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Foreign ownership, privatization and subsidization with shadow cost of public funds
North American Journal of Economics and Finance xxx (xxxx) xxx–xxx
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Foreign ownership, privatization and subsidization with shadow cost of public funds Ding Chena,1, Leonard F.S. Wangb, , Jen-yao Leec ⁎
a b c
School of Economics and Management, Xi’an Shiyou University, X’ian, Shaanxi, China Wenlan School of Business, Zhongnan University of Economics and Law, Wuhan, Hubei, China Department of International Business, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
ARTICLE INFO
ABSTRACT
JEL classification: F13 H21 L13
We examine how the shadow cost of public funds will affect the privatization policy in the presence of strategic tax/subsidy policies in a mixed oligopoly model with foreign ownership. We show that (1) When the dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large; (2) When the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relative small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Additionally, we show that the influence of foreign ownership on the privatization and subsidization policies are dependent upon the cost structures, ownership types, distribution of firms, and policy pairs.
Keywords: Foreign ownership Privatization The shadow of the public fund Production subsidy Social welfare
1. Introduction Over the past few decades, there has been a proliferation of theoretical literature involving the exploration of privatization. De Fraja and Delbono (1989) in a mixed oligopoly model showed that the privatization of welfare-maximizing public firms might improve social welfare. Matsumura (1998) explicitly considered the possibility of partial privatization.2 In the literature on mixed oligopolies, Capuano and De Feo (2010), Wang and Chen (2011b) and Matsumura and Tomaru (2013, 2015) have tackled the policy burden issue by examining the welfare effect of a change in a public firm's objective function when the government takes into account the shadow cost of public funds (or excess taxation burden, ETB). Wang and Chen (2011b) considered only the case of Cournot competition with cost efficiency gap, while Matsumura and Tomaru (2013) compared the optimal subsidies and the resulting welfare levels among four regimes: mixed and private Cournot duopolies and Stackelberg competition with public
⁎ Corresponding author at: Wenlan School of Business, Zhongnan University of Economics and Law, 182# Nanhu Avenue, East Lake High-tech Development Zone, Wuhan 430074, China. E-mail address: [email protected] (L.F.S. Wang). 1 Ding Chen acknowledges the financial support from National Social Science Research Program (Item No. 18VSJ094) and Scientific Research Program Funded by Shaanxi Provincial Education Department (Item No. 16JK1584). The authors would also like to thank the editor, two anonymous referees, Angela C. Chao and Chenhang Zeng for their helpful comments and suggestions. 2 In a free-entry market, Matsumura and Kanda (2005) assessed the welfare implications of partial privatization in a homogeneous oligopoly, and can be an alternative to direct regulation to avoid the excess entry problem. Wang and Chen (2010) highlighted the importance of the cost-efficiency gap between public and private firms, and showed the relation of the cost-efficiency gap and foreign competition with optimal privatization in a free-entry market.
https://doi.org/10.1016/j.najef.2018.10.017 Received 10 July 2018; Received in revised form 23 October 2018; Accepted 29 October 2018 1062-9408/ © 2018 Elsevier Inc. All rights reserved.
Please cite this article as: Chen, D., North American Journal of Economics and Finance, https://doi.org/10.1016/j.najef.2018.10.017
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and private leaderships. Further, Matsumura and Tomaru (2015) examined the effect of product differentiation, while Xu, Lee, and Wang (2016), Lee and Wang (2018) considered the relationships with foreign competition. Looking at the influence of environmental policies on privatization in a free-entry mixed market taking account of excess burden of taxation, Xu and Lee (2018) showed that when the excess burden of taxation is small (large), ex-post taxation imposes a lower (higher) tax level than ex-ante taxation, which results in a larger (smaller) number of firms and higher (lower) environmental damage. What motivates us is providing a generalized framework not only to synthesize the existing models, but to also deal with the five issues: partial privatization, subsidization, competiveness, foreign penetration, and excess taxation burden (shadow cost of public funds). In this paper, we examine how the competition and shadow cost of public funds will affect the privatization and subsidization policies in a mixed oligopoly model with foreign ownership. We show two main propositions that (1) when the dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large; and (2) when the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relatively small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Additionally, we show that the influence of foreign ownership on the privatization and subsidization policies are dependent upon the cost structures, ownership types, distribution of firms, and policy pairs. Clearly, some of our results are new derived from a generalized model setting and which should be noticed by academic researchers and policy decision-makers. This paper is organized as follows. Review of relevant literature is given in Section 2. Basic modeling is provided in Section 3. Section 4 explores how the shadow cost of public funds and foreign ownership will affect the privatization policy in the presence of strategic tax/subsidy policies. Section 5 provides comparisons of policy choice and social welfare. Section 6 concludes the paper. 2. Review of relevant literature In the literature on the optimal subsidy in mixed oligopoly, White (1996) showed that the same subsidy rate yields the first-best outcome in both mixed and private oligopoly in his Cournot setting (privatization neutrality theorem). This privatization neutrality theorem (PNT) was supported by Tomaru (2006), who showed that the optimal subsidy, all firms’ output, profits and social welfare are identical regardless of the share in a state-owned enterprise (SOE), and Matsumura and Okumura (2013), who also showed the optimal output floor regulation, concluded that privatization does not affect welfare regardless of the time structure and the degree of privatization. Wang and Chen (2011a) and Matsumura and Tomaru (2013) introduced an excess-taxation burden to describe the violation of the PNT. The violation of the PNT means privatization can work to enhance welfare. Tomaru and Wang (2018) then examined the optimal privatization policy. They showed that the optimal policy is partial privatization when the technical improvement is small. Matsumura (1998) showed that partial privatization is optimal in a mixed duopoly. A crucial difference between them is that Tomaru and Wang (2018) considered subsidization and a technical improvement resulting from privatization. Subsidization adjusts the production allocation, and privatization plays an auxiliary role in enhancing welfare by further adjusting the production allocation and improving the technology of the privatized firm. We have observed that beside the open-door policy in product marker, recent capital liberalization that is prevalent globally has enabled not only domestic investors but also foreign investors to own domestic private firms in many mixed markets. To see how the foreign penetration affects the privatization policy, Wang and Chen (2011a) showed that in the short-run, the government should increase the degree of privatization when the equity share held by foreign investor is increasing, which increases all domestic private firms’ profit and social welfare. Cato and Matsumura (2012) investigated how foreign penetration in the domestic market affects the privatization policy and showed that the optimal degree of privatization is increasing in foreign penetration in the long-run. The implications of Wang and Chen (2011a) and Cato and Matsumura (2012) are that the open capital market policy and privatization are complementary whether no entry barrier exists or entry or exit is possible in the market. The country with a more open capital market should privatize the firms more, even though this temporally reduces welfare. Matsumura and Tomaru (2012) found that under the optimal tax-subsidy policy, the government’s privatization decision depends on how many private firms in the product market and the equity share are held by foreign investor. In particular, when the equity share held by the foreign investors is low, the government should privatize the public firm in the absence of free entry of private firms. Wang and Lee (2013) examined how the order of the firm’s moves affects the social efficiency with foreign ownership and free entry in a mixed oligopoly market. In particular, they showed that when the foreign shareholding ratio is low, the entry of private followers will lead to lower consumer welfare and higher social welfare, but the profit of the incumbent nationalized firm is higher under entry than under no entry. Furthermore, they found that there always exists the problem of excessive entry under public leadership regardless of the degree of foreign ownership, which has important implications for industrial and market-opening policies. Wang and Tomaru (2015) showed that partial privatization is optimal for small extents of foreign penetration and the optimal degree of privatization is not monotonically related to foreign penetration. This result is in sharp contrast to the existing works that suggest either the positive or negative relationship. Xu, Lee, and Matsumura (2017) investigated the impact of the timing of privatization and liberalization policies on the degree of privatization and number of entering firms in free-entry mixed markets. They formulated two models: ex-post privatization and ex-ante privatization. In the former, the government liberalizes the market and then privatizes the public firm, whereas the order of the policies is reversed in the latter. They showed that ex-ante privatization yields a higher (lower) level of privatization and a larger (smaller) equilibrium number of entering private firms when foreign ownership in private firms is high (low).
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3. Basic model Consider a domestic market for a homogeneous good produced by one public firm, and n domestic firms. The linear demand function is specified as P = a
Q . The supply equation is given by Q = q0 +
n
i=1
qi , where q0 , and qi denote, respectively, the output
of public firm, and domestic firms. As in many existing studies on mixed oligopoly, we assume that all firms use an identical q2
technology and have the increasing marginal cost function: 0 , and 2 The profits of domestic public and private firms are given by: n 0
= a
q0 +
q0 +
, respectively.3
2
n
= a
2
q02
qi + s q0 i=1
i
qi2
(1)
qi2
qi + s qi
2
i=1
(2)
where s is the unit subsidy rate. The social welfare is defined as, n
SW = CS + (1
n
)
(1 + ) s
i i=1
qi + sq0
0
(3)
i=1
where the consumer surplus is given by CS = Q2/2 , is the shareholding ratio of the foreigners, and signifies the shadow cost of public funds for representing administrative inefficiency of government bureaucracy.4 As explained in Matsumura and Tomaru (2012), when all private firms are symmetric and denotes the share of foreign investors in the private firms, then there are n ) n domestic private firms. As such, two formulations yield exactly the same equilibrium outcomes.5 foreign private firms and (1 [0, ) . As pointed out in Matsumura and Tomaru (2013), the social welfare can be decomposed into the welfare We assume that without excess taxation burden and the distortion due to taxation. Moreover, we can rewrite Eq. (3) to obtain n
SW ( ) = CS + (1
n
)
(1 + ) s
i i=1
i=1
n
qi + sq0
= CS + (1
0
) i=1
n
n i
s i=1
qi
sq0 +
0
n
s i=1
qi + sq0
0
= SW ( = 0) +
s
0
i=1
qi
sq0
The right-hand side of the equation states that the excess burden applies on the subsidy paid to the private firms. As easily inferred from this social welfare, an increase in makes the official putting greater emphasis on the profit of SOE. The government sells all or a part of shares in firm 0 in the first stage (shares-selling stage). This means that the revenue from selling the shares is fixed in the later stage, where the output-setting stage follows the shares-selling stage. The government finances the subsidies for the firms from the partial profits of the privatized firm, and the revenue from selling the stocks of firms. We assume that the financial markets are perfect. V is the revenue from selling the stocks of firm 0. Assume the degree of ) 0 and 0 , respectively. 0 . The profit sharing of the government and the private investors are (1 privatization is , and 1 Then, the government sets s and to maximize the following social welfare: n
SW = CS + (1
n
)
i
+
0
V + (1 + ) (1
)
0
+V
i=1
sq0
s
qi
The government maximizes the social welfare, SW , expecting (i) the equilibrium result in the subgames and (ii) V = the private investors’ rationality and the assumption of perfect stock markets. When government privatizes the public firm partially, the optimization problem for the semi-public firm is:
max. {q0 }
=
0
+ (1
(4)
i=1
) SW
0
due to
(5)
3 See Matsumura and Kanda (2005), Wang et al. (2009) and Wang and Chen (2010) for using the specification of increasing marginal costs (decreasing returns to scale technology) in mixed oligopolies. In the current paper, we use a homogeneous demand function with decreasing returns to scale technology, which is not a general specification of the demand and the cost side of the model. Once the two assumptions are relaxed, our results may qualitatively differ. 4 The similar specification can be found in Capuano and De Feo (2010), Wang and Chen (2011b), and Matsumura and Tomaru (2013). 5 Foreign ownership of public firms is not considered in this paper. Lin and Matsumura (2012) also investigated the presence of foreign investors in privatized firms and confirmed Wang and Chen’s finding that an increase in the stockholding ratio of foreign investors in a privatized firm increases the optimal degree of privatization, whereas an increase in the penetration of foreign firms in product markets reduces it. These results imply that the degree of openness of financial markets and that of product markets have contrasting implications for the optimal privatization policy.
