國際混合寡占下貿易自由化、民營化與管制政策分析：環境稅、股權管制與併購

全文

(1)國立高雄大學經濟管理研究所碩士論文. 國際混合寡占下貿易自由化、民營化與管制政策分析：環境稅、股權管制與併購 TRADE LIBERALIZATION, PRIVATIZATION AND REGULATION POLICIES IN AN INTERNATIONAL MIXED OLIGOPOLY: ENVIRONMENTAL TAXATION, EQUITY REGULATION, AND MERGER. 研究生:陳泰良撰指導教授:王鳳生博士中華民國九十七年六月.

(2) 國際混合寡占下貿易自由化、民營化與管制政策分析：環境稅、股權管制與併購指導教授：王鳳生博士國立高雄大學應用經濟學系學生: 陳泰良國立高雄大學經濟管理研究所摘要近年來，發展中國家如中國、印度和東南亞國協等利用課稅、股權管制或民營化政策來保護國內產業、環境和追求社會福利；本論文將在一個國際混合寡占市場下的架構下分別探討環境稅、對外國投資廠商的股權管制與併購等議題。在環境議題上，Lai (2004)探討在一個雙占市場中貿易和環境稅的關係，而 Ohori (2006)擴充 Lai 的模型至一混合雙占市場。我們在兩篇文獻基礎上探討當存在消費外部性造成環境損害時，不同寡占市場結構(純粹寡占、混合寡占)與財貨性質下最適環境稅率的訂定與貿易自由化對環境損害的影響。結果顯示，無論在雙占市場或是寡占市場，存在低效率的公營廠商下所課徵的環境稅高於純民營市場；此外，在市場高度開放後，純粹寡占市場相較於混合寡占市場，環境損害程度將減少。在股權管制議題上，我們在一國際混合寡占模型下討論最適民營化比例與股權管制的影響。我們發現嚴厲股權管制措施會增加民營企業產出、利潤、市場價格和社會福利，但會降低公營企業的產出；又隨著股權管制的增加，政府將提升民營化的程度，且廠商家數越高亦將提升政府民營化的程度；此外，我們證明出 Fjell and Pal (1996)文中所指出的部份結論並非完全無誤，即無論外國廠商是否再投資於本國，公營廠商的產出將隨著外國私營廠商的進入而增加。最後，Méndez-Naya (2008)指出當部份廠商參與成為水平併購者之一且有利可圖，而非市場並構成唯一個獨佔市場時，合併的矛盾(merger paradox)是可被修正的。我們 I.

(3) 在一個國際混合寡占市場架構且廠商間生產水平異質產品下，發現在存在足夠併購誘因而達成併購時，大部分市不存在併購矛盾；對政府而言，當存在足夠誘因可達成併購時，藉由併購方式來進行民營化的策略將使福利高過公營廠商直接進行民營化的策略。關鍵字：貿易自由化；民營化；環境稅；股權控制；併購。. II.

(4) TRADE LIBERALIZATION, PRIVATIZATION AND REGULATION POLICIES IN AN INTERNATIONAL MIXED OLIGOPOLY: ENVIRONMENTAL TAXATION, EQUITY REGULATION, AND MERGER Advisor: Dr. Leonard F.S. Wang Department of Applied Economics National University of Kaohsiung Student: Tai-Liang Chen Institute of Economics and Management National University of Kaohsiung ABSTRACT For developing countries or those in transition, to protect domestic firms, environment, and social welfare, the government always steps in to affect market, such as taxation, equity control/regulation or privatization. For instance, China, India and the Association of South-East Asian Nations (ASEAN) not only choose privatization policy, but have passed legislation which implements taxations on controlling pollution, limits private shareholding, and/or the upper limit of foreign investment. This thesis will consider the issues of public policy－environmental taxation, equity control on foreign competitors, and merger for partial privatization－in an international mixed oligopoly. Concerning the environmental issue, Lai (2004) examined trade and environmental policies in a pure duopoly market, while Ohori (2006) extended Lai’s work in a mixed duopoly model. We investigated the environment tax and trade liberalization with different market structures (pure oligopoly or mixed oligopoly) juxtaposing the substitutability of the goods (homogenous goods and differentiated goods), wherein environmental damage is III.

(5) associated with consumption. It shows that the environmental tax in mixed oligopoly is higher than in pure oligopoly irrespective of the properties of goods. In addition, it demonstrates 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. Subsequently, concerning the issue on equity control, we demonstrated that the stringent control on domestic equity increases private firms’ outputs, profits, market price and social welfare, but decreases public firm’s output. Furthermore, along with the stringent control on domestic equity, the government ought to increase the degree of privatization. In an opening market, intensive competition from private firms in general will enhance the degree of privatization. It is shown that for the result in Fjell and Pal (1996): the public firm’s output always increases with an additional foreign private firm even if foreign firms reinvest in the home country; may not hold. Finally, Méndez-Naya (2008) found the “merger paradox” is qualified by showing that there are profitable gains for the firms participating in a horizontal merger that is not a merger to a monopoly. We considered in a single international mixed oligopoly market, firms produce horizontal differentiated commodity, and found that most merger cases are profitable under considering the incentives for mergers, and do not exist “The Merger Paradox”. For government, if enough incentives for all insiders, namely, public and private owners, the privatization strategy should be chosen to merge. Therefore, the way is more profitable and welfare-improving than privatizing directly. Keywords: Trade Liberalization; Privatization; Environmental Taxation; Equity Control; Merger.. IV.

(6) TABLE OF CONTENTS CHAPTER ONE：AN INTRODUCTION ..............................................................................1 1.1 Research Background .....................................................................................................1 1.2 Literature Review............................................................................................................2 1.2.1 Privatization .............................................................................................................2 1.2.2 Privatization and Environmental Taxation...............................................................3 1.2.3 Privatization and Equity Regulation ........................................................................4 1.2.4 Privatization and Merger..........................................................................................5 1.3 Structure of Thesis ..........................................................................................................6 CHAPTER TWO：PRIVATIZATION WITH CONSUMPTION EXTERNALITIES. AND. ENVIRONMENTAL TAXATION ...................................................................................8 2.1 Basic Model ....................................................................................................................9 2.2 Environmental Tax in Oligopoly...................................................................................11 2.2.1 Pure Oligopoly .......................................................................................................11 2.2.2 Mixed Oligopoly....................................................................................................12 2.3 The Effect of Trade Liberalization................................................................................13 2.4 Concluding Remarks.....................................................................................................15 CHAPTER THREE：PARTIAL PRIVATIZATION AND EQUITY REGULATION...........16 3.1 Basis Model ..................................................................................................................16 3.2 Privatization and an Open-door Policy .........................................................................18 3.2.1 Optimal Degree of Privatization ............................................................................20 3.2.2 Free Entry...............................................................................................................23 3.2.3 Effects of an Open-door Policy..............................................................................24 3.3 Concluding Remarks.....................................................................................................25 CHAPTER FOUR ： PARTIAL PRIVATIZATION, FOREIGN COMPETITORS, AND INCENTIVES FOR MERGERS ....................................................................................27 4.1 Basic Model ..................................................................................................................27 4.2 Merger Profitability and Partial Privatization...............................................................30 4.2.1 Benchmark .............................................................................................................30 4.2.2 Public Firm Privatizes Directly..............................................................................31 4.2.3 Merging Firm and Partial Privatization .................................................................34 V.

