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Rent dissipation and social benefit in regulated entry contests
European Journal of Political Economy Vol. 21 (2005) 205 – 219 www.elsevier.com/locate/econbase
Rent dissipation and social benefit in regulated entry contests Sanghack Lee a,*, Kiwoong Cheong b a
School of Economics, Kookmin University, Seoul 136-702, South Korea School of Business, Keimyung University, Taegu 704-701, South Korea
b
Received 21 September 2003; received in revised form 2 April 2004; accepted 16 April 2004 Available online 30 July 2004
Abstract This paper examines entry contests in oligopoly with regulatory barriers to entry when government seeks to issue additional licenses. The entry contests are modeled as a two-stage rentseeking game between incumbents and potential entrants, with incumbents opposing issuance of additional licenses while the potential entrants try to obtain them. We derive conditions under which the resources expended in the entry contest exceed or fall short of the expected increase in social benefit. Entry deregulation is more likely to increase expected social benefit when incumbents employ a non-cooperative Nash strategy in rent seeking than when they collude. D 2004 Elsevier B.V. All rights reserved. JEL classification: D72; D73; L13 Keywords: Entry barrier; Entry contest; Rent seeking; Partial deregulation
1. Introduction This paper considers entry contests in oligopoly with regulatory barriers to entry. The contests are between incumbents and potential entrants when government seeks to partially deregulate entry barriers by issuing additional licenses. We derive conditions under which the partial deregulation of entry barriers laden with rent seeking increases or decreases expected social benefit. The entry deregulation is more likely to increase social benefit when the incumbents employ a non-cooperative Nash strategy in rent seeking than when they collude. * Corresponding author. Tel.: +82-2-910-4546; fax: +82-2-910-4519. E-mail address: [email protected] (S. Lee). 0176-2680/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejpoleco.2004.04.001
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Deregulation of entry barriers is an important issue in the literature of regulation. Indeed, entry barriers are the regulatory form preferred by incumbents (Rasmusen and Zupan, 1991). Economists usually support unlimited entry of new firms into oligopolies. However, many papers show that there are circumstances in which entry of firms decreases social benefit. Mankiw and Whinston (1986) find that excessive entry is likely to occur when there are setup costs and firms enter the industry simultaneously. Nachbar et al. (1998) examine the effects of entry in a Cournot oligopoly when some of incumbents’ costs are sunk. They find that a small portion of sunk costs can reverse a welfare assessment in cases where entry reduces social benefit. Several papers have previously examined the social benefit effects of deregulation. McCormick et al. (1984) propose that the gains from deregulation of monopoly are much lower than those conventionally thought if the initial effort to establish monopoly has dissipated the monopoly profit. Their argument is labeled the ‘‘disinterest in deregulation’’ proposition. Crew and Rowley (1986, 1988) and Poitras and Sutter (1997, 2000) show that the ‘‘disinterest in deregulation’’ proposition holds only when the deregulation is unanticipated. In particular, Poitras and Sutter (1997) analyze the efficiency gains from deregulation of monopolies when reformers expend resources to secure deregulation and the monopolist expends resources to maintain the status quo. They find that the potential welfare gains of deregulation exceed the cost of deregulation. However, their analysis is limited to complete deregulation of entry into the industry. In more realistic circumstances, governments might allow for entry of a limited number of additional firms instead of completely dismantling the entry barriers. Poitras and Sutter (2000) examine the welfare gains from the reform of distortions induced by government. They show that the welfare gains of reform over the status quo exist whenever deregulation occurs. Governments are not likely to take away licenses already given to firms in regulated industries. However, they can issue more licenses to potential entrants. Indeed, many governments have issued licenses to potential entrants to the provision of telecommunication services, which had previously been viewed as a natural monopoly. This has raised a conflict of interest between the incumbent monopolists and potential entrants.1 Quite naturally, the incumbents try to maintain the status quo while the potential entrants try to induce the government to issue more licenses. The deregulation process in such a situation can be modeled as a contest. Poitras and Sutter (1997, 2000) model the deregulation process as a contest between the monopolist and the reformer. As in Kang and Lee (2001), we model the deregulation process as a two-stage game between incumbents and potential entrants in oligopoly. In the first stage, the group of potential entrants competes against the group of incumbents to secure entry licenses. We allow for issuance of an arbitrary number of licenses. If the incumbents win, the regulation
1 For example, the Korean government has recently issued licenses to new entrants in telecommunication service industries and broadcasting industries. The state-run Korea Telecom was the only supplier of telephone services until the late 1980s in Korea. Competition was first introduced in 1990 with the entry of DACOM into the international telephone service market. The Ministry of Information and Communication of Korea introduced competition in the cellular phone service market in 1994 and in the long distance telephone service market in 1995, respectively. For a detailed explanation, see the White Paper (1998) of the Ministry of Information and Communication of Korea.
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regime remains the same. If the potential entrants win in the first stage, however, the second-stage contest takes place between the potential entrants to obtain the licenses.2 We do not adopt any specific assumptions on the behavior of firms and demand conditions, whereas Kang and Lee (2001) examine a Cournot oligopoly with a linear demand and identical costs. Our results stand in sharp contrast with those of Kang and Lee (2001). The paper is organized as follows. Section 2 sets out the basic model. Section 3 analyzes the contest between the incumbents and the potential entrants. We consider three kinds of interaction between incumbents and potential entrants. In the first case, firms adopt a non-cooperative Nash strategy in the entry contest. In the second case, firms collude within their respective groups. In the third case, incumbents collude while potential entrants adopt a non-cooperative Nash strategy. We find that the firms expend more on rent seeking when they collude than when they employ a non-cooperative Nash strategy. We also show that complete deregulation is hard to obtain. Section 4 examines the effect of the entry contest on expected social benefit. We derive conditions under which the resources expended in the entry contest exceed or fall short of the expected increase in social benefit. We show that the entry deregulation is likely to increase social benefit when the incumbents employ a non-cooperative Nash strategy in rent seeking and when the decrease in profits of the incumbents caused by entry is small. Section 5 offers concluding remarks.
2. Oligopoly with regulatory barriers to entry Consider an oligopoly consisting of n (identical) incumbent firms with regulatory barriers to entry.3 There are m potential entrants, where m ( z 1) is exogenously given.4 Government may issue k more license(s) to the potential entrants, where 1 V k V m. The firms produce a homogeneous product. Production takes place only once.5 The inverse
2 Examples of such contests can be found in utility rate hearings. Regarding these, Wenders (1987, p. 457) notes that: ‘‘Various consumer groups initially present a united front, often with explicit cooperation, in trying to keep the allowed increase in utility revenues as small as possible. However, once the allowed revenue increase is set by the commission, the various consumer groups turn on one another and try to deflect as much of the increase as possible to others. Lions and wolves cooperate in the hunt, but scrap over the kill.’’ Thus, Wenders (1987) recognizes the possibility of rent-defending activity by consumers. However, his analysis ignores the effect of consumer expenditures on the behavior of the other participants. Building on Hillman and Riley (1989), Ellingsen (1991) derives conditions under which consumer participation in a rent-seeking game is socially beneficial. 3 In the present paper, we simply take the oligopoly structure, i.e., the number of firms, as given. Thus, we abstract from the question of how and why government has issued n licenses. McCormick et al. (1984) and Poitras and Sutter (1997, 2000) assume that government has issued a single license. 4 The number of potential entrants, m, can be endogenously determined following Higgins et al. (1985). The first-stage in their model is the qualifying contest. In the second stage, the qualified bidders compete for the monopoly franchise. We thank the anonymous referee for introducing the paper to us. Another interesting possibility noted by the referee is that ‘‘government also determines m by requiring potential entrants to ‘prequalify’ to compete for service provision rights.’’ 5 In focusing on a single-period model, we assume away problems associated with multi-period models, one of which is whether oligopoly is contestable or not. Several papers deal with issues related to deregulation in multi-period models. See Crew and Rowley (1986, 1988) and Poitras and Sutter (1997, 2000).