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where is the weight assigned to the profits in the decision-making process of the firm.6 The difference between us and Matsumura (1998) is that the government can directly control through its shareholding. The fully privatized firm only seeks the profit if = 1; contrarily, a fully nationalized firm maximizes the social welfare if = 0 . The government chooses the subsidy rate and the degree of privatization to maximize social welfare. We construct a two-stage game. In the first stage of the game, the government decides the subsidy rate and the degree of privatization. In the second stage, the firms engage in Cournot competition. The backward induction is used to derive the sub-game perfect Nash equilibrium (SPNE). 4. Foreign ownership, privatization and social welfare The outputs of the domestic private firms and the public firm are obtained by partially differentiating Eqs. (2) and (5) with respect to qi , and q0 , the first-order conditions are: i
qi
=a+s
q0
=a+s +a
q0
2qi a
2
2
+( 2
(6)
+ 3( 1 + ) ) q0
+n ( 1 +
+ ( 1 + ) ) qi = 0
2
q02
We have |H| =
nqi = 0
q0 qi 2
i
> 0 . According to the positive Hessian, the second-order conditions and stable condition of the game
i qi2
qi q0
are satisfied.7 The equilibrium outputs are:
qi (s , ) =
a + 2s + a + (2a + 3s )(1 ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1
q0 (s , ) = a + s
(8)
)
(2 + n)(a + 2s + a + (2a + 3s )(1 ) ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1 )
(9)
We analyze joint choices of privatization and subsidization policy in three regimes. In regime A and B, the government employs either a privatization level or an out subsidy. In regime C, the government simultaneously employs dual policy instruments of subsidization and privatization. 4.1. Regime A: The privatization policy is employed Letting s = 0 and substituting Eqs. (8) and (9) into Eq. (4) and then differentiating with respect to , the degree of privatization is given as A
=
n (1 2 2 + (n 1 + (n 2) )) n 4 + n (1 + 2(1 ) + (5 + n + (n 2) )) ,
0
+2
> nA n
+2 2 (1 + )
1
. (10)
n A.
As it can easily observed, full nationalization is optimal for a large and a small and n . It is straightforward, when the number of private firms is relatively large, partial privatization is employed due to the market compete is intensive. nA
= > 0 . When the shadow cost of public fund Taking differentiation of n A with respect to , and we obtain (1 + )2 increases, the critical value of number of private firms raises. Other thing being equal, the possibility of the public firm being fully nationalized increases to enhance the consumer surplus. As Matsumura and Tomaru (2013) pointed out, the government confronts two effects when it privatizes its public firm. One is that the shadow cost of public fund (excess burden of taxation) increases and the consumer surplus decreases, owing to the private and privatized firms’ disincentive to produce more, which is a negative welfare effect of privatization. The other is that privatization equalizes (or makes closer) the outputs of both firms, which reduces the sum of total costs. This is a positive welfare effect of privatization. Whether or not privatization improves welfare depends on which effect is stronger. Privatization increases the shadow cost of public fund, reduces consumer surplus, and induces output substitution from the public firm to the private firms. The former two effects reduce welfare whereas the last one improves welfare. The former two effects dominate the last one under our setting of the framework. 0 . Taking differentiation of A with respect to According to Eq. (10), we assume 2 2 1 > 0 to ensure n A > 0 if , we obtain that
A
=
n
1+2 2 1 + (n 2)
1+
+ 2 (2 + )
< 0 . When the ratio of foreign ownership increases, the optimal degree of privatization declines. The
6 Public firms may have other different targets, such as maximizing the profit, income, employee’s income or management of license, etc. See De Fraja and Delbono (1989), and Pal and White (1998) on the modeling of a public firm as a social welfare maximizer. 7 For example, see Etro (2006).
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intuition is that when the ratio of foreign ownership in the private firms is high, the role of the private firms is acting like foreign firms. This is simply because if a private firm is foreign-owned, its profit is sweated out of the country. This provides the government with an incentive to nationalize the privatized firm, thereby government will reduce the degree of privatization and transferal of profits to the (previously) privatized firm. 4.2. Regime B: The subsidization policy is employed as
Letting
= 0 and substituting Eqs. (8) and (9) into Eq. (4) and then differentiating with respect to s , the optimum subsidy is given
sB =
a (2
if n < nB
2 (n
+ 2n ) + (n 6 21 3(6 + n) 2) (2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 +
(2 + 3 )( 1 + 2 + 6 2 + (3 + 6 )) (1 ) (1 + 2 2 ) (4 + 3 ) 2 4
2
(1 + 18 (1 + ) + n (1 + 2 ) 2)) >0 + 2 + 3 (1 + ))) (11)
3
According to Eq. (11), when the number of private firms is relatively small, a positive subsidy is necessary to expand the output of the market due to the market compete is insufficient. As in Matsumura and Tomaru (2013), a higher cost of public funding reduces the optimal subsidy rate, and it becomes negative if is large. An increase in reduces the output of the public firm and increases that of the private firm through strategic interaction. The output substitution from the public firm to the private firm improves production efficiency because the marginal cost of the public firm is higher than that of the private firm. In our framework, we extend their model by taking into account the foreign penetration and competition involving more than one private firms. As in Matsumura and Tomaru (2012) without taxation burden in mixed oligopoly, the optimal subsidy s B can be either positive or negative, which is dependent on the value of . The intuitions are the following. In mixed oligopoly, the output of each private firm is too low for domestic welfare; thus, the government has an incentive to raise s so as to stimulate the output of private firms. On the other hand, an increase in s raises the outflow of surplus to the foreign investors and reduces domestic welfare. The latter effect becomes more significant when and n are large. Our result confirm the robustness of Matsumura and Tomaru (2012) with excess taxation burden. 4.3. Regime C: The dual policies are employed Substituting Eqs. (8) and (9) into Eq. (4) and then differentiating with respect to s and , the optimum subsidy and degree of privatization are given as
sC = C
=
a (1 (3 + 6 ) (2 + n + (6 + n) )) > 0, if n < nC n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )
1
3
2 6 (1 + )
6
2
n (1 + ) <1 6+n+n
(12) (13)
The intuition of dual policies will be explained later. We have the following lemma immediately. Lemma 1:. (i) qi are increasing in while q0 , and q0 + nqi are decreasing in when the privatization policy is employed. (ii) qi , and q0 + nqi are increasing in s , and q0 is decreasing in s when the subsidization policy is employed. (iii) When the dual policies are employed, qi , and q0 + nqi are increasing in s , and q0 is decreasing in s if the shareholding ratio of the foreigners is relatively small. qi are increasing in while q0 , and q0 + nqi are decreasing in . Proof. See the Appendix I. A higher degree of privatization will shift the output from the privatized firm to the private firms, which increases that of the private firm, and declines the output of the public firm and total output through strategic interaction. Thus, privatization can induce welfare-improving output-substitution effect between privatized firm and domestic private firms. The output of the private firms is increasing in . An increase in s lowers the production cost of the private firm, which increases the output of the private firm and total output. Thus, subsidization can induce welfare-improving output-expansion effect of the output of the private firm and total output. The output of the private firms and total output are increasing in s . When the dual policies are employed, the output of the privatized firm is decreasing in s , if the shareholding ratio of the foreigners is relatively small. Due to the output-substitution effect between the privatized firm and the private firms, the output of the privatized firm is decreasing in . The output of the private firms and total output are increasing in , due to the output-substitution effect shifting production from the privatized firm to the private firms. We have the following proposition 1. Proposition 1:. When the dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large. 5
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We can see from proposition 1 that *C tends to increase with n. This means that more competitive markets call for greater privatization policies, which is qualitatively the same as the result from De Fraja and Delbono (1989). Proposition 1 suggests that regardless of the number of domestic private firms, the partial privatization of a public firm is always desirable from a welfare point of view in the presence of the shadow of the public fund. This is in sharp contrast to the existing literature. Capuano and De Feo (2010) demonstrated that with nil or large efficiency gains, an inefficient public firm that maximizes welfare may still be preferred where there exists the shadow of the public fund in the government's objective function. Wang and Chen (2011b) found that for an imposition of the optimal subsidy, the level of welfare with privatization depends on the level of the cost-efficiency gap and the excess burden of taxation. Comparing privatization with mixed duopoly, Matsumura and Tomaru (2013) investigated optimal tax-subsidy policies with the excess burden of taxation. They focused on both the optimal tax-subsidy policies with endogenous timing of production, as well as the privatization neutrality theorem. They showed that mixed-oligopoly welfare reduction does not hold with the shadow of the public fund. Hence, the PNT does not hold even when they compared the resulting outcomes before and after privatization. They did not extend the study to the situation in which the public firm competes with multiple private firms as we do in this paper. *C
= (6 + n + n )2 > 0 . When the shadow cost of public fund inTaking differentiation of *C with respect to , we obtain that creases, the degree of privatization rises. The intuition is the same as we provided in regime A. sC*
6n
a (15 + n (7 + n) + 3n + 9 2 + 2(4 + n)(6 + n) + (6 + n)(7 + n
3 ) 2)
= < 0. Taking differentiation of s C* with respect to , we obtain that (n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))2 When the shadow cost of public fund increases, the subsidy rate declines due to the subsidy policy being more costly. We further show that the production tax may be used if the shadow of the public fund is relatively large. This result coincides with Matsumura and Tomaru (2013), Lee and Wang (2018): s is not always positive (i.e., the government may impose a production tax). When is small, s > 0 . However, when is large, s is negative. Naturally, a higher cost of public funding reduces the optimal subsidy rate, and it becomes negative if is large. In our modelling, there are two distortions thereby needing two policy instruments concurrently to deal with these: firstly, the domestic market is under oligopolistic competition and output of domestic private firm is less than the one under perfect competition, and it needs output subsidy to increase the private firm’s output; secondly, for the public firm, it cares about social welfare, which leads to more output and higher marginal cost needing higher degree of privatization to curtail the output of public firm. We have the following proposition 2. Proposition 2:. When the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relative small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Proof:. Taking differentiation of A