(7) 4.2.4 Incentives for Mergers ...........................................................................................35 4.3 Concluding Remarks.....................................................................................................38 CHAPTER FIVE：CONCLUSION.......................................................................................39 REFERENCES .......................................................................................................................41 APPENDIX A .........................................................................................................................44 APPENDIX B .........................................................................................................................46 APPENDIX C .........................................................................................................................47. VI.

(8) LIST OF FINGURES Figure 3.1 Game Structure of Cournot Competition Model with Equity Control............................18 Figure 3.2. The Effect of Number of Private Firms on the Degree of Privatization...............23 Figure 4.1 Game Structure of Cournot Competition Model ..........................................................30 Figure 4.2. Private Firm’s Incentives to Merge............................................................................37. VII.

(9) CHAPTER ONE: AN INTRODUCTION. 1.1 Research Background For developing countries or those in transition, privatization is one of the biggest issues toward market liberalization. Intensive competition between public and private firms exists in many industries such as air transportation, rail, telecommunications, electricity, and so on. Yet in addition to privatize directly, government could make public firm merge with private firm to enhance competitiveness. Therefore, the issues about incentives for mergers will be more interesting to discuss. To protect domestic firms, environment, social welfare, the government always steps in to affect market, such as taxation, equity control/regulation or privatization. The government of developing or newly emerging countries like China, India and the Association of South-East Asian Nations (ASEAN) not only choose privatization policy, but have passed legislation which implements subsidies on production, limits private shareholding, and/or the upper limit of foreign investment. In addition, for some strategic industries like military, astronavigation, navigation, and nuclear industry, more developing countries also pass legislation of control on domestic equity of foreign firms to protect national security, like Germany, Russia and Austria. Moreover, controlling pollution emission has become the most important and pressing issue for most governments to deal with. In particular, many developing countries face the alternatives between poor environmental-quality improvement and development of the economy. With market opening, the impact of trade liberalization on the environment has become the focus of much attention and debate.. 1.

(10) 1.2 Literature Review 1.2-1 Privatization Many papers have focused on the privatization issue and related policies. De Fraja and Delbono (1989) in a mixed oligopoly model showed that the privatization of welfare-maximizing public firms may improve social welfare. Many problems of privatization in developing countries result from the lack of information about the situation of the economy, and from the lack of determination on their path of privatization. Bös (1997) presented a theory of incomplete privatization contracts to postulate an elaborate system of price regulation of privatized monopolies, which typically is missing in developing countries. Matsumura (1998) explicitly considered the possibility of partial privatization, and shows that neither full privatization nor full nationalization is optimal. Lee and Hwang (2003) elaborated on the framework of Matsumura (1998) by allowing managerial inefficiency and showed that partial privatization is a reasonable choice of government in a monopoly as well as a mixed duopoly. Fjell and Heywood (2004) demonstrated that there are no consequences from privatization in a mixed oligopoly when the government uses a subsidy to ensure first best. Recently, Hindriks and Claude (2006) considered mixed oligopoly markets for differentiated goods where private and public firms compete either in prices or quantities, and studied the welfare effect of privatization which is interpreted as partial strategic delegation of the public firm to a private manager with profit concern. They found that public and private firms should be taxed the same, and that price regulation is better than quantity regulation. Fujiwara (2007) develops a differentiated mixed oligopoly model to establish what implication product differentiation has for the optimal privatization policy and shows that the short-run optimal policy is non-monotonic in the degree of love of variety, while the optimal degree of privatization is monotonically increasing in the consumer’s preference for variety in the long run. 2.

(11) In an international oligopoly market, many studies on privatization have concerned government policies that included tariff, taxation, and equity distribution.. Serizawa (2000). showed that even when there are only a few firms in the market, the government may first use an optimal tariff, then full privatization to improve domestic social welfare. Norbäck and Persson (2005) argued that equal treatment of foreign investors will be detrimental to domestic welfare by shifting profits from domestic to foreign firms which is shown to be less relevant in privatization auctions than for Greenfield FDI. They also showed that small local equity requirements are likely to be beneficial, but large ones counterproductive, preventing welfare-enhancing foreign acquisitions. Chang (2005) used a mixed duopoly model with cost asymmetry to examine optimal trade policy (import tariff) and full/partial privatization policy. Chao and Yu (2006) constructed a mixed oligopoly model to examine how partial privatization or foreign competition affects the optimal import tariff. Beladi and Chao (2006) showed that an increase in partial privatization may lower welfare in the long term through capital inflow. Dadpay and Heywood (2006) considered a mixed oligopoly with two countries each with public and private firms competing in a single market, and presented the usual reasons to imagine a public firm in a mixed oligopoly, though intended to enhance welfare, is actually lost when such firms compete in the interest of their respective countries. Sepahvand and Cornes (2007) examined the impact of timing of the game on the welfare gains of privatization in the presence of strategic trade policy. They argued that only if the public enterprise acts as a Cournot player will it generate an additional distortion that could outweigh the distortion caused by the oligopolistic behavior of private firms. However, with a first-mover advantage, it can serve as an effective regulatory device comparable with a production subsidy.. 1.2-2 Privatization and Environmental Taxation Many existing studies are concerned about internalizing pollution externalities by using 3.

