entry preventing price is p
C xj r s F eÿrR : xj xj 1 ÿ eÿrR
(2)
In the extreme case s 0 this price coincides with average cost, and obviously, as s ! 0, the entry preventing price converges towards average cost. Baumol et al. (1983, p. 494), therefore, conclude, ``where there are almost no sunk costs, markets are almost perfectly contestable.'' But this assertion has to be qualified because, even in the limiting case s 0 and R > 0, a unique statement on the effectiveness of potential competition is not possible. In this case, the entry preventing price equals average cost, but the question still remains whether it would be optimal for established firms to actually charge it. To decide that question, one would first have to investigate whether p AC corresponds to a Nash equilibrium of the entry game, i.e. whether the profit resulting from any strategy p > AC is less than the damage caused by new entry.1 1
AC denotes average cost.
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Under the assumption of absolute costless market exit, the mere existence of an entry lag, however small, contradicts the optimality of a sustainable price.2 If retirement from the market involves a time lag, too, that would induce exit costs because of temporarily uncovered fixed costs. Thus, hit-and-run entry would create a loss to established firms. Yet newcomers and, consequently, the profitability of market entry would be affected by such exit costs as well. It is this ambiguity which this paper is concerned with. 3. A model of hit-and-run entry with time lags In order to stick to the main features of the contestable market approach, namely a situation where strategic behaviour is irrelevant, we will retain Assumptions 1 to 5 and consider the structure of one entry process in isolation, starting at t 0. The time of the earliest possible entry of a newcomer firm is denoted as t0 and the earliest possible exit for both the entrant and the incumbent as tE. The incumbent can respond to the entry at the earliest at tR.3 The existence of a reaction lag (contract period), that is tR > t0, in connection with the absence of any entry and exit costs ensures the feasibility of hit-and-run entry. If the market price is above average cost and a new firm enters as a Bertrand competitor, the existence of a sustainable configuration will imply the displacement of the incumbent at t0, because no residual demand will remain to ensure the survival of the established firm.4 But this would not be the end of the story. Since the (delayed) price response by the incumbent can be regarded as its re-entry, the newcomer would be forced to exit on his part in tR. Otherwise there would be a contradiction within the Bertrand framework. An entry lag would correspond to t0 > 0. Instead of applying the original sunk-cost approach, we allow for an exit lag which is an alternative representation of imperfect contestability. Obviously, every exit lag is equivalent to a certain amount of sunk costs, and vice versa.5 It is assumed that the exit lag, which is reflected by tE > t0, results from technological or institutional reasons, i.e. is exogenous. Thus, if there are market exit costs, they may reduce the payoff associated with hit-and-run entry, but they do not offer the possibility of strategic commitment. The beginning, t0, and the length of an exit lag are the same for both the monopolist and the newcomer.6 2 Incumbent firms could charge a price p > AC during the entry lag, leaving the market without incurring any loss at the moment when entry takes place. See Schwartz and Reynolds (1983). 3 t0, tE and tR are points in time. 4 Because the entrant faces no disadvantage vis-aÁ-vis the incumbent with respect to the available production techniques he is able to replicate the incumbent's output. Thus, firm j only needs to undercut the prevailing price by an arbitrarily small amount. 5 For example, Spence (1983, p. 986) associates sunk costs with ``the period for which a new entrant's costs are sunk, after the investment is costlessly.'' This analogy is also emphasized by Schwartz (1986). 6 A realistic example may be the period of notice for rented capital, employment contracts, or the average time spent on selling production capital or equipment. This means, t0 is the earliest moment in time to both enter the market and to take precautions to ensure reversibility of all investments at the earliest time (i.e. tE). For the monopolist, the necessity of liquidating capital goods or terminating hire and employment contracts only arises in the case of entry. But this may occur at the earliest in t0. Accordingly, t0 marks the beginning of the exit lag for both the newcomer and the incumbent.
