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Undesirable competition
Economics Letters 114 (2012) 175–177
Contents lists available at SciVerse ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Undesirable competition Leonard F.S. Wang a , Arijit Mukherjee b,c,∗ a
Department of Applied Economics, National University of Kaohsiung, Taiwan
b
University of Nottingham and the Leverhulme Centre for Research in Globalisation and Economic Policy, UK
c
CESifo, Germany
article
info
Article history: Received 1 November 2010 Received in revised form 27 August 2011 Accepted 22 September 2011 Available online 5 October 2011
abstract We show that the entry of private profit-maximising firms makes the consumers worse off compared to having a nationalised monopoly. Such entry increases the nationalised firm’s profit, industry profit, and social welfare, at the expense of the consumers. Our result is important for competition policy. © 2011 Elsevier B.V. All rights reserved.
JEL classification: L32 L44 L13 L11 H00 D43 Keywords: Competition Consumer surplus Nationalised firm
1. Introduction It is generally believed that higher competition benefits consumers1 (Metzenbaum, 1993; Hausman and Leibtag, 2007), and encourages antitrust authorities to foster competition. However, using a model with a welfare-maximising nationalised firm, we show that the entry of private profit-maximising firms makes consumers worse off compared to having a nationalised monopoly.2 Such entry increases the nationalised firm’s profit, industry profit, and social welfare, at the expense of the consumers. Nationalised or state-owned firms in industries such as the airline and rail industries are common in many developing, developed, and transitional economies. Although many of these
∗ Correspondence to: School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Tel.: +44 115 951 4733; fax: +44 115 951 4159. E-mail address: [email protected] (A. Mukherjee). 1 Promotion of consumer welfare is the common goal of consumer protection and competition policies, which can be evidenced by the document of the US Department of Justice. (www.justice.gov/atr/public/div_stats/276198.pdf). 2 In a repeated game between a public and a private firm, Wen and Sasaki (2001) show how strategic excess capacity installation in the public firm helps to improve welfare compared to the static competition between these firms. 0165-1765/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2011.09.021
industries were initially characterised by restrictions on private entry, several countries such as India, Taiwan, and Japan have relaxed entry regulation in recent years. Hence, a proper account of the effects of competition in industries with nationalised firms deserves attention. While the existence of nationalised firms is viewed as an indirect regulatory mechanism (Cremer et al., 1989; De Fraja and Delbono, 1989), we show that the effect of competition on consumers is non-trivial, and that it may go against the consumers. There are some other papers challenging the price-reducing effects of competition. The factors responsible for the price-raising effects of competition in the previous papers are consumers’ search costs (Janssen and Moraga-González, 2004), the presence of loyal and switching buyer groups (Rosenthal, 1980), and the consumers’ preferences for differentiated products (Chen and Riordan, 2008).3 In contrast, our result is due to output shifting from a less costefficient public firm to more cost-efficient private firms, thus creating the trade-off between productive efficiency and allocative inefficiency. Hence, our paper is more closely related to Gans
3 See Chen and Riordan (2008) for references to papers showing the price-raising effects of competition in the spatial models of product differentiation.
176
L.F.S. Wang, A. Mukherjee / Economics Letters 114 (2012) 175–177
and Quiggin (2003), which shows that if a large regulated firm with increasing returns to scale technology faces competition from a competitive fringe, competition increases price by reducing the output of the large firm. Our result is due to the strategic behaviour between the public and the private firms, and does not depend on the increasing returns to scale technology. Thus, our analysis suggests that the price-raising effect of competition under a regulatory mechanism may be a common phenomenon.
q1 +nqi
∫ Max q1
P (q) − cq1 .