(12) environmental tax like Krutilla (1991) who has focused attention on the determination of environmental regulations, and disregard the effect of trade liberalization on pollution control. Few studies have considered negative externalities associated with consumption of the good such as gum-chewing, cigarette smoking and gasoline consumption that cause environmental damage. Anderson (1992) showed that liberalizing trade in a good whose consumption gives rise to pollution will cause a country’s environment to deteriorate if the good is imported. Metcalfe and Beghin (1998) argued that when pollution intensities emitted in consumption endogenously respond to environmental policy, and when this policy differs between trading partners, an additional policy instrument is required to cap pollution intensities, such as a standard or a prohibitive tax on any increase in the intensity of consumption pollution. Lai (2004) examined trade and environmental policies in a pure duopoly market, while Ohori (2006) extended Lai’s work in a mixed duopoly model and showed that the optimal environmental tax in a mixed duopoly is higher than the Pigouvian level and the optimal tax in a pure duopoly. Furthermore, Lai and Hu (2005) demonstrated that trade liberalization will enhance global welfare if transboundary pollution-associated consumption is sufficiently strong as well as if bilateral reduction in tariffs is beneficial to the global environment.. 1.2-3 Privatization and Equity Regulation Chakrabarti and Heywood (2004) presented a spatial model in which a foreign firm and local government behave strategically in setting a local equity requirement. Norbäck and Persson (2005) argued that equal treatment of foreign investors will be detrimental to domestic welfare by shifting profits from domestic to foreign firms which is shown to be less relevant in privatization auctions than for Greenfield FDI. They also showed that small local equity requirements are likely to be beneficial, but large ones counterproductive, preventing 4.

(13) welfare-enhancing foreign acquisitions. Actually, most papers on equity issue are general equilibrium setting, Hill and Mendez (1992) provided an exploration of the impact on local resource allocation and employment of laws which regulate the degree of local ownership of multinational subsidiaries. Chao and Yu (2000) examined the welfare effect of domestic equity requirements on multinational firms in the presence of alternative types of trade instruments and varying degrees of the mobility of foreign capital. Chao and Yu (2007) further examined the effects of trade liberalization on firm ownership and the environment for a small open economy.. 1.2-4 Privatization and Merger Most literatures on merger issues focus on private firms and extensively analyze the private incentives of mergers, and also their impact on welfare, however it has not considered the decision to merge by private and public firms. González-Maestre and López-Cuñat (2001) assume that owners delegate output decisions to managers. Faulí-Oller (2002) assumes that when two firms with different costs merge, the merged entity produces at the cost of the more efficient firm. However, Bárcena-Ruiz and Garzón (2003) assumed that when a private and a public firm merge, and set up a jointly owned multiproduct firm. The decisions to merge depend on the degree to which goods are substitutes and on the percentage of the shares that the government owns in the multiproduct firm. Huck and Konard (2004) showed that merger can be profitable and welfare enhancing, even though it would not be profitable in a laissez-faire economy. A key element is a change in the government’s incentives to give subsidies to their local firms. Norman et. al. (2005) showed that if the merger occurs in a vertical differentiated market, then the merger will lead to a reduction in product offerings, and in such markets, two-firm mergers will lead to higher prices in spite of the merger’s cost saving. Coloma (2006) develops an oligopoly model with firms that may potentially be state-owned or privately owned and solves it for different cases in which the number and 5.

(14) ownership of those firms vary. Moreover, traditionally it was well known that the profitability of horizontal mergers with quantity competition is scarce, but profits of non-merging firms increase. This result has grown to take prominent places in text book such as that by Pepall, Richard, and Norman (1999, Chapter 8) and took the name, “The Merger Paradox”. Subsequently, many papers used different methods on applied merger issues to revise merger paradox. Ziss (2001) showed that the profitability of merger in oligopoly enhanced if firms delegate the output decision to an agent. Creane and Davidson (2004) found different result from “Paradox” by allowing for a parent company that can play each insider off one another with quantity competition. Esccrihuela-Villar and Faulí-Oller (2008) expressed mergers among followers become profitable when the followers are insufficient enough. Heywood and McGinty (2008) examined the consequence of a Stackelberg leader merging with followers when costs are convex. Such mergers are always profitable for the participants, and the followers often do better merging than remaining excluded rivals. Méndez-Naya (2008) studies the incentive to merge for both, private and public firms, when non-merging firms change their strategies as a consequence of the merger and finds the “merger paradox” is qualified by showing that there are profitable gains for the firms participating in a horizontal merger that is not a merger to a monopoly and presents that it is shown that merger sustainability depends on both, the privatization degree of the mixed firm and the number of non-merging firms. However, when firms produce differentiated product, the results turn to ambiguous because of the degree of differentiation.. 1.3 Structure of Thesis This thesis will consider the issues of public policy－environmental taxation, equity control on foreign competitors, and merger for partial privatization－in an international 6.

(15) mixed oligopoly. Based on the studies of environmental taxation in Lai (2004) and Ohori (2006), welfare model in Fjell and Pal (1996), partial privatization with differentiated commodity in Fujiwara (2007) and merger profitability in Méndez-Naya (2008), we will extend the past results to be more completed by apt models. The remaining chapters are organized as follows. In chapter 2, presents privatization with consumption externalities and legislation of environmental taxation. In Chapter 3, analyzes the effects of equity control on foreign competitors and compares the results with Fjell and Pal (1996). In chapter 4, studies the partial privatization and the merging incentives derived from the privatization of the mixed firm. Chapter 5 summarizes our main conclusions.. 7.

(16) CHAPTER TWO：PRIVATIZATION WITH CONSUMPTION EXTERNALITIES AND ENVIRONMENTAL TAXATION1. In this paper, we investigate the optimal environmental tax and the environmental effect of trade liberalization in a mixed oligopoly and pure oligopoly, wherein firms produce the differentiated goods and the environmental damage is associated with consumption.2 As a benchmark, we used the study conducted by Lai (2004), who demonstrates that trade liberalization on “dirty” goods leads to environmental improvement and Ohori (2006), who demonstrates that trade liberalization on such dirty goods has no influence on environmental improvement. We then compared the environmental tax before privatization with that after privatization, and that of producing differentiated goods with homogeneous goods. We found 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. This chapter is organized as follows. Section 2.1 provides the basic model. Section 2.2 includes the results of the analysis in oligopoly with differentiated goods and does a comparison. Section 2.3 analyzes the effects of trade liberalization. Section 2.4 presents concluding remarks.. 1. This chapter has been published in Economics Bulletin: Wang, Wang, and Chen (2007). Mixed oligopoly models with foreign competition, see Fjell and Pal (1996), Pal and White (1998), and Fjell and Heywood (2002). 2. 8.

