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(1)國立高雄大學應用經濟學系碩士班 碩士論文. 混合寡占市場下污染、所有權與貿易分析 Pollution, Ownership, and Trade in Mixed Oligopoly. 研究生:陳政聖 撰 指導教授:王鳳生 博士. 中 華 民 國. 九 十 九 年. 七 月.

(2) 致謝 時光飛逝,在高大短短兩年的日子即將劃下句號。回首第一次走進教室那ㄧ 天,ㄧ切都是那麼的陌生,與學校老師和同學間的生疏還清晰的在腦海裡浮現。 隨著日子ㄧ天天過去,與同學漸漸熟悉,向老師學習,這一點一滴都在我的人生 中留下豐富的ㄧ頁。而今,驪歌輕唱,就要與大家告別。 ㄧ路走來,首先要感謝辛苦指導我的王鳳生教授,這些日子在老師身上學到 的不侷限於學業的範圍,與擔任RA或者與老師聊天的過程中,讓我認識許多新 鮮的事物,也對於事物有不同的看法。此外,老師親切的笑容,讓學生覺得與老 師之間沒有距離,與老師相處感覺輕鬆沒有壓力。再來要感謝兩位辛苦的口試委 員蔡穎義教授與廖肇寧教授,您們的建議讓我論文更為完備。還有同學間相互幫 忙及學弟妹的協助,期待你們未來都能發光發熱,並且順利的完成論文。 最後,謝謝我的家人,你們的支持與鼓勵是我的精神支柱,未來我會繼續努 力,用行動回報你們。. 陳政聖. 謹誌於. 國立高雄大學應用經濟學系 99年 仲夏.

(3) 混合寡占市場下污染,所有權與貿易分析 指導教授:王鳳生 博士 國立高雄大學應用經濟系. 學生:陳政聖 國立高雄大學應用經濟系. 摘要. 近年來,發展中國家利用課徵環境稅和民營化政策來保護國內環境和追求社 會福利;本論文將在一個混合寡占市場下的架構分別探討民營化、環境稅與國外 廠商的進入模式議題。 在混合同質雙占市場,公營廠商存在著無效率的問題。而公營廠商民營化後 可以改善民營化前的生產無效率,但是依然會低於民營廠商的生產效率。而每個 廠商可以藉由污染的減量來降低生產過程所製造的汙染。結果顯示,當民營化後 可以大量改善無效率時,將藉由產出與環境稅的增加使得消費者剩餘及污染減量 措施上升。 在內部管理效率的議題上,我們發現內部管理措施可能不會降低環境傷害,除 非內部管理可以充分的降低邊際環境傷害。然而,有效率的內部管理將會提升消 費者剩餘及社會福利。 在國外的進入模式議題下,在政府沒有課徵環境稅並且國外民營廠商擁有較 大的生產優勢時,國外廠商將會選擇以兼併方式進入本國市場。若政府課徵環境 稅時國外廠商將會選擇以直接投資方式進入本國市場。 關鍵字:民營化、環境稅、污染減量、內部管理效率、無效率、進入模式、 兼併 I.

(4) Pollution, Ownership, and Trade in Mixed Oligopoly Advisor: Dr. Leonard F.S. Wang Department of Applied Economics National University of Kaohsiung Student: JHEN, JHENG-SHENG Department of Applied Economics National University of Kaohsiung ABSTRACT In recent years, developing countries to protect environment and social welfare, the government always steps in to affect market, taking policy instruments such as environmental tax and privatization. This thesis will consider the issues of public policy-degree of privatization, environmental taxation, and entry mode in a mixed oligopoly setting. Under mixed duopoly market with a homogeneous good, allowing the public firm has an efficiency gap between preprivatization and postprivatization, the postprivatization improves the public firm’s production inefficiency than the preprivatization, but it exists less production inefficiency than the private firm. Each firm can prevent pollution by undertaking abatement measures. We find that when the privatization improves production inefficiency more, an increase in output results in higher consumer surplus, and more pollution abatement is devoted by all the firms coupled with higher environmental tax. Concerning the issue of governance efficiency, we show that better governance may not decrease the environmental damage unless it could sufficiently reduce marginal environmental damage. The effect of better governance increases consumer surplus and social welfare.. II.