(5)
0
Firm 1’s equilibrium output is given by
∂ qi P 1+n ∂ q1
= c,
∂q
(6)
P ′ +q P ′′
where ∂ q i = − (n+1)P ′ +i nq P ′′ < 0. 1 i
∂q
The total output under entry is given by P 1 + n ∂ q i
1
+ n(P +
2. The model and the results
qi P ′ ) = c or
2.1. Nationalised monopoly
∂ qi = c, (7) P 1+n ∂ q1 since P + qi P ′ = 0. ∂q Since ∂ q i < 0, (2) and (6) show that the entry of the profit1
Consider the monopoly of a welfare-maximising nationalised firm (called firm 1) that produces with a constant marginal cost of production c > 0. Assume that the inverse market demand function is P (q) with P ′ < 0 and P ′′ ≤ 0, where P is price and q is the total output. Firm 1 determines its output to maximise social welfare, which is sum of the industry profit and consumer surplus. Hence, firm 1’s objective is qm
∫
P (q)dq − cqm .
Max qm
(1)
0
The equilibrium output is given by P m = c,
(2)
implying zero profit of firm 1 under a nationalised monopoly. 2.2. Entry of private profit-maximising firms Now consider the entry of n private profit-maximising firms, each of them producing homogeneous goods at the marginal cost of d, with d < c, where d is assumed to be zero for simplicity. The following game under entry is considered and solved through backward induction. At stage 1, the nationalised firm determines the output to maximise welfare. At stage 2, all private firms choose outputs simultaneously. At least two justifications can be given for the above game structure. The first justification comes from the empirical side. As mentioned in Fjell and Heywood (2002), many industries such as telecommunications and electricity industries are dominated by former nationalised firms with a first mover advantage, thus justifying the role of the nationalised firm as a Stackelberg leader and the private profit-maximising firms as Stackelberg followers. The second justification comes from the theoretical side. Following Pal (1998), Jacques (2004), and Lu (2007), our analysis uses an observable delay game of Hamilton and Slutsky (1990) that creates an equilibrium where the nationalised firm and the private firms behave like a Stackelberg leader and Stackelberg followers, respectively.4 Then we determine the firms’ equilibrium outputs under entry. The ith private firm determines the output to maximise (3): Max P (q)qi , qi
i = 2, 3, . . . , n + 1.
(3)
The equilibrium output of the ith follower is P + qi P ′ = 0,
i = 2, 3, . . . , n + 1.
maximising firms reduces firm 1’s equilibrium output. Since (7) shows that equilibrium P is greater than c, the equilibrium price is lower under a nationalised monopoly than under entry with Stackelberg competition. Hence, competition makes the consumers worse off if the nationalised firm behaves like a Stackelberg leader. Since P > c in (7), this also implies that the nationalised firm’s profit is positive under entry, while it is zero under a nationalised monopoly. Hence, such entry increases the profit of the incumbent nationalised firm. It is intuitive to argue that entry increases welfare compared to a nationalised monopoly. Under entry, the welfare-maximising nationalised firm could increase welfare compared to a nationalised monopoly by choosing its monopoly output, while the profitmaximising firms choose respective positive outputs. Since the nationalised firm’s equilibrium output under entry is different from its monopoly output, it is trivial that the equilibrium welfare under entry is higher compared to the situation where the nationalised firm produces its monopoly output under entry. Hence, it is immediate that entry increases welfare compared to a nationalised monopoly, and such improvement in welfare is created at the expense of the consumers. Then, we have the following. Proposition 1. If c > 0, entry by private profit-maximising firms behaving like Stackelberg followers, (i) reduces the output of the nationalised firm, (ii) increases the profit of the nationalised firm, (iii) reduces the consumer surplus, and (iv) increases the welfare of the economy, compared to a nationalised monopoly. Considering all profit-maximising firms, Pal and Sarkar (2001) and Mukherjee and Zhao (2009) show that the entry of a firm can raise the profits of some incumbents by stealing market share from other incumbents. In contrast, such entry in our analysis increases the profit of the incumbent nationalised firm in the absence of other incumbents. Lower total output under entry is responsible for our result. 2.3. An example An example with a linear demand function, P = a − q, is provided for the aforementioned analysis. Straightforward calculation shows that, under a nationalised monopoly, firm 1’s equilibrium output, the product price, firm 1’s profit, and welfare are, respectively, qm = a − c , P m = c , π1m = 0, (a−c )2
(4)
Due to the symmetry of the private firms, the nationalised firm (firm 1) maximises (5) to determine the output:
4 See De Fraja and Delbono (1989) for an earlier work on Stackelberg competition in a mixed oligopoly.
and W m = 2 . Under Cournot competition, since P + qi P ′ = 0, the total output is given by P + n(P + qi P ′ ) = c or P = c.