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From the prospect of a potential competitor an exit lag only matters if tE > tR. Then, the newcomer loses all demand to the monopolist in tR, but cannot resell production capital or terminate contracts before tE. Consequently, he bears exit costs R t because of uncovered fixed costs during the time interval [tR, tE]. They amount to tRE F eÿrt dt. If tE tR, the entrant can leave the market prior to any aggressive reaction by the incumbent. Losses due to temporary uncovered fixed costs do not accrue. Thus, exit costs for an entrant only arise during the interval [tR, max{tE, tR}]. The incumbent's exit lag is bounded by tR, because at this time the newcomer retreats, and the whole demand falls back to the monopolist. The established firm has to bear losses due to uncovered fixed costs only during the period [t0, min{tE, tR}]. If tR > tE, the newcomer would delay his exit until tR to exhaust the contract period that protects him from price responses. Therefore, the incumbents's profit over [tE, tR] is 0 since he has to bear no additional costs while he is unable to drive out the entrant. Summing up thus far, two different lag structures may appear: 0 t0 < tR < tE
or 0 t0 tE tR
with
t0 < tR
In t 0, the incumbent has to choose one of the strategies p AC or, p > AC. The first strategy is sufficient to deter entry, for it constitutes a sustainable equilibrium which does not offer any profitable entry option. With p > AC, hit-and-run entry might be possible. In t0 the newcomer chooses between enter or not enter. The beforementioned time lags imply sequential moves. Obviously, an extensive game structure is appropriate to model the entry situation (Fig. 1). The strategy combination (p AC, enter) will not be taken into account, because enter is dominated by not enter as long as the monopolist plays p AC.
Fig. 1. An extensive entry game to model hit-and-run behaviour.
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The following payoff functions have to be specified: Z t0 Z ÿrt pe dt ÿ Vi p > AC; enter Z Vj p > AC; enter
t0 tR
t0
peÿrt dt ÿ Z
Vi p > AC; not enter
tR
t0
Z
min tE ;tR
t0 max tE ;tR
tR
F eÿrt dt
(3)
F eÿrt dt
(4)
peÿrt dt
(5)
(p) denotes the profit stream which is identical for both the incumbent and the newcomer since we assume ! 0. In order to establish (p AC, not enter) as an unique equilibrium of the entry game, it has to be shown that, first, hit-and-run attacks are profitable if the incumbent plays p > AC and, second, the incumbent would suffers a loss. Bearing (4) in mind, the first condition implies Z max tE ;tR Z tR peÿrt dt > F eÿrt dt for p > AC (6) t0
tR
and, using (3), the second condition becomes Z t0 Z min tE ;tR peÿrt dt < F eÿrt dt t0
t0
for
p > AC:
(7)
These inequalities can be expressed as a two-sided condition on (p)/F:7 eÿrtR ÿ eÿr maxftE ;tR g p eÿrt0 ÿ eÿr minftE ;tR g < < eÿrt0 ÿ eÿrtR 1 ÿ eÿrt0 F
for
p > AC
(8)
In the absence of an entry lag, every positive exit lag makes (7) to hold. However, if the exit lag is zero, every arbitrarily small entry lag would prevent (p AC, not enter) from being optimal. It turns out, therefore, that under the hit-and-run hypothesis potential competition requires a sufficient exit lag to be effective. However, the consequences of an exit lag are ambiguous, because in view of (6) it may also impair the profitability of hit-and-run entry. Accordingly, the next two sections will focus on the consequences of exit lags of different lengths, or more precisely, on the two cases tE tR and tE > tR. 3.1. The case tE tR If tE tR, the second integral in (4) vanishes. The existence of an exit lag does not affect the entrant since he may leave the market prior to any price response. If the established firm chooses p > AC, hit-and-run entry will be profitable, i.e. Z tR peÿrt dt > 0: (9) Vj p > AC; enter t0
7
This was pointed out by an anonymous referee.