(5) Finally, concerning the entry mode of foreign firm and see how it would affect the environmental damage and the domestic welfare. When the government dose not set an environmental tax to control pollution and firms do not abate emissions, foreign firm will choose to acquire a domestic private firm with foreign firm has sufficiently higher production advantage. If the government sets an environmental tax to protect the environment, foreign firm never chooses to acquire.. Keywords: Privatization, Environmental Tax, Pollution Abatement, Governance Efficiency, Efficiency Gap, Entry Mode.. III.

(6) CONTENTS CHAPTER ONE: AN INTRODUCTION ………….………………………..1 1.1 Research Background……………………………………………………………1 1.2 Literature Review………………………………………………………………..2 1.2.1 Privatization…………………………………………………………………2 1.2.2 Environmental policy and R&D investment in a mixed oligopoly…………3 1.2.3 Entry Mode…………………………………………………………………..5 1.3 Structure of Thesis………………………………………………………………..6. CHAPTER TWO: Environmental Taxes in a Mixed Duopoly with Asymmetric Costs …...…………………………………………………………8 2.1 Basic Model ………………………………………………………………………9 2.2 Mixed Duopoly and Private Duopoly ...…………………………………………10 2.2.1 Case I: Mixed Duopoly (Preprivatization) ..….……………………………..10 2.2.2 Case II: Private Duopoly (Postprivatization) ..….…………………………..13 2.3 Effects of privatization ..…………………….…………………………………...15 2.4 Concluding Remark ..……………………………………………………………18. CHAPTER Three: Governance, Environmental Taxes in a Mixed Duopoly ………………………………………………………………………..19 3.1 Basic Model ...……………………………………………………………………20 3.2 Privatization and Environmental tax Policy ...…………………………………...21 3.3 Optimal Degree of Privatization and Environmental tax ...……………………...22 3.3.1 Effects of privatization ...……………………………………………………24 3.4 Conclusion ...……………………………………………………………………..28. CHAPTER FOUR: Entry Mode, Pollution and Host Country Welfare in Mixed Oligopoly ...………………………………...…………………………30 IV.

(7) 4.1 Basic Model ...……………………………………………………………………31 4.2 Case I: No environmental policy ...………………………………………………33 4.3.1 Foreign firm chooses to FDI ...……………………………………………...33 4.3.2 Foreign firm chooses to M&A ……………………………………………...34 4.2.3 Foreign firm’s preferred mode of entry ...…………………………………...35 4.3 Case II: The government implements an environmental policy ...……………….36 4.3.1 Foreign firm chooses to FDI ...……………………………………………...36 4.3.2 Foreign firm chooses to M&A ……………………………………………...38 4.3.3 Choice of Entry Mode ...…………………………………………………….40 4.4 Conclusion ...…………………………………………………….……………….43. CHAPTER FIVE: CONCLUDSIONS…………………………………..44 References .………..…………………………………………………….…………46 Appendix A ……...………………………………………………………….……..48 Appendix B ..….…………………………………………………………….……..49. V.

(8) LIST OF FIGURE Figure 1.1 The structure of Thesis ...………………………………………………….7 Figure 2.1 Illustration of Proposition 2.1 (i) ...…………………….………………...15 Figure 2.2 Illustration of Proposition 2.1 (ii) ………………….……………………16 Figure 2.3 Illustration of Lemma 2 ………………………………………………….17 Figure 3.1 The effect of public firm’s governance …………..……………………...28 Figure 3.2 The effect of foreign firm’s governance ...…………..…………………...28 Figure 4.1 Illustration of Proposition 4.1 ...……………………….…………….......36. VI.