(17) 2.1 Basic Model The model follows Ohori’s (2006) basic set-up but includes product differentiation. Consider a single international market in which there exists one domestic firm (firm 0) and several private foreign firms (firm i , i = 1,..., n ) competing in a domestic country. Under the. Cournot-Nash assumption, if the domestic firm is public, it selects its output in order to maximize the sum of consumer surplus and its own profit U ；if the domestic firm is private, it chooses its output in order to maximize its own profit π 0 . The domestic and foreign firms produce a differentiated good, given by qi ( i =0, 1… n), and this leads to pollution. The domestic government sets the environmental tax t to control the pollution that results from environmentally harmful consumption. We assume that all consumers in the domestic country are the same, and normalize the size of the population in the domestic country to one. The representative consumer derives utility from consuming the good under consideration, and suffers from consumption-type pollution. The utility function of the representative consumer in the domestic country is as follows Häckner (2000)3 in generalizing the utility function to allow for n foreign firms and one domestic firm producing differentiated goods, n n 1 V = a(q0 + ∑ qi ) − (q02 + ∑ qi 2 + 2γ ∑ qi q j ) + I − θ Q 2 i =1 i =1 i≠ j. (2.1). Where I is the composite goods, and θ is the coefficient of the marginal pollution damage. By solving the optimization problem of the domestic consumer, we can derive the n. domestic inverse demand function for the good, pi ≡ pi (Q) , where Q = q0 + γ ∑ qi . Q i =1. denotes the aggregate output. We assume p′ < 0 . In order to sharpen the study, it is also. 3. Häckner assumed the utility function is quadratic in the consumption of q-goods and for simplicity let β1 = β 2 = 1 , which is more concise than the utility in Sing and Vives (1984), namely, 1 U (q1 , q2 ) = q1 + q2 − ( β1q12 + β 2 q22 + 2γ q1q2 ) . 2. 9.

(18) assumed that the inverse demand function is linear (i.e. p (Q) = a − Q ). The profit function of firm 0,. π 0 = ( p − c0 − t )q0 , where c0 is the constant marginal production cost. The public firm’s objective function is defined as the sum of consumer surplus and the firm’s profit,. U = CS + π 0 =. 1 2 n 2 (q0 + ∑ qi ) + γ ∑ qi q j + π 0 . 2 i =1 i≠ j. (2.2). The environmental damage function is given by D = θ Q , where θ denotes the marginal environmental damage and θ ≥ 1 . Social welfare in the domestic country is n. W = CS + π 0 + tQ + τ ∑ qi − D .. (2.3). i =1. The foreign private firm selects its own output in order to maximize its profit,. π i = ( p − c f − t − τ )qi , i = 1, 2,......, n ,. (2.4). where c f is the constant marginal production cost and τ is the tariff rate, τ ≥ 0 .When we examine the duopoly case, in equation (2.2)、(2.3) and (2.4) assuming n = 1 to represent one. foreign firm. For simplicity, each firm does not have fixed cost. It also assumes that the marginal production cost of the domestic firm is higher than that of the foreign firm ( c0 > c f > 0 ).4 Moreover, as in Lai and Ohori, we consider trade liberalization to be a form of tariff reduction. 4. See Cremer et al (1989) for a justification of this assumption. 10.

(19) 2.2 Environmental Tax in Oligopoly We extend the basic model concerning the number of foreign firms in which there is one domestic firm and n foreign private firms producing differentiated goods.. 2.2-1 Pure Oligopoly Case We first derive the optimal environmental tax in the pure oligopoly with differentiated goods. Under the Cournot-Nash assumption, the domestic private firm selects its output in order to maximize its own profit π 0 , while the foreign private firm chooses its output in order to maximize its own profit π i . We obtain the following first-order conditions: p − c0 − t + p′q0 = 0 , and. (2.5). p − c f − t − τ + p′γ qi = 0 , i = 1, 2,......, n .. (2.6). The output effects of the taxes are obtained by differentiating (2.5) and (2.6) with respect to. t. and. qi , δ q0 δ t = 1 (n + 2) p′. and. n. ∑ (δ q i =1. i. δ t ) = n γ (n + 2) p′ . This. demonstrates that an increase in the environmental tax reduces the market share of all firms. Having obtained these results, we differentiate social welfare equation with respect to t and set dW / dt = 0 to obtain optimal environmental tax,. t DP =. 1 n n + 2γ + 1 [2n(c0 − c f ) − (n − 1) p′Q* ] − [ ]τ + θ , 2 (n + 1) n + 1 γ (n + 1). (2.7). where Q* denotes optimal aggregate output5. 5. (a) We use the superscripts M 、 P 、 DM and DP for the mixed Cournot-Nash with homogeneous goods, pure Cournot-Nash homogeneous goods, mixed Cournot-Nash with differentiated goods, and pure Cournot-Nash with differentiated goods oligopoly respectively. (b) Because the form of optimal environmental tax in pure duopoly is not as usual, there exists a Therefore, we supply a special case to simplify this equation in appendix B. 11. p 'Q* term..

(20) 2.2-2 Mixed Oligopoly Case We derive the optimal environmental tax in the mixed oligopoly with differentiated goods. Under the Cournot-Nash assumption, the domestic firm selects its output in order to maximize the sum of consumer surplus and its own profits U , while the foreign private firm chooses its output in order to maximize its own profit π i . We obtain the following first-order conditions, n. p − c0 − t − p′γ ∑ qi = 0 , and. (2.8). p − c f − t − τ + p′γ qi = 0 , i = 1, 2,......, n .. (2.9). i =1. The output effects of the taxes are obtained by differentiating (2.8) and (2.9) with n. respect to t and qi , δ q0 / δ t = 1/ p and ∑ (δ qi / δ t ) = 0 . These demonstrate that an '. i =1. increase in the environmental tax reduces the market share of the less efficient public firm. Having obtained these results, we differentiate social welfare equation with respect to t and set dW / dt = 0 to obtain optimal environmental tax,. t DM =. n(c0 − c f − τ ) n +1. +θ .. (2.10). From equation (2.7)、(2.10)、(A.1.4) and (A.2.4)6, we find that the optimal environmental tax in different market with different properties of goods is, t M = t DM > t P > t DP . We have the following proposition.. 6. See appendix A. for deriving optimal tax rate in pure and mixed oligopoly homogeneous goods. 12.

