Using the simple linear demand model, part of our findings are consistent with what has been shown in Lai (2004) and Ohori (2006), even though they considered all firms producing homogeneous goods. In an international oligopoly market wherein the environmental damage is associated with consumption, the order of optimal environmental tax parallels the results of the duopoly model irrespective of the properties of the goods. In addition, we have shown that when the domestic market increases its openings, the tariff reduction does not always bring positive effects on the environment in mixed oligopoly; but, in pure oligopoly with homogeneous goods, the tariff reduction is bad for the environment.
CHAPTER THREE： PARTIAL PRIVATIZATION AND EQUITY REGULATION
In this chapter, we consider in an international oligopoly market with a homogeneous good, one partially privatized domestic public firm competing with n domestic private firms and m foreign private firms. To protect domestic firms in this single market, the government decides on the proportion of domestic equity for foreign competitors.
The chapter is organized as follows: Section 3.1 presents the model. Section 3.2 studies the market equilibrium and analyzes the effects of equity control policies and free entry.
Section 3.3 includes concluding remarks.
3.1 Basic Model
Consider in an international oligopoly market, one domestic public firm with partial privatization (firm 0), n private firms (firm i ; i=1, 2,...,n) and m foreign private firms (firm j ; j=1, 2,...,m) compete. Each firm with identical technology, as represented by the cost function as C q( )= +f (1 2)q2, produces a homogeneous commodity, and the inverse demand function for the product in the domestic country is given
by 0 is the output of the foreign firm. Furthermore, the fixed cost f is assumed to be zero for simplicity7. Each domestic private firm i maximizes its own profit denoted by
(1 2) 2
i Pqi qi
π = − , and each foreign firm j maximizes its own profit denoted by
7 Fjell and Pal (1996) also assumed f =0, then indicated the results change for f >0 in footnote 3 and 5.
(1 2) 2
j Pqj qj
π = − .8 In this paper, government decides the proportion of domestic equity for foreign competitors to protect domestic firms. Therefore, domestic social welfare is the
summation of the consumer surplus, 0 2
1 1
profit, and partial foreign firms’ profits.
0 represents the extent of domestic ownership of a private firm. When α =1, foreign investments are not allowed, so that foreign firms are owned by domestic equity. α =0 corresponds to the case in which government does not limit foreign competitors by deciding the proportion of domestic equity for foreign firms. If 0< <α 1, a foreign firm is considered as a joint ownership enterprise. It is natural to consider that 100α percent of foreign firms’
profits should be attributed to domestic resident. Fjell and Pal (1996) mentioned that the foreign firms may reinvest some of their profits in the public firm’s home country so the domestic social welfare is the summation of the consumer surplus, domestic firm’s profit, and the part of the foreign firm’s profit that remains in the public firm’s home country.9 Zhao (2000) considered the case in that the repatriation tax imposed by the government on the multinational firm’s downstream branch profits.
When the government owns a share of 1− ∈θ [0,1], the manager of this firm will maximize the weighted average of social welfare and the profit. We define the objective function of firm 0 as
8 Note that because equity control on foreign firm solely changes the internal equity structure, the firms still maximize πj, j=1, 2,...,m.
9 See Fjell and Pal (1996) footnote 2.
0 (1 )
V =θπ + −θ W；θ∈[0,1], (3.2)
where θ denotes the degree of privatization.
Note that the manager of fully privatized firm (θ =1) seeks the firm’s profit, while the manager of a fully nationalized firm (θ =0) maximizes social welfare. The game is constructed by two-stage decision-making. The government maximizes social welfare to chooses the level of privatization, θ , in the first-stage. In the second stage, all private firms simultaneously maximize its own profits to choose its quantity, while the privatized public firm maximizes the objective function V to choose its quantity. We use the method of backward induction and solve the equilibriums from the second stage.
3.2 Privatization and an Open-door Policy
In the second stage, given the policy variables α and θ , all private firms maximize their own profits to choose their quantity, while the privatized public firm maximizes the objective function V to choose its quantity simultaneously.
0
Each firm simultaneously maximizes their objective function to select the quantities
Government maximizes social welfare to choose the degree of privatization.