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demand function for the product is denoted g( Q), where Q is the aggregate output of the industry and gV( Q) < 0. The incumbents and potential entrants have the same variable cost function given by c( q), where q is each firm’s output. The profit of each incumbent with no entry is denoted P(n). With n incumbents and k entrants, the profit of a representative incumbent is denoted P(n,k), given by Pðn; kÞ ¼ PðQÞq cðqÞ F;
ð1Þ
where F is the fixed cost. For simplicity, we assume that F is sunk so that it does not affect firms’ output decision. Each entrant’s cost function is given by c( q) + Fe, where Fe denotes the fixed cost. Note that each entrant is assumed to possess the same cost function as the incumbents except for the fixed cost.6 Thus, if the entrant’s fixed cost is smaller than the incumbents’, then the entrants are more efficient than the incumbents and vice versa. The representative entrant’s profit Pe(n,k) can be expressed as a proportion of each incumbent’s profit, Pe ðn; kÞ ¼ aPðn; kÞ; where 0 V a. Of course, a is related to the size of Fe relative to F. If F > Fe, then a >1 and vice versa. We impose no specific restrictions on behavior of firms. However, both the behavior of firms and the demand and cost conditions are assumed to yield positive outputs and nonnegative profits for all the incumbents and entrants. Social benefit is measured by the sum of aggregate profits and consumer surplus. The consumer surplus in the case without entry is denoted, CSðnÞ ¼
Z
gðqÞdq gðQÞQ;
ð2Þ
where Q is the industry output. In the case of no entry, social benefit is denoted SW(n), and is given by SW(n) = CS(n) + nP(n,k). With entry of k firms, social benefit SW(n,k) is given by SWðn; kÞ ¼ CSðn; kÞ þ nPðn; kÞ þ kPe ðn; kÞ ¼ CSðn; kÞ þ ðn þ kaÞPðn; kÞ;
ð3Þ
where CS(n,k) denotes consumer surplus with n incumbents and k entrants. If SW(n,k)> SW(n), then entry of k firms increases social benefit if there is no cost associated with deregulation of entry barriers. However, rent-seeking costs are likely to be incurred in the process of entry.
6 This assumption is adopted so that new entrants produce the same quantity as the incumbents. The only difference between the incumbents and the new entrants is the size of fixed costs. This assumption can be relaxed without affecting the qualitative results.
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3. Entry contests This section examines the contest over partial deregulation of entry barriers. Government deliberates on issuing k more licenses to m potential entrants.7 Following Katz and Tokatlidu (1996) and Kang and Lee (2001), we model the entry contest as a two-stage game as follows. In the first stage, group of incumbents and group of potential entrants compete over entry of firms.8 Unlike Ellingsen (1991) and Poitras and Sutter (1997, 2000), consumers have no influence on the deregulation process. If the incumbents win, the regulation regime remains the same with no more licenses being issued. If the potential entrants win, all of them become eligible for the entry licenses. In the second stage, they compete with one another for the licenses. For each incumbent firm, the prize of the contest is the profit differential secured by maintaining the status quo. With k entrants, each incumbent’s profit decreases by DPk(n,k) (u P(n) P(n,k)). In other words, DPk (n,k) denotes the benefit to each incumbent firm of maintaining the status quo. Note that the sign of DPk is the opposite of conventional differential P(n,k) P(n). Where no confusion arises, the arguments of DPk(n,k) will be omitted. For each potential entrant, the prize of the first-stage contest is the expected benefit of participation in the second-stage contest for the licenses. The incumbent firm i contributes xi to entry-preventing activity, for i = 1,. . .,n. The potential entrant j contributes yj to entry-promoting activity, for j = 1,. . .,m. Following Tullock (1980), the probability that the incumbents succeed in entry blocking, PX, is given by a logit-form function of the aggregate outlays of the two groups: PX ¼ X =ðX þ Y Þ;
ð4Þ
where X (= Sixi) and Y (= Sk yk) denote, respectively, the aggregate outlay of the incumbents and the potential entrants. Note that consumers have no influence on the probability. The probability that the government will issue k more licenses is denoted PY (u 1 PX). If the government decides not to issue k more licenses, the contest is over. Social benefit decreases by the amount r(X + Y) where the parameter r, 0 V r V 1, denotes the extent of wastefulness of rent-seeking expenditures. In one extreme case, (X + Y) can be treated as a mere transfer so that r = 0. In the other extreme case, as in the literature on rent seeking, (X + Y) are all wasted so that r = 1. Real circumstances may be somewhere between the two extreme cases, i.e., 0 < r < 1. If the government decides to issue k more licenses, the second-stage contest takes place between the potential entrants. While consumer surplus increases, additional rent-seeking costs are incurred as well. We employ a subgame-perfect equilibrium as a solution concept. As usual, we first examine the second-stage contest. This result is then utilized to analyze the first-stage contest. 7 Government may choose k that maximizes expected social benefit. In the present paper, however, we do not examine how government determines k. For a related discussion, see footnote 4. 8 While we focus on interaction between groups of firms, there can be a variety of deregulatory process scenarios. For example, Poitras and Sutter (1997, 2000) consider interaction between the reformer and the monopolist.
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3.1. Second-stage contest Assume that the government has decided to issue k more licenses to m potential entrants. The government can distribute the licenses in various ways. One simple way is for the government to randomly distribute them to potential entrants. There is no secondstage rent seeking in such a case. Each potential entrant receives the license with probability k/m. Another possible way is that the government distributes them through rent-seeking contests. In this case, the potential entrant j spends y2j to obtain the entry license, for j = 1,. . .,m. The problem of the risk-neutral potential entrant j is: Max P2j aPðn; kÞ y2j ; y2j
ð5Þ
where P2j denotes the probability that potential entrant j receives the license. Following Katz and Tokatlidu (1996), we assume that the first-stage expenditures have no carryover effect on the second-stage probability of winning.9 If m = 1, of course, there is no secondstage contest. If k = 1, the conventional Tullock contest-success-function can be employed. However, if k >1, more specific assumptions should be employed. As one of such models, Berry (1993) offers a model of contest with multiple identical prizes. In the model of Berry (1993), the probability of any particular combination of k potential entrants being given licenses is equal to the sum of rent-seeking expenditures of the potential entrants in that combination divided by the aggregate sum of rent-seeking expenditures in all possible combinations of k potential entrants. Without any specific assumptions on the way the licenses are distributed, we express the expected benefit of participation in the secondstage contest as a fraction of the entrant’s profit. Let EW2 denote the expected pay-off of the second-stage contest to each potential entrant. Then, EW2 ¼ bPe ðn; kÞ ¼ abPðn; kÞ
ð6Þ
The expression EW2 given in Eq. (6) can encompass a variety of scenarios on the way the licenses are distributed. If we adopt the model of Berry (1993), then b = (mk m + k)/ m2. When k = 1 and P2j is given by a logit-form function as in Eq. (4), then b = 1/m2. If the government distributes the licenses randomly to the potential entrants, each potential entrant has the same chance of obtaining the license so that b = (k/m). 3.2. First-stage contest The first-stage contest between the two groups of firms is now examined. Depending upon institutional setting, there can be a variety of possible interaction between the group of incumbents and the group of potential entrants. We focus on three cases, which seem to 9 In some multi-stage contests, efforts are carried over to next stages in the sense that they are effective in the next stages as well. Baik and Lee (2000) examine the effect of carryovers in a two-stage contest.
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be most plausible.10 In the first case, the firms of the two groups employ, respectively, a non-cooperative Nash strategy when determining their level of contribution to the rentseeking activity of the group. In the second case, both the incumbents and the potential entrants, respectively, collude in rent seeking, each group behaving as a cartel. In the third case, the incumbents collude while the potential entrants employ a non-cooperative Nash strategy. 3.2.1. Case 1: non-cooperative Nash incumbents and potential entrants In this case, both the incumbents and the potential entrants employ a non-cooperative Nash strategy. This assumption is adopted in many papers in the literature on collective rent seeking. See, for example, Katz and Tokatlidu (1996), Lee (1993, 1995) and Nitzan (1991). The objective of the risk-neutral incumbent firm i is: Max Vi ¼ PX PðnÞ þ ð1 PX ÞPðn; kÞ xi ; xi
for i ¼ 1; . . . ; n:
ð7Þ
Similarly, the objective of the risk-neutral potential entrant j is Max Wj ¼ PY ½abPðn; kÞ yj ; yj
for k ¼ 1; . . . ; m:
ð8Þ
The first-order conditions for Eqs. (7) and (8) are, respectively: BVi =Bxi ¼ Y DPk =ðX þ Y Þ2 1 ¼ 0;
for i ¼ 1; . . . ; n:
BWj =Byj ¼ X abPðn; kÞ=ðX þ Y Þ2 1 ¼ 0;
for j ¼ 1; . . . ; m:
ð9Þ ð10Þ
Simultaneous solution of Eqs. (9) and (10) gives X N ¼ abPðn; kÞðDPk Þ2 =½DPk þ abPðn; kÞ2 ;
ð11Þ
Y N ¼ a2 b2 DPk ðPðn; kÞÞ2 =½DPk þ abPðn; kÞ2 and
ð12Þ
X N þ Y N ¼ abPðn; kÞDPk =½DPk þ abPðn; kÞ:
ð13Þ
The superscript N indicates that X N and Y N are the solutions for the non-cooperative Nash equilibrium. Substituting X N and Y N into PX and PY , the equilibrium probability of each group’s winning is obtained.