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Entry can only be deterred by exercising strategy p AC. Thus, if the incumbent plays p > AC, the monopoly price would be a dominant strategy, since smaller prices above average cost do not affect the optimality of hit-and-run entry. The optimal strategy of the incumbent, therefore, depends on the sign of Z t0 Z tE pM eÿrt dt ÿ F eÿrt dt; (10) Vi p pM ; enter t0
t0
M
where p denotes the monopoly price. As regards the various cases conforming with the constellation tE t0 0, it is easy to see that in general only a sufficiently long exit lag may prevent the incumbent from monopoly pricing. However, the case tE t0 0 calls for a more detailed explanation. At first glance, it would appear that the incumbent is indifferent to p AC and p pM, as Vi(p AC, not enter) Vi(p pM, enter) 0. Both strategy combinations form a Nash equilibrium.8 It can be argued, however, that (p pM, enter) is the preferred solution since it complies with Selten's (1975) `trembling-hand' criterion.9 If the monopolist plays p AC, he is sure of getting 0, whereas if he chose the monopoly price, instead, he would keep the chance of exploiting the possibility that the newcomer will stay out by mistake, without taking any risk of a lower payoff than 0. 3.2. The case tE > tR In this situation, the upper limit of the second integral in (4) is given by tE. The monopolist is now able to deter entry by means of a price, ^p, which meets the restriction Z tR Z tE p; enter ^ peÿrt dt ÿ F eÿrt dt 0: (11) Vj p ^ t0
tR
In the case of p^ pM this constraint would not be binding since firm i possesses a safe monopoly position. On the other hand, the constraint is binding if AC < ^p < pM , but it would still be possible to discourage entry by setting a price above average cost. However, the optimality of whether or not to deter entry now depends on which of the two payoffs Z tR p; not enter ^peÿrt dt (12) Vi p ^ t0
and Vi p pM ; enter
8
Z
t0 t0
pM eÿrt dt ÿ
Z
tR t0
F eÿrt dt:
(13)
Since none of them rests on an incredible threat, both equilibria are also subgame perfect. The basic idea of this concept is that there always exists a small probability that a player will take a choice by `mistake'. Consequently, every pure strategy of the game is chosen with a positive probability, even if it can be reached only after a deviation from equilibrium. An equilibrium is `perfect', if each player's equilibrium strategy is optimal against both the equilibrium strategies of his opponents, and some slight perturbations. Note that this criterion is an appropriate refinement even under perfect information. 9
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is larger. In the absence of an entry lag the incumbent will always play p ^p, whereas for p pM to be optimal, a sufficiently long entry lag is necessary. 4. Summary and conclusion The preceding analysis suggests that a market into which entry is absolutely free and exit is absolutely costless cannot be perfectly contestable. The possibility to leave a market absolutely costlessly and without any delay strengthens the strategical position of hit-and-run entrants, because they need not fear retaliatory price responses if they enter to exploit transient profit options. At the same time, the established firm is protected against losses from hit-and-run attacks as well since it can leave the market on the same terms. Without an exit lag, the incumbent sets the price pM to exploit any entry lag. If this motivates a hit-and-run attack he will leave the market costlessly in t0 and will come back in tR. No oligopolistic interaction will occur, because the entrant exits prior to a reaction by the established firm. The same holds in the absence of an entry lag since the incumbent, still charging pM, will maintain the chance to profit from the non-appearance of any newcomer without taking a risk. In the extreme case tR tE > t0, average cost pricing may appear as an equilibrium. Given the main assumptions of contestability theory, the power of potential competition reaches its theoretical maximum only if market exit costs are sufficiently high. This contradicts the assertion of Baumol, Panzar and Willig that potential competition which appears as hitand-run entry, will force market price down to average cost where there are no sunk costs. Although the exit lag approach is equivalent to a certain amount of sunk costs, the constellation tR tE > t0 involves an important feature, which cannot be represented by the sunk cost approach. If the monopolist loses the whole demand to an entrant which means that he is temporarily displaced, he has to bear exit costs. Contrarily, this does not apply to the newcomer since the exit lag does not exceed the reaction lag which just prevents him from a retaliatory price response. Only this unlikely asymmetry, in connection with one further condition, namely, that market exit costs exceed the profit which can be earned by the monopolist during the entry lag, yields a motivation to carry out strategy p AC. However, if the exit lag surpasses the reaction lag, entry deterrence by means of a price above average cost becomes possible. In conclusion, it may be said that within the scope of contestability theory, market exit costs may not only increase the effectiveness of potential competition, but they are even a necessary condition for any impact of an entry threat at all. The inverse relationship between sunk costs and the power of potential competition which has not been challenged up to now, should be reconsidered. Acknowledgements The author gratefully acknowledges helpful comments and suggestions by Michael Braulke, Friedrich Breyer, Udo Broll, JoÈrg Schimmelpfennig, Heinrich Ursprung, and an anonymous referee.
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