=
A
,
C
and s C with respect to 2
, we obtain
2
2n ( 4( + 2 ) + n ( 1 + 3( 2 + n) 2 ( 3 + n + 12 ))) < 0, (4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) )))2
when
4 + n ( 3 + n + 12 ) +
< C
sC
=
=
16 + n (n3
24(1 + 4 ) + 6(n + 2n )2 + n ( 7 + 24 (1 + 4 ))) 6( 2 + n) n
6n >0 (6 + n + n ) 2 a (15 + n (7 + n) + 3n + 9 2 + 2(4 + n)(6 + n) + (6 + n)(7 + n (n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )) 2
3 ) 2)
<0
When the dual policies are employed, if the social cost of public fund is more severe, and the degree of privatization and production subsidy are complementary instruments for a given degree of foreign ownership; the production subsidy should decrease and the degree of privatization should increase in order to mitigate the policy distortion. However, when only the privatization policy is employed, due to the official putting greater emphasis on the profit of the privatized firm, the degree of privatization is decreasing in the shadow cost of public funds, when the share of foreign investors in the private firms is relatively small. As in lemma 1, we have that qi are increasing in , while q0 , and q0 + nqi are decreasing in when the privatization policy is employed. On one hand, the output of the privatized firm is decreasing in , due to the output-substitution effect when the privatization policy is employed. A lower degree of privatization will lead the profit of the privatized firm higher. On the other hand, an increase in raises the outflow of surplus to the foreign investors and reduces domestic welfare. The latter effect becomes more significant when the share of foreign investors in the private firms is relatively large. Thus, we have the degree of privatization is increasing in the shadow cost of public funds, when the share of foreign investors in the private firms is relatively large. This result is in line with Lee and Wang (2018): The optimal degree of privatization is increasing in the shadow cost of public funds if the shadow cost of public funds is relatively large. In that framework, a higher shadow cost of public funds will cause a lower subsidy rate and a higher degree of privatization, due to the subsidy policy being more costly. The output subsidy-induced effect on total output is decreasing while the tariff-induced output effect is increasing in the domestic output market. When is relatively 6
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small, in this case, the government does care more about the consumer surplus. Thus, a lower degree of privatization is needed to enhance the total market output. When is relatively large, in this case, the government cares less about the consumer surplus; thus, a higher degree of privatization is adopted to enhance the total revenue of the government. However, in this framework, the tariff policy is not adopted due to the close-door policy. The tariff-induced output effect doesn’t exist in the policy options, and the government has to increase the degree of privatization to lower the output of the privatized firm and decline the cost inefficiency of the privatized firm. [0, ) in our analysis, here we consider what would happen if Although we assume . Taking limit of , and s we have
lim
C
= lim
lim s C = lim
n (1 + ) =1 6+n+n
a (1 (3 + 6 ) (2 + n + (6 + n) )) = n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )
a 2
The optimal degree of privatization is 1, and the output subsidy is negative, 2 ; that is, a production tax is adopted. Due to officials putting a greater emphasis on the profit of SOE, they do not care about consumer surplus anymore. The government’s objective reduces to maximize their revenue (production tax, and profit of the privatized firm), and full privatization is chosen. Wang and Chen (2011a) showed that in the short-run, the government should increase the degree of privatization when the equity share held by foreign investors is increasing in the absence of subsidization policy and the shadow cost of public funds. In their framework, not all of the private firms are held by foreign investors, and an output-substitution will be realized by the other private firm. So, an increase in the degree of privatization is called for from the welfare viewpoint. Next, we consider some comparative analysis result of the influence of foreign ownership on the degree of privatization and subsidization. We have the following proposition in the case that is 0. a
Proposition 3:. When the privatization policy is employed, the degree of privatization is decreasing in the shareholding ratio of the foreigners; when the dual policies are employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, while the degree of privatization is irrelevant to the shareholding ratio of the foreigners. Proof:. Taking differentiation of A
,
C
and s C with respect to , we obtain that
=
2n (2 + n) <0 (4 + n + n (5 + n) ) 2
=
3a (4 + n) <0 (n + 2) 2
=0
C
A
=0
sC =0
Our result is different from Wang and Chen (2011a): when only the privatization policy is employed, the degree of privatization is decreasing in the shareholding ratio of the foreigners. The reasoning is that, a higher of the shareholding ratio of the foreigners raises the outflow of surplus to the foreign investors and reduces domestic welfare. A decreasing increases the output of the privatized firm, and thus, we have that the optimum degree of privatization is decreasing in the shareholding ratio of the foreigners. As mentioned in proposition 2, when the dual policies are employed in mixed oligopoly with partial privatization, an increase in s raises the outflow of surplus to the foreign investors and reduces domestic welfare, becoming more significant when is large. Thus, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners. Wang and Tomaru (2015) in a linear-demand and constant marginal-cost setting, showed that an increase in makes firm 0 have a greater incentive to produce due to the terms-of-trade effect, if is relatively small. This aggressive behavior of firm 0 increases the total production cost incurred by the domestic country. A decrease in makes firm 0 reduce its output via the terms-of-trade effect and the profit-motivation effect. Thus, to decrease the welfare loss from the increased production cost, the government tries to reduce when is increased. If is in an intermediate range, firm 0 overproduces by the terms-of-trade effect. Accordingly, an increase in makes the price so low that firm 0 earns negative profits for a wider range of . However, if is sufficiently large, increase makes an impact of the dividends on welfare more negligible, and so, only the consumer surplus matters for welfare. The government chooses full nationalization, and the consumer surplus improves due to firm 0′s greater incentive to produce. However, in the case of increasing marginal cost with subsidization policy, the public firm cares about social welfare, which leads to more output and the higher marginal cost needing higher degree of privatization to curtail the output of public firm. The effect of partial privatization amends the cost inefficiency caused by over-production of public firm. Although an increase in raises the outflow of surplus to the foreign investors and reduces domestic welfare, the lower subsidy rate revises the outflow of surplus. The privatized firm’s output is increasing in , whereas the private firm’s output is decreasing in it. Accordingly, the degree of privatization is irrelevant to the shareholding ratio of the foreigners. To see whether production subsidy or production tax will be chosen along with privatization policy, we have the following proposition in the case that is 0. 7
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Proposition 4:. When the subsidization policy is employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, if the number of private firm is relatively small; when the dual policies are employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners. Proof. Taking differentiation of s B , s C and
sB
= =0
with respect to , we obtain:
a (24 + n (4 + 8 + n ( 1 + (2 + )))) <0 2(2 + n + 6 + n 2)2
(2 + 3 )( 1 + 2 + 6 2 + (3 + 6 )) ( 1 + ) + + 2 2 + (4 + 3 ) 2 + 4
if n < sC
= =0
C
C
3
3a (4 + n) <0 (n + 2) 2
= 0.
As mentioned in proposition 3, an increase in raises the outflow of surplus to the foreign investors and reduces domestic welfare, but the lower subsidy rate revises the outflow of surplus. In our model, production subsidy and partial privatization policy are concurrently adopted from the welfare point of view.8 However, when the subsidization policy is employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, if the number of private firm is relatively small. This is consistent with Matsumura and Tomaru (2013) who showed the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, if the number of private firm is relatively small. When the number of private firm is larger,
s B*
=0
is ambiguous. The public firm’s output is increasing in , whereas the private firm’s
output is decreasing in it. Note that the public firm’s profit can be negative when is sufficiently larger. In the case of a sufficiently large , the optimal subsidy rate s B* becomes negative, i.e. a production tax is imposed on all firms. Recall that the public firm becomes more aggressive toward improving the terms of trade if increases. 5. Comparisons of policy choice and social welfare We compare the optimal subsidies, the degree of privatization and the resulting welfare among the three policy regimes. Computation yields the following:
W
A
=
a2 ((2 + n) 2 + (8 + n (7 + n 3 )) + 4 2) 2(8 + 12 + n (5 + n + 3 + (8 + n) ))
W
B
=
a2 (1 + ) 2 ((2 + 3 )(1 + 3 + 4 ) + n (2 + 2(2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 +
W
C
=
a2 (1 + ) 2 (1 + n + 3 + (4 + n) ) 2(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))
2 2
+2 +2
+ (5 + 4 ))) + 3 (1 + )))
First, we compare the optimal subsidies and the degree of privatization. This comparison leads to the following proposition. Proposition 5:. Suppose that demand is linear, firms’ costs are quadratic. The optimal subsidies in the three regimes have the following properties. (1) s C < s B , (2) C > A, i f
>
1
(2 + n + (6 + n) ) 3+6
Proof:.
sC C
sB = A
=
an (1 + ) 2 ( + )(n (1 + )(1 + ) + (1 + + 2 )(2 + 3 )) (2 + 3 )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))((2 + 3 )(1 + 3 + 4 ) + n (1 + 2 + 2
2n ( 1 + (3 + 6 ) + (2 + n + (6 + n) )) > 0, if (6 + n + n )(4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) )))
>
1
+ 3 (1 + )))
<0
(2 + n + (6 + n) ) 3+6
We explain the intuition behind Proposition 5. Due to the shadow cost of public fund and foreign ownership, the social cost of 8 The similar result can be seen in Lin and Matsumura (2018) in the presence of foreign ownership, and Tomaru and Wang (2018) in the presence of endogenous cost asymmetry.
8
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subsidization is high. The social cost of the privatization policy is relatively low. Accordingly, the optimal subsidy rate is low under a dual policies regime. When the ratio of foreign ownership is high, it will decrease the degree of privatization under regime A. However, in regime B, the government can use the lower subsidy rate to mitigate the negative effect of foreign ownership. Hence, with a higher ratio of foreign ownership, the degree of privatization will not be affected and it appears that C * > *A . It shall be noted that the optimal policy can be full nationalization in regime A, while it is necessarily partial privatization in regime B. Next, we compare the welfare level among the three types of regimes. We obtain a clear result with regard to welfare ranking. Regardless of and , dual policies yield the highest welfare level. Proposition 6:. Suppose that demand is linear, firms’ costs are quadratic, and
> 0 . Then,W C > max{W A, W B}
Proof.