10
Real-world circumstances may be expressed as a combination of the three cases examined in this paper.
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Lemma 1. If the incumbents and the potential entrants employ a non-cooperative Nash strategy in the entry contest, the equilibrium probability of each group’s winning is, respectively, given by PXN = DPk /[DPk + abP(n,k)], PYN = abP(n,k)/[DPk + abP(n,k)]. Note that Lemma 1 holds regardless of the form of oligopoly and demand conditions. From Lemma 1 and Eq. (13), we find that X N + Y N = P YN DPk . The larger the profit differential DPk, the higher is the probability of winning for the incumbents. It is easy to find that BPXN =Ba < 0 and BPXN =Bb < 0:
ð14Þ
These results are in accordance with our intuition. The expected pay-off to each potential entrant, EW2, increases in a and b. Thus, an increase in a or b induces the potential entrants to spend more in the first-stage contest, thereby decreasing the incumbents’ winning probability. An increase in m would decrease b in most plausible situations where the greater extent of the entrant’s profit is dissipated in the second stage with more potential entrants. Thus, it would also decrease rent-seeking efforts of the potential entrants in the first stage, thereby increasing the incumbents’ winning probability. The effect of an increase in n cannot be easily determined, however. With more incumbents, the entry-blocking activity of the incumbents would decline. This is because the profit differential tends to decrease in n, lowering the incentives of the incumbents to block entry. However, the increase in n would also reduce the incentives of the potential entrants in most circumstances as abj(n,k) tends to decrease in n. Thus, the net effect of an increase in n on the equilibrium probability of entry blocking cannot be determined a priori. 3.2.2. Case 2: well-organized incumbents vs. well-organized potential entrants We now consider the first-stage contest when the two groups are organized well. In this case, each group behaves as a cartel. The incumbents jointly solve: X Max V ¼ PX nPðnÞ þ ð1 PX ÞnPðn; kÞ X i i X
¼ PX nDPk þ nPðn; kÞ X
ð15Þ
Note that the incumbents try to maximize the joint profit differentials, nDPk. Similarly, the objective of the cartel of the potential entrants is X Max Wk ¼ PY mabPðn; kÞ Y ð16Þ k Y
The first-order conditions to Eqs. (15) and (16) are, respectively, given by X B V BX ¼ nY DPk =ðX þ Y Þ2 1 ¼ 0; i i B
X
Wk k
BY ¼ XmabPðn; kÞ=ðX þ Y Þ2 1 ¼ 0;
ð17Þ
ð18Þ
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Simultaneous solution of Eqs. (17) and (18) gives X C ¼ abmn2 Pðn; kÞðDPk Þ2 =½nDPk þ mabPðn; kÞ2 ;
ð19Þ
Y C ¼ m2 na2 b2 ðPðn; kÞÞ2 DPk =½nDPk þ mabPðn; kÞ2 and
ð20Þ
X C þ Y C ¼ mnabPðn; kÞDPk =½nDPk þ mabPðn; kÞ:
ð21Þ
The superscript C indicates that X C and Y C are the solutions for the collusive case. Comparing X C + Y C in Eq. (21) with X N + Y N in Eq. (13), it is easy to find that X C + Y C z X N + Y N, where the equality holds only when m = n = 1. Substituting X C and Y C into PX and PY , the equilibrium probability of each group’s winning is obtained. Lemma 2. When the incumbents and the potential entrants collude, respectively, in the entry contest, the equilibrium probability of each group’s winning is, respectively PXC = nDPk /[nDPk + mabP(n,k)], PYC = mabP(n,k)/[nDPk + mabP(n,k)]. From Lemma 2 and Eq. (21), we find that X C + Y C = PYCnDPk. The following comparative static results are also obtained. BPXC =Ba < 0 and BPXC =Bb < 0:
ð22Þ
These inequalities are qualitatively the same as those in Eq. (14). The effect of an increase in m cannot be easily determined. If b decreases in m fast enough, however, then an increase in m increases the winning probability of the incumbents. For example, when k = 1 and P2j is given by a logit-form function as PX in Eq. (4), then b = 1/m2. In this case, an increase in m increases PXC. If the government distributes the licenses randomly, then a change in m has no effect on PXC since b = k/m and mabP(n,k) (= kaP(n,k)) is not affected by m. 3.2.3. Case 3: collusive incumbents vs. non-cooperative potential entrants In this, case the incumbents are organized well while the potential entrants adopt a noncooperative Nash strategy. The incumbents jointly determine the level of contribution to entry-blocking activity. They solve the following problem: Max
X i
Vi ¼ PX nPðnÞ þ ð1 PX ÞnPðn; kÞ X
X
¼ PX nDPk þ nPðn; kÞ X
ð15Þ
Note that the incumbents try to maximize the joint profit differentials, nDPk as in Case 2.
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Each potential entrant determines the level of his or her own contribution, employing a non-cooperative Nash strategy. The objective of the risk-neutral potential entrant j is Max Wj ¼ PY ½abPðn; kÞ yj ; for k ¼ 1; . . . ; m:
ð8Þ
yj
which is the same as in Case 1. The first-order conditions are given by X
BX ¼ nY DPk =ðX þ Y Þ2 1 ¼ 0;
ð17Þ
BWj =Byj ¼ X abPðn; kÞ=ðX þ Y Þ2 1 ¼ 0; for j ¼ 1; . . . ; m:
ð10Þ
B
V i i
Simultaneous solution of Eqs. (10) and (17) gives X M ¼ n2 abPðn; kÞðDPk Þ2 =½nDPk þ abPðn; kÞ2 ;
ð23Þ
Y M ¼ na2 b2 DPk ðPðn; kÞÞ2 =½nDPk þ abPðn; kÞ2 and
ð24Þ
X M þ Y M ¼ nabPðn; kÞDPk =½nDPk þ abPðn; kÞ:
ð25Þ
The superscript M indicates that X M and Y M are the solutions for the mixed case. Substituting X M and Y M into PX and PY, the equilibrium probability of each group’s winning is obtained. Lemma 3. When the incumbents collude and the potential entrants employ a noncooperative Nash strategy, the equilibrium probability of each group’s winning is, respectively, PXM = nDPk /[nDPk + abP(n,k)], PYM = abP(n,k)/[nDPk + abP(n,k)]. As in the collusive case, we find that X M + Y M = PYMnDPk. From Lemma 3, the following comparative static results are easily obtained. BPXM =Ba < 0 and BPXM =Bb < 0:
ð26Þ
These inequalities are qualitatively the same as those in Eqs. (14) and (22). An increase in a or b would decrease the winning probability of the incumbents. An increase in m would decrease b, and thus increase the winning probability of the incumbents. The effect of an increase in the number of incumbents cannot be determined. The three cases, Lemmas 1– 3, are now compared with one another to find out when the incumbents are more likely to win. The result is reported in Lemma 4. Lemma 4. (1) If n>m, then PXM z PXC>PXN, where the first equality holds when m = 1. (2) If n = m, then PXM z PXC = PXN, where the first equality holds when m = n = 1. (3) If n < m, PXM z PXN>PXC, where the first equality holds when n = 1.
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Note that Lemma 4 is obtained without any restrictions on demand and the behavior of firms in oligopoly. When n>m, the incumbents are more susceptible to the free-rider problem than the potential entrants. In this case, the incumbents are more likely to win in the collusive case than in the non-cooperative Nash case, since collusion can mitigate the free-rider problem effectively. The analysis in this section shows that complete deregulation is not likely to occur. Complete deregulation corresponds to the case in which the government sets the largest number of k that satisfies the non-negativity constraint of the entrant, i.e., abj(n,k) z 0. In this case, the profits of the incumbents and the new entrants are driven very close to zero. The difference in the profits of the incumbents, DPk, would be greater in the case of complete deregulation than in the case of partial deregulation. Therefore, the incumbents would spend more on rent seeking than in the case of partial deregulation examined in this section. Moreover, in case of complete deregulation, the potential entrants have little incentive to spend on rent seeking, since profits after complete deregulation are very close to zero. As a result, the incumbents are likely to win the contest. That is, complete deregulation is very unlikely to occur.
