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Competition and privatization policies revisited: the payoff interdependence approach

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Abstract

We investigate the relationship between competition and privatization policies. Existing studies measure the strength of competition based on the number of firms, and show that the optimal degree of privatization is higher in more competitive markets. We introduce an interdependent payoff structure into a mixed oligopoly and revisit this problem. Here, we assume that firms consider their own and other firms’ profits. In the model, competition increases when firms are negatively affected by rivals’ profits. We find that under the assumption of quadratic production costs, which is popular in mixed oligopolies, the optimal degree of privatization is higher when there is less market competition. This finding contrasts with those of prior studies. However, this result may be reversed when we adopt alternative model formulation. Furthermore, in the constant marginal cost case, the optimal degree of privatization is always lower when there is less market competition, which is opposite to the result in the quadratic cost case. Our results suggest that the relationship between an optimal privatization policy and the strength of competition crucially depends on the market structure, including the cost conditions.

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Notes

  1. This interest in mixed oligopolies is the result of their importance to European, Canadian, and Japanese economies. Although they are less significant, there are some examples of mixed oligopolies in the United States, such as the packaging and overnight-delivery industries. Analyses of mixed oligopolies date back to at least (Merrill and Schneider 1966), although it is only more recently that the literature in this field has become richer and more diverse. See Gil-Moltó et al. (2011) and Bose and Gupta (2013), and the works referenced therein, for recent developments in this field.

  2. Partial ownership in privatized firms has become increasingly popular worldwide and, as a result, partial privatization has been discussed intensively in the literature. For a general discussion, see Matsumura (1998). In addition, see Ishibashi and Kaneko (2008) for quality-improving investments, Kato (2006, 2013) for environmental problems, Matsumura and Kanda (2005), Fujiwara (2007), Wang and Chen (2010) and Cato and Matsumura (2012) for free-entry markets, Bárcena-Ruiz and Garzón (2003) for merger problems, and Matsumura and Ogawa (2010), Bárcena-Ruiz and Garzón (2010), and Naya (2015), who examine the endogenous timing game.

  3. A typical example is R&D competition. For R&D competition in mixed oligopolies, see Nishimori and Ogawa (2002), Matsumura and Matsushima (2004), and Ishibashi and Matsumura (2006).

  4. Even in private oligopolies, an increase in the number of firms can increase the profits of dominant firms. See Mukherjee and Zhao (2009) and Ishida et al. (2011).

  5. See Cato and Matsumura (2013, (2015) and the works referenced therein for recent developments in mixed oligopolies.

  6. For a general discussion of this approach, see Matsumura et al. (2013).

  7. Under the standard conditions in a Cournot oligopoly, the ratio between profit margin (price less marginal cost) and the price, known as Lerner index, is decreasing in \(\alpha \). This index is popular in the empirical literature as a measure of the intensity of market competition in product markets. Furthermore, Matsumura and Matsushima (2012) show that collusion is less stable when \(\alpha \) is larger under moderate conditions. In this sense, a larger \(\alpha \) again indicates a more competitive market.

  8. The conjectural variation approach is another possibility, and contains three models as special cases. However, the conjectural variation model assumes that firm 1’s output affects that of firm 2, and vice versa. Needless to say, this assumption is inconsistent in any static model. One advantage of the interdependent payoff approach is that it does not suffer from this problem.

  9. See Gibbons and Murphy (1990) for empirical evidence. The payoff function based on relative wages or relative wealth status has also been intensively discussed in the macroeconomics context.

  10. See Armstrong and Huck (2010), and the works referenced therein.

  11. See Vega-Redondo (1997) for an evolutionary game model in this regard. He considers a quantity-setting model in a homogeneous product market, and shows that if firms myopically imitate the most profitable firm’s strategy, the industry converges to a highly competitive outcome.

  12. See Fumas (1992) and Kockesen et al. (2000). Although we do not endogenize this parameter, we presume that the owners of private firms set \(\alpha \) as positive if they are able to do so. However, the owner of a public firm may have little incentive to choose a positive \(\alpha \). From this viewpoint, the alternative model formulation of payoffs discussed in Sect. 4 is important.

  13. This formulation of demand and cost is popular in mixed oligopoly literature. See, among others, De Fraja and Delbono (1989) and Fjell and Pal (1996). We adopt another popular model formulation in Sect. 4.

  14. If we replace \(V_i\) with \(\pi _i\), this becomes the standard formulation of the payoff for a semi-public firm (Matsumura 1998). See also Fujiwara (2007) for recent works adopting this approach. We assume that W represents the sum of the consumer surplus and the profits of firms, rather than the sum of the consumer surplus and the payoff of all firms, \(V_0+V_1+\cdots +V_n\). CEOs of firms might be concerned with the relative performance of their firms because good relative performance will increase their current and future incomes. However, we regard this simply as an income transfer.

  15. The neutrality of privatization is also discussed in detail in the different context of a subsidized mixed oligopoly. For recent developments in this field, see Matsumura and Tomaru (2012, 2013), and the works referenced therein.

  16. For example, De Fraja and Delbono (1989) discuss the case of \(\alpha =0\), and show that there exists m such that a private oligopoly (\(\theta =1\)) yields greater welfare than a mixed oligopoly (\(\theta =0\)) if and only if \(n>m\).

  17. In this setting, the payoff of each private firm is non-negative in the symmetric equilibrium, whereas it could have been negative in the original setting. This might be another advantage of this alternative formulation over the original formulation. However, in the alternative formulation, \(\theta =1\) does not imply a symmetric private oligopoly. In contrast, in the original formulation, we can treat a symmetric private oligopoly as a special case. This is an advantage of the original formulation discussed in Sect. 3.

  18. See Mujumdar and Pal (1998), Pal (1998), Matsumura (2003), and Matsumura and Ogawa (2010).

  19. If \(c_0 = 0\), the first-best outcome is achieved and the optimal degree of privatization is zero. See Bárcena-Ruiz (2012).

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Authors and Affiliations

  1. Institute of Social Science, The University of Tokyo, Tokyo, Japan

    Toshihiro Matsumura

  2. Economics Department, Hiroshima University, 1-2-1, Kagamiyama, Higashihiroshima, Hiroshima, 739-8525, Japan

    Makoto Okamura

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  1. Toshihiro Matsumura
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  2. Makoto Okamura
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Correspondence to Makoto Okamura.

Additional information

We are indebted to two anonymous referees and the editor for their valuable and constructive suggestions. We also thank seminar participants at annual meeting of Japanese Economic Association, National Dong Hwa University, Osaka University, and The University of Tokyo for their helpful comments. Needless to say, we are responsible for any remaining errors. This work was supported by Murata Science Foundation and JSPS KAKENHI Grant Numbers 15k03347.

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Matsumura, T., Okamura, M. Competition and privatization policies revisited: the payoff interdependence approach. J Econ 116, 137–150 (2015). https://doi.org/10.1007/s00712-015-0445-5

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