(21) Proposition 2.1: In an international oligopoly market wherein the environmental damage is. associated with consumption, the optimal environmental tax in mixed market is maximum, and the optimal environmental tax with differentiated good in pure market is minimum.. 2.3 The Effect of Trade Liberalization We now consider the impact of a change in the tariff rate on the outputs of one domestic firm and n foreign private firms in the domestic market. We derive the total impact of trade liberalization on the environment by differentiating the environmental damage function with respect toτ , dD δ D δ D δ t = + = 0. dτ δτ δ t δτ We obtained the following four results for different market structures and commodities properties:. Case (i): pure oligopoly with homogeneous goods. dD (n + 2n − 11n − 4n) = dτ (n + 2) 2 (n + 1) 2 p′ P. 4. 3. 2. ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩. dD P > 0 if dτ. n≤2. dD P < 0 if dτ. n≥3. δ t P −(n3 + 8n 2 + 3n) = <0 δτ ( n + 1) 2 (n + 2). Case (ii): mixed oligopoly with homogeneous goods dD M = 0； dτ. 13.

(22) δtM −n = <0 δτ n +1. Case (iii): pure oligopoly with differentiated goods dD DP −[(γ − 1) 2 n 4 + (−4γ 2 + 4γ − 3)n3 + (−8γ 2 + 4γ − 2)n 2 + (−5γ 2 + 2γ )n] = > 0； (n + 2) 2 (n + 1) 2 γ 2 p′ dτ. δ t DP −[n3 + 3(γ + 1)n 2 + (3γ + 2)n] = <0 δτ γ (n + 1) 2 (n + 2). Case (iv): mixed oligopoly with differentiated goods dD DM (1 − γ )nθ = <0； (n + 1)γ p′ dτ. δ t DM −n = <0 δτ n +1 According to the above results, we know no matter what types of market structures, there is a negative relationship between tariff rate τ and environmental taxes t ; that is, if the government opens the market wholly to make the numbers of foreign firms increase from 1 to n , it may cause more pollution; hence, the government should raise the environmental tax. In pure oligopoly with homogeneous goods, if the numbers of firms are equal and less than two (i.e. n ≤ 2 ), a tariff reduction will improve the environment；however, if the numbers of firms are equal and greater than three (i.e. n ≥ 3 ), a tariff reduction has harmful effect on the environment. In mixed oligopoly with homogeneous goods, a tariff reduction has no effect on the environmental damage associated with consumption, which is the same as Ohori’s (2006) result. However, in the pure oligopoly with differentiated goods, a tariff reduction has a positive impact on the environment; but, in mixed oligopoly with differentiated goods, a tariff reduction has harmful effect on the environment. When exogenous variables n or γ equal 1, we obtain the same results as in the duopoly market (Lai and Ohori’s work). We have the following proposition. 14.

(23) Proposition 2.2: The effects of trade liberalization in oligopoly coincide with that in duopoly;. except for the one in pure oligopoly with homogeneous goods. 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.. 2.4 Concluding Remarks 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.. 15.

(24) 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)q 2 , produces a homogeneous commodity, and the inverse demand. function. for. the. n. m. i =1. j =1. product. in. the. domestic. country. is. given. by P = a − Q = a − (q0 + ∑ qi + ∑ q j ) , where P is market price, Q is total output, q0 is the output of the domestic public firm, qi is the output of the domestic private firm, and q j is the output of the foreign firm. Furthermore, the fixed cost f is assumed to be zero for simplicity 7 . Each domestic private firm i maximizes its own profit denoted by. π i = Pqi − (1 2)qi2 , 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. 16.

(25) π j = Pq j − (1 2)q 2j .8 In this paper, government decides the proportion of domestic equity for foreign competitors to protect domestic firms. Therefore, domestic social welfare is the n. m. i =1. j =1. summation of the consumer surplus, CS = (1 2)(q0 + ∑ qi + ∑ q j ) 2 , the domestic firms’ profit, and partial foreign firms’ profits. n. m. i =1. j =1. W = CS + π 0 + ∑ π i + α ∑ π j ; α ∈ [0,1) ,. (3.1). where π 0 = Pq0 − (1 2)q02 denotes the profit of the privatized public firm, and α 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 100 α 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 π j , j = 1, 2,..., m . 9. See Fjell and Pal (1996) footnote 2. 17.

(26) V = θπ 0 + (1 − 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.. Stage II. Stage I. Time. Government maximizes social welfare to choose the degree of privatization.. Each firm simultaneously maximizes their objective function to select the quantities. Figure 3.1 Game Structure of Cournot Competition Model with Equity Control. 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.. q0 =. a(2 + m(1 − α )(1 − θ )) a(1 + θ ) 2a(1 + θ ) , qi = q j = ; P= , Η Η Η 18. (3.3).

(27) where Η = 4 + n + m(2 + α (−1 + θ )) + (2 + n)θ > 0 . The effects of privatization is given by,. ∂q0 2a (2 + m + n)(1 + m(1 − α )) =− < 0, ∂θ Η2 ∂qi ∂q j 2a(1 + m − mα ) = = > 0; ∂θ ∂θ Η2. (3.4). ∂P 4a(1 + m − mα ) = > 0. ∂θ Η2 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,. π0 =. a 2 (2 + m(1 − α )(1 − θ ))(2 − m(1 − α )(1 − θ ) + 4θ , 2Η 2. πi = π j = CS =. 3a 2 (1 + θ ) 2 ; 2Η 2. (3.5). a 2 (2 + n + m(2 − α (1 − θ )) + nθ ) 2 . 2Η 2. Lump-sum transfer from consumer to firm 0 may be conducted when π 0 takes a negative value. The comparative static results include ∂π 0 Φ = , ∂θ Η 3 ∂π i ∂π j 6a 2 (1 + m(1 − α ))(1 + θ ) = = > 0; ∂θ ∂θ Η3. (3.6). ∂CS 4a 2 (1 + m(1 − α ))(2 + n + m(2 + α (−1 + θ )) + nθ ) =− <0, ∂θ Η3 where Φ = 2a 2 (1 + m(1 − α ))(4 + m(4 + m + n)(1 − α + αθ ) − (4 + 2n + m(6 + m + n))θ ) . Equation (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 19.