W
A
W
B
=
1 2 (2 + n)2 + (8 + n (7 + n 3 )) + 4 2 a 2 8 + 12 + n (5 + n + 3 + (8 + n) ) (1 + ) 2 ((2 + 3 )(1 + 3 + 4 ) + n (2 + (2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 +
W
A
WC =
W
B
WC
=
2 2
+2 +2
+ (5 + 4 ))) + 3 (1 + )))
a2n ( 1 + (3 + 6 ) + (2 + n + (6 + n) )) 2 <0 2(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))(8 + 12 + n (5 + n + 3 + (8 + n) ))
a2n2 (1 + ) 4 ( + )2 2(2 + 3 )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))((2 + 3 )(1 + 3 + 4 ) + n (1 +
2
+2
+ 3 (1 + )))
<0
Regime A is a constraint equilibrium at the subsidy rate is 0 and regime B is also a constraint equilibrium at the degree of privatization is 0. As mentioned above, there are two distortions in our framework: 1) the total output of domestic private firms is less than the one under perfect competition; and 2) the public firm is less efficient than the private firms. For each policy objective, one policy instrument is needed, and one only. Naturally, the social welfares of regimes A and B will be lower than regime C. 6. Conclusions We have used a mixed oligopoly model with foreign ownership examining how the shadow cost of public funds and competition will affect privatization policy in the presence of strategic tax/subsidy policies. We showed two main propositions that (1) when dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large; and (2) when the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relatively small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Additionally, we show that the influence of foreign ownership on the privatization and subsidization policies are dependent upon the cost structures, ownership types, distribution of firms, and policy pairs. In this study, we assumed that all private firms are partially owned by foreign investors. Lee and Wang (2018) have considered how subsidization, tariff and privatization policies could be influenced by the entry of foreign firms who are competing with domestic firms due to the open-door policy of domestic country. It might be interesting to investigate whether the results will be changed if the foreign investors are allowed to invest in both public and private firms concurrently with or without the same share-holding ratio.9 Appendix I:. Proof of Lemma 1 Proof:. Regime A: The Privatization Policy is Employed We evaluate the comparative analysis at = A and s = 0
qi (s, )
9
2(a + an s (2 + n (1 + )3 )) (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) ))) 2 = > 0, 2(1 + n )(8 + 12 + n (5 + n + 3 + (8 + n) )) 2 =
See Lin and Matsumura (2012), who investigated the presence of foreign investors in privatized firms. 9
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D. Chen et al.
q0 (s, )
2(2 + n)(a + an (4 + n + n + 2 + n a (2 + n)(4 + n (1 2( 2(1 + n )(8 + 12
= =
Q (s , )
s (2 + n (1 + )3 )) (1 ) + 2(3 + n)(1 ) )2 1 + ) + (5 + n + ( 2 + n) )))2 < 0, + n (5 + n + 3 + (8 + n) ))2
4(2 + n) s 4(a + n (a + s ) ) + 4(3 + n) s (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) ))) 2 = < 0. (1 + n )(8 + 12 + n (5 + n + 3 + (8 + n) ))2 =
Regime B: The subsidization policy is employed We evaluate the comparative analysis at = 0 and
+ 2n ) + ( 6 + n 21 3(6 + n) 2) (1 + 18 (1 + ) + n (1 + 2 ) 2)) qi (s , ) 2 (2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 + + 2 + 3 (1 + ))) s 2 + 3(1 ) 2(a + an ) = = > 0, 4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) (4 + n + n + 2(3 + n) ) 2
s = sB =
q0 (s, ) s
2 (n
a (2
=1 =
(2 + n)(2 + 3(1 ) ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) 2a (2 + n)(1 + )( + )(6 + 9 + n (1 + + 2 )) (2 + 3 )(4 + n + n + 2(3 + n) )((2 + 3 )(1 + 3 + 4 ) + n (1 + 2 + 2
) + 2 (1 )) ) + 2(3 + n)(1 ) 4a (1 + )( + )(6 + 9 + n (1 + + 2 )) (2 + 3 )(4 + n + n + 2(3 + n) )((2 + 3 )(1 + 3 + 4 ) + n (1 +
+ 3 (1 + )))
< 0,
Q (s , ) 2 + n (1 + + (1 = s 4 + n + n + 2 + n (1 =
Regime C: The dual policies are employed We evaluate the comparative analysis at =
qi (s , ) s q0 (s , ) s
if
<
=
2 + 3(1 4 + n + n + 2 + n (1
+2
+ 3 (1 + )))
> 0,
and s = s
) ) + 2(3 + n)(1
)
(2 + n)(2 + 3(1 ) ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1
=1
2
=
)
6 + n + (9 + n) 12 + 6n + n2 + 3n + (3 + n)(6 + n) =
> 0,
n (3 2(1 + )) 12 + 6n + n2 + 3n + (3 + n)(6 + n)
< 0,
2(1 + ) 3
Q (s , ) 2 + n (1 + + (1 = s 4 + n + n + 2 + n (1 qi (s, )
q0 (s, )
)
=
n (4 + n + 3 + (7 + n) ) 12 + 6n + n2 + 3n + (3 + n)(6 + n)
2(a + an s (2 + n (1 + )3 )) (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (1 + )( + )(6 + n + n )2 = > 0, 2(12 + 6n + n2 + 3n + (3 + n)(6 + n) )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )) =
= =
Q (s , )
) + 2 (1 )) ) + 2(3 + n)(1
2(2 + n)(a + an s (2 + n (1 + )3 )) (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (2 + n)(1 + )( + )(6 + n + n ) 2 < 0, 2(12 + 6n + n2 + 3n + (3 + n)(6 + n) )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))
4(2 + n) s 4(a + n (a + s ) ) + 4(3 + n) s (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (1 + )( + )(6 + n + n ) 2 = < 0, 2 (12 + 6n + n + 3n + (3 + n)(6 + n) )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )) =
Appendix B. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.najef.2018.10.017.
10
> 0,
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References Capuano, C., & De Feo, G. (2010). Privatization in oligopoly: The impact of the shadow cost of public funds. Rivista Italiana Degli Economisti, 15, 175–208. Cato, S., & Matsumura, T. (2012). Long-run effects of foreign penetration on privatization policies. Journal of Institutional and Theoretical Economics, 168, 444–454. De Fraja, G., & Delbono, F. (1989). Alternative strategies of a public enterprise in oligopoly. Oxford Economic Papers, 41, 302–311. Etro, F. (2006). Aggressive leaders. RAND Journal of Economics, 37, 146–154. Lee, J. Y., & Wang, Leonard F. S. (2018). Foreign competition and optimal privatization with excess burden of taxation. Journal of Economics, 125(2), 189–204. Lin, M. S., & Matsumura, T. (2012). Presence of foreign investors in privatized firms and privatization policy. Journal of Economics, 107, 71–80. Lin, M. S., & Matsumura, T. (2018). Optimal privatization and uniform subsidy policies: A note. Journal of Public Economic Theory, 20, 416–423. Matsumura, T. (1998). Partial privatization in a mixed duopoly. Journal of Public Economics, 70, 473–483. Matsumura, T., & Kanda, O. (2005). Mixed oligopoly at free entry markets. Journal of Economics, 84, 27–48. Matsumura, T., & Okumura, Y. (2013). Privatization neutrality theorem revisited. Economics Letters, 118, 324–326. Matsumura, T., & Tomaru, Y. (2012). Market structure and privatization policy under International competition. Japanese Economic Review, 63, 244–258. Matsumura, T., & Tomaru, Y. (2013). Mixed duopoly, privatization, and subsidization with excess burden of taxation. Canadian Journal of Economics, 46, 526–554. Matsumura, T., & Tomaru, Y. (2015). Mixed duopoly, location choice, and shadow cost of public funds. Southern Economic Journal, 82, 416–429. Pal, D., & White, M. D. (1998). Mixed oligopoly, privatization, and strategic trade policy. Southern Economic Journal, 65, 264–281. Tomaru, Y. (2006). Mixed oligopoly, partial privatization and subsidization. Economics Bulletin, 12(5), 1–6. Tomaru, Y., & Wang, L. F. S. (2018). Optimal privatization and subsidization policy in mixed oligopoly: Relevance of an efficiency gap. Journal of Institutional and Theoretical Economics, 174, 189–203. Wang, L. F. S., & Chen, T.-L. (2010). Do cost efficiency gap and foreign competitors matter concerning optimal privatization policy at the free entry market? Journal of Economics, 100, 33–49. Wang, L. F. S., & Chen, T.-L. (2011a). Mixed oligopoly, optimal privatization, and foreign penetration. Economic Modelling, 28, 1465–1470. Wang, L. F. S., & Chen, T.-L. (2011b). Privatization, efficiency gap, and subsidization with excess taxation burden. Hitotsubashi Journal of Economics, 52, 55–68. Wang, Leonard F. S., & Lee, J. Y. (2013). Foreign penetration and undesirable competition. Economic Modelling, 30, 729–732. Wang, L. F. S., & Tomaru, Y. (2015). The feasibility of privatization and foreign penetration. International Review of Economics and Finance, 39, 36–46. Wang, L. F. S., Wang, Y. C., & Zhao, L. (2009). Privatization and efficiency gain in an international mixed oligopoly with asymmetric costs. Japanese Economic Review, 60, 539–559. White, M. D. (1996). Mixed oligopoly, privatization and subsidization. Economics Letters, 53, 189–195. Xu, L., & Lee, S. H. (2018). Environmental policies with excess burden of taxation in free-entry mixed markets. International Review of Economics and Finance. (forthcoming). Xu, L., Lee, S.-H., & Matsumura, T. (2017). Ex-ante versus ex-post privatization policies with foreign penetration in free-entry mixed markets. International Review of Economics and Finance, 50, 1–7. Xu, L., Lee, S. H., & Wang, L. F. S. (2016). Free trade agreements and privatization policy with an excess burden of taxation. Japan and World Economy, 37–38, 55–64.