Figure 3.1 Game Structure of Cournot Competition Model with Equity Control
whereΗ = + +4 n m(2+ − +α( 1 θ)) (2+ +n)θ > . The effects of privatization is given by, 0
Hence, the higher degree of privatization increases market price and firm i ’s output, but decreases firm 0’s output. The range of decrease in firm 0’s output is larger than the increase in firm i ’s output. The profit and consumer surplus in the second stage are,
2
Lump-sum transfer from consumer to firm 0 may be conducted when π0 takes a negative value. The comparative static results include
0 (3.6) shows that while privatization serves to increase firm i ’s profit, its effect on the firm 0’s profit is ambiguous. For a purely public firm, privatization can raise the mixed firm’s
(firm 0) profit,
This result is quite different from Fershtman’s (1990) result in a closed duopoly market, privatization deteriorates the mixed firm’s profit.
3.2.1 Optimal Degree of Privatization
In the first stage, the government chooses the level of privatization of public firm 0 maximize social welfare with respect to θ ; submitting (3.3) and (3.5) into (3.1), the objective function of the government, social welfare is given as,
2 2
We obtain the optimal degree of privatization as
( 2 )(1 )
To see how the equity control affects the degree of privatization, we have the following
expression, increases social welfare and consequently, promotes the degree of privatization.
Proposition 3.1: Along with the stringent control on the domestic equity of foreign firms, the government should increase the degree of privatization.
The sub-game perfect Nash equilibrium of the model is shown as follows:
0
By comparing welfare differential, the government will push forward on its privatization path.
where W denotes the social welfare without partial privatization* 10. To see the effect of equity control on outputs and price, we have,
10 See Appendix (C.1)
2
The stringent control on domestic equity will increase private firms’ outputs and market price, but decrease public firm’s output. The reason is that stringent control on domestic equity for foreign firms literally shifts the reaction function of all private firms outward, so it makes public firm’s quantity decrease and private firms’ quantities increase. In addition, we obtain the following results:
2 2 2
The stringent control of domestic equity on foreign firms will increase private firms’
outputs and social welfare, but the effect on public firm’s profit is ambiguous subject to the number of private firms. Because foreign firms could earn more profits, they do have the incentive to invest, even though government legislates stringent controls on domestic equity for foreign firms. Note that if the public firm without privatization competes with private firms, then the results of the stringent control on the domestic equity of foreign firms parallel the partial privatization case. Moreover, the effect of control always increases the public firm’s profit.11
Proposition 3.2: The stringent control of domestic equity on foreign firms increases private
11 See Appendix (C.2)
firms’ outputs, profits, market price and social welfare; decreases public firm’s output, but the effect on its profit is ambiguous.
3.2.2 Free Entry
In an opening market, private firms can enter the market freely. Intensive competition from private firms affecting the degree of privatization is given as per the following equations,
An increase in the number of domestic firms definitely raises the degree of privatization, but when more foreign firms enter the domestic market, this may also increase the degree of privatization except in a small likelihood of ( , )n m . See Fig. 3.2 for geometric depiction.
20
Fig. 3.2. The Effect of Number of Private Firms on the Degree of Privatization
Proposition 3.3: Intensive competition from private firms in general will enhance the degree of privatization.
3.2.3 Effects of an Open-door Policy
Allowing foreign firms enter domestic market and the effects of adding a new foreign firm in the market are,
0
Under an open-door policy, public firm’s profit increases if and only if {(2 3 ) 6 /(4 3 )}
m< − α n− α − α , that is, if and only if the number of foreign private firms is small relative to the number of domestic private firms. The reason is that an additional foreign firm literally shifts the reaction function of all private firms outward, but it also shifts public firm’s reaction function outward due to the public firm producing more if the output comes from a foreign firm. However, if the reaction function of all private shifts outward more than the public firm’s, the public firm’s output decreases with the entrance of foreign
firms. Hence, the result obtained in Fjell and Pal (1996): the public firm’s output always increase with an additional foreign private firm even if foreign firms reinvest in the home country; is not robust.
Moreover, social welfare increases if and only if m>{(2 3 )− α n−6 /(4 3 )}α − α , that is, if and only if the number of foreign private firms is large relative to the number of domestic private firms.12 Entry of an additional foreign private firm reduces price, public firm’s profit, and all private firms’ profit respectively. Although there is social welfare loss because the loss in domestic profits is transferred by the additional foreign firm, yet the domestic equity control on foreign firms may improve social welfare even though more foreign firms enter the market.13 We have the following proposition.14
Proposition 3.4: Under an open-door policy, public firm’s profit increases if and only if the number of foreign private firms is small relative to the number of domestic private firms;
social welfare increases if and only if the number of foreign private firms is large relative to the number of domestic private firms.