(28) (firm 0) profit, ∂π 0 ∂θ. = θ = 0+. 2a 2 (1 + m(1 − α ))(4 + m(4 + m + n)(1 − α )) >0. (4 + n + m(2 − α ))3. 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, W = (a 2 (1 + θ )(8 + m 2 (3 − 2α (1 − θ ) − θ ) + n(7 + n + (3 + n)θ ) +. (3.7). m(8 − α + 2n(2 − α (1 − θ )) − 4θ + 7αθ ))) / 2Η 2 .. We obtain the optimal degree of privatization as. θ=. n + m + (m 2 + mn)(1 − α ) , 4 + n + m(6 + m + n − (5 + m + n)α ). (3.8). and from (3.8), θ ∈ [0,1] for n ≥ 1, m ≥ 1 and 0 ≤ α < 1 , and the second-order condition is satisfied, ∂ 2W = −(2a 2 (1 + m(1 − α ))((4 + n + m(6 + m + n) − m(5 + 2 ∂θ m + n)α )(4 + n + m(2 + α (−1 + θ )) + (2 + n)θ ) + 3(2 + n + mα )(n + m(m + n + α − (m + n)α ) − 4θ + (−n − m(6 +. <0.. (3.9). m + n) + m(5 + m + n)α )θ )) / Η 4 To see how the equity control affects the degree of privatization, we have the following 20.

(29) expression, ∂θ 2m(2 + m + n) = >0, ∂α (4 + n + m(6 + m + n − (5 + m + n)α )) 2 for. (3.10). n ≥ 1, m ≥ 1 and 0 ≤ α < 1 . The stringent control of domestic equity on foreign firms. 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:. q0 =. a (4 + n + m(4 − 3α )) a(2 + m + n) 2a(2 + m + n) , qi = q j = , P= ; Ψ Ψ Ψ. a 2 (4 + n + 4m − 3mα )(4 + 3n + 3mα ) 3a 2 (2 + n + m) 2 π0 = , πi = π j = ; 2Ψ 2 2Ψ 2. (3.11). a 2 (2 + n + m) 2 W= , 2Ψ where Ψ = 8 + m 2 + n(5 + n) + m(8 + 2n − 3α ) > 0 . By comparing welfare differential, the government will push forward on its privatization path. W −W * =. a 2 (n + m(m + n + α − (m + n)α )) 2 > 0, 2(8 + m 2 + n(5 + n) + m(8 + 2n − 3α ))(4 + n + m(2 − α )) 2. where W * denotes the social welfare without partial privatization10. To see the effect of equity control on outputs and price, we have,. 10. See Appendix (C.1) 21. (3.12).

(30) ∂q0 ∂qi ∂q j 3am(2 + n + m) 3am(2 + n + m) 2 =− <0, = = >0; 2 ∂α Ψ ∂α ∂α Ψ2 ∂P 6am(2 + n + m) = >0, ∂α Ψ2 for any n ≥ 1, m ≥ 1 and 0 ≤ α < 1 .. (3.13). 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: ∂π 0 3a 2 m(2 + n + m)(8 + 12m + 2m 2 + mn − n 2 − 3m(4 + m + n)α ) = , ∂α Ψ3 ∂π i ∂π j 9a 2 m(2 + n + m) 2 = = > 0; ∂α ∂α Ψ3. (3.14). ∂W 3a 2 m(2 + n + m) 2 = >0. ∂α 2Ψ 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) 22.

(31) 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, ∂θ 2(1 + m(1 − α ))(2 + 3m(1 − α )) = >0, ∂n (4 + n + m(6 + m + n − (5 + m + n)α )) 2 and ∂θ 2(4m(1 − α ) − n(1 − α ) + 3m 2 (1 − α ) 2 + 2α ) = > 0 , if and only if ∂m (4 + n + m(6 + m + n − (5 + m + n)α )) 2. 1 ≤ n < 4m + 3m 2 (1 − α ) +. (3.15). 2α . 1−α. 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.. 0.95 θ 0.9. 100 80. 0.85 40. 20. 60 m. 40 n. 20. 60 80 100. Fig. 3.2. The Effect of Number of Private Firms on the Degree of Privatization. 23.

(32) 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, ∂q0 a(2 + m + n)(2n − 3(2 + n)α + m(−4 + 3α )) = > 0 , if and only if (8 + m 2 + n(5 + n) + m(8 + 2n − 3α )) 2 ∂m m<. (2 − 3α )n − 6α ; 4 − 3α. ∂W a 2 (2 + m + n)(−2n + 3(2 + n)α + m(4 − 3α )) = > 0 , if and only if ∂m 2(8 + m 2 + n(5 + n) + m(8 + 2n − 3α )) 2. m>. (2 − 3α )n − 6α ; 4 − 3α. ∂P 2a (8 + m 2 + 2m(2 + n) + n(7 + n) − 3(2 + n)α ) =− < 0, ∂m (8 + m 2 + n(5 + n) + m(8 + 2n − 3α )) 2. (3.16). ∂π 0 = −(a 2 (64 + 3m 2 (8 + 3n(2 − α )) − 48α + 3m3α (4 − 3α ) + ∂m 3n(4 + n)(6 + (−2 + n)α ) + 3m(4 + n)(8 + 2α (−5 + 3α ) + 3n(2 + < 0 , (−2 + α )α ))) /(8 + m 2 + n(5 + n) + m(8 + 2n − 3α ))3 ∂π i ∂π j 3a 2 (2 + m + n)(8 + m 2 + n(7 + n) + (2m − 3α )(2 + n)) = =− < 0. ∂m ∂m (8 + m 2 + n(5 + n) + m(8 + 2n − 3α ))3. Under an open-door policy, public firm’s profit increases if and only if. m < {(2 − 3α )n − 6α /(4 − 3α )} , 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 24.

(33) 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 − 3α )n − 6α /(4 − 3α )} , 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 Note that if the public firm competes only with foreign private firms ( n = 0 ), then entry by a new foreign ∂W a 2 (2 + m)(6α + m(4 − 3α )) = > 0 . The case of a public firm firm always increases welfare, namely, ∂m n = 0 2(8 + m(8 + m − 3α )) 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. 12. 25.

(34) 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.. 26.

(35) 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. 27.

(36) differentiated goods15, m m 1 U (qa , qb , q1 , q2 ,..., qm ) = (qa + qb + ∑ q j ) − (q a2 + q b2 + ∑ q 2j + 2γ ∑ qi q j ) + I ; 2 j =1 j =1 i≠ j. (4.1). i, j = a, b,1, 2,..., m , where I is the composite goods. If the parameter γ ∈ (0,1) products are substitutes while if γ ∈ (−1, 0) products are complementary. The inverse demand function is given by Pi = 1 − (qi + γ Q−i ) ; i = a, b,1, 2,..., m ,. (4.2) m. where qi is output and Q− i = (qa + qb + ∑ q j ) − qi . j =1. Therefore, consumer surplus is given by CS ≡ U − ( Pa qa + Pb qb + Pq 1 1 + ... + Pm qm ) m 1 = (qa2 + qb2 + ∑ q 2j ) + γ ∑ qi q j 2 j =1 i≠ j. .. (4.3). All firms share identical cost function with increasing marginal cost represented by the following quadratic function.. C (qi ) =. 1 2 qi ； i = a, b,1, 2,..., m . 2. (4.4). The profit function of firm i is given by 1 2. π i = Pq qi2 ； i = a, b,1, 2,..., m . i i −. (4.5). 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 β1 = β 2 = 1 , which is more concise than the utility in Sing and Vives (1984), namely, 1 U (q1 , q2 ) = q1 + q2 − ( β1q12 + β 2 q22 + 2γ q1q2 ) . 2. 28.