11
Contents lists available at ScienceDirect
North American Journal of Economics and Finance journal homepage: www.elsevier.com/locate/najef
Foreign ownership, privatization and subsidization with shadow cost of public funds Ding Chena,1, Leonard F.S. Wangb, , Jen-yao Leec ⁎
a b c
School of Economics and Management, Xi’an Shiyou University, X’ian, Shaanxi, China Wenlan School of Business, Zhongnan University of Economics and Law, Wuhan, Hubei, China Department of International Business, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
ARTICLE INFO
ABSTRACT
JEL classification: F13 H21 L13
We examine how the shadow cost of public funds will affect the privatization policy in the presence of strategic tax/subsidy policies in a mixed oligopoly model with foreign ownership. We show that (1) When the dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large; (2) When the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relative small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Additionally, we show that the influence of foreign ownership on the privatization and subsidization policies are dependent upon the cost structures, ownership types, distribution of firms, and policy pairs.
Keywords: Foreign ownership Privatization The shadow of the public fund Production subsidy Social welfare
1. Introduction Over the past few decades, there has been a proliferation of theoretical literature involving the exploration of privatization. De Fraja and Delbono (1989) in a mixed oligopoly model showed that the privatization of welfare-maximizing public firms might improve social welfare. Matsumura (1998) explicitly considered the possibility of partial privatization.2 In the literature on mixed oligopolies, Capuano and De Feo (2010), Wang and Chen (2011b) and Matsumura and Tomaru (2013, 2015) have tackled the policy burden issue by examining the welfare effect of a change in a public firm's objective function when the government takes into account the shadow cost of public funds (or excess taxation burden, ETB). Wang and Chen (2011b) considered only the case of Cournot competition with cost efficiency gap, while Matsumura and Tomaru (2013) compared the optimal subsidies and the resulting welfare levels among four regimes: mixed and private Cournot duopolies and Stackelberg competition with public
⁎ Corresponding author at: Wenlan School of Business, Zhongnan University of Economics and Law, 182# Nanhu Avenue, East Lake High-tech Development Zone, Wuhan 430074, China. E-mail address: [email protected] (L.F.S. Wang). 1 Ding Chen acknowledges the financial support from National Social Science Research Program (Item No. 18VSJ094) and Scientific Research Program Funded by Shaanxi Provincial Education Department (Item No. 16JK1584). The authors would also like to thank the editor, two anonymous referees, Angela C. Chao and Chenhang Zeng for their helpful comments and suggestions. 2 In a free-entry market, Matsumura and Kanda (2005) assessed the welfare implications of partial privatization in a homogeneous oligopoly, and can be an alternative to direct regulation to avoid the excess entry problem. Wang and Chen (2010) highlighted the importance of the cost-efficiency gap between public and private firms, and showed the relation of the cost-efficiency gap and foreign competition with optimal privatization in a free-entry market.
https://doi.org/10.1016/j.najef.2018.10.017 Received 10 July 2018; Received in revised form 23 October 2018; Accepted 29 October 2018 1062-9408/ © 2018 Elsevier Inc. All rights reserved.
Please cite this article as: Chen, D., North American Journal of Economics and Finance, https://doi.org/10.1016/j.najef.2018.10.017
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and private leaderships. Further, Matsumura and Tomaru (2015) examined the effect of product differentiation, while Xu, Lee, and Wang (2016), Lee and Wang (2018) considered the relationships with foreign competition. Looking at the influence of environmental policies on privatization in a free-entry mixed market taking account of excess burden of taxation, Xu and Lee (2018) showed that when the excess burden of taxation is small (large), ex-post taxation imposes a lower (higher) tax level than ex-ante taxation, which results in a larger (smaller) number of firms and higher (lower) environmental damage. What motivates us is providing a generalized framework not only to synthesize the existing models, but to also deal with the five issues: partial privatization, subsidization, competiveness, foreign penetration, and excess taxation burden (shadow cost of public funds). In this paper, we examine how the competition and shadow cost of public funds will affect the privatization and subsidization policies in a mixed oligopoly model with foreign ownership. We show two main propositions that (1) when the dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large; and (2) when the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relatively small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Additionally, we show that the influence of foreign ownership on the privatization and subsidization policies are dependent upon the cost structures, ownership types, distribution of firms, and policy pairs. Clearly, some of our results are new derived from a generalized model setting and which should be noticed by academic researchers and policy decision-makers. This paper is organized as follows. Review of relevant literature is given in Section 2. Basic modeling is provided in Section 3. Section 4 explores how the shadow cost of public funds and foreign ownership will affect the privatization policy in the presence of strategic tax/subsidy policies. Section 5 provides comparisons of policy choice and social welfare. Section 6 concludes the paper. 2. Review of relevant literature In the literature on the optimal subsidy in mixed oligopoly, White (1996) showed that the same subsidy rate yields the first-best outcome in both mixed and private oligopoly in his Cournot setting (privatization neutrality theorem). This privatization neutrality theorem (PNT) was supported by Tomaru (2006), who showed that the optimal subsidy, all firms’ output, profits and social welfare are identical regardless of the share in a state-owned enterprise (SOE), and Matsumura and Okumura (2013), who also showed the optimal output floor regulation, concluded that privatization does not affect welfare regardless of the time structure and the degree of privatization. Wang and Chen (2011a) and Matsumura and Tomaru (2013) introduced an excess-taxation burden to describe the violation of the PNT. The violation of the PNT means privatization can work to enhance welfare. Tomaru and Wang (2018) then examined the optimal privatization policy. They showed that the optimal policy is partial privatization when the technical improvement is small. Matsumura (1998) showed that partial privatization is optimal in a mixed duopoly. A crucial difference between them is that Tomaru and Wang (2018) considered subsidization and a technical improvement resulting from privatization. Subsidization adjusts the production allocation, and privatization plays an auxiliary role in enhancing welfare by further adjusting the production allocation and improving the technology of the privatized firm. We have observed that beside the open-door policy in product marker, recent capital liberalization that is prevalent globally has enabled not only domestic investors but also foreign investors to own domestic private firms in many mixed markets. To see how the foreign penetration affects the privatization policy, Wang and Chen (2011a) showed that in the short-run, the government should increase the degree of privatization when the equity share held by foreign investor is increasing, which increases all domestic private firms’ profit and social welfare. Cato and Matsumura (2012) investigated how foreign penetration in the domestic market affects the privatization policy and showed that the optimal degree of privatization is increasing in foreign penetration in the long-run. The implications of Wang and Chen (2011a) and Cato and Matsumura (2012) are that the open capital market policy and privatization are complementary whether no entry barrier exists or entry or exit is possible in the market. The country with a more open capital market should privatize the firms more, even though this temporally reduces welfare. Matsumura and Tomaru (2012) found that under the optimal tax-subsidy policy, the government’s privatization decision depends on how many private firms in the product market and the equity share are held by foreign investor. In particular, when the equity share held by the foreign investors is low, the government should privatize the public firm in the absence of free entry of private firms. Wang and Lee (2013) examined how the order of the firm’s moves affects the social efficiency with foreign ownership and free entry in a mixed oligopoly market. In particular, they showed that when the foreign shareholding ratio is low, the entry of private followers will lead to lower consumer welfare and higher social welfare, but the profit of the incumbent nationalized firm is higher under entry than under no entry. Furthermore, they found that there always exists the problem of excessive entry under public leadership regardless of the degree of foreign ownership, which has important implications for industrial and market-opening policies. Wang and Tomaru (2015) showed that partial privatization is optimal for small extents of foreign penetration and the optimal degree of privatization is not monotonically related to foreign penetration. This result is in sharp contrast to the existing works that suggest either the positive or negative relationship. Xu, Lee, and Matsumura (2017) investigated the impact of the timing of privatization and liberalization policies on the degree of privatization and number of entering firms in free-entry mixed markets. They formulated two models: ex-post privatization and ex-ante privatization. In the former, the government liberalizes the market and then privatizes the public firm, whereas the order of the policies is reversed in the latter. They showed that ex-ante privatization yields a higher (lower) level of privatization and a larger (smaller) equilibrium number of entering private firms when foreign ownership in private firms is high (low).
2
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3. Basic model Consider a domestic market for a homogeneous good produced by one public firm, and n domestic firms. The linear demand function is specified as P = a
Q . The supply equation is given by Q = q0 +
n
i=1
qi , where q0 , and qi denote, respectively, the output
of public firm, and domestic firms. As in many existing studies on mixed oligopoly, we assume that all firms use an identical q2
technology and have the increasing marginal cost function: 0 , and 2 The profits of domestic public and private firms are given by: n 0
= a
q0 +
q0 +
, respectively.3
2
n
= a
2
q02
qi + s q0 i=1
i
qi2
(1)
qi2
qi + s qi
2
i=1
(2)
where s is the unit subsidy rate. The social welfare is defined as, n
SW = CS + (1
n
)
(1 + ) s
i i=1
qi + sq0
0
(3)
i=1
where the consumer surplus is given by CS = Q2/2 , is the shareholding ratio of the foreigners, and signifies the shadow cost of public funds for representing administrative inefficiency of government bureaucracy.4 As explained in Matsumura and Tomaru (2012), when all private firms are symmetric and denotes the share of foreign investors in the private firms, then there are n ) n domestic private firms. As such, two formulations yield exactly the same equilibrium outcomes.5 foreign private firms and (1 [0, ) . As pointed out in Matsumura and Tomaru (2013), the social welfare can be decomposed into the welfare We assume that without excess taxation burden and the distortion due to taxation. Moreover, we can rewrite Eq. (3) to obtain n
SW ( ) = CS + (1
n
)
(1 + ) s
i i=1
i=1
n
qi + sq0
= CS + (1
0
) i=1
n
n i
s i=1
qi
sq0 +
0
n
s i=1
qi + sq0
0
= SW ( = 0) +
s
0
i=1
qi
sq0
The right-hand side of the equation states that the excess burden applies on the subsidy paid to the private firms. As easily inferred from this social welfare, an increase in makes the official putting greater emphasis on the profit of SOE. The government sells all or a part of shares in firm 0 in the first stage (shares-selling stage). This means that the revenue from selling the shares is fixed in the later stage, where the output-setting stage follows the shares-selling stage. The government finances the subsidies for the firms from the partial profits of the privatized firm, and the revenue from selling the stocks of firms. We assume that the financial markets are perfect. V is the revenue from selling the stocks of firm 0. Assume the degree of ) 0 and 0 , respectively. 0 . The profit sharing of the government and the private investors are (1 privatization is , and 1 Then, the government sets s and to maximize the following social welfare: n
SW = CS + (1
n
)
i
+
0
V + (1 + ) (1
)
0
+V
i=1
sq0
s
qi
The government maximizes the social welfare, SW , expecting (i) the equilibrium result in the subgames and (ii) V = the private investors’ rationality and the assumption of perfect stock markets. When government privatizes the public firm partially, the optimization problem for the semi-public firm is:
max. {q0 }
=
0
+ (1
(4)
i=1
) SW
0
due to
(5)
3 See Matsumura and Kanda (2005), Wang et al. (2009) and Wang and Chen (2010) for using the specification of increasing marginal costs (decreasing returns to scale technology) in mixed oligopolies. In the current paper, we use a homogeneous demand function with decreasing returns to scale technology, which is not a general specification of the demand and the cost side of the model. Once the two assumptions are relaxed, our results may qualitatively differ. 4 The similar specification can be found in Capuano and De Feo (2010), Wang and Chen (2011b), and Matsumura and Tomaru (2013). 5 Foreign ownership of public firms is not considered in this paper. Lin and Matsumura (2012) also investigated the presence of foreign investors in privatized firms and confirmed Wang and Chen’s finding that an increase in the stockholding ratio of foreign investors in a privatized firm increases the optimal degree of privatization, whereas an increase in the penetration of foreign firms in product markets reduces it. These results imply that the degree of openness of financial markets and that of product markets have contrasting implications for the optimal privatization policy.
