Abstract
This study formulates a new model of mixed oligopolies in free entry markets. A state-owned public enterprise is established before the game, private enterprises enter the market, and then the government chooses the degree of privatization of the public enterprise (termed the entry-then-privatization model herein). We find that under general demand and cost functions, the timing of privatization does not affect consumer surplus or the output of each private firm, while it does affect the equilibrium degree of privatization, number of entering firms, and output of the public firm. The equilibrium degree of privatization is too high (low) for both domestic and world welfare if private firms are domestic (foreign).
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Notes
Nippon Telecom and Telecommunication (NTT) was a typical example of a public monopolist (it was a monopolist until 1985).
Examples include United States Postal Service, Deutsche Post AG, Areva, NTT, Japan Tobacco (JT), Volkswagen, Renault, Electricite de France, Japan Postal Bank, Kampo, Korea Development Bank, and Korea Investment Corporation.
Xu et al. (2017) is one exception, as it discussed the timing of privatization, showing that earlier privatization is better for domestic and world social welfare in a very specific model with a linear demand and a specific symmetric quadratic cost. Regarding the timing of commitment, Ino and Matsumura (2012) discussed two Stackelberg models in private oligopolies. In the strongly (weakly) persistent leadership model, Stackelberg leaders produce their outputs before (after) the entry of followers. However, they showed that the two models yield similar welfare results (i.e., leadership improves welfare in both models).
However, there are also examples suggesting that the timeline of existing papers is reasonable. For example, the Japanese government fully privatized J-Power in 2004 before opening the electricity market in 2017 and has not thus far renationalized it.
Moreover, the government plans to sell its share in Japan Post, too.
In Japan, the government rarely increases its ownership of partially privatized enterprises except when they face financial problems. However, this is not the case in France. For example, the French government increased its ownership of Renault from 15 to 19.4% in 2015.
In many contexts, the nationality of the private firms affects the optimal policies in mixed oligopolies. Pal and White (1998); Bárcena-Ruiz and Garzón (2005a, b) discussed trade policies. Wang and Lee (2013) introduced foreign firms into the framework of Ino and Matsumura (2010) showing that foreign ownership matters in Stackelberg models. Matsumura and Tomaru (2012) revisited the privatization neutrality theorem presented by White (1996) showing that his result does not hold under foreign ownership of the private firms.
In this study, we allow a cost difference between public and private firms, although we do not allow a cost difference among private firms. While some readers might think that the public firm must be less efficient than the private firm, not all empirical papers support this view. See Megginson and Netter (2001) and Stiglitz (1988). In addition, Martin and Parker (1997) suggested that corporate performance can either increase or decrease after privatization, based on their study in the United Kingdom. See Matsumura and Matsushima (2004) for a theoretical discussion of the endogenous cost differences between public and private enterprises.
In the literature on mixed oligopolies, quadratic production costs are popular and they satisfy these assumptions (Fraja and Delbono 1989; Matsumura and Shimizu 2010). In the literature, constant marginal costs with the cost disadvantage of the public firm are also popular (Pal 1998; Matsumura 2003a) but they do not satisfy these assumptions. The model with constant marginal costs yields a problem in free entry markets. For example, suppose that \(\theta =0\). As discussed in Matsumura and Kanda (2005), when the marginal cost of firm 0 is constant, firm 0’s production level is zero if \(c_0^{\prime } >p(Q^*)\) and the number of entering firms is zero if \(c_0^{\prime } <p(Q^*)\). Therefore, mixed oligopolies do not appear (either a public monopoly or a private oligopoly appears) unless \(c_0^{\prime }=p(Q^*)\). To avoid this technical problem, most papers of mixed oligopolies analyzing free entry markets of homogeneous products assume increasing marginal costs. Therefore, increasing marginal costs are crucial in our analysis.
We do not assume that the strategy of the public firm is a strategic substitute because the public firm can be a strategic complement under plausible assumptions when private firms are foreign. See Matsumura (2003b).
However, this is not true if the degree of privatization is determined before the entries of the private firms and \(\theta =0\). This is shown in Matsumura and Kanda (2005).
Again this result is not new in the literature on mixed oligopolies. Matsumura and Kanda (2005) showed it in the case of \(\theta =0\).
Again, this result is not new in the literature on mixed oligopolies. Lin and Matsumura (2012) showed it in non-free entry markets under specific demand and cost functions.