(8)
Firm 1’s equilibrium output, the ith entrant’s equilibrium output, total equilibrium outputs, product price, firm 1’s profit, the ith entrant’s profit, and welfare are, respectively, qc1 = a − c (n + 1), qci = c , qc = a − c , P c = c , π1c = 0, πic = c 2 , and W c = (a−c )2 +2c 2 n 2
. If firm 1 and the entrants behave like a Stackelberg
L.F.S. Wang, A. Mukherjee / Economics Letters 114 (2012) 175–177
177
under entry changes from Cournot competition to Stackelberg competition. Thus, we get P m = P c < P s . 3. Conclusion In contrast to the general belief that greater competition makes consumers better off, we show that the entry of profit-maximising firms makes the consumers worse off in the presence of a nationalised firm behaving like a Stackelberg leader under entry. Hence, antitrust authorities should be careful when considering entry in industries with nationalised firms. In our analysis, the entry of the profit-maximising firms increases the profit of the nationalised firm, industry profit, and social welfare at the expense of the consumers. However, it is trivial that, if the nationalised firm’s purpose is to maximise consumer surplus instead of social welfare, competition does not affect the consumers, since the nationalised firm always produces in a way that reduces the price to the minimum. Acknowledgement Fig. 1. Comparison of nationalised monopoly, Cournot and Stackelberg.
leader and Stackelberg followers, firm 1’s equilibrium output, the ith entrant’s equilibrium output, total output, product price, firm 1’s profit, the ith entrant’s profit, and welfare are, respectively, qs1 = a − c (n + 1)2 , qsi = c (n + 1), qs = a − c (n + 1), P s = c (n + 1), π1s = cn(a − c (n + 1)2 ), πis = c 2 n(n + 1)2 and W s = a2 −2ac +c 2 (n+1)2 . 2
From the above calculations, the total output, product price, and firm 1’s profit are the same under a nationalised monopoly and Cournot competition under entry. Since the cost-efficient entrants produce positive outputs, while the total output remains the same under a nationalised monopoly and entry, such entry increases welfare compared to a nationalised monopoly by saving the production cost. Thus, this shows that Stackelberg competition under entry is important for Proposition 1. Fig. 1 provides the reason for P m = P c < P s . The reaction curves of firm 1 and the profit-maximising firms taken together are R1 M and R−1 A, respectively. The intersection of these curves, C , represents Cournot equilibrium, whereas the intersection of R1 M and the horizontal axis shows the output under a nationalised monopoly. It follows from (8) that the slope of the nationalised firm’s reaction curve with respect to the total outputs of the profitmaximising firms is exactly −1. Hence, entry does not change the total outputs and consumer surplus compared to a nationalised monopoly. However, the Stackelberg equilibrium in Fig. 1 is denoted as S, where the iso-welfare function WW ′ is tangent to R−1 A.5 Since the absolute slope of R−1 A (i.e., the reaction function of the profit-maximising firms taken together) is less than 1, the total output reduces when the product–market competition
5 The shape and properties of the iso-welfare function can be found from the q +nq welfare function W = 0 1 i P (q) − cq1 .