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where is the weight assigned to the profits in the decision-making process of the firm.6 The difference between us and Matsumura (1998) is that the government can directly control through its shareholding. The fully privatized firm only seeks the profit if = 1; contrarily, a fully nationalized firm maximizes the social welfare if = 0 . The government chooses the subsidy rate and the degree of privatization to maximize social welfare. We construct a two-stage game. In the first stage of the game, the government decides the subsidy rate and the degree of privatization. In the second stage, the firms engage in Cournot competition. The backward induction is used to derive the sub-game perfect Nash equilibrium (SPNE). 4. Foreign ownership, privatization and social welfare The outputs of the domestic private firms and the public firm are obtained by partially differentiating Eqs. (2) and (5) with respect to qi , and q0 , the first-order conditions are: i
qi
=a+s
q0
=a+s +a
q0
2qi a
2
2
+( 2
(6)
+ 3( 1 + ) ) q0
+n ( 1 +
+ ( 1 + ) ) qi = 0
2
q02
We have |H| =
nqi = 0
q0 qi 2
i
> 0 . According to the positive Hessian, the second-order conditions and stable condition of the game
i qi2
qi q0
are satisfied.7 The equilibrium outputs are:
qi (s , ) =
a + 2s + a + (2a + 3s )(1 ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1
q0 (s , ) = a + s
(8)
)
(2 + n)(a + 2s + a + (2a + 3s )(1 ) ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1 )
(9)
We analyze joint choices of privatization and subsidization policy in three regimes. In regime A and B, the government employs either a privatization level or an out subsidy. In regime C, the government simultaneously employs dual policy instruments of subsidization and privatization. 4.1. Regime A: The privatization policy is employed Letting s = 0 and substituting Eqs. (8) and (9) into Eq. (4) and then differentiating with respect to , the degree of privatization is given as A
=
n (1 2 2 + (n 1 + (n 2) )) n 4 + n (1 + 2(1 ) + (5 + n + (n 2) )) ,
0
+2
> nA n
+2 2 (1 + )
1
. (10)
n A.
As it can easily observed, full nationalization is optimal for a large and a small and n . It is straightforward, when the number of private firms is relatively large, partial privatization is employed due to the market compete is intensive. nA
= > 0 . When the shadow cost of public fund Taking differentiation of n A with respect to , and we obtain (1 + )2 increases, the critical value of number of private firms raises. Other thing being equal, the possibility of the public firm being fully nationalized increases to enhance the consumer surplus. As Matsumura and Tomaru (2013) pointed out, the government confronts two effects when it privatizes its public firm. One is that the shadow cost of public fund (excess burden of taxation) increases and the consumer surplus decreases, owing to the private and privatized firms’ disincentive to produce more, which is a negative welfare effect of privatization. The other is that privatization equalizes (or makes closer) the outputs of both firms, which reduces the sum of total costs. This is a positive welfare effect of privatization. Whether or not privatization improves welfare depends on which effect is stronger. Privatization increases the shadow cost of public fund, reduces consumer surplus, and induces output substitution from the public firm to the private firms. The former two effects reduce welfare whereas the last one improves welfare. The former two effects dominate the last one under our setting of the framework. 0 . Taking differentiation of A with respect to According to Eq. (10), we assume 2 2 1 > 0 to ensure n A > 0 if , we obtain that
A
=
n
1+2 2 1 + (n 2)
1+
+ 2 (2 + )
< 0 . When the ratio of foreign ownership increases, the optimal degree of privatization declines. The
6 Public firms may have other different targets, such as maximizing the profit, income, employee’s income or management of license, etc. See De Fraja and Delbono (1989), and Pal and White (1998) on the modeling of a public firm as a social welfare maximizer. 7 For example, see Etro (2006).
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intuition is that when the ratio of foreign ownership in the private firms is high, the role of the private firms is acting like foreign firms. This is simply because if a private firm is foreign-owned, its profit is sweated out of the country. This provides the government with an incentive to nationalize the privatized firm, thereby government will reduce the degree of privatization and transferal of profits to the (previously) privatized firm. 4.2. Regime B: The subsidization policy is employed as
Letting
= 0 and substituting Eqs. (8) and (9) into Eq. (4) and then differentiating with respect to s , the optimum subsidy is given
sB =
a (2
if n < nB
2 (n
+ 2n ) + (n 6 21 3(6 + n) 2) (2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 +
(2 + 3 )( 1 + 2 + 6 2 + (3 + 6 )) (1 ) (1 + 2 2 ) (4 + 3 ) 2 4
2
(1 + 18 (1 + ) + n (1 + 2 ) 2)) >0 + 2 + 3 (1 + ))) (11)
3
According to Eq. (11), when the number of private firms is relatively small, a positive subsidy is necessary to expand the output of the market due to the market compete is insufficient. As in Matsumura and Tomaru (2013), a higher cost of public funding reduces the optimal subsidy rate, and it becomes negative if is large. An increase in reduces the output of the public firm and increases that of the private firm through strategic interaction. The output substitution from the public firm to the private firm improves production efficiency because the marginal cost of the public firm is higher than that of the private firm. In our framework, we extend their model by taking into account the foreign penetration and competition involving more than one private firms. As in Matsumura and Tomaru (2012) without taxation burden in mixed oligopoly, the optimal subsidy s B can be either positive or negative, which is dependent on the value of . The intuitions are the following. In mixed oligopoly, the output of each private firm is too low for domestic welfare; thus, the government has an incentive to raise s so as to stimulate the output of private firms. On the other hand, an increase in s raises the outflow of surplus to the foreign investors and reduces domestic welfare. The latter effect becomes more significant when and n are large. Our result confirm the robustness of Matsumura and Tomaru (2012) with excess taxation burden. 4.3. Regime C: The dual policies are employed Substituting Eqs. (8) and (9) into Eq. (4) and then differentiating with respect to s and , the optimum subsidy and degree of privatization are given as
sC = C
=
a (1 (3 + 6 ) (2 + n + (6 + n) )) > 0, if n < nC n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )
1
3
2 6 (1 + )
6
2
n (1 + ) <1 6+n+n
(12) (13)
The intuition of dual policies will be explained later. We have the following lemma immediately. Lemma 1:. (i) qi are increasing in while q0 , and q0 + nqi are decreasing in when the privatization policy is employed. (ii) qi , and q0 + nqi are increasing in s , and q0 is decreasing in s when the subsidization policy is employed. (iii) When the dual policies are employed, qi , and q0 + nqi are increasing in s , and q0 is decreasing in s if the shareholding ratio of the foreigners is relatively small. qi are increasing in while q0 , and q0 + nqi are decreasing in . Proof. See the Appendix I. A higher degree of privatization will shift the output from the privatized firm to the private firms, which increases that of the private firm, and declines the output of the public firm and total output through strategic interaction. Thus, privatization can induce welfare-improving output-substitution effect between privatized firm and domestic private firms. The output of the private firms is increasing in . An increase in s lowers the production cost of the private firm, which increases the output of the private firm and total output. Thus, subsidization can induce welfare-improving output-expansion effect of the output of the private firm and total output. The output of the private firms and total output are increasing in s . When the dual policies are employed, the output of the privatized firm is decreasing in s , if the shareholding ratio of the foreigners is relatively small. Due to the output-substitution effect between the privatized firm and the private firms, the output of the privatized firm is decreasing in . The output of the private firms and total output are increasing in , due to the output-substitution effect shifting production from the privatized firm to the private firms. We have the following proposition 1. Proposition 1:. When the dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large. 5
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We can see from proposition 1 that *C tends to increase with n. This means that more competitive markets call for greater privatization policies, which is qualitatively the same as the result from De Fraja and Delbono (1989). Proposition 1 suggests that regardless of the number of domestic private firms, the partial privatization of a public firm is always desirable from a welfare point of view in the presence of the shadow of the public fund. This is in sharp contrast to the existing literature. Capuano and De Feo (2010) demonstrated that with nil or large efficiency gains, an inefficient public firm that maximizes welfare may still be preferred where there exists the shadow of the public fund in the government's objective function. Wang and Chen (2011b) found that for an imposition of the optimal subsidy, the level of welfare with privatization depends on the level of the cost-efficiency gap and the excess burden of taxation. Comparing privatization with mixed duopoly, Matsumura and Tomaru (2013) investigated optimal tax-subsidy policies with the excess burden of taxation. They focused on both the optimal tax-subsidy policies with endogenous timing of production, as well as the privatization neutrality theorem. They showed that mixed-oligopoly welfare reduction does not hold with the shadow of the public fund. Hence, the PNT does not hold even when they compared the resulting outcomes before and after privatization. They did not extend the study to the situation in which the public firm competes with multiple private firms as we do in this paper. *C
= (6 + n + n )2 > 0 . When the shadow cost of public fund inTaking differentiation of *C with respect to , we obtain that creases, the degree of privatization rises. The intuition is the same as we provided in regime A. sC*
6n
a (15 + n (7 + n) + 3n + 9 2 + 2(4 + n)(6 + n) + (6 + n)(7 + n
3 ) 2)
= < 0. Taking differentiation of s C* with respect to , we obtain that (n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))2 When the shadow cost of public fund increases, the subsidy rate declines due to the subsidy policy being more costly. We further show that the production tax may be used if the shadow of the public fund is relatively large. This result coincides with Matsumura and Tomaru (2013), Lee and Wang (2018): s is not always positive (i.e., the government may impose a production tax). When is small, s > 0 . However, when is large, s is negative. Naturally, a higher cost of public funding reduces the optimal subsidy rate, and it becomes negative if is large. In our modelling, there are two distortions thereby needing two policy instruments concurrently to deal with these: firstly, the domestic market is under oligopolistic competition and output of domestic private firm is less than the one under perfect competition, and it needs output subsidy to increase the private firm’s output; secondly, for the public firm, it cares about social welfare, which leads to more output and higher marginal cost needing higher degree of privatization to curtail the output of public firm. We have the following proposition 2. Proposition 2:. When the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relative small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Proof:. Taking differentiation of A