4. Social benefit and the cost of entry contests We now examine the effect of entry contest on expected social benefit. When the incumbents win, the market structure remains the same. Ex post social benefit decreases by the wasted portion of the first-stage expenditures on entry contest. When the potential entrants win, they expend resources to win the licenses. However, consumer surplus increases due to an increase in output. In this case, the change in social benefit, ignoring the first-stage rent-seeking expenditures, is given by DSW ¼ ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ ½CSðnÞ þ nPðnÞ:
ð27Þ
Note that the second-stage expenditure on rent seeking is taken into account in DSW. If there is no second-stage contest, then DSW is equal to the conventional change in social benefit resulting from the entry of firm(s). Moreover, if we adopt the model of Berry (1993) so that b =(mk m + k)/m2, then it is easy to find that DSW is decreasing in m since mb= (k 1) + k/m. This result can be explained as follows. With a smaller number of potential entrants, the second-stage rent seeking is mitigated to a large extent. This increases the expected payoff to the potential entrants. The expected social benefit E(SW) is given by EðSWÞ ¼ PX ½SWðnÞ rðX þ Y Þ þ ð1 PX Þ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ rðX þ Y Þ ¼ PX SWðnÞ þ ð1 PX Þ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ rðX þ Y Þ: ð28Þ Notice that E(SW) takes suitably into account the second-stage rent-seeking expenditures and the increase in consumer surplus. We now calculate the expected social benefit
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E(SW) in the non-cooperative Nash case, the collusive case and the mixed case, respectively. E(SWN) in the non-cooperative Nash case is given by EðSWN Þ ¼ PXN SWðnÞ þ ð1 PXN Þ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ rðX N þ Y N Þ; where the superscript N is used to denote the non-cooperative Nash case. Compare E(SWN) with the social benefit SW(n) ( = CS(n) + nP(n)). It is easy to find that EðSWN Þzð<ÞSWðnÞ
ð29 1Þ
Zð1 PXN ÞDSW zð<ÞrðX N þ Y N Þ
ð29 2Þ
ZDSW zð<ÞrDPk :
ð29 3Þ
(Lemma 1 and Eq. (13)). With the entry contest, the condition under which social benefit increases becomes more stringent. The inequality (29-2) compares the expected benefit of the entry contest with the social cost of entry contest. The term (1PXN)DSW in Eq. (29-2) is the expected increase in social benefit, whereas r(XN+YN) is the social cost of entry contest. Only when DSW is greater than r proportion of the incumbent’s profit differential does the entry contest increase social benefit (Eq. (29-3)). The higher is r, the less likely is it that the entry contest increases expected social benefit. When r=0, the inequalities (29-1), (29-2) and (29-3) are equivalent to the condition that entry of firms increases social benefit, as in Mankiw and Whinston (1986). For the collusive case, straightforward calculation, utilizing Lemma 2 and Eq. (21), gives EðSW C Þzð<ÞSWðnÞ
ð30 1Þ
Zð1 PXC ÞDSW zð<ÞrðX C þ Y C Þ
ð30 2Þ
ZDSW zð<ÞrnDPk :
ð30 3Þ
In the collusive case, the condition under which the entry contest increases social benefit becomes more stringent than in the non-cooperative Nash case. This is so because the incumbents and the potential entrants are more heavily engaged in the entry contest in the collusive case than in the non-cooperative Nash case. Thus, collusion in entry contest as well as that in the output market is harmful to society.
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For the mixed case, we obtain EðSWM Þzð<ÞSWðnÞ
ð31 1Þ
Zð1 PXM ÞDSW zð<ÞrðX M þ Y M Þ
ð31 2Þ
ZDSW zð<ÞrnDPk :
ð31 3Þ
Note that Eqs. (31-1) –(31-3) is equivalent to Eqs. (30-1) – (30-3). We summarize the 29-1) (29-2) (29-3), (30-1) (30-2) (30-3) and (31-1) (31-2) (31-3) by Proposition 1. If DSW < rDPk , the partial deregulation of entry barriers laden with rent seeking decreases expected social benefit. (2) If rDPk < DSW < rnDPk , the partial deregulation increases expected social benefit when the incumbents employ a noncooperative Nash strategy, and decreases expected social benefit when the incumbents collude in entry contest. (3) If DSW >rnDPk , the partial deregulation increases expected social benefit. It is well known in the literature on excessive entry that there are circumstances in which entry of firms decreases social benefit. The above proposition shows that the entry contest enlarges the set of circumstances where entry of firms is socially harmful. If DSW>0, then the entry of firms increases social benefit when there is no rent seeking. With rent seeking in the deregulation process, the entry of firms increases social benefit only when the increase in conventional social benefit, DSW, is greater than the threshold level. For a given k, a decrease in m increases DSW, thereby making it more likely that deregulation is socially beneficial. The threshold level increases in r, the extent of wastefulness of rent-seeking expenditures. The higher is r, the more likely is it that partial deregulation laden with rent seeking decreases social benefit. The threshold level also increases in the incumbent’s profit differential, DPk. Moreover, the threshold level in the collusive rent seeking case is higher than the threshold level when the incumbents employ the non-cooperative Nash strategy in rent seeking. In a nutshell, the entry contest makes it less likely that entry of firms increases social welfare. If the increase in social benefit is very large, however, the partial deregulation laden with heavy rent seeking can still increase social benefit. This result is in contrast with that of Kang and Lee (2001) who examine entry contests in a Cournot oligopoly with a linear demand. Focusing on the case of single issuance, they show that the entry contest always decreases social benefit. Unlike Kang and Lee (2001), the above proposition shows that deregulation can increase social benefit under some circumstances. Thus, the result of Kang and Lee (2001) is shown to stem from specific assumptions of their model. Poitras and Sutter (2000) show that welfare gains over the status quo exist whenever deregulation occurs. The difference between the above proposition and their result stems from several differences in the modeling of the deregulation process. Firstly, the model in the present paper considers the contest between incumbents and potential entrants while
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Poitras and Sutter (2000) consider the contest between the monopolist and the reformer who represents consumers. Secondly, we have considered essentially a single-stage game while Poitras and Sutter (2000) consider a two-period dynamic process. Thirdly, the model in the present paper considers oligopoly while their model is focused on monopoly. Finally, the scope of deregulation is different between the present paper and Poitras and Sutter (2000). The present paper examines partial deregulation, the limit of which corresponds to complete deregulation examined by Poitras and Sutter (2000).
5. Concluding remarks We have examined entry contests in oligopoly with regulatory barriers to entry. The paper has derived conditions under which the partial deregulation of entry barriers laden with rent seeking decreases or increases expected social benefit for a general demand function. We have shown that entry deregulation is more likely to be socially beneficial when the incumbents employ a non-cooperative Nash strategy in rent seeking and when the decrease in profits of the incumbents caused by entry is small. We have also shown that entry deregulation alone does not guarantee an increase in social benefit if a rent-seeking contest takes place between incumbents and potential entrants. Our analysis serves, at least, as a counter-example to the assertion that partial deregulation always increases social benefit. Through careful design of deregulation processes, however, the reformer can reduce the extent of rent seeking. For example, in the USA, some of new licenses are auctioned off. This could reduce the rent-seeking losses in the second stage. Still, the change of regulation regime might incur some costs. An interesting issue not dealt with in this paper is the optimal competition policy of the government. The government may determine the number of entrants, k, with which the increase in expected social benefit is maximized. The larger the value of k, the greater is the increase in social benefit if the deregulation succeeds. The larger the value of k, however, the higher the probability that the deregulation attempt fails. The optimal competition policy should balance these offsetting effects.
Acknowledgements For their helpful comments and suggestions, we would like to thank an anonymous referee, an editor and participants of seminars at Kookmin University and the annual meeting of Korea International Economic Association. Financial support from Korea Research Foundation is gratefully acknowledged (KRF-2001-041-C00240). The usual disclaimer applies.
References Baik, K.H., Lee, S., 2000. Two-stage rent-seeking contests with carryovers. Public Choice 103, 285 – 296. Berry, S.K., 1993. Rent-seeking with multiple winners. Public Choice 77, 437 – 443.