The government may commit to not reducing public ownership after entry by enacting a law with a minimal public ownership share obligation. For example, the government must hold more than one-third of shares in NTT by law. In the JT case, the government needed to hold a two-thirds share in JT until 2012; however, this was reduced to one-third thereafter. Thus, committing to not setting the public share in the future can be challenging.
In the proof of Proposition 2, we show that a marginal increase in \(\alpha ^{**}\) from \(\alpha ^{*}\) improves welfare if and only if \(p-c_0^{\prime }<0\) when \(\alpha ^{**}=\alpha ^{*}.\) Because Q is independent of \(\theta \) and \(c_0^{{\prime }{\prime }}>0\), such \(\bar{\theta } \in (0,1)\) exists if \(q_0^{*}\) is increasing in \(\theta \).
For the oligopoly version in mixed oligopolies, see Haraguchi and Matsumura (2016).
For discussions on the negative externality, see Matsumura and Ogawa (2017) and the papers cited therein. For discussions on the tax subsidy in mixed oligopolies, see White (1996). On regulations, see Matsumura (2012) and Matsumura and Okumura (2013, 2017). Chen (2017) incorporated the cost-reducing effect of privatization into a free entry market.
References
Anderson SP, de Palma A, Thisse JF (1997) Privatization and efficiency in a differentiated industry. Eur Econ Rev 41(9):1635–1654
Bárcena-Ruiz JC, Garzón MB (2005a) Economic integration and privatization under diseconomies of scale. Eur J Polit Economy 21(1):247–267
Bárcena-Ruiz JC, Garzón MB (2005b) International trade and strategic privatization. Rev Dev Econ 9(4):502–513
Cato S, Matsumura T (2012) Long-run effects of foreign penetration on privatization policies. J Inst Theor Econ 168(3):444–454
Cato S, Matsumura T (2013a) Long-run effects of tax policies in a mixed market. FinanzArchiv 69(2):215–240
Cato S, Matsumura T (2013b) Merger and entry-license tax. Econ Lett 119(1):11–13
Cato S, Matsumura T (2015) Optimal privatization and trade policies with endogenous market structure. Econ Rec 91(294):309–323
Chen TL (2017) Privatization and efficiency: a mixed oligopoly approach. J Econ 120(3):251–268
Colombo S (2016) Mixed oligopoly and collusion. J Econ 118(2):167–184
Corneo G, Jeanne O (1994) Oligopole mixte dans un marche commun. Annal Econ Stat 33:73–90
De Fraja G, Delbono F (1989) Alternative strategies of a public enterprise in oligopoly. Oxford Econ Pap 41:302–311
Fjell K, Pal D (1996) A mixed oligopoly in the presence of foreign private firms. Can J Econ 29(3):737–743
Fujiwara K (2007) Partial privatization in a differentiated mixed oligopoly. J Econ 92(1):51–65
Fujiwara K (2015) Mixed oligopoly and privatization in general equilibrium. Kwansei Gakuin University Discussion Paper No. 137
Ghosh A, Morita H (2007a) Free entry and social efficiency under vertical oligopoly. RAND J Econ 38(2):541–554
Ghosh A, Morita H (2007b) Social desirability of free entry: a bilateral oligopoly analysis. Int J Ind Organ 25(5):925–934
Hattori K, Yoshikawa T (2016) Free entry and social inefficiency under co-opetition. J Econ 118(2):97–119
Haraguchi J, Matsumura T (2016) Cournot–Bertrand comparison in a mixed oligopoly. J Econ 117(2):117–136
Ino H, Matsumura T (2010) What role should public enterprises play in free-entry markets? J Econ 101(3):213–230
Ino H, Matsumura T (2012) How many firms should be leaders? Beneficial concentration revisited. Int Econ Rev 53(4):1323–1340
Ishibashi I, Matsumura T (2006) R&D competition between public and private sectors. Eur Econ Rev 50(6):1347–1366
Ishida J, Matsushima N (2009) Should civil servants be restricted in wage bargaining? A mixed-duopoly approach. J Public Econ 93(3–4):634–646
Lahiri S, Ono Y (1988) Helping minor firms reduces welfare. Econ J 98:1199–1202