=
A
,
C
and s C with respect to 2
, we obtain
2
2n ( 4( + 2 ) + n ( 1 + 3( 2 + n) 2 ( 3 + n + 12 ))) < 0, (4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) )))2
when
4 + n ( 3 + n + 12 ) +
< C
sC
=
=
16 + n (n3
24(1 + 4 ) + 6(n + 2n )2 + n ( 7 + 24 (1 + 4 ))) 6( 2 + n) n
6n >0 (6 + n + n ) 2 a (15 + n (7 + n) + 3n + 9 2 + 2(4 + n)(6 + n) + (6 + n)(7 + n (n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )) 2
3 ) 2)
<0
When the dual policies are employed, if the social cost of public fund is more severe, and the degree of privatization and production subsidy are complementary instruments for a given degree of foreign ownership; the production subsidy should decrease and the degree of privatization should increase in order to mitigate the policy distortion. However, when only the privatization policy is employed, due to the official putting greater emphasis on the profit of the privatized firm, the degree of privatization is decreasing in the shadow cost of public funds, when the share of foreign investors in the private firms is relatively small. As in lemma 1, we have that qi are increasing in , while q0 , and q0 + nqi are decreasing in when the privatization policy is employed. On one hand, the output of the privatized firm is decreasing in , due to the output-substitution effect when the privatization policy is employed. A lower degree of privatization will lead the profit of the privatized firm higher. On the other hand, an increase in raises the outflow of surplus to the foreign investors and reduces domestic welfare. The latter effect becomes more significant when the share of foreign investors in the private firms is relatively large. Thus, we have the degree of privatization is increasing in the shadow cost of public funds, when the share of foreign investors in the private firms is relatively large. This result is in line with Lee and Wang (2018): The optimal degree of privatization is increasing in the shadow cost of public funds if the shadow cost of public funds is relatively large. In that framework, a higher shadow cost of public funds will cause a lower subsidy rate and a higher degree of privatization, due to the subsidy policy being more costly. The output subsidy-induced effect on total output is decreasing while the tariff-induced output effect is increasing in the domestic output market. When is relatively 6
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small, in this case, the government does care more about the consumer surplus. Thus, a lower degree of privatization is needed to enhance the total market output. When is relatively large, in this case, the government cares less about the consumer surplus; thus, a higher degree of privatization is adopted to enhance the total revenue of the government. However, in this framework, the tariff policy is not adopted due to the close-door policy. The tariff-induced output effect doesn’t exist in the policy options, and the government has to increase the degree of privatization to lower the output of the privatized firm and decline the cost inefficiency of the privatized firm. [0, ) in our analysis, here we consider what would happen if Although we assume . Taking limit of , and s we have
lim
C
= lim
lim s C = lim
n (1 + ) =1 6+n+n
a (1 (3 + 6 ) (2 + n + (6 + n) )) = n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )
a 2
The optimal degree of privatization is 1, and the output subsidy is negative, 2 ; that is, a production tax is adopted. Due to officials putting a greater emphasis on the profit of SOE, they do not care about consumer surplus anymore. The government’s objective reduces to maximize their revenue (production tax, and profit of the privatized firm), and full privatization is chosen. Wang and Chen (2011a) showed that in the short-run, the government should increase the degree of privatization when the equity share held by foreign investors is increasing in the absence of subsidization policy and the shadow cost of public funds. In their framework, not all of the private firms are held by foreign investors, and an output-substitution will be realized by the other private firm. So, an increase in the degree of privatization is called for from the welfare viewpoint. Next, we consider some comparative analysis result of the influence of foreign ownership on the degree of privatization and subsidization. We have the following proposition in the case that is 0. a
Proposition 3:. When the privatization policy is employed, the degree of privatization is decreasing in the shareholding ratio of the foreigners; when the dual policies are employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, while the degree of privatization is irrelevant to the shareholding ratio of the foreigners. Proof:. Taking differentiation of A
,
C
and s C with respect to , we obtain that
=
2n (2 + n) <0 (4 + n + n (5 + n) ) 2
=
3a (4 + n) <0 (n + 2) 2
=0
C
A
=0
sC =0
Our result is different from Wang and Chen (2011a): when only the privatization policy is employed, the degree of privatization is decreasing in the shareholding ratio of the foreigners. The reasoning is that, a higher of the shareholding ratio of the foreigners raises the outflow of surplus to the foreign investors and reduces domestic welfare. A decreasing increases the output of the privatized firm, and thus, we have that the optimum degree of privatization is decreasing in the shareholding ratio of the foreigners. As mentioned in proposition 2, when the dual policies are employed in mixed oligopoly with partial privatization, an increase in s raises the outflow of surplus to the foreign investors and reduces domestic welfare, becoming more significant when is large. Thus, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners. Wang and Tomaru (2015) in a linear-demand and constant marginal-cost setting, showed that an increase in makes firm 0 have a greater incentive to produce due to the terms-of-trade effect, if is relatively small. This aggressive behavior of firm 0 increases the total production cost incurred by the domestic country. A decrease in makes firm 0 reduce its output via the terms-of-trade effect and the profit-motivation effect. Thus, to decrease the welfare loss from the increased production cost, the government tries to reduce when is increased. If is in an intermediate range, firm 0 overproduces by the terms-of-trade effect. Accordingly, an increase in makes the price so low that firm 0 earns negative profits for a wider range of . However, if is sufficiently large, increase makes an impact of the dividends on welfare more negligible, and so, only the consumer surplus matters for welfare. The government chooses full nationalization, and the consumer surplus improves due to firm 0′s greater incentive to produce. However, in the case of increasing marginal cost with subsidization policy, the public firm cares about social welfare, which leads to more output and the higher marginal cost needing higher degree of privatization to curtail the output of public firm. The effect of partial privatization amends the cost inefficiency caused by over-production of public firm. Although an increase in raises the outflow of surplus to the foreign investors and reduces domestic welfare, the lower subsidy rate revises the outflow of surplus. The privatized firm’s output is increasing in , whereas the private firm’s output is decreasing in it. Accordingly, the degree of privatization is irrelevant to the shareholding ratio of the foreigners. To see whether production subsidy or production tax will be chosen along with privatization policy, we have the following proposition in the case that is 0. 7
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Proposition 4:. When the subsidization policy is employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, if the number of private firm is relatively small; when the dual policies are employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners. Proof. Taking differentiation of s B , s C and
sB
= =0
with respect to , we obtain:
a (24 + n (4 + 8 + n ( 1 + (2 + )))) <0 2(2 + n + 6 + n 2)2
(2 + 3 )( 1 + 2 + 6 2 + (3 + 6 )) ( 1 + ) + + 2 2 + (4 + 3 ) 2 + 4
if n < sC
= =0
C
C
3
3a (4 + n) <0 (n + 2) 2
= 0.
As mentioned in proposition 3, an increase in raises the outflow of surplus to the foreign investors and reduces domestic welfare, but the lower subsidy rate revises the outflow of surplus. In our model, production subsidy and partial privatization policy are concurrently adopted from the welfare point of view.8 However, when the subsidization policy is employed, the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, if the number of private firm is relatively small. This is consistent with Matsumura and Tomaru (2013) who showed the optimum subsidy rate is decreasing in the shareholding ratio of the foreigners, if the number of private firm is relatively small. When the number of private firm is larger,
s B*
=0
is ambiguous. The public firm’s output is increasing in , whereas the private firm’s
output is decreasing in it. Note that the public firm’s profit can be negative when is sufficiently larger. In the case of a sufficiently large , the optimal subsidy rate s B* becomes negative, i.e. a production tax is imposed on all firms. Recall that the public firm becomes more aggressive toward improving the terms of trade if increases. 5. Comparisons of policy choice and social welfare We compare the optimal subsidies, the degree of privatization and the resulting welfare among the three policy regimes. Computation yields the following:
W
A
=
a2 ((2 + n) 2 + (8 + n (7 + n 3 )) + 4 2) 2(8 + 12 + n (5 + n + 3 + (8 + n) ))
W
B
=
a2 (1 + ) 2 ((2 + 3 )(1 + 3 + 4 ) + n (2 + 2(2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 +
W
C
=
a2 (1 + ) 2 (1 + n + 3 + (4 + n) ) 2(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))
2 2
+2 +2
+ (5 + 4 ))) + 3 (1 + )))
First, we compare the optimal subsidies and the degree of privatization. This comparison leads to the following proposition. Proposition 5:. Suppose that demand is linear, firms’ costs are quadratic. The optimal subsidies in the three regimes have the following properties. (1) s C < s B , (2) C > A, i f
>
1
(2 + n + (6 + n) ) 3+6
Proof:.
sC C
sB = A
=
an (1 + ) 2 ( + )(n (1 + )(1 + ) + (1 + + 2 )(2 + 3 )) (2 + 3 )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))((2 + 3 )(1 + 3 + 4 ) + n (1 + 2 + 2
2n ( 1 + (3 + 6 ) + (2 + n + (6 + n) )) > 0, if (6 + n + n )(4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) )))
>
1
+ 3 (1 + )))
<0
(2 + n + (6 + n) ) 3+6
We explain the intuition behind Proposition 5. Due to the shadow cost of public fund and foreign ownership, the social cost of 8 The similar result can be seen in Lin and Matsumura (2018) in the presence of foreign ownership, and Tomaru and Wang (2018) in the presence of endogenous cost asymmetry.
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subsidization is high. The social cost of the privatization policy is relatively low. Accordingly, the optimal subsidy rate is low under a dual policies regime. When the ratio of foreign ownership is high, it will decrease the degree of privatization under regime A. However, in regime B, the government can use the lower subsidy rate to mitigate the negative effect of foreign ownership. Hence, with a higher ratio of foreign ownership, the degree of privatization will not be affected and it appears that C * > *A . It shall be noted that the optimal policy can be full nationalization in regime A, while it is necessarily partial privatization in regime B. Next, we compare the welfare level among the three types of regimes. We obtain a clear result with regard to welfare ranking. Regardless of and , dual policies yield the highest welfare level. Proposition 6:. Suppose that demand is linear, firms’ costs are quadratic, and
> 0 . Then,W C > max{W A, W B}
Proof.
