Taxation on a mixed oligopoly in the presence of foreign ownership

Abstract

This paper analyzes the optimal taxation policy in a mixed duopoly when the private firm is jointly owned by domestic and foreign investors. The optimal policy is tax if the foreign shareholding is high enough; otherwise, it should be subsidy. Besides, to obtain a higher welfare, the taxation policy is superior to the privatization policy only when the private firm is mainly domestically owned. However, when full foreign shareholding of the private firm is allowed, the taxation and privatization can obtain the same level of social welfare regardless of the public firm’s marginal cost.

Keywords:

• Taxation
• mixed oligopoly
• foreign shareholding
• privatization

Acknowledgment

We are indebted to the anonymous referees and Toshihiro Matsumura for their constructive comments and suggestions. We also thank the participants at University of Tokyo and National Taiwan University Joint Conference on Industrial Organization, especially Professor Hwang Hong for their useful comments and suggestions. The financial support from the Tatung University is greatly appreciated.

Notes

1. For example, there are state-owned companies and an increasing presence of foreign ownership (mainly from China) in Canada’s mining industry. In addition, there are many industries belongs to this case, such as education, energy, medical care, banking, and life insurance.

2. Numerous paper on mixed oligopoly has extensively assumed that a public firm competes with the private firms who are pure domestic firms, pure foreign firms, or some domestic and some foreign firms (see Mujumdar and Pal 1998; Pal and White 1998; Ohori 2004; Bárcena-Ruiz and Garzón 2006; Chao and Yu 2006). However, little attention in the body of literature has been paid to the effect of the foreign investors in private firm on the optimal taxation policy. In order to incorporate reality into the situation, we take up an issue, in which a private firm is jointly owned by domestic and foreign investors, in this paper.

3. The analysis of a privatization policy has also received significant attention in the literature recently (see De Fraja and Delbono 1989; Cremer, Marchand, and Thisse 1991; White 1996; Matsumura 1998; Pal and White 1998; Bárcena-Ruiz and Garzón 2006; Chao and Yu 2006; Ishibashi and Matsumura 2006; Jiang 2006; Ohori 2006; Fujiwara 2007; Mukherjee and Suetrong 2009).

4. They investigate the data of six network industries of 30 OECD countries (1975–2007) and find that right-wing parties have a higher proportion to implement privatization policy than left-wing parties.

5. In reality, the process of privatization may encounter difficulties. For example, the culture of the state-owned enterprise is totally different from that of private enterprises. Conflicts arise between two groups of people when the state-owned enterprise undergoes partial privatization. Compared with a privatization policy, a taxation policy is practically easier to impose. Thus, if a taxation policy can achieve higher welfare, then it implies that the government can implement taxation instead of privatization when the privatization policy is not easy to implement.

6. White (1996) considers the production subsidies in mixed oligopoly industry and shows that the privatization neutrality theorem is hold. Numerous paper also find that the privatization neutrality theorem is hold. For example, Kato and Tomaru (2007) consider several types of objectives of private firm; Hashimzade, Khodavaisi, and Myles (2007) discussed heterogeneous goods; Tomaru and Saito (2010) analyzed the endogenous timing. However, Fjell and Heywood (2004) and Matsumura and Tomaru (2013) derived a non-neutral result.

7. Matsumura and Matsushima (2004) provide a justification for this assumption.

8. Note that ϕ > 1 is necessary to the positive production of the private firm (if τ = 0). If the efficiency level of the public firm is the same as that of the private firm (ϕ = 1), then the public firm will monopolize the entire market and the private firm will exit the market.

9. This is because the public firm does not care about firm 1’s profit when firm 1 is a pure foreign firm. In addition, the taxation policy is just like money transfer from the right-hand side pocket to the left-hand side one for firm 0, so firm 0’s output is not affected by the taxation policy.

10. We obtain the same result as Mujumdar and Pal (1998) when β = 1; however, in the case of 0 < β < 1, we find that the total output decrease with the tax.

11. By (2) and (3), the slope of R₀ is dq₁/dq₀ = −1/β and the slope of R₁ is dq₁/dq₀ = −1/2.

12. One can image that this is quite different to the privatization policy. Under a privatization regime, although the privatization leads to a reduction in firm 0’s output, firm 0’s output will be positive, even if the privatization policy is full nationalization.

13. Unless the demand function is very convex, the property of the Cournot competition is strategic substitutes.

14. It is worth to point out that even the optimal taxation policy is subsidy; the public firm does not exit the market. This is because is lower than the non-negative output constraint of β, which is defined as .

15. If a < a^∗, so as the public firm cannot survive in the market, then the optimal tax imposed on the private firm is (a − c)(1 − 2β)/(3 − 2β). In this case, the private firm’s equilibrium output is  = {(2β − 1)a + [(3 − 2β)ϕ − 2]c}/[(3 − 2β)(2 − β)]. Note that if β = 1, then the optimal subsidy and equilibrium output are τ = −(a − c) and a − c, respectively.

16. In the privatization literature, there are two popular model formulations of firms’ marginal cost: constant marginal cost and increasing marginal cost. Matsumura and Okamura (2015) investigate the relationship between competition and privatization policies under these two popular models and yield the contracting results. We discuss the relationship between the inefficiency level of public firm and which policy should be adopted under these two models and also obtain the different results. In the increasing marginal cost model, whether a tax or a subsidy should be adopted depends on the inefficiency level of the public firm. The reason is as follows. If the marginal cost is constant, then the marginal cost of per unit output is the same. Therefore, the distortion of production inefficiency can be totally corrected by the public firm’s output decision that is reallocating the output from the public firm to the private firm. However, if the marginal cost is increasing, then the marginal cost of any unit of output is different. The distortion of production inefficiency cannot be totally corrected by the public firm’s output decision. Hence, our result does not hold in the increasing marginal cost model.

17. A higher marginal cost for the public firm leads to less of its output and more of the private firm’s output. Therefore, the domestic government has an incentive to set a higher tax to extract the foreign country’s profit. On the contrary, the government has an incentive to encourage the private firm to produce more when domestic country ownership is sufficiently high, and so it sets a higher subsidy.

18. Matsumura and Tomaru (2012) has a similar result that the optimal policy could be subsidy or tax; however, we further point out that whether a subsidy or a tax should be adopt is independent with the pubic firm’s inefficiency level.

19. Note that the equilibrium price is higher than firm 1’s marginal cost c, because of ϕ > 1, and so firm 1 achieves a positive profit. However, if ϕ = 1, then the equilibrium price is equal to c and firm 1 earns zero profit.

20. If the public firm’s marginal cost is the same as the foreign one’s (ϕ = 1), then the equilibrium price is equal to c, the public firm will serve the entire market, and the foreign one will exit the market.

21.

22.

23. There is no reason for the domestic government to privatize the public firm, since firm 1 can choose an output to achieve the first best level of welfare without any inefficiency.

24. An extreme case is β → 1. In this case, the first best situation is setting the price at p = c, so the government has an incentive to increase firm 1’s output to get q₁ = a − c as close as possible. From Figures 1 and 2, we see that the magnitude of a rise in q₁ under the taxation () is larger than that under the privatization (). Therefore, a subsidizing is better than privatization. Nevertheless, the market is only served by the efficient firm (firm 1).

25. In the increasing marginal cost model, this result does not hold. The reason has been mentioned in footnote 13.