(9) CHAPTER ONE: AN INTRODUCTION 1.1 Research Background Since the 1980s, in order to improve production efficiency and economic growth, each government has engaged in privatization policy. The public and private firms have different objective function: public firms maximize social welfare while private maximize profits. Thus, the total output of market will decrease when public firms are privatized. As a result, it reduces the consumer surplus and increases the producer surplus. When the producer surplus increase and the consumer surplus simultaneously reduce, the social welfare will increase and government will engage in privatization policy. In recent years, Greenhouse effect gained more and more attention globally. In order to reduce the pollution damage, the Kyoto Protocol is an international agreement linked to the United Nations Framework Convention on Climate Change (UNFCCC or FCCC) in 1997. In many developing countries as well as Japanese and European countries, their governments and investors have concerned about environmental issue and the common (global) environmental tax. To protect environment, the government conducts environmental regulation by imposing taxes and uses its proceeds to pay the expense of clean up firm-generated pollution. Moreover, the imposition of certain restrictive pollution standard requires adoption of costly abatement technology by the firms. Although the government sets a tax protect the environment, the firm’s governance maybe inefficiency. In this year, the BP oil spillover is a massive ongoing oil spill in the Gulf of Mexico. Many experts fear that spill result in an environmental damage,. 1.

(10) with extensive impact already on ocean and wildlife habits. The spill has also damaged Gulf of Mexico fishery and tourism industry. It caused the most serious environmental damage for a dozen years in United States. Recently, controlling pollution emission has become the most important and pressing issue for most government to deal with. In many developing countries to protect environment and social welfare, each government always steps in to affect market, such as environmental tax and privatization. With a mixed oligopolistic market, the affect of privatization on the environment has become the focus of much attention and debate.. 1.2 Literature Review. 1.2.1 Privatization. Many papers have focused on the privatization issue and related policies. Matsumura (1998) explicitly considered the possibility of partial privatization, and shows that neither full privatization nor full nationalization is optimal. It is commonly know that the government should increasingly private the public firm as the market becomes more competitive. In the literature on mixed oligopoly, the public firm’s objection includes their profits and social welfare. In mixed oligopoly literature, Fujiwara (2007) explore the optimal privatization policy different between the short-run and the long-run in differentiated mixed oligopoly. They find that the short-run optimal privatization policy is non-monotonic in the degree of love of variety, while the long-run optimal degree of privatization is monotonically decreasing in the degree of love of variety, and the privatization policy is monotonically of the number of private firms. Matsumura and Okamara (2009) 2.

(11) adopted a relative performance approach and investigate the relationship between competition and privatization policy in mixed oligopoly. They find that increase of the intensity of competition reduces the optimal degree of privatization. At the same time, increase of the intensity reduces the number of firms at free entry market, and it indirectly reduces the optimal privatization policy. HEYWOOD and YE (2009) assume that one domestic private firm, one foreign private firm, and one public firm competing against each other in a domestic, and this model established by Hamilton and Slutsky (1990). They find that the public firm as follower has the higher domestic welfare but privatization will always lower domestic welfare. As we known, public firm are usually less efficient than private firms. Wang and Wang and Zhao (2009) examine the privatization and trade policies in a domestic market consisting of domestic public firm and one or more foreign private firms with asymmetric cost structure. They find that the government decision on privatization is associated with the magnitude of efficiency gain by privatization. In general, the privatization of public firms often takes place in conjunction with reforms of the competition policy. Matsumura and Tomaru (2010) investigate the relationship among market structure, privatization and tax-subsidy policies. They find that if there are no foreign investors in private firms, as result in the degree of optimal privatization is neutrality. And public leadership more likely yields a large domestic welfare when the foreign presence in the product market is large and the number of private firms is large.. 1.2.2 Environmental policy and R&D investment in a mixed oligopoly. The literature on R&D has widely handled with the issue of firms invest 3.