3.3 Concluding Remarks
We considered in an international oligopoly market with a homogeneous good, one partially privatized domestic public firm competes with n domestic private firms and m foreign private firms. To protect domestic firms in this single market, the government determines the proportion of domestic equity on foreign competitors. We have shown that
12 Note that if the public firm competes only with foreign private firms (n=0), then entry by a new foreign firm always increases welfare, namely,
2
without partial privatization still has the same result as a partial privatization case. See appendix (C.4)
13 The case of a public firm without partial privatization still has the same result as the partial privatization case.
See appendix (C.3)
14 Proposition 2 of Fjell and Pal (1996) does not always hold.
stringent control of domestic equity on foreign firms increases private firms’ outputs, profits, market price and social welfare, but decreases the public firm’s output. Furthermore, along with the stringent control on the domestic equity of foreign firms, the government should increase the degree of privatization. In an opening market, intensive competition from private firms in general will enhance the degree of privatization.
Comparing our results with the result in Fjell and Pal (1996), we found that the effect of the number of foreign firms on the public firm’s profit is ambiguous. The public firm’s profit increases if and only if the number of foreign private firms is small relative to the number of domestic private firms; social welfare increases if and only if the number of foreign private firms is large relative to the number of domestic private firms.
CHAPTER FOUR： PARTIAL PRIVATIZATION, FOREIGN COMPETITORS, AND INCENTIVES FOR MERGER
This chapter considers a single international differentiated mixed oligopoly market where there exists one domestic public firm with partial privatization, one domestic private firm and several private foreign firms competing in a domestic country. Firms produce horizontal differentiated commodity. To be more efficient, the public firm is allowing for partial privatization. Public firm will proceed partial privatizing through a program with two distinct measures: (i) privatizing directly, and (ii) deciding to merge with domestic private firm. However, there exist some incentives for domestic firm to choose to merge.
The chapter is organized as follow. Section 4.1 presents the models. Section 4.2 analyses the partial privatization and the merging incentives derived from the privatization of the mixed firm. Section 4.3 summarizes our main conclusions.
4.1 Basic Model
Consider a single international mixed oligopoly market in which there exist one domestic public firm (firm a) with partial privatization, one domestic private firm (firm b) and several private foreign firms (firm j , j=1,...,m) without considering transport cost and paying the tariff in the presence of trade liberalization, and all firms compete in a domestic country. Under the Cournot-Nash assumption, the private firm aims at maximizing the firm’s profit, and the public firm maximizes social welfare when the domestic government owns it.
Due to firms produce horizontal differentiated commodities, the utility function of the representative consumer in the domestic country is following Häckner (2000) in generalizing the utility function to allow for two domestic firms and m foreign firms producing
differentiated goods15, if ( 1,0)γ∈ − products are complementary. The inverse demand function is given by
1 ( )
Therefore, consumer surplus is given by
1 1
All firms share identical cost function with increasing marginal cost represented by the following quadratic function.
1 2
Domestic social welfare is measured as the summation of the consumer surplus and the
15 Häckner assumed the utility function is quadratic in the consumption of q-goods and for simplicity let
1 2 1
domestic firm’s profit,
a b
W =CS+π + , π (4.6)
where πa represents the profits of public firm and πb the profits of domestic private firm.
To be more efficient, the public firm allows for partial privatization. In the following, public firm will proceed partial privatizing through a program with two distinct measures: (i) privatizing directly, and (ii) deciding to merge with domestic private firm.
If public firm allow for partial privatizing directly, i.e. case (i), we follow the assumption in Matsumura (1998), which the government owns a share of (1− ∈δ) [0,1] and the manager of this firm will maximize the weighted average of social welfare and the profit. Then, we define the objective function of firmaas
(1 δ)W δπa
Ω = − + ；δ∈[0,1]. (4.7.1)
Note that the manager of fully privatized firm (δ =1) seeks the firm’s profit, while the manager of a fully nationalized firm (δ =0) maximizes social welfare.
If there exists enough incentives for both public firm and domestic private firm to make them choose to merge with each other, i.e. case (ii), we follow the assumption in Mé ndez-Naya (2008), which is assumed that, the merging firm is partially owned by private and public owners. The private owner owns a percentage of the shares of the merging firm which depends on the degree of privatization of the merged firm. Therefore, assuming that the domestic firms merge, the objective function of the merged firm is given by,
(1 δ)W δ π( a πb)
Ω = − + + ；δ∈[0,1]. (4.7.2)
Identically, the merged firm would be a public firm if δ=0, and as δ increases, the degree of privatization of the mixed firm increases, becoming a private one if δ=1.