We thank an anonymous referee for helpful comments and suggestions. The usual disclaimer applies. References Chen, Y., Riordan, M., 2008. Price-increasing competition. RAND Journal of Economics 39, 1042–1058. Cremer, H., Marchand, M., Thisse, J.F., 1989. The public firm as an instrument for regulating an oligopolistic market. Oxford Economic Papers 41, 283–301. De Fraja, G., Delbono, F., 1989. Alternative strategies of a public enterprise in oligopoly. Oxford Economic Papers 41, 302–311. Fjell, K., Heywood, J.S., 2002. Public Stackelberg leadership in a mixed oligopoly with foreign firms. Australian Economic Papers 41, 267–281. Gans, J., Quiggin, J., 2003. A technological and organisational explanation of the size distribution of firms. Small Business Economics 21, 243–256. Hamilton, J.H., Slutsky, S.M., 1990. Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games and Economic Behavior 2, 29–46. Hausman, J., Leibtag, E., 2007. Consumer benefits from increased competition in shopping outlets: measuring the effect of Wal-Mart. Journal of Applied Econometrics 7, 1157–1177. Jacques, A., 2004. Endogenous timing in a mixed oligopoly: a forgotten equilibrium. Economics Letters 83, 147–148. Janssen, M.C., Moraga-González, J.L., 2004. Strategic pricing, consumer search and the number of firms. Review of Economic Studies 71, 1089–1118. Lu, Y., 2007. Endogenous timing in a mixed oligopoly: another forgotten equilibrium. Economics Letters 94, 226–227. Metzenbaum, H.M., 1993. Antitrust enforcement: putting the consumers first. Health Affairs, Fall 137–143. Mukherjee, A., Zhao, L., 2009. Profit raising entry. Journal of Industrial Economics 57, 870. Pal, D., 1998. Endogenous timing in a mixed oligopoly. Economics Letters 61, 181–185. Pal, D., Sarkar, J., 2001. A Stackelberg oligopoly with nonidentical firms. Bulletin of Economic Research 53, 127–134. Rosenthal, R.W., 1980. A model in which an increase in the number of sellers leads to a higher price. Econometrica 48, 1575–1579. Wen, M., Sasaki, D., 2001. Would excess capacity in public firms be socially optimal. Economic Record 77, 283–290.
Contents lists available at SciVerse ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Undesirable competition Leonard F.S. Wang a , Arijit Mukherjee b,c,∗ a
Department of Applied Economics, National University of Kaohsiung, Taiwan
b
University of Nottingham and the Leverhulme Centre for Research in Globalisation and Economic Policy, UK
c
CESifo, Germany
article
info
Article history: Received 1 November 2010 Received in revised form 27 August 2011 Accepted 22 September 2011 Available online 5 October 2011
abstract We show that the entry of private profit-maximising firms makes the consumers worse off compared to having a nationalised monopoly. Such entry increases the nationalised firm’s profit, industry profit, and social welfare, at the expense of the consumers. Our result is important for competition policy. © 2011 Elsevier B.V. All rights reserved.
JEL classification: L32 L44 L13 L11 H00 D43 Keywords: Competition Consumer surplus Nationalised firm
1. Introduction It is generally believed that higher competition benefits consumers1 (Metzenbaum, 1993; Hausman and Leibtag, 2007), and encourages antitrust authorities to foster competition. However, using a model with a welfare-maximising nationalised firm, we show that the entry of private profit-maximising firms makes consumers worse off compared to having a nationalised monopoly.2 Such entry increases the nationalised firm’s profit, industry profit, and social welfare, at the expense of the consumers. Nationalised or state-owned firms in industries such as the airline and rail industries are common in many developing, developed, and transitional economies. Although many of these
∗ Correspondence to: School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Tel.: +44 115 951 4733; fax: +44 115 951 4159. E-mail address: [email protected] (A. Mukherjee). 1 Promotion of consumer welfare is the common goal of consumer protection and competition policies, which can be evidenced by the document of the US Department of Justice. (www.justice.gov/atr/public/div_stats/276198.pdf). 2 In a repeated game between a public and a private firm, Wen and Sasaki (2001) show how strategic excess capacity installation in the public firm helps to improve welfare compared to the static competition between these firms. 0165-1765/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2011.09.021
industries were initially characterised by restrictions on private entry, several countries such as India, Taiwan, and Japan have relaxed entry regulation in recent years. Hence, a proper account of the effects of competition in industries with nationalised firms deserves attention. While the existence of nationalised firms is viewed as an indirect regulatory mechanism (Cremer et al., 1989; De Fraja and Delbono, 1989), we show that the effect of competition on consumers is non-trivial, and that it may go against the consumers. There are some other papers challenging the price-reducing effects of competition. The factors responsible for the price-raising effects of competition in the previous papers are consumers’ search costs (Janssen and Moraga-González, 2004), the presence of loyal and switching buyer groups (Rosenthal, 1980), and the consumers’ preferences for differentiated products (Chen and Riordan, 2008).3 In contrast, our result is due to output shifting from a less costefficient public firm to more cost-efficient private firms, thus creating the trade-off between productive efficiency and allocative inefficiency. Hence, our paper is more closely related to Gans
3 See Chen and Riordan (2008) for references to papers showing the price-raising effects of competition in the spatial models of product differentiation.