Lahiri S, Ono Y (1998) Foreign direct investment, local content requirement, and profit taxation. Econ J 108:444–457
Lin MH, Matsumura T (2012) Presence of foreign investors in privatized firms and privatization policy. J Econ 107(1):71–80
Mankiw NG, Whinston MD (1986) Free entry and social inefficiency. RAND J Econ 17(1):48–58
Martin S, Parker D (1997) The impact of privatisation: ownership and corporate performance in the UK. Routledge, London
Matsumura T (1998) Partial privatization in mixed duopoly. J Public Econ 70(3):473–483
Matsumura T (2003a) Endogenous role in mixed markets: a two-production period model. South Econ J 70(2):403–413
Matsumura T (2003b) Stackelberg mixed duopoly with a foreign competitor. Bull Econ Res 55(3):275–287
Matsumura T (2012) Welfare consequences of an asymmetric regulation in mixed Bertrand duopoly. Econ Lett 115(1):94–96
Matsumura T, Kanda O (2005) Mixed oligopoly at free entry markets. J Econ 84(1):27–48
Matsumura T, Matsushima N (2004) Endogenous cost differentials between public and private enterprises: a mixed duopoly approach. Economica 71(284):671–688
Matsumura T, Matsushima N, Ishibashi I (2009) Privatization and entries of foreign enterprises in a differentiated industry. J Econ 98(3):203–219
Matsumura T, Ogawa A (2012) Price versus quantity in a mixed duopoly. Econ Lett 116(2):174–177
Matsumura T, Ogawa A (2017) Inefficient but robust public leadership (forthcoming). J Ind Compet Trade. doi:10.1007/s10842-017-0248-1
Matsumura T, Okumura Y (2013) Privatization neutrality theorem revisited. Econ Lett 118(2):324–326
Matsumura T, Okumura Y (2017) Privatization neutrality theorem in free entry markets. BE J Theor Econ 17(2). doi:10.1515/bejte-2015-0130
Matsumura T, Shimizu D (2010) Privatization waves. Manch Sch 78(6):609–625
Matsumura T, Tomaru Y (2012) Market structure and privatization policy under international competition. Jpn Econ Rev 63(2):244–258
Matsumura T, Yamagishi A (2017) Long-run welfare effect of energy conservation regulation. Econ Lett 154:64–68
Matsushima N, Matsumura T (2006) Mixed oligopoly, foreign firms, and location choice. Reg Sci Urban Econ 36(6):753–772
Megginson W, Netter J (2001) From state to market: a survey of empirical studies on privatization. J Econ Lit 39(2):321–389
Pal D (1998) Endogenous timing in a mixed oligopoly. Econ Lett 61(2):181–185
Pal D, White MD (1998) Mixed oligopoly, privatization, and strategic trade policy. South Econ J 65(2):264–281
Singh N, Vives X (1984) Price and quantity competition in a differentiated duopoly. RAND J Econ 15(4):546–554
Stiglitz JE (1988) Economics of the public sector, 2nd edn. Norton, New York
Wang LFS, Lee JY (2013) Foreign penetration and undesirable competition. Econ Model 30(1):729–732
White MD (1996) Mixed oligopoly, privatization and subsidization. Econ Lett 53(2):189–195
Xu L, Lee SH, Matsumura T (2017) Ex-ante versus ex-post privatization policies with foreign penetration in free-entry mixed markets. Int Rev Econ Financ 50:1–7
Acknowledgements
We are indebted to two anonymous referees for their valuable and constructive suggestions. This work was supported by National Research Foundation of Korea Grant (NRF-2014S1A2A2028188), JSPS KAKENHI (15K03347), and the Zengin Foundation. Needless to say, we are responsible for any remaining errors.
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Appendix
Appendix
In the following proofs, we suppress the arguments of functions.
Proof of Result 1
First, note that \(\sum _{i \ne 0}q_i = n q = Q-q_0\). By differentiating (2), (3), and (7), we obtain
where
From (6) and the second-order condition for \(q_0\), we obtain
By applying Cramer’s rule to (18), we obtain
\(\square \)
Proof of Result 2
By using (8), (2), and Result 1(ii), we obtain
This implies Result 2(i).