(37) domestic firm’s profit, W = CS + π a + π b ,. (4.6). where π a represents the profits of public firm and π b 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 firm a as Ω = (1 − δ )W + δπ a ； 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 + π ) ； δ ∈ [0,1] . Ω a b. (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 . 29.

(38) 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.. Stage II. Stage I. Time. Government maximizes social welfare to choose the degree of privatization.. Each firm simultaneously maximizes their objective function to select the quantities. Figure 4.1 Game Structure of Cournot Competition Model. 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,. qa =. 3 + (m − 1)γ , 6 + 2mγ − γ 2. qb = q j = Pa =. 2−γ , 6 + 2mγ − γ 2. (4.8). 3 − (1 + m(1 − γ ))γ , 6 + 2mγ − γ 2. 30.

(39) Pb = Pj =. 2(2 − γ ) , 6 + 2mγ − γ 2. (3 + (m − 1)γ )(3 − γ (1 + m(3 − 2γ ))) , 2(6 + 2mγ − γ 2 ) 2. πa =. 3(2 − γ ) 2 , 2(6 + 2mγ − γ 2 ) 2. π =π = b. j. 34 + 4m + 4γ (m − 1)(4 + m) − (4 + m(3 + 2m))γ 2 + (2 + (m − 1) m)γ 3 ; 2(6 + 2mγ + γ 2 ) 2 j = 1, 2,..., m .. W=. 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 ,. qaD =. 3 + γ (−1 + m(1 − δ )) , 3(2 + δ ) + mγ (2 + (1 − γ )δ ) − γ 2. Q− a =. (1 + m)(2 + δ − γ ) 3(2 + δ ) + mγ (2 + (1 − γ )δ ) − γ 2. qbD = q Dj =. (4.9). 2+δ −γ . 3(2 + δ ) + mγ (2 + (1 − γ )δ ) − γ 2. Concerning the optimal result, we have,. ∂q aD ∂δ. =−. (3 − γ )(1 + mγ )(3 + mγ ) <0, (3(2 + δ ) + mγ (2 + (1 − γ )δ ) − γ 2 ) 2 (4.10). ∂q b ∂δ. ∂q j. D. D. =. ∂δ. =. γ (3 − γ )(1 + mγ ) >0. (3(2 + δ ) + mγ (2 + (1 − γ )δ ) − γ 2 ) 2 31.

(40) 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,. γ (2 − γ )(1 + m + m 2γ ) δ= . 9 + γ (−4 + m(11 + (−4 + m(2 − γ ))γ )). (4.11). Proof: (9 + γ (−4 + m(11 + (−4 + m(2 − γ ))γ ))) − (γ (2 − γ )(1 + m + m 2γ )) = (3 − γ )(3 + (3m − 1)γ ) > 0 , so 0 < δ <1 Then, ∂δ = (2(3 − γ )(3 − 2γ ) + m(γ 2 + 18(1 − γ )) + γ m 2 (6 − γ )(γ 2 + 6(1 − γ )) + ∂γ > 0;. 3γ 2 m3 (γ 2 + 6(1 − γ ))) /( −9 + γ (4 + m( −11 + (4 + m( −2 + γ ))γ ))) 2 ∂δ γ (3 − γ )(2 − γ )(3 + γ (3m − 2)(2 + γ m)) = >0. ∂m (−9 + γ (4 + m(−11 + (4 + m(−2 + γ ))γ ))) 2 16. See Matsumura and Kanda (2005). 32. (4.12).

(41) 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,. q aD =. 9 + γ (−4 + m(5 − γ )) , 18 + γ (−4γ + m(12 + γ (−1 + m(2 − γ ) − γ ))). q bD = q Dj = PaD =. (2 − γ )(3 + mγ ) , 18 + γ (−4γ + m(12 + γ (−1 + m(2 − γ ) − γ ))). 9 + γ (m(1 + γ ) − 2 − γ ) , 18 + γ (−4γ + m(12 + γ (−1 + m(2 − γ ) − γ ))). PbD = PjD =. πD = a. (4.13). (9 + γ (−4 + m(5 − γ )))(9 + 3m( −1 + γ )γ − 2γ 2 ) , 2(18 + γ (−4γ + m(12 + γ (−1 + m(2 − γ ) − γ )))) 2. πD =πD = b. 2(2 − γ )(3 + mγ ) , 18 + γ (−4γ + m(12 + γ (−1 + m(2 − γ ) − γ ))). j. 3(−2 + γ ) 2 (3 + mγ ) 2 , 2(18 + γ ( −4γ + m(12 + γ ( −1 + m(2 − γ ) − γ )))) 2. 17 − 8γ + m(2 + 2(3 + m)γ − (2 + m)γ 2 ) ; 36 + 2γ ( −4γ + m(12 + γ (−1 + m(2 − γ ) − γ ))) j = 1, 2,..., m .. WD =. 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. 33.

(42) 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 . 3 + γ (−1 + m(1 − δ )) , (2 + γ )(3 + (m − 1)γ ) + (3 + γ (2 + m(1 − γ ) + γ ))δ 2 − γ + (1 + γ )δ q Mj = . (2 + γ )(3 + (m − 1)γ ) + (3 + γ (2 + m(1 − γ ) + γ ))δ. q aM = q bM =. (4.14). Concerning the optimal result, we have,. ∂q aM ∂q bM (3 + (m − 1)γ )(3 + γ (2 + 3m − γ )) = =− < 0, (3(2 + δ ) + γ (1 + 2δ − γ (1 + δ ) + m(2 + γ + δ − γδ ))) 2 ∂δ ∂δ. (4.15) ∂q j 2γ (3 + γ (2 + 3m − γ )) = > 0. ∂δ (3(2 + δ ) + γ (1 + 2δ − γ (1 + δ ) + m(2 + γ + δ − γδ ))) 2 M. At the first stage of the game, the government maximizes social welfare to choose the optimal degree of partial privatization,. δ =. γ m(2 − γ )(1 + (m − 1)γ ) . 9 + γ (3 + m(11 − γ ) − (5 − γ )γ + m 2 (2 − γ )γ ). (4.16). Then, ∂δ = (2m(9 + γ (9γ m 2 (1 − γ )) + γ (14 + γ − γ 2 ) + m(18 + γ (−26 + ∂γ. γ (8 + γ ))) − 27)) /(9 + γ (3 + m(11 − γ ) − (5 − γ )γ + m (2 − γ )γ )) 2. 34. > 0; 2. (4.17).