176
L.F.S. Wang, A. Mukherjee / Economics Letters 114 (2012) 175–177
and Quiggin (2003), which shows that if a large regulated firm with increasing returns to scale technology faces competition from a competitive fringe, competition increases price by reducing the output of the large firm. Our result is due to the strategic behaviour between the public and the private firms, and does not depend on the increasing returns to scale technology. Thus, our analysis suggests that the price-raising effect of competition under a regulatory mechanism may be a common phenomenon.
q1 +nqi
∫ Max q1
P (q) − cq1 .
(5)
0
Firm 1’s equilibrium output is given by
∂ qi P 1+n ∂ q1
= c,
∂q
(6)
P ′ +q P ′′
where ∂ q i = − (n+1)P ′ +i nq P ′′ < 0. 1 i
∂q
The total output under entry is given by P 1 + n ∂ q i
1
+ n(P +
2. The model and the results
qi P ′ ) = c or
2.1. Nationalised monopoly
∂ qi = c, (7) P 1+n ∂ q1 since P + qi P ′ = 0. ∂q Since ∂ q i < 0, (2) and (6) show that the entry of the profit1
Consider the monopoly of a welfare-maximising nationalised firm (called firm 1) that produces with a constant marginal cost of production c > 0. Assume that the inverse market demand function is P (q) with P ′ < 0 and P ′′ ≤ 0, where P is price and q is the total output. Firm 1 determines its output to maximise social welfare, which is sum of the industry profit and consumer surplus. Hence, firm 1’s objective is qm
∫
P (q)dq − cqm .
Max qm
(1)
0
The equilibrium output is given by P m = c,
(2)
implying zero profit of firm 1 under a nationalised monopoly. 2.2. Entry of private profit-maximising firms Now consider the entry of n private profit-maximising firms, each of them producing homogeneous goods at the marginal cost of d, with d < c, where d is assumed to be zero for simplicity. The following game under entry is considered and solved through backward induction. At stage 1, the nationalised firm determines the output to maximise welfare. At stage 2, all private firms choose outputs simultaneously. At least two justifications can be given for the above game structure. The first justification comes from the empirical side. As mentioned in Fjell and Heywood (2002), many industries such as telecommunications and electricity industries are dominated by former nationalised firms with a first mover advantage, thus justifying the role of the nationalised firm as a Stackelberg leader and the private profit-maximising firms as Stackelberg followers. The second justification comes from the theoretical side. Following Pal (1998), Jacques (2004), and Lu (2007), our analysis uses an observable delay game of Hamilton and Slutsky (1990) that creates an equilibrium where the nationalised firm and the private firms behave like a Stackelberg leader and Stackelberg followers, respectively.4 Then we determine the firms’ equilibrium outputs under entry. The ith private firm determines the output to maximise (3): Max P (q)qi , qi
i = 2, 3, . . . , n + 1.