(12) environmental R&D that reduce emissions, and the emission tax is lower than environmental. damages.. Poyago-Theotoky. (2003). examines. the. optimal. environmental policy in a differentiated goods duopoly with either price or quantity setting firms, where firms invest in environmental R&D that reduces emissions. Beladi and Chao (2006) restricted discussion to the case of monopoly without considering pollution abatement, and proved that privatization paradoxically exerts a negative effect upon the environment. Wang et al (2007) used a two-country trade model with consumption externalities to show that the environmental taxes in mixed oligopoly are larger than in the pure oligopoly, whether the nature of good is homogeneous or differentiated. Besides, strategic behavior of pollution abatement and privatization issue had discussed by Ohori (2006) explores the optimal environmental tax and level of privatization in an international duopolistic market. They showed that privatization leads to a decrease in the abatement level of the domestic firm but increase in the output of domestic firm. They fund that privatization leads to an increase in the emission level of the domestic firm and a decrease in that if the foreign firm. Bárcena-Ruiz and Garzón (2006) consider a single industry made up of one public firm and number of private firms producing a homogeneous good. They showed that when governments set a tax to protect environment, the tax is lower in the mixed oligopoly than in the private one, and environmental damage is greater; Wang and Wang (2009) re-examines whether privatization improves (or deteriorates) the environment in a mixed duopolistic framework with differentiated product and pollution abatement. They showed that when the product is highly substitutable, industry profits increase because this softens the intensity of the product market, but social welfare deteriorates accompanied with path of privatization because the loss of consumer surplus and tax revenue exceeds the increases in profits, even if the 4.

(13) environment is less damaged.. 1.2.3 Entry Mode. In general, foreign firm has technology advantage than domestic firms, and they always consider entry mode in order to maximizing their profits. Sometimes, the foreign firm’s entry mode will conflict with the domestic welfare. Mattoo et al. (2004) develop a three-stage game where FDI can occur through either direct entry or M&A. The foreign firm decides the R&D investment after choosing the mode of entry. The final stage of the game is the output competition in which the foreign firm competes in the host country with domestic firms. Their analysis indicates that a foreign firm can find acquisition of an existing domestic profitable under oligopoly when it is accompanied by technology transfer and that conflict between the foreign firm’s objective and the preferences of a welfare maximizing government can serve a basis for policy intervention in such market. They showed that a purely welfaremaximizing government might use FDI restrictions in order to influence the foreign firm’s chose between different modes of entry. Mukherjee and Shinha (2004) showed that cost efficiency in the domestic industry may reduce domestic welfare if it changes foreign firm’s production strategy form foreign investment to export. They find that if the domestic market is sufficiently small, domestic cost reduction always reduces domestic welfare. However, if the domestic cost reduction is either very large or it is very small such that it dose not affect the mode of operation of the foreign firm then domestic cost reduction always increases domestic welfare. Recently, Mukherjee (2010) showed that whether or not better governance in the host-country increase FDI may depend on the way it affects the costs of the firms. Further, better governance may reduce the host-country welfare, thus providing a 5.

(14) strategic reason for the existence of poor governance. 1.3 Structure of Thesis. This thesis will consider the issue of public policy- degree of privatization, environmental taxation, pollution abatement and governance efficiency. Based on studies of environmental taxation in Ohori (2006), abatement level in Wang and Wang (2009), governance efficiency in Mukherjee and Maiti (2010), partial privatization in Matsumura (1998) and foreign firm’s entry mode in Mattoo (2004), we will extend the past results to be more completed by apt models. The remaining chapters are organized as follows. In chapter 2, we investigate the public firm has an efficiency gap between preprivatization and postprivatization. The postprivatization improves the public firm’s production inefficiency than the preprivatization, but it exists less production inefficiency than the private firm. Each firm can prevent pollution by undertaking abatement measures. In chapter 3, analyzes the effects of better governance reduce the environmental damage and government decides the degree of privatization. In chapter 4, analyzes the entry mode of foreign firm affect the environmental damage and the domestic welfare. Chapter 5 summarizes our main conclusions.. 6.