By substituting \(\theta =1\) into (8) and using (2), we obtain
From Result 1(iii), we obtain \(dq_0/d\alpha + n (dq/d\alpha ) <0.\) Because \(p^{\prime }<0\) and \(q_0 >0\), we find that (19) is negative and thus \(\alpha =1\) is not an equilibrium outcome. \(\square \)
Proof of Result 3
Substituting \(\theta =0\) into (8) yields
Because \(d q_0/d \alpha <0\), \(d q/d \alpha > 0\) (Result 1(ii)) and \(p^{\prime }<0\), we find that \(p-c_0^{\prime }\) is positive.
Substituting \(\theta =1\) into (8) yields
From Result 1(iii), we obtain \(dq_0/d\alpha + n (dq/d\alpha ) <0.\) From Result 1(i), we obtain \(dq_0/d \alpha <0.\) Under these conditions, \(p-c_0^{\prime }\) must be negative. \(\square \)
Proof of Result 4
In Eqs. (15) and (16), there are only two unknown variables, \(Q^{**}\) and \(q^{**}\). Thus, these two equations determine \(Q^{**}\) and \(q^{**}\). Because neither \(\alpha ^{**}\) nor \(\theta \) appears in these equations, \(Q^{**}\) and \(q^{**}\) must not depend on these two. This implies (i).
Because these two equations are common with equation system (9)–(13), \(Q^{**}=Q^{*}\) and \(q^{**}=q^{*}.\) This implies (ii).
By differentiating (14), we obtain
This implies (iii). Note that \(Q^{**}\) is independent of \(\alpha ^{**}\) and that \(d q_0^{**}/d\alpha ^{**} = - q^{**}(d n^{**}/d\alpha ^{**})\) (because \(Q^{**}=q_0^{**}+ n^{**}q^{**}\)).
Because neither \(Q^{**}\) nor \(q^{**}\) depends on \(\alpha ^{**}\) and \(q_0^{**}\) is decreasing in \(\alpha ^{**}\), (17) implies that \(n^{**}\) is increasing in \(\alpha ^{**}\). This implies (iv).
Obviously, if \(\alpha ^{*}=\alpha ^{**}\), then \(n^{*}=n^{**}\). Thus, Result 4(iv) implies Result 4(v). \(\square \)
Proof of Result 5
(i) is proven in the proof of Result 4(i).
Because (15) and (16) determine \(q^{**}\) and \(Q^{**}\), the remaining unknown variables \(q_0^{**}\) and \(n^{**}\) are determined by (14) and (16). By differentiating (14) and (17), we obtain
By applying Cramer’s rule to (20), we obtain
and the equalities hold if and only if \(\alpha ^{**}=1\). This implies (ii) and (iii). \(\square \)
Proof of Proposition 2
where we use Result 4 and (16). Thus, (23) is positive if and only if \(p-c_0^{\prime } <0\). Result 3 implies Proposition 2. \(\square \)
Proof of Proposition 3
We show that \(q^*_0\) is increasing in \(\theta \). In the proof of Proposition 2, we showed that a marginal increase in \(\alpha ^{**}\) from \(\alpha ^{*}\) improves welfare if and only if \(p-c_0^{\prime }<0\) when \(\alpha ^{**}=\alpha ^{*}.\) Because p is independent of \(\alpha \) and \(c_0^{\prime }\) is increasing in \(q_0\), the result that \(q^*_0\) is increasing in \(\theta \) implies Proposition 3.
By substituting \(p(Q) = a-bQ\), \(c_0(q_0) = (k_0/2)q^2_0\), and \(c(q_i) = (k/2)q^2_i\) into (3) and using (7), we obtain
and thus
We now consider the first-order condition for \(\alpha \) in the privatization stage. By using (24), the first-order condition (8) for \(\alpha \) is rewritten as
Since \(dq_0/d\alpha <0\), and \(q^*\) and \(Q^*\) are independently determined by (11) and (12), the following two equations determine \(q^*_0\) and \(n^*\):
By substituting \(n^* = (Q^*-q^*_0)/q^*\) into (25), we obtain
By rearranging it, we obtain the quadratic equation
We obtain the equilibrium output of the public firm \(q^*_0\) from
where
and
We obtain
and
Finally, we obtain
Thus, \(q^*_0\) is increasing in \(\theta \). \(\square \)
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Lee, SH., Matsumura, T. & Sato, S. An analysis of entry-then-privatization model: welfare and policy implications. J Econ 123, 71–88 (2018). https://doi.org/10.1007/s00712-017-0559-z
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DOI: https://doi.org/10.1007/s00712-017-0559-z