(3)
The equilibrium output of the ith follower is P + qi P ′ = 0,
i = 2, 3, . . . , n + 1.
maximising firms reduces firm 1’s equilibrium output. Since (7) shows that equilibrium P is greater than c, the equilibrium price is lower under a nationalised monopoly than under entry with Stackelberg competition. Hence, competition makes the consumers worse off if the nationalised firm behaves like a Stackelberg leader. Since P > c in (7), this also implies that the nationalised firm’s profit is positive under entry, while it is zero under a nationalised monopoly. Hence, such entry increases the profit of the incumbent nationalised firm. It is intuitive to argue that entry increases welfare compared to a nationalised monopoly. Under entry, the welfare-maximising nationalised firm could increase welfare compared to a nationalised monopoly by choosing its monopoly output, while the profitmaximising firms choose respective positive outputs. Since the nationalised firm’s equilibrium output under entry is different from its monopoly output, it is trivial that the equilibrium welfare under entry is higher compared to the situation where the nationalised firm produces its monopoly output under entry. Hence, it is immediate that entry increases welfare compared to a nationalised monopoly, and such improvement in welfare is created at the expense of the consumers. Then, we have the following. Proposition 1. If c > 0, entry by private profit-maximising firms behaving like Stackelberg followers, (i) reduces the output of the nationalised firm, (ii) increases the profit of the nationalised firm, (iii) reduces the consumer surplus, and (iv) increases the welfare of the economy, compared to a nationalised monopoly. Considering all profit-maximising firms, Pal and Sarkar (2001) and Mukherjee and Zhao (2009) show that the entry of a firm can raise the profits of some incumbents by stealing market share from other incumbents. In contrast, such entry in our analysis increases the profit of the incumbent nationalised firm in the absence of other incumbents. Lower total output under entry is responsible for our result. 2.3. An example An example with a linear demand function, P = a − q, is provided for the aforementioned analysis. Straightforward calculation shows that, under a nationalised monopoly, firm 1’s equilibrium output, the product price, firm 1’s profit, and welfare are, respectively, qm = a − c , P m = c , π1m = 0, (a−c )2
(4)
Due to the symmetry of the private firms, the nationalised firm (firm 1) maximises (5) to determine the output:
4 See De Fraja and Delbono (1989) for an earlier work on Stackelberg competition in a mixed oligopoly.
and W m = 2 . Under Cournot competition, since P + qi P ′ = 0, the total output is given by P + n(P + qi P ′ ) = c or P = c.
(8)
Firm 1’s equilibrium output, the ith entrant’s equilibrium output, total equilibrium outputs, product price, firm 1’s profit, the ith entrant’s profit, and welfare are, respectively, qc1 = a − c (n + 1), qci = c , qc = a − c , P c = c , π1c = 0, πic = c 2 , and W c = (a−c )2 +2c 2 n 2
. If firm 1 and the entrants behave like a Stackelberg
L.F.S. Wang, A. Mukherjee / Economics Letters 114 (2012) 175–177
177
under entry changes from Cournot competition to Stackelberg competition. Thus, we get P m = P c < P s . 3. Conclusion In contrast to the general belief that greater competition makes consumers better off, we show that the entry of profit-maximising firms makes the consumers worse off in the presence of a nationalised firm behaving like a Stackelberg leader under entry. Hence, antitrust authorities should be careful when considering entry in industries with nationalised firms. In our analysis, the entry of the profit-maximising firms increases the profit of the nationalised firm, industry profit, and social welfare at the expense of the consumers. However, it is trivial that, if the nationalised firm’s purpose is to maximise consumer surplus instead of social welfare, competition does not affect the consumers, since the nationalised firm always produces in a way that reduces the price to the minimum. Acknowledgement Fig. 1. Comparison of nationalised monopoly, Cournot and Stackelberg.