(15) Private Policy. Chapter 2 Preprivatization & Postprivatization Efficiency Gap Chapter 5 Chapter 3. Conclusions Partial privatization Governance Efficiency. Chapter 4. No Privatization Entry Mode. Figure 1.1 The structure of Thesis. 7.

(16) CHAPTER TWO: Environmental Taxes in a Mixed Duopoly with Asymmetric Costs. We adopt the same framework in Wang and Wang (2009) to investigate the optimal environmental tax and pollution abatement in a mixed duopoly and pure duopoly with asymmetric cost, wherein firms produce the homogeneous goods and environmental damage is associated with consumption and pollution abatement. Wang and Wang (2009) demonstrated that when the product is highly substitutable, industry profits are increased, but social welfare deteriorates accompanied with the path of privatization because the loss of consumer surplus and tax revenue exceeds the increased in profits even if the environment is less damage. We find that when the privatization improves production efficiency, the output increase result in consumer surplus addition and more pollution abatement is devoted by all the firms coupled with high environmental tax. This chapter is organized as follows. Section 2.1 provides the basic model. In section 2.2 we set up a two-stage model in a mixed duopoly and pure duopoly. Section 2.3 analyzes the effect of privatization. Section 2.4 presents concluding remarks.. 8.

(17) 2.1 Basic Model. We consider a single market made up of one public firm (indexed by 0) and one private firm (indexed by 1) producing homogeneous good. The inverse demand function is given by p = A − Q , where Q = q0 + q1 is the total output of the market. Accordingly, total consumer surplus is CS = Q 2 / 2 . The cost function of private firm is c ( q1 ) = q12 / 2 . We postulate that public firms are usually less efficient than private firms. Even though the public firm is privatized, small efficiency gap still exist. We assume that the public firm has the cost function c ( q0 ) = σ q02 / 2 and privatized firm has the cost function c* ( q0 ) = kq02 / 2 , which follows Pal and White (1998). The assumption σ ≥ k ≥ 1. indicates that there has an efficiency gap between. preprivatization and postprivatization of the public firm. Furthermore, we allow that postprivatization improves the public firm’s production efficiency than the preprivatization, but it exist less production inefficiency than the private firm. We assume that a pollutant is associated with the production of the good and each unit of good produced gives rise to one unit of pollution. However, each firm can prevent pollution by undertaking abatement measures. If firm i choose pollution abatement level ai , pollutant emissions by firm i are ei = qi − ai ( i = 0,1 ). The environmental damage is measured by a quadratic form ED = ( e0 + e1 ) / 2 , and the 2. total cost of pollution abatement of firm i is ai2 / 2 . Each firm has to pay an. environmental tax per unit of pollutant emitted, the profit of firm i is given by: ai2 π i = ( A − Q ) qi − ci − tei − , i = 0,1 2. (2.1). As in Beladi and Chao (2006), the public firms’ objective functions are defined as the. 9.

(18) sum of consumer surplus and firm’s profit, given as G = CS + π 0. (2.2). The social welfare function considered by government comprises the comprises the consumer surplus, the producer surplus π 0 + π 1 , and the tax revenues collected by the government are T = t (e0 + e1 ) , less the environmental damage ED . Thus, the social welfare can be expressed: W = CS + π 0 + π 1 + T − ED. (2.3). We consider two cases. First, the public firm is not privated and second, it is privated. For each case, we propose a two-stage game with the following timing. In the first stage, the government set the environmental tax. In the second stage, the two firms compete in the market by choosing output and abatement level. The public and private firms have different objectives: the former maximizes the sum of consumer surplus and the firm’s profit while the latter maximize its own profit. If the public firm transfers the privatized then it exists small cost inefficiency and competing in the market with another private firm. 2.2 Mixed Duopoly and Private Duopoly. 2.2.1 Case I: Mixed Duopoly (Preprivatization). The backward induction method is used for finding Subgame Perfect Nash Equilibriums (SPNE). In the second stage, both firms choose output and abatement level, qi and ai ( i = 0,1 ), simultaneously. In the first stage of the game, the government sets the environmental tax to maximize the social welfare. In the second stage of the game, both firms choose output and abatement level simultaneously. Differencing (2.2) with respect to q0 and a0 for public firm, we 10.