W
A
W
B
=
1 2 (2 + n)2 + (8 + n (7 + n 3 )) + 4 2 a 2 8 + 12 + n (5 + n + 3 + (8 + n) ) (1 + ) 2 ((2 + 3 )(1 + 3 + 4 ) + n (2 + (2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 +
W
A
WC =
W
B
WC
=
2 2
+2 +2
+ (5 + 4 ))) + 3 (1 + )))
a2n ( 1 + (3 + 6 ) + (2 + n + (6 + n) )) 2 <0 2(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))(8 + 12 + n (5 + n + 3 + (8 + n) ))
a2n2 (1 + ) 4 ( + )2 2(2 + 3 )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))((2 + 3 )(1 + 3 + 4 ) + n (1 +
2
+2
+ 3 (1 + )))
<0
Regime A is a constraint equilibrium at the subsidy rate is 0 and regime B is also a constraint equilibrium at the degree of privatization is 0. As mentioned above, there are two distortions in our framework: 1) the total output of domestic private firms is less than the one under perfect competition; and 2) the public firm is less efficient than the private firms. For each policy objective, one policy instrument is needed, and one only. Naturally, the social welfares of regimes A and B will be lower than regime C. 6. Conclusions We have used a mixed oligopoly model with foreign ownership examining how the shadow cost of public funds and competition will affect privatization policy in the presence of strategic tax/subsidy policies. We showed two main propositions that (1) when dual policies are employed, the privatization policy is partial privatization and the production tax may be used if the shadow of the public fund is relatively large; and (2) when the privatization policy is employed, the degree of privatization is decreasing in the shadow cost of public funds if the share of foreign investors in the private firms is relatively small; however, when the dual policies are employed, the degree of privatization is increasing in the shadow cost of public funds. Additionally, we show that the influence of foreign ownership on the privatization and subsidization policies are dependent upon the cost structures, ownership types, distribution of firms, and policy pairs. In this study, we assumed that all private firms are partially owned by foreign investors. Lee and Wang (2018) have considered how subsidization, tariff and privatization policies could be influenced by the entry of foreign firms who are competing with domestic firms due to the open-door policy of domestic country. It might be interesting to investigate whether the results will be changed if the foreign investors are allowed to invest in both public and private firms concurrently with or without the same share-holding ratio.9 Appendix I:. Proof of Lemma 1 Proof:. Regime A: The Privatization Policy is Employed We evaluate the comparative analysis at = A and s = 0
qi (s, )
9
2(a + an s (2 + n (1 + )3 )) (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) ))) 2 = > 0, 2(1 + n )(8 + 12 + n (5 + n + 3 + (8 + n) )) 2 =
See Lin and Matsumura (2012), who investigated the presence of foreign investors in privatized firms. 9
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q0 (s, )
2(2 + n)(a + an (4 + n + n + 2 + n a (2 + n)(4 + n (1 2( 2(1 + n )(8 + 12
= =
Q (s , )
s (2 + n (1 + )3 )) (1 ) + 2(3 + n)(1 ) )2 1 + ) + (5 + n + ( 2 + n) )))2 < 0, + n (5 + n + 3 + (8 + n) ))2
4(2 + n) s 4(a + n (a + s ) ) + 4(3 + n) s (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (4 + n (1 2( 1 + ) + (5 + n + ( 2 + n) ))) 2 = < 0. (1 + n )(8 + 12 + n (5 + n + 3 + (8 + n) ))2 =
Regime B: The subsidization policy is employed We evaluate the comparative analysis at = 0 and
+ 2n ) + ( 6 + n 21 3(6 + n) 2) (1 + 18 (1 + ) + n (1 + 2 ) 2)) qi (s , ) 2 (2 + 3 )((2 + 3 )(1 + 3 + 4 ) + n (1 + + 2 + 3 (1 + ))) s 2 + 3(1 ) 2(a + an ) = = > 0, 4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) (4 + n + n + 2(3 + n) ) 2
s = sB =
q0 (s, ) s
2 (n
a (2
=1 =
(2 + n)(2 + 3(1 ) ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) 2a (2 + n)(1 + )( + )(6 + 9 + n (1 + + 2 )) (2 + 3 )(4 + n + n + 2(3 + n) )((2 + 3 )(1 + 3 + 4 ) + n (1 + 2 + 2
) + 2 (1 )) ) + 2(3 + n)(1 ) 4a (1 + )( + )(6 + 9 + n (1 + + 2 )) (2 + 3 )(4 + n + n + 2(3 + n) )((2 + 3 )(1 + 3 + 4 ) + n (1 +
+ 3 (1 + )))
< 0,
Q (s , ) 2 + n (1 + + (1 = s 4 + n + n + 2 + n (1 =
Regime C: The dual policies are employed We evaluate the comparative analysis at =
qi (s , ) s q0 (s , ) s
if
<
=
2 + 3(1 4 + n + n + 2 + n (1
+2
+ 3 (1 + )))
> 0,
and s = s
) ) + 2(3 + n)(1
)
(2 + n)(2 + 3(1 ) ) 4 + n + n + 2 + n (1 ) + 2(3 + n)(1
=1
2
=
)
6 + n + (9 + n) 12 + 6n + n2 + 3n + (3 + n)(6 + n) =
> 0,
n (3 2(1 + )) 12 + 6n + n2 + 3n + (3 + n)(6 + n)
< 0,
2(1 + ) 3
Q (s , ) 2 + n (1 + + (1 = s 4 + n + n + 2 + n (1 qi (s, )
q0 (s, )
)
=
n (4 + n + 3 + (7 + n) ) 12 + 6n + n2 + 3n + (3 + n)(6 + n)
2(a + an s (2 + n (1 + )3 )) (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (1 + )( + )(6 + n + n )2 = > 0, 2(12 + 6n + n2 + 3n + (3 + n)(6 + n) )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )) =
= =
Q (s , )
) + 2 (1 )) ) + 2(3 + n)(1
2(2 + n)(a + an s (2 + n (1 + )3 )) (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (2 + n)(1 + )( + )(6 + n + n ) 2 < 0, 2(12 + 6n + n2 + 3n + (3 + n)(6 + n) )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 ))
4(2 + n) s 4(a + n (a + s ) ) + 4(3 + n) s (4 + n + n + 2 + n (1 ) + 2(3 + n)(1 ) )2 a (1 + )( + )(6 + n + n ) 2 = < 0, 2 (12 + 6n + n + 3n + (3 + n)(6 + n) )(n (1 + )(1 + 2 ) + (2 + 3 )(1 + 3 + 4 )) =
Appendix B. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.najef.2018.10.017.
10
> 0,
North American Journal of Economics and Finance xxx (xxxx) xxx–xxx
D. Chen et al.
References Capuano, C., & De Feo, G. (2010). Privatization in oligopoly: The impact of the shadow cost of public funds. Rivista Italiana Degli Economisti, 15, 175–208. Cato, S., & Matsumura, T. (2012). Long-run effects of foreign penetration on privatization policies. Journal of Institutional and Theoretical Economics, 168, 444–454. De Fraja, G., & Delbono, F. (1989). Alternative strategies of a public enterprise in oligopoly. Oxford Economic Papers, 41, 302–311. Etro, F. (2006). Aggressive leaders. RAND Journal of Economics, 37, 146–154. Lee, J. Y., & Wang, Leonard F. S. (2018). Foreign competition and optimal privatization with excess burden of taxation. Journal of Economics, 125(2), 189–204. Lin, M. S., & Matsumura, T. (2012). Presence of foreign investors in privatized firms and privatization policy. Journal of Economics, 107, 71–80. Lin, M. S., & Matsumura, T. (2018). Optimal privatization and uniform subsidy policies: A note. Journal of Public Economic Theory, 20, 416–423. Matsumura, T. (1998). Partial privatization in a mixed duopoly. Journal of Public Economics, 70, 473–483. Matsumura, T., & Kanda, O. (2005). Mixed oligopoly at free entry markets. Journal of Economics, 84, 27–48. Matsumura, T., & Okumura, Y. (2013). Privatization neutrality theorem revisited. Economics Letters, 118, 324–326. Matsumura, T., & Tomaru, Y. (2012). Market structure and privatization policy under International competition. Japanese Economic Review, 63, 244–258. Matsumura, T., & Tomaru, Y. (2013). Mixed duopoly, privatization, and subsidization with excess burden of taxation. Canadian Journal of Economics, 46, 526–554. Matsumura, T., & Tomaru, Y. (2015). Mixed duopoly, location choice, and shadow cost of public funds. Southern Economic Journal, 82, 416–429. Pal, D., & White, M. D. (1998). Mixed oligopoly, privatization, and strategic trade policy. Southern Economic Journal, 65, 264–281. Tomaru, Y. (2006). Mixed oligopoly, partial privatization and subsidization. Economics Bulletin, 12(5), 1–6. Tomaru, Y., & Wang, L. F. S. (2018). Optimal privatization and subsidization policy in mixed oligopoly: Relevance of an efficiency gap. Journal of Institutional and Theoretical Economics, 174, 189–203. Wang, L. F. S., & Chen, T.-L. (2010). Do cost efficiency gap and foreign competitors matter concerning optimal privatization policy at the free entry market? Journal of Economics, 100, 33–49. Wang, L. F. S., & Chen, T.-L. (2011a). Mixed oligopoly, optimal privatization, and foreign penetration. Economic Modelling, 28, 1465–1470. Wang, L. F. S., & Chen, T.-L. (2011b). Privatization, efficiency gap, and subsidization with excess taxation burden. Hitotsubashi Journal of Economics, 52, 55–68. Wang, Leonard F. S., & Lee, J. Y. (2013). Foreign penetration and undesirable competition. Economic Modelling, 30, 729–732. Wang, L. F. S., & Tomaru, Y. (2015). The feasibility of privatization and foreign penetration. International Review of Economics and Finance, 39, 36–46. Wang, L. F. S., Wang, Y. C., & Zhao, L. (2009). Privatization and efficiency gain in an international mixed oligopoly with asymmetric costs. Japanese Economic Review, 60, 539–559. White, M. D. (1996). Mixed oligopoly, privatization and subsidization. Economics Letters, 53, 189–195. Xu, L., & Lee, S. H. (2018). Environmental policies with excess burden of taxation in free-entry mixed markets. International Review of Economics and Finance. (forthcoming). Xu, L., Lee, S.-H., & Matsumura, T. (2017). Ex-ante versus ex-post privatization policies with foreign penetration in free-entry mixed markets. International Review of Economics and Finance, 50, 1–7. Xu, L., Lee, S. H., & Wang, L. F. S. (2016). Free trade agreements and privatization policy with an excess burden of taxation. Japan and World Economy, 37–38, 55–64.
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