leader and Stackelberg followers, firm 1’s equilibrium output, the ith entrant’s equilibrium output, total output, product price, firm 1’s profit, the ith entrant’s profit, and welfare are, respectively, qs1 = a − c (n + 1)2 , qsi = c (n + 1), qs = a − c (n + 1), P s = c (n + 1), π1s = cn(a − c (n + 1)2 ), πis = c 2 n(n + 1)2 and W s = a2 −2ac +c 2 (n+1)2 . 2
From the above calculations, the total output, product price, and firm 1’s profit are the same under a nationalised monopoly and Cournot competition under entry. Since the cost-efficient entrants produce positive outputs, while the total output remains the same under a nationalised monopoly and entry, such entry increases welfare compared to a nationalised monopoly by saving the production cost. Thus, this shows that Stackelberg competition under entry is important for Proposition 1. Fig. 1 provides the reason for P m = P c < P s . The reaction curves of firm 1 and the profit-maximising firms taken together are R1 M and R−1 A, respectively. The intersection of these curves, C , represents Cournot equilibrium, whereas the intersection of R1 M and the horizontal axis shows the output under a nationalised monopoly. It follows from (8) that the slope of the nationalised firm’s reaction curve with respect to the total outputs of the profitmaximising firms is exactly −1. Hence, entry does not change the total outputs and consumer surplus compared to a nationalised monopoly. However, the Stackelberg equilibrium in Fig. 1 is denoted as S, where the iso-welfare function WW ′ is tangent to R−1 A.5 Since the absolute slope of R−1 A (i.e., the reaction function of the profit-maximising firms taken together) is less than 1, the total output reduces when the product–market competition
5 The shape and properties of the iso-welfare function can be found from the q +nq welfare function W = 0 1 i P (q) − cq1 .
We thank an anonymous referee for helpful comments and suggestions. The usual disclaimer applies. References Chen, Y., Riordan, M., 2008. Price-increasing competition. RAND Journal of Economics 39, 1042–1058. Cremer, H., Marchand, M., Thisse, J.F., 1989. The public firm as an instrument for regulating an oligopolistic market. Oxford Economic Papers 41, 283–301. De Fraja, G., Delbono, F., 1989. Alternative strategies of a public enterprise in oligopoly. Oxford Economic Papers 41, 302–311. Fjell, K., Heywood, J.S., 2002. Public Stackelberg leadership in a mixed oligopoly with foreign firms. Australian Economic Papers 41, 267–281. Gans, J., Quiggin, J., 2003. A technological and organisational explanation of the size distribution of firms. Small Business Economics 21, 243–256. Hamilton, J.H., Slutsky, S.M., 1990. Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games and Economic Behavior 2, 29–46. Hausman, J., Leibtag, E., 2007. Consumer benefits from increased competition in shopping outlets: measuring the effect of Wal-Mart. Journal of Applied Econometrics 7, 1157–1177. Jacques, A., 2004. Endogenous timing in a mixed oligopoly: a forgotten equilibrium. Economics Letters 83, 147–148. Janssen, M.C., Moraga-González, J.L., 2004. Strategic pricing, consumer search and the number of firms. Review of Economic Studies 71, 1089–1118. Lu, Y., 2007. Endogenous timing in a mixed oligopoly: another forgotten equilibrium. Economics Letters 94, 226–227. Metzenbaum, H.M., 1993. Antitrust enforcement: putting the consumers first. Health Affairs, Fall 137–143. Mukherjee, A., Zhao, L., 2009. Profit raising entry. Journal of Industrial Economics 57, 870. Pal, D., 1998. Endogenous timing in a mixed oligopoly. Economics Letters 61, 181–185. Pal, D., Sarkar, J., 2001. A Stackelberg oligopoly with nonidentical firms. Bulletin of Economic Research 53, 127–134. Rosenthal, R.W., 1980. A model in which an increase in the number of sellers leads to a higher price. Econometrica 48, 1575–1579. Wen, M., Sasaki, D., 2001. Would excess capacity in public firms be socially optimal. Economic Record 77, 283–290.