(19) have ∂G = A − t − q0 − σ q0 = 0 ∂q0. (2.4). ∂G = t − a0 = 0 ∂a0. Turning to the private firm, we differencing (2.1) with respect to q1 and a1 , and obtain that ∂π 1 = A − t − q0 − 3q1 = 0 ∂q1. (2.4). ∂π 1 = t − a1 = 0 ∂a1 From the above first-order conditions, we obtain the results q0 =. σ ( A−t) g ( A−t) ; q1 = ; a0 = a1 = t 3 (1 + σ ) (1 + σ ). (2.5). Equation (2.5) shows that both public and private firms abate pollution to the point where marginal abatement cost equals the tax. In the first stage, the government sets the environmental tax to maximize the social welfare. We substitute (2.5) into (2.3), and thus social welfare is given by: W=. A2σ + 2 A ( 9 + 2σ ) t − ( 36 + 23σ ) t 2 , 6 (1 + σ ). and differentiating it with respect to t, we obtain the optimal environmental tax, t=. A ( 9 + 2σ ). (2.6). 36 + 23σ. Substituting (2.6) into (2.1), (2.3) and (2.5), we get the Cournot-Nash equilibrium outcomes as follows: a0MC = a1MC = t MC =. A ( 9 + 2σ ) 36 + 23σ. 11.

(20) q0MC =. π. MC 0. π. MC 1. 3 A ( 9 + 7σ ). (1 + σ )( 36 + 23σ ). (. , q1MC =. (. 2 (1 + σ ) ( 36 + 23σ ) 2. (. =. 2 (1 + σ ) ( 36 + 23σ ) 2. W. MC. =. =. 2. 2. , ED. (1 + σ )( 36 + 23σ ). )). 2. 2. 2 (1 + σ ) ( 36 + 23σ ). A ( 3 + σ )( 9 + 7σ ). 2. (. A2 ( 3 + σ ) ( 9 + 7σ ). , Q MC =. )). A2 81 + σ 198 + σ ( 400 + σ ( 422 + 151σ ) ). 2. CS. (1 + σ )( 36 + 23σ ). A2 81 + σ 441 + σ ( 535 + σ (191 + 4σ ) ). =. MC. Ag ( 9 + 7σ ). MC. =. A2 ( 9 + σ ( 8 + 3σ ) ). 2. 2 (1 + σ ) ( 36 + 23σ ) 2. 2. 3 A2 ( 9 + σ ( 8 + 3σ ) ) 2 (1 + σ )( 36 + 23σ ). where the superscripts MC denote mixed duopolies under Cournot competition. Lemma 2.1. An increase of σ reduces the consumer surplus, environmental tax, environmental damage, social welfare, but producer surplus increases in mixed duopoly model. Proof: See Appendix A .1. ∂W MC ∂CS MC ∂PS MC ∂T MC ∂ED MC = + + − ∂σ ∂σ ∂σ ∂σ ∂σ ( -) ( -) ( +) ( -) ( -) Intuitively, an increase of production inefficiency in the mixed duopoly induce the public firm decrease its output and private increase its output, but public firm’s output decrease more than private firm’s output increase, resulting in decreased total output, which leads to consumer surplus, environmental tax, environmental damage and social welfare decreases.. 2.2.2 Case II: Private Duopoly (Postprivatization) We first derive the optimal environmental tax in the private duopoly. Under. 12.