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Crew, M.A., Rowley, C.K., 1986. Deregulation as an instrument in industrial policy. Journal of Institutional and Theoretical Economics 142, 52 – 70. Crew, M.A., Rowley, C.K., 1988. Dispelling the disinterest in deregulation. In: Rowley, C.K., Tollison, R.D., Tullock, G. (Eds.), The Political Economy of Rent Seeking. Kluwer, Boston, MA, USA, pp. 163 – 178. Ellingsen, T., 1991. Strategic buyers and the social cost of monopoly. American Economic Review 81, 648 – 657. Higgins, R.S., Shughart II, W.F., Tollison, R.D., 1985. Free entry and efficient rent-seeking. Public Choice 46, 247 – 258. Hillman, A.L., Riley, J.G., 1989. Politically contestable rents and transfers. Economics and Politics 1, 17 – 39. Kang, J.H., Lee, S., 2001. The social cost of entry contest in Cournot-Nash oligopoly. Journal of Economics and Business 53, 139 – 152. Katz, E., Tokatlidu, J., 1996. Group competition for rents. European Journal of Political Economy 12, 599 – 607. Lee, S., 1993. Inter-group competition for a pure private rent. Quarterly Review of Economics and Finance 33, 261 – 266. Lee, S., 1995. Endogenous sharing rules in collective-group rent-seeking. Public Choice 85, 31 – 44. Mankiw, N.G., Whinston, M.D., 1986. Free entry and social inefficiency. Rand Journal of Economics 17, 48 – 58. McCormick, R.E., Shughart II, W.F., Tollison, R.D., 1984. The disinterest in deregulation. American Economic Review 74, 1075 – 1079. Ministry of Information and Communication of Korea, 1998. White Paper. Seoul. Nachbar, J.H., Petersen, B., Hwang, I., 1998. Sunk costs, accommodation, and the welfare effects of entry. Journal of Industrial Economics 46, 317 – 332. Nitzan, S., 1991. Collective rent dissipation. Economic Journal 101, 1522 – 1534. Poitras, M., Sutter, D., 1997. The efficiency gains from deregulation. Journal of Regulatory Economics 12, 81 – 89. Poitras, M., Sutter, D., 2000. Enhancing efficiency or crying over spilled milk: the benefits of reform. Public Choice 105, 23 – 40. Rasmusen, E., Zupan, M., 1991. Extending the economic theory of regulation to the form of policy. Public Choice 72, 167 – 191. Tullock, G., 1980. Efficient rent seeking. In: Buchanan, J.M., Tollison, R.D., Tullock, G. (Eds.), Toward a Theory of the Rent-Seeking Society. Texas A&M University Press, College Station, TX, USA, pp. 269 – 282. Wenders, J.T., 1987. On perfect rent dissipation. American Economic Review 77, 456 – 459.
Rent dissipation and social benefit in regulated entry contests Sanghack Lee a,*, Kiwoong Cheong b a
School of Economics, Kookmin University, Seoul 136-702, South Korea School of Business, Keimyung University, Taegu 704-701, South Korea
b
Received 21 September 2003; received in revised form 2 April 2004; accepted 16 April 2004 Available online 30 July 2004
Abstract This paper examines entry contests in oligopoly with regulatory barriers to entry when government seeks to issue additional licenses. The entry contests are modeled as a two-stage rentseeking game between incumbents and potential entrants, with incumbents opposing issuance of additional licenses while the potential entrants try to obtain them. We derive conditions under which the resources expended in the entry contest exceed or fall short of the expected increase in social benefit. Entry deregulation is more likely to increase expected social benefit when incumbents employ a non-cooperative Nash strategy in rent seeking than when they collude. D 2004 Elsevier B.V. All rights reserved. JEL classification: D72; D73; L13 Keywords: Entry barrier; Entry contest; Rent seeking; Partial deregulation
1. Introduction This paper considers entry contests in oligopoly with regulatory barriers to entry. The contests are between incumbents and potential entrants when government seeks to partially deregulate entry barriers by issuing additional licenses. We derive conditions under which the partial deregulation of entry barriers laden with rent seeking increases or decreases expected social benefit. The entry deregulation is more likely to increase social benefit when the incumbents employ a non-cooperative Nash strategy in rent seeking than when they collude. * Corresponding author. Tel.: +82-2-910-4546; fax: +82-2-910-4519. E-mail address: [email protected] (S. Lee). 0176-2680/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejpoleco.2004.04.001
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Deregulation of entry barriers is an important issue in the literature of regulation. Indeed, entry barriers are the regulatory form preferred by incumbents (Rasmusen and Zupan, 1991). Economists usually support unlimited entry of new firms into oligopolies. However, many papers show that there are circumstances in which entry of firms decreases social benefit. Mankiw and Whinston (1986) find that excessive entry is likely to occur when there are setup costs and firms enter the industry simultaneously. Nachbar et al. (1998) examine the effects of entry in a Cournot oligopoly when some of incumbents’ costs are sunk. They find that a small portion of sunk costs can reverse a welfare assessment in cases where entry reduces social benefit. Several papers have previously examined the social benefit effects of deregulation. McCormick et al. (1984) propose that the gains from deregulation of monopoly are much lower than those conventionally thought if the initial effort to establish monopoly has dissipated the monopoly profit. Their argument is labeled the ‘‘disinterest in deregulation’’ proposition. Crew and Rowley (1986, 1988) and Poitras and Sutter (1997, 2000) show that the ‘‘disinterest in deregulation’’ proposition holds only when the deregulation is unanticipated. In particular, Poitras and Sutter (1997) analyze the efficiency gains from deregulation of monopolies when reformers expend resources to secure deregulation and the monopolist expends resources to maintain the status quo. They find that the potential welfare gains of deregulation exceed the cost of deregulation. However, their analysis is limited to complete deregulation of entry into the industry. In more realistic circumstances, governments might allow for entry of a limited number of additional firms instead of completely dismantling the entry barriers. Poitras and Sutter (2000) examine the welfare gains from the reform of distortions induced by government. They show that the welfare gains of reform over the status quo exist whenever deregulation occurs. Governments are not likely to take away licenses already given to firms in regulated industries. However, they can issue more licenses to potential entrants. Indeed, many governments have issued licenses to potential entrants to the provision of telecommunication services, which had previously been viewed as a natural monopoly. This has raised a conflict of interest between the incumbent monopolists and potential entrants.1 Quite naturally, the incumbents try to maintain the status quo while the potential entrants try to induce the government to issue more licenses. The deregulation process in such a situation can be modeled as a contest. Poitras and Sutter (1997, 2000) model the deregulation process as a contest between the monopolist and the reformer. As in Kang and Lee (2001), we model the deregulation process as a two-stage game between incumbents and potential entrants in oligopoly. In the first stage, the group of potential entrants competes against the group of incumbents to secure entry licenses. We allow for issuance of an arbitrary number of licenses. If the incumbents win, the regulation
1 For example, the Korean government has recently issued licenses to new entrants in telecommunication service industries and broadcasting industries. The state-run Korea Telecom was the only supplier of telephone services until the late 1980s in Korea. Competition was first introduced in 1990 with the entry of DACOM into the international telephone service market. The Ministry of Information and Communication of Korea introduced competition in the cellular phone service market in 1994 and in the long distance telephone service market in 1995, respectively. For a detailed explanation, see the White Paper (1998) of the Ministry of Information and Communication of Korea.
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regime remains the same. If the potential entrants win in the first stage, however, the second-stage contest takes place between the potential entrants to obtain the licenses.2 We do not adopt any specific assumptions on the behavior of firms and demand conditions, whereas Kang and Lee (2001) examine a Cournot oligopoly with a linear demand and identical costs. Our results stand in sharp contrast with those of Kang and Lee (2001). The paper is organized as follows. Section 2 sets out the basic model. Section 3 analyzes the contest between the incumbents and the potential entrants. We consider three kinds of interaction between incumbents and potential entrants. In the first case, firms adopt a non-cooperative Nash strategy in the entry contest. In the second case, firms collude within their respective groups. In the third case, incumbents collude while potential entrants adopt a non-cooperative Nash strategy. We find that the firms expend more on rent seeking when they collude than when they employ a non-cooperative Nash strategy. We also show that complete deregulation is hard to obtain. Section 4 examines the effect of the entry contest on expected social benefit. We derive conditions under which the resources expended in the entry contest exceed or fall short of the expected increase in social benefit. We show that the entry deregulation is likely to increase social benefit when the incumbents employ a non-cooperative Nash strategy in rent seeking and when the decrease in profits of the incumbents caused by entry is small. Section 5 offers concluding remarks.
2. Oligopoly with regulatory barriers to entry Consider an oligopoly consisting of n (identical) incumbent firms with regulatory barriers to entry.3 There are m potential entrants, where m ( z 1) is exogenously given.4 Government may issue k more license(s) to the potential entrants, where 1 V k V m. The firms produce a homogeneous product. Production takes place only once.5 The inverse
2 Examples of such contests can be found in utility rate hearings. Regarding these, Wenders (1987, p. 457) notes that: ‘‘Various consumer groups initially present a united front, often with explicit cooperation, in trying to keep the allowed increase in utility revenues as small as possible. However, once the allowed revenue increase is set by the commission, the various consumer groups turn on one another and try to deflect as much of the increase as possible to others. Lions and wolves cooperate in the hunt, but scrap over the kill.’’ Thus, Wenders (1987) recognizes the possibility of rent-defending activity by consumers. However, his analysis ignores the effect of consumer expenditures on the behavior of the other participants. Building on Hillman and Riley (1989), Ellingsen (1991) derives conditions under which consumer participation in a rent-seeking game is socially beneficial. 3 In the present paper, we simply take the oligopoly structure, i.e., the number of firms, as given. Thus, we abstract from the question of how and why government has issued n licenses. McCormick et al. (1984) and Poitras and Sutter (1997, 2000) assume that government has issued a single license. 4 The number of potential entrants, m, can be endogenously determined following Higgins et al. (1985). The first-stage in their model is the qualifying contest. In the second stage, the qualified bidders compete for the monopoly franchise. We thank the anonymous referee for introducing the paper to us. Another interesting possibility noted by the referee is that ‘‘government also determines m by requiring potential entrants to ‘prequalify’ to compete for service provision rights.’’ 5 In focusing on a single-period model, we assume away problems associated with multi-period models, one of which is whether oligopoly is contestable or not. Several papers deal with issues related to deregulation in multi-period models. See Crew and Rowley (1986, 1988) and Poitras and Sutter (1997, 2000).