In order to develop the analysis, we set up two stage game. Government decides the degree of partial privatization for public firm or merged firm at the first stage. All firms simultaneously choose their output at the second stage. The game is solved by backwards induction.
4.2 Merger Profitability and Partial Privatization 4.2.1 Benchmark
In a single international mixed oligopoly market with differentiated commodity, full-stated firm does not privatize and maximize the social welfare to produce as well as all private maximize profit simultaneously,
2
Each firm simultaneously maximizes their objective function to select the quantities
Government maximizes social welfare to choose the degree of privatization.
Figure 4.1 Game Structure of Cournot Competition Model
2
The following sections will discuss the strategies for public firm to privatize: direct privatization or merger for privatizing.
4.2.2 Public Firm Privatizes Directly
In this case, at the second stage of the game, the public firm maximizes Ω to choose the output and all private firms maximize their profits to choose the output simultaneously.
We then obtain the following equilibrium values which are denoted by the superscript D ,
2
Concerning the optimal result, we have,
2 2
As an auxiliary result, one can obtain qualitatively the same result as that stated in lemma 1 in Matsumura and Kanda (2005) and Fujiwara (2007):
Lemma 4.1: Privatization makes the public firm’s share lower and that of each private firm higher.
According to Lemma 4.1, this completes laying out the basic model. The intuition behind Lemma 4.1 is that a profit-maximizing owner has a strong incentive to increase its output than welfare-maximizing owner. Since the reaction function of private firms is increasing in the output of public firm, the equilibrium output of each private firm increase;
thus the output of each private firm is increasing in δ .16
At the first stage of the game, the government maximizes social welfare to choose the optimal degree of partial privatization,
(2 )(1 2 )
Suppose that the number of foreign firms and the degree of product differentiated are exogenously given. Then with the utility assumption in Häckner (2000), the optimal privatization policy is monotonic in the differentiated degree of character of commodities,
γ .17 Moreover, the degree of privatization is monotonically increasing with the more the number of foreign private firm entry.
Proposition 4.1: The optimal privatization policy is monotonic in the differentiated degree of character of commodities. The degree of privatization is monotonically increasing with the more the number of foreign private firm entry.
Concerning the optimal degree of partial privatization we obtained, the sub-game perfect Nash equilibriums (SPNE) are as follows,
9 ( 4 (5 ))
17 This result is different from the result in Fujiwara (2007), where his utility function is assumed by Ottaviano et al. (2002) and Vives (2001) similarly.
4.2.3 Merging Firm and Partial Privatization
Without loss of generality, the public firm a and the domestic private firm b merge, they set up a new firm that chooses its strategy to maximize its objective function (4.7.2), Ω , at the second stage of the game. Simultaneously, all foreign private firms maximize their profits to choose output. Then we obtain the following equilibrium values which are denoted by the superscript M .
Concerning the optimal result, we have,
2
At the first stage of the game, the government maximizes social welfare to choose the optimal degree of partial privatization,
2
2 2
Suppose that the number of foreign firms and the degree of product differentiated are exogenously given. The optimal privatization policy is monotonic in the differentiated degree of character of commodities, γ . Moreover, the degree of privatization is monotonically increasing with the more the number of foreign private firm entry.
Concerning the optimal degree of partial privatization we obtained, the sub-game perfect Nash equilibriums (SPNE) are as follows,
2
4.2.4 Incentives for Mergers
In an international mixed oligopoly market, there exist one domestic public firm with partial privatization, one domestic private firm and several private foreign firms. Public firm has more incentives to merge because of social welfare improving, namely, social welfare
after merging is better than both the social welfare of pre-merger and of direct privatization.
Lemma 4.2: Post-merger social welfare is the best; the social welfare of no privatization is worst.
Therefore, public firm have to please to merge and when domestic firm’s readiness to merge.
For domestic private owner who would like to merge with the public firm, only if, the fraction of that private owner owns profits of the mixed firm after merging, ( )
a b
M M
δ π +π , is higher enough than the profit obtained by domestic private firm before merging, πb. Therefore, for any m∈N there exist δΓ∈(0,1)which denotes the value of the degree of privatization such that ( )
a b
With the proceeding of privatization, domestic private owner choose to merge with public firm when δ δ> Γ.18
With the proceeding of privatization, domestic private owner choose to merge with public firm when δ δ> Γ.18