Privatization of a multi-product public firm

ABSTRACT

This study considers a public firm that provides a profitable service and an unprofitable service. In our model, only the public firm supplies the unprofitable service, while both the public firm and multiple private firms supply the profitable service. The two services may be substitutes, complements, or independent in demand, and the public firm has inferior technology. We examine whether the public firm should privatize either the profitable service or the service that faces competition from private firms. We obtain the following results. When the two services are complementary, the critical cost of the public firm such that privatizing the profitable service is socially preferable increases with the degree of complementarity. When the two services are substitutes, the critical cost decreases (increases) with the degree of substitution for a low (high) degree of substitution. For a sufficiently high degree of substitution, the critical cost becomes small.

KEYWORDS:

• Multi-product firm
• privatization
• substitute goods
• complementary goods

Acknowledgments

The authors would like to thank the associate editor and an anonymous referee for their constructive and helpful comments. We thank Noriaki Matsushima and Yoshihiro Tomaru for their useful comments. We gratefully acknowledge the financial support of JSPS KAKENHI Grant Number 18K01613. We are responsible for any remaining errors.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. In Kumamoto City, both public and private firms competed in the provision of bus services.

2. While Barcena-Ruiz and Garzon (2003) consider a multi-product case using a mixed duopoly market, they assume that when public and private firms merge, the result is a multi-product firm.

3. Studies such as Matsumura (1998), Fujiwara (2007), Wang and Chen (2010, 2011), Cato and Matsumura (2012), and Wang and Tomaru (2015) address the partial privatization problem.

4. Recently, Matsumura and Matsushima (2012), Mantin (2012), Lin and Mantin (2015), and Kawasaki (2017) show the need for airport privatization, while Matsushim:a and Takauchi (2014) and Czerny, Hoffer, and Mun (2014) show the need for port privatization.

5. For example, Wang and Tomaru (2015) argue that if we consider the non-negative profit condition of the public firm, nationalization can be socially preferable, even if foreign capital flows into domestic private firms.

6. This case also differs from that in which the public firm produces only one good.

7. For example, Matsumura and Shimizu (2010) assume that the public firm’s production technology improves after privatization. See Matsumura and Shimizu (2010), footnote 9.

8. We assume $a=1$ and $n=5$ without loss of generality.

9. Note that because the market size of each service decreases with the degree of substitution, the private and privatized firms have less incentive to supply their services.

10. Without loss of generality, we assume $a=1$ and $n=5$ in Figure 2.

11. See Matsumura and Kanda (2005); Fujiwara (2007); and Lee, Matsumura, and Sato (2018).