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demand function for the product is denoted g( Q), where Q is the aggregate output of the industry and gV( Q) < 0. The incumbents and potential entrants have the same variable cost function given by c( q), where q is each firm’s output. The profit of each incumbent with no entry is denoted P(n). With n incumbents and k entrants, the profit of a representative incumbent is denoted P(n,k), given by Pðn; kÞ ¼ PðQÞq cðqÞ F;
ð1Þ
where F is the fixed cost. For simplicity, we assume that F is sunk so that it does not affect firms’ output decision. Each entrant’s cost function is given by c( q) + Fe, where Fe denotes the fixed cost. Note that each entrant is assumed to possess the same cost function as the incumbents except for the fixed cost.6 Thus, if the entrant’s fixed cost is smaller than the incumbents’, then the entrants are more efficient than the incumbents and vice versa. The representative entrant’s profit Pe(n,k) can be expressed as a proportion of each incumbent’s profit, Pe ðn; kÞ ¼ aPðn; kÞ; where 0 V a. Of course, a is related to the size of Fe relative to F. If F > Fe, then a >1 and vice versa. We impose no specific restrictions on behavior of firms. However, both the behavior of firms and the demand and cost conditions are assumed to yield positive outputs and nonnegative profits for all the incumbents and entrants. Social benefit is measured by the sum of aggregate profits and consumer surplus. The consumer surplus in the case without entry is denoted, CSðnÞ ¼
Z
gðqÞdq gðQÞQ;
ð2Þ
where Q is the industry output. In the case of no entry, social benefit is denoted SW(n), and is given by SW(n) = CS(n) + nP(n,k). With entry of k firms, social benefit SW(n,k) is given by SWðn; kÞ ¼ CSðn; kÞ þ nPðn; kÞ þ kPe ðn; kÞ ¼ CSðn; kÞ þ ðn þ kaÞPðn; kÞ;
ð3Þ
where CS(n,k) denotes consumer surplus with n incumbents and k entrants. If SW(n,k)> SW(n), then entry of k firms increases social benefit if there is no cost associated with deregulation of entry barriers. However, rent-seeking costs are likely to be incurred in the process of entry.
6 This assumption is adopted so that new entrants produce the same quantity as the incumbents. The only difference between the incumbents and the new entrants is the size of fixed costs. This assumption can be relaxed without affecting the qualitative results.
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3. Entry contests This section examines the contest over partial deregulation of entry barriers. Government deliberates on issuing k more licenses to m potential entrants.7 Following Katz and Tokatlidu (1996) and Kang and Lee (2001), we model the entry contest as a two-stage game as follows. In the first stage, group of incumbents and group of potential entrants compete over entry of firms.8 Unlike Ellingsen (1991) and Poitras and Sutter (1997, 2000), consumers have no influence on the deregulation process. If the incumbents win, the regulation regime remains the same with no more licenses being issued. If the potential entrants win, all of them become eligible for the entry licenses. In the second stage, they compete with one another for the licenses. For each incumbent firm, the prize of the contest is the profit differential secured by maintaining the status quo. With k entrants, each incumbent’s profit decreases by DPk(n,k) (u P(n) P(n,k)). In other words, DPk (n,k) denotes the benefit to each incumbent firm of maintaining the status quo. Note that the sign of DPk is the opposite of conventional differential P(n,k) P(n). Where no confusion arises, the arguments of DPk(n,k) will be omitted. For each potential entrant, the prize of the first-stage contest is the expected benefit of participation in the second-stage contest for the licenses. The incumbent firm i contributes xi to entry-preventing activity, for i = 1,. . .,n. The potential entrant j contributes yj to entry-promoting activity, for j = 1,. . .,m. Following Tullock (1980), the probability that the incumbents succeed in entry blocking, PX, is given by a logit-form function of the aggregate outlays of the two groups: PX ¼ X =ðX þ Y Þ;
ð4Þ
where X (= Sixi) and Y (= Sk yk) denote, respectively, the aggregate outlay of the incumbents and the potential entrants. Note that consumers have no influence on the probability. The probability that the government will issue k more licenses is denoted PY (u 1 PX). If the government decides not to issue k more licenses, the contest is over. Social benefit decreases by the amount r(X + Y) where the parameter r, 0 V r V 1, denotes the extent of wastefulness of rent-seeking expenditures. In one extreme case, (X + Y) can be treated as a mere transfer so that r = 0. In the other extreme case, as in the literature on rent seeking, (X + Y) are all wasted so that r = 1. Real circumstances may be somewhere between the two extreme cases, i.e., 0 < r < 1. If the government decides to issue k more licenses, the second-stage contest takes place between the potential entrants. While consumer surplus increases, additional rent-seeking costs are incurred as well. We employ a subgame-perfect equilibrium as a solution concept. As usual, we first examine the second-stage contest. This result is then utilized to analyze the first-stage contest. 7 Government may choose k that maximizes expected social benefit. In the present paper, however, we do not examine how government determines k. For a related discussion, see footnote 4. 8 While we focus on interaction between groups of firms, there can be a variety of deregulatory process scenarios. For example, Poitras and Sutter (1997, 2000) consider interaction between the reformer and the monopolist.
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3.1. Second-stage contest Assume that the government has decided to issue k more licenses to m potential entrants. The government can distribute the licenses in various ways. One simple way is for the government to randomly distribute them to potential entrants. There is no secondstage rent seeking in such a case. Each potential entrant receives the license with probability k/m. Another possible way is that the government distributes them through rent-seeking contests. In this case, the potential entrant j spends y2j to obtain the entry license, for j = 1,. . .,m. The problem of the risk-neutral potential entrant j is: Max P2j aPðn; kÞ y2j ; y2j
ð5Þ
where P2j denotes the probability that potential entrant j receives the license. Following Katz and Tokatlidu (1996), we assume that the first-stage expenditures have no carryover effect on the second-stage probability of winning.9 If m = 1, of course, there is no secondstage contest. If k = 1, the conventional Tullock contest-success-function can be employed. However, if k >1, more specific assumptions should be employed. As one of such models, Berry (1993) offers a model of contest with multiple identical prizes. In the model of Berry (1993), the probability of any particular combination of k potential entrants being given licenses is equal to the sum of rent-seeking expenditures of the potential entrants in that combination divided by the aggregate sum of rent-seeking expenditures in all possible combinations of k potential entrants. Without any specific assumptions on the way the licenses are distributed, we express the expected benefit of participation in the secondstage contest as a fraction of the entrant’s profit. Let EW2 denote the expected pay-off of the second-stage contest to each potential entrant. Then, EW2 ¼ bPe ðn; kÞ ¼ abPðn; kÞ
ð6Þ
The expression EW2 given in Eq. (6) can encompass a variety of scenarios on the way the licenses are distributed. If we adopt the model of Berry (1993), then b = (mk m + k)/ m2. When k = 1 and P2j is given by a logit-form function as in Eq. (4), then b = 1/m2. If the government distributes the licenses randomly to the potential entrants, each potential entrant has the same chance of obtaining the license so that b = (k/m). 3.2. First-stage contest The first-stage contest between the two groups of firms is now examined. Depending upon institutional setting, there can be a variety of possible interaction between the group of incumbents and the group of potential entrants. We focus on three cases, which seem to 9 In some multi-stage contests, efforts are carried over to next stages in the sense that they are effective in the next stages as well. Baik and Lee (2000) examine the effect of carryovers in a two-stage contest.