(43) ∂δ = (γ (2 − γ )(9 + γ (−6 + 2m(−3 + γ ) 2 (1 + γ ) + γ m 2 (9 + γ (2 − γ )) − >0. ∂m 2 2 γ (4 − γ )(2 − γ ))) /(9 + γ (3 + m(11 − γ ) − (5 − γ )γ + m (2 − γ )γ )). 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,. q aM = qbM = q Mj =. 9 + γ (−6 + γ + m(5 − γ )) , 18 + γ (−3 + 12m − (4 − γ )γ + γ m 2 (2 − γ )). (2 − γ )(3 + (m − 1)γ ) , 18 + γ (−3 + 12m − (4 − γ )γ + γ m 2 (2 − γ )). PaM = PbM = PjM =. 9 + γ (−6 + γ + m + γ m) , 18 + γ (−3 + 12m − (4 − γ )γ + γ m 2 (2 − γ )). 2(2 − γ )(3 + (m − 1)γ ) , 18 + γ (−3 + 12m − (4 − γ )γ + γ m 2 (2 − γ )). πM =πM = a. b. πM = j. (4.18). (9 + γ (−6 + γ + m(5 − γ )))(9 + γ (−6 + γ + 3m(−1 + γ ))) , 2(18 + γ (−3 + 12m − (4 − γ )γ + γ m 2 (2 − γ ))) 2. 3(−2 + γ ) 2 (3 + (m − 1)γ ) 2 , 2(18 + γ (−3 + 12m − (4 − γ )γ + γ m 2 (2 − γ ))) 2. 2(−3 + γ ) 2 + γ m 2 (2 − γ ) + m(2 + (7 − γ )γ ) ; 36 + 2γ (−3 + 12m − (4 − γ )γ + γ m 2 (2 − γ )) j = 1, 2,..., m .. WM =. 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 35.

(44) 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.. Proof: W M − W D = ((2 − γ )(3 + (3m − 1)γ ) 2 ) / 2(18 + γ (−3 + 12m + (−4 + γ )γ +. γ m 2 (2 − γ )))(18 + γ (−4γ + m(12 + γ (−1 + m(2 − γ ) − γ ))). > 0;. W D − W = (γ 2 (2 − γ ) 2 (1 + m + γ m 2 ) 2 ) / 2(6 + 2mγ − γ 2 ) 2 (18 + > 0. γ (−4γ + m(12 + γ (−1 + m(2 − γ ) + γ )))). 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, δ (π aM + π bM ) , is higher enough than the profit obtained by domestic private firm before merging, π b . Therefore, for any m ∈ N there exist δ Γ ∈ (0,1) which denotes the value of the degree of privatization such that δ Γ (π aM + π bM ) = π b . Concerning this we obtain δ Γ is given by. δ Γ = (3(−2 + γ ) 2 (18 + γ (−3 + 12m + (−4 + γ )γ + γ m 2 (2 − γ ))) 2 ) / (2(9 + γ (−6 + m(5 − γ ) + γ ))(9 + γ (6 + 3m(1 − γ ) − γ ))(6 + 2mγ + γ 2 ) 2 ). .. (4.19). With the proceeding of privatization, domestic private owner choose to merge with public firm when δ > δ Γ .18. 18. See the proof of proposition 2 in Méndez-Naya (2008). 36.

(45) Proposition 4.2: In an international differentiated mixed oligopoly, domestic private firm. decide to merge with public firm when δ (π aM + π bM ) > π b if and only if δ > δ Γ .. Proof:. δ − δ Γ = {γ m(2 − γ )(1 + (m − 1)γ ) /(9 + γ (3 + m(11 − γ ) − γ (5 − γ ) + m 2 (2 − γ )γ ))} + {(3(−2 + γ ) 2 (18 + γ (−3 + 12m + (−4 + γ )γ + γ m 2 (2 − γ ))) 2 ) /. .. (2(9 + γ (−6 + m(5 − γ ) + γ ))(9 + γ (6 + 3m(1 − γ ) − γ ))(6 + 2mγ + γ ) )} 2 2. The ambiguous comparison is subject to both the differentiated degree of commodity and numbers of foreign private firm. Proposition 4.2 is illustrated in Fig 4.2. 1 0.8. δ − δ Γ = 0. 0.6. γ. I. 0.4 0.2 0 -0.2 0 -0.4 -0.6. II 5. 10. 15. 20. 25. δ − δ Γ = 0. 30. 35. 40. 45. 50. m. III. -0.8 -1. Fig 4.2. Private Firm’s Incentives to Merge. Region I and III represent δ − δ Γ > 0 , that is, δ (π aM + π bM ) > π b . In other words, the nature of commodity and number of foreign firm could influence private owner’s incentives to merge. When products are substitutes, the private owner chooses to merge in region I. Identically, when products are complementary, the private owner chooses to merge in region III. In general, more foreign private firms competing in the domestic market will promote private owner’s merging decision. The degree of substitution of commodity which is too higher or lower would not influence private owner’s decision. Higher degree of complement. 37.

(46) of commodity promotes private owner’s merging decision.. Proposition 4.3: In general, more foreign private firms and higher degree of complement of. commodity will promote private owner’s merging decision. The degree of substitution of commodity which is too higher or lower cannot be incentives for private owner to merge.. 4.3 Concluding Remarks This chapter considered that there exist one domestic public firm, one domestic private firm and several private foreign firms in an international mixed oligopoly market. To be more efficient, the public firm allowed for partial privatization and through a program with two distinct measures, privatizing directly, or deciding to merge with domestic private firm. Under the utility assumption of differentiated commodity in Häckner (2000), we found whether public firm merger with domestic private firm or not, 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. Moreover, there exist some incentives for domestic firm to choose to merge. For public firm, the incentives are explicit because of welfare improving. For private owner, generally, more foreign private firms and higher degree of complement of commodity will promote private owner’s merging decision. The degree of substitution of commodity which is too higher or lower cannot be incentives for private owner to merge.. 38.