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be most plausible.10 In the first case, the firms of the two groups employ, respectively, a non-cooperative Nash strategy when determining their level of contribution to the rentseeking activity of the group. In the second case, both the incumbents and the potential entrants, respectively, collude in rent seeking, each group behaving as a cartel. In the third case, the incumbents collude while the potential entrants employ a non-cooperative Nash strategy. 3.2.1. Case 1: non-cooperative Nash incumbents and potential entrants In this case, both the incumbents and the potential entrants employ a non-cooperative Nash strategy. This assumption is adopted in many papers in the literature on collective rent seeking. See, for example, Katz and Tokatlidu (1996), Lee (1993, 1995) and Nitzan (1991). The objective of the risk-neutral incumbent firm i is: Max Vi ¼ PX PðnÞ þ ð1 PX ÞPðn; kÞ xi ; xi
for i ¼ 1; . . . ; n:
ð7Þ
Similarly, the objective of the risk-neutral potential entrant j is Max Wj ¼ PY ½abPðn; kÞ yj ; yj
for k ¼ 1; . . . ; m:
ð8Þ
The first-order conditions for Eqs. (7) and (8) are, respectively: BVi =Bxi ¼ Y DPk =ðX þ Y Þ2 1 ¼ 0;
for i ¼ 1; . . . ; n:
BWj =Byj ¼ X abPðn; kÞ=ðX þ Y Þ2 1 ¼ 0;
for j ¼ 1; . . . ; m:
ð9Þ ð10Þ
Simultaneous solution of Eqs. (9) and (10) gives X N ¼ abPðn; kÞðDPk Þ2 =½DPk þ abPðn; kÞ2 ;
ð11Þ
Y N ¼ a2 b2 DPk ðPðn; kÞÞ2 =½DPk þ abPðn; kÞ2 and
ð12Þ
X N þ Y N ¼ abPðn; kÞDPk =½DPk þ abPðn; kÞ:
ð13Þ
The superscript N indicates that X N and Y N are the solutions for the non-cooperative Nash equilibrium. Substituting X N and Y N into PX and PY , the equilibrium probability of each group’s winning is obtained.
10
Real-world circumstances may be expressed as a combination of the three cases examined in this paper.
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Lemma 1. If the incumbents and the potential entrants employ a non-cooperative Nash strategy in the entry contest, the equilibrium probability of each group’s winning is, respectively, given by PXN = DPk /[DPk + abP(n,k)], PYN = abP(n,k)/[DPk + abP(n,k)]. Note that Lemma 1 holds regardless of the form of oligopoly and demand conditions. From Lemma 1 and Eq. (13), we find that X N + Y N = P YN DPk . The larger the profit differential DPk, the higher is the probability of winning for the incumbents. It is easy to find that BPXN =Ba < 0 and BPXN =Bb < 0:
ð14Þ
These results are in accordance with our intuition. The expected pay-off to each potential entrant, EW2, increases in a and b. Thus, an increase in a or b induces the potential entrants to spend more in the first-stage contest, thereby decreasing the incumbents’ winning probability. An increase in m would decrease b in most plausible situations where the greater extent of the entrant’s profit is dissipated in the second stage with more potential entrants. Thus, it would also decrease rent-seeking efforts of the potential entrants in the first stage, thereby increasing the incumbents’ winning probability. The effect of an increase in n cannot be easily determined, however. With more incumbents, the entry-blocking activity of the incumbents would decline. This is because the profit differential tends to decrease in n, lowering the incentives of the incumbents to block entry. However, the increase in n would also reduce the incentives of the potential entrants in most circumstances as abj(n,k) tends to decrease in n. Thus, the net effect of an increase in n on the equilibrium probability of entry blocking cannot be determined a priori. 3.2.2. Case 2: well-organized incumbents vs. well-organized potential entrants We now consider the first-stage contest when the two groups are organized well. In this case, each group behaves as a cartel. The incumbents jointly solve: X Max V ¼ PX nPðnÞ þ ð1 PX ÞnPðn; kÞ X i i X
¼ PX nDPk þ nPðn; kÞ X
ð15Þ
Note that the incumbents try to maximize the joint profit differentials, nDPk. Similarly, the objective of the cartel of the potential entrants is X Max Wk ¼ PY mabPðn; kÞ Y ð16Þ k Y
The first-order conditions to Eqs. (15) and (16) are, respectively, given by X B V BX ¼ nY DPk =ðX þ Y Þ2 1 ¼ 0; i i B
X
Wk k
BY ¼ XmabPðn; kÞ=ðX þ Y Þ2 1 ¼ 0;
ð17Þ
ð18Þ
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Simultaneous solution of Eqs. (17) and (18) gives X C ¼ abmn2 Pðn; kÞðDPk Þ2 =½nDPk þ mabPðn; kÞ2 ;
ð19Þ
Y C ¼ m2 na2 b2 ðPðn; kÞÞ2 DPk =½nDPk þ mabPðn; kÞ2 and
ð20Þ
X C þ Y C ¼ mnabPðn; kÞDPk =½nDPk þ mabPðn; kÞ:
ð21Þ
The superscript C indicates that X C and Y C are the solutions for the collusive case. Comparing X C + Y C in Eq. (21) with X N + Y N in Eq. (13), it is easy to find that X C + Y C z X N + Y N, where the equality holds only when m = n = 1. Substituting X C and Y C into PX and PY , the equilibrium probability of each group’s winning is obtained. Lemma 2. When the incumbents and the potential entrants collude, respectively, in the entry contest, the equilibrium probability of each group’s winning is, respectively PXC = nDPk /[nDPk + mabP(n,k)], PYC = mabP(n,k)/[nDPk + mabP(n,k)]. From Lemma 2 and Eq. (21), we find that X C + Y C = PYCnDPk. The following comparative static results are also obtained. BPXC =Ba < 0 and BPXC =Bb < 0:
ð22Þ
These inequalities are qualitatively the same as those in Eq. (14). The effect of an increase in m cannot be easily determined. If b decreases in m fast enough, however, then an increase in m increases the winning probability of the incumbents. For example, when k = 1 and P2j is given by a logit-form function as PX in Eq. (4), then b = 1/m2. In this case, an increase in m increases PXC. If the government distributes the licenses randomly, then a change in m has no effect on PXC since b = k/m and mabP(n,k) (= kaP(n,k)) is not affected by m. 3.2.3. Case 3: collusive incumbents vs. non-cooperative potential entrants In this, case the incumbents are organized well while the potential entrants adopt a noncooperative Nash strategy. The incumbents jointly determine the level of contribution to entry-blocking activity. They solve the following problem: Max
X i
Vi ¼ PX nPðnÞ þ ð1 PX ÞnPðn; kÞ X
X
¼ PX nDPk þ nPðn; kÞ X
ð15Þ
Note that the incumbents try to maximize the joint profit differentials, nDPk as in Case 2.
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Each potential entrant determines the level of his or her own contribution, employing a non-cooperative Nash strategy. The objective of the risk-neutral potential entrant j is Max Wj ¼ PY ½abPðn; kÞ yj ; for k ¼ 1; . . . ; m:
ð8Þ
yj
which is the same as in Case 1. The first-order conditions are given by X
BX ¼ nY DPk =ðX þ Y Þ2 1 ¼ 0;
ð17Þ
BWj =Byj ¼ X abPðn; kÞ=ðX þ Y Þ2 1 ¼ 0; for j ¼ 1; . . . ; m:
ð10Þ
B
V i i
Simultaneous solution of Eqs. (10) and (17) gives X M ¼ n2 abPðn; kÞðDPk Þ2 =½nDPk þ abPðn; kÞ2 ;
ð23Þ
Y M ¼ na2 b2 DPk ðPðn; kÞÞ2 =½nDPk þ abPðn; kÞ2 and
ð24Þ
X M þ Y M ¼ nabPðn; kÞDPk =½nDPk þ abPðn; kÞ:
ð25Þ
The superscript M indicates that X M and Y M are the solutions for the mixed case. Substituting X M and Y M into PX and PY, the equilibrium probability of each group’s winning is obtained. Lemma 3. When the incumbents collude and the potential entrants employ a noncooperative Nash strategy, the equilibrium probability of each group’s winning is, respectively, PXM = nDPk /[nDPk + abP(n,k)], PYM = abP(n,k)/[nDPk + abP(n,k)]. As in the collusive case, we find that X M + Y M = PYMnDPk. From Lemma 3, the following comparative static results are easily obtained. BPXM =Ba < 0 and BPXM =Bb < 0:
ð26Þ
These inequalities are qualitatively the same as those in Eqs. (14) and (22). An increase in a or b would decrease the winning probability of the incumbents. An increase in m would decrease b, and thus increase the winning probability of the incumbents. The effect of an increase in the number of incumbents cannot be determined. The three cases, Lemmas 1– 3, are now compared with one another to find out when the incumbents are more likely to win. The result is reported in Lemma 4. Lemma 4. (1) If n>m, then PXM z PXC>PXN, where the first equality holds when m = 1. (2) If n = m, then PXM z PXC = PXN, where the first equality holds when m = n = 1. (3) If n < m, PXM z PXN>PXC, where the first equality holds when n = 1.
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Note that Lemma 4 is obtained without any restrictions on demand and the behavior of firms in oligopoly. When n>m, the incumbents are more susceptible to the free-rider problem than the potential entrants. In this case, the incumbents are more likely to win in the collusive case than in the non-cooperative Nash case, since collusion can mitigate the free-rider problem effectively. The analysis in this section shows that complete deregulation is not likely to occur. Complete deregulation corresponds to the case in which the government sets the largest number of k that satisfies the non-negativity constraint of the entrant, i.e., abj(n,k) z 0. In this case, the profits of the incumbents and the new entrants are driven very close to zero. The difference in the profits of the incumbents, DPk, would be greater in the case of complete deregulation than in the case of partial deregulation. Therefore, the incumbents would spend more on rent seeking than in the case of partial deregulation examined in this section. Moreover, in case of complete deregulation, the potential entrants have little incentive to spend on rent seeking, since profits after complete deregulation are very close to zero. As a result, the incumbents are likely to win the contest. That is, complete deregulation is very unlikely to occur.
4. Social benefit and the cost of entry contests We now examine the effect of entry contest on expected social benefit. When the incumbents win, the market structure remains the same. Ex post social benefit decreases by the wasted portion of the first-stage expenditures on entry contest. When the potential entrants win, they expend resources to win the licenses. However, consumer surplus increases due to an increase in output. In this case, the change in social benefit, ignoring the first-stage rent-seeking expenditures, is given by DSW ¼ ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ ½CSðnÞ þ nPðnÞ:
ð27Þ
Note that the second-stage expenditure on rent seeking is taken into account in DSW. If there is no second-stage contest, then DSW is equal to the conventional change in social benefit resulting from the entry of firm(s). Moreover, if we adopt the model of Berry (1993) so that b =(mk m + k)/m2, then it is easy to find that DSW is decreasing in m since mb= (k 1) + k/m. This result can be explained as follows. With a smaller number of potential entrants, the second-stage rent seeking is mitigated to a large extent. This increases the expected payoff to the potential entrants. The expected social benefit E(SW) is given by EðSWÞ ¼ PX ½SWðnÞ rðX þ Y Þ þ ð1 PX Þ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ rðX þ Y Þ ¼ PX SWðnÞ þ ð1 PX Þ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ rðX þ Y Þ: ð28Þ Notice that E(SW) takes suitably into account the second-stage rent-seeking expenditures and the increase in consumer surplus. We now calculate the expected social benefit
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E(SW) in the non-cooperative Nash case, the collusive case and the mixed case, respectively. E(SWN) in the non-cooperative Nash case is given by EðSWN Þ ¼ PXN SWðnÞ þ ð1 PXN Þ½CSðn; kÞ þ ðn þ mabÞPðn; kÞ rðX N þ Y N Þ; where the superscript N is used to denote the non-cooperative Nash case. Compare E(SWN) with the social benefit SW(n) ( = CS(n) + nP(n)). It is easy to find that EðSWN Þzð<ÞSWðnÞ
ð29 1Þ
Zð1 PXN ÞDSW zð<ÞrðX N þ Y N Þ
ð29 2Þ
ZDSW zð<ÞrDPk :
ð29 3Þ
(Lemma 1 and Eq. (13)). With the entry contest, the condition under which social benefit increases becomes more stringent. The inequality (29-2) compares the expected benefit of the entry contest with the social cost of entry contest. The term (1PXN)DSW in Eq. (29-2) is the expected increase in social benefit, whereas r(XN+YN) is the social cost of entry contest. Only when DSW is greater than r proportion of the incumbent’s profit differential does the entry contest increase social benefit (Eq. (29-3)). The higher is r, the less likely is it that the entry contest increases expected social benefit. When r=0, the inequalities (29-1), (29-2) and (29-3) are equivalent to the condition that entry of firms increases social benefit, as in Mankiw and Whinston (1986). For the collusive case, straightforward calculation, utilizing Lemma 2 and Eq. (21), gives EðSW C Þzð<ÞSWðnÞ
ð30 1Þ
Zð1 PXC ÞDSW zð<ÞrðX C þ Y C Þ
ð30 2Þ
ZDSW zð<ÞrnDPk :
ð30 3Þ
In the collusive case, the condition under which the entry contest increases social benefit becomes more stringent than in the non-cooperative Nash case. This is so because the incumbents and the potential entrants are more heavily engaged in the entry contest in the collusive case than in the non-cooperative Nash case. Thus, collusion in entry contest as well as that in the output market is harmful to society.
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For the mixed case, we obtain EðSWM Þzð<ÞSWðnÞ
ð31 1Þ
Zð1 PXM ÞDSW zð<ÞrðX M þ Y M Þ
ð31 2Þ
ZDSW zð<ÞrnDPk :
ð31 3Þ
Note that Eqs. (31-1) –(31-3) is equivalent to Eqs. (30-1) – (30-3). We summarize the 29-1) (29-2) (29-3), (30-1) (30-2) (30-3) and (31-1) (31-2) (31-3) by Proposition 1. If DSW < rDPk , the partial deregulation of entry barriers laden with rent seeking decreases expected social benefit. (2) If rDPk < DSW < rnDPk , the partial deregulation increases expected social benefit when the incumbents employ a noncooperative Nash strategy, and decreases expected social benefit when the incumbents collude in entry contest. (3) If DSW >rnDPk , the partial deregulation increases expected social benefit. It is well known in the literature on excessive entry that there are circumstances in which entry of firms decreases social benefit. The above proposition shows that the entry contest enlarges the set of circumstances where entry of firms is socially harmful. If DSW>0, then the entry of firms increases social benefit when there is no rent seeking. With rent seeking in the deregulation process, the entry of firms increases social benefit only when the increase in conventional social benefit, DSW, is greater than the threshold level. For a given k, a decrease in m increases DSW, thereby making it more likely that deregulation is socially beneficial. The threshold level increases in r, the extent of wastefulness of rent-seeking expenditures. The higher is r, the more likely is it that partial deregulation laden with rent seeking decreases social benefit. The threshold level also increases in the incumbent’s profit differential, DPk. Moreover, the threshold level in the collusive rent seeking case is higher than the threshold level when the incumbents employ the non-cooperative Nash strategy in rent seeking. In a nutshell, the entry contest makes it less likely that entry of firms increases social welfare. If the increase in social benefit is very large, however, the partial deregulation laden with heavy rent seeking can still increase social benefit. This result is in contrast with that of Kang and Lee (2001) who examine entry contests in a Cournot oligopoly with a linear demand. Focusing on the case of single issuance, they show that the entry contest always decreases social benefit. Unlike Kang and Lee (2001), the above proposition shows that deregulation can increase social benefit under some circumstances. Thus, the result of Kang and Lee (2001) is shown to stem from specific assumptions of their model. Poitras and Sutter (2000) show that welfare gains over the status quo exist whenever deregulation occurs. The difference between the above proposition and their result stems from several differences in the modeling of the deregulation process. Firstly, the model in the present paper considers the contest between incumbents and potential entrants while
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Poitras and Sutter (2000) consider the contest between the monopolist and the reformer who represents consumers. Secondly, we have considered essentially a single-stage game while Poitras and Sutter (2000) consider a two-period dynamic process. Thirdly, the model in the present paper considers oligopoly while their model is focused on monopoly. Finally, the scope of deregulation is different between the present paper and Poitras and Sutter (2000). The present paper examines partial deregulation, the limit of which corresponds to complete deregulation examined by Poitras and Sutter (2000).
5. Concluding remarks We have examined entry contests in oligopoly with regulatory barriers to entry. The paper has derived conditions under which the partial deregulation of entry barriers laden with rent seeking decreases or increases expected social benefit for a general demand function. We have shown that entry deregulation is more likely to be socially beneficial when the incumbents employ a non-cooperative Nash strategy in rent seeking and when the decrease in profits of the incumbents caused by entry is small. We have also shown that entry deregulation alone does not guarantee an increase in social benefit if a rent-seeking contest takes place between incumbents and potential entrants. Our analysis serves, at least, as a counter-example to the assertion that partial deregulation always increases social benefit. Through careful design of deregulation processes, however, the reformer can reduce the extent of rent seeking. For example, in the USA, some of new licenses are auctioned off. This could reduce the rent-seeking losses in the second stage. Still, the change of regulation regime might incur some costs. An interesting issue not dealt with in this paper is the optimal competition policy of the government. The government may determine the number of entrants, k, with which the increase in expected social benefit is maximized. The larger the value of k, the greater is the increase in social benefit if the deregulation succeeds. The larger the value of k, however, the higher the probability that the deregulation attempt fails. The optimal competition policy should balance these offsetting effects.
Acknowledgements For their helpful comments and suggestions, we would like to thank an anonymous referee, an editor and participants of seminars at Kookmin University and the annual meeting of Korea International Economic Association. Financial support from Korea Research Foundation is gratefully acknowledged (KRF-2001-041-C00240). The usual disclaimer applies.
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