(21) Cournot-Nash assumption, the privatized firm and private firm selects its output and abatement level in order to maximize its own profit, while the privatized firm is exist small cost inefficiency k . In the second stage of the game, both firms choose output and abatement level simultaneously. Differencing (2.1) with respect to q0 and a0 for public firm, we have ∂π 0 = A − t − ( 2 + k ) q0 − q1 = 0 ∂q0. (2.7). ∂π 0 = t − a0 = 0 ∂a0. Turning to the private firm, we differencing (2.1) with respect to q1 and a1 , and obtain that ∂π 1 = A − t − q0 − 3q1 = 0 ∂q1. (2.8). ∂π 1 = t − a1 = 0 ∂a1 From the above first-order conditions, we obtain the results q0 =. 2( A − t) 5 + 3k. ; q1 =. (1 + k )( A − t ) ; 5 + 3k. a0 = a1 = t. (2.9). In the first two stage, the government sets the environmental tax to maximize the social welfare. We substitute (2.9) into (2.3), and thus social welfare is given by: W=. A2 k + 2 A (18 + 5k ) t − ( 92 + 39k ) t 2 , 8(2 + k ). and differentiating it with respect to t, we obtain the optimal environmental tax, t=. 2 A (17 + k (16 + 3k ) ). (2.10). 229 + k ( 254 + 69k ). Substituting (2.10) into (2.1), (2.3) and (2.9), we get the Cournot-Nash equilibrium outcomes as follows:. 13.

(22) a0PC = a1PC = t PC =. 2 A (17 + k (16 + 3k ) ) 229 + k ( 254 + 69k ). 6 A (13 + 7k ). q0PC =. 229 + k ( 254 + 69k ). π. PC 0. π. PC 1. (. , q1PC =. (. (. ( 229 + k ( 254 + 69k ) ). (. W. PC. , Q PC =. =. =. 2 ( 229 + k ( 254 + 69k ) ). =. 2. 2 ( 229 + k ( 254 + 69k ) ). 2. , ED. 229 + k ( 254 + 69k ). 2. (. 9 A2 ( 3 + k ) (13 + 7k ). 3 A ( 3 + k )(13 + 7 k ). ))). A2 5719 + k 16216 + k (17146 + 3k ( 2648 + 453k ) ). 2. CS. 229 + k ( 254 + 69k ). 2 A2 3331 + k 5341 + k 2878 + 537 k + 9k 2. =. PC. 3 A (1 + k )(13 + 7k ). PC. =. )). 2. A2 ( 49 + k ( 38 + 9k ) ). 2. 2 ( 229 + k ( 254 + 69k ) ). 2. 3 A2 ( 49 + k ( 38 + 9k ) ) 458 + 2k ( 254 + 69k ). where the superscripts PC denote private duopolies under Cournot competition.. Lemma 2.2. An increase of σ (k) reduce the public (privated) firm’s profit and increase the other firms’ profit.. (. ). 3 A2 σ ( 3267 + σ ( 4255 + 1307 g ) − 1683) − 2106 ∂π 0MC =− <0 3 3 ∂σ 2 (1 + σ ) ( 36 + 23σ ). ( (. ). ). 2 ∂π 1MC 3 A σ 1611 + σ ( 5319 + σ ( 4707 + 1352σ ) ) − 405 = >0 3 3 ∂σ (1 + σ ) ( 36 + 23σ ). (. (. 6 A2 156353 + k 319282 + 3k ( 81852 + k ( 28058 + 3609k ) ) ∂π 0PC =− 3 ∂k ( 229 + k ( 254 + 69k ) ). (. (. 2 ∂π 1PC 6 A 67351 + k 179630 + 3k ( 58356 + k ( 24902 + 3951k ) ) = 3 ∂k ( 229 + k ( 254 + 69k ) ). 14. )) < 0. )) > 0.

(23) An increase of production inefficiency reduce the public firm’s profit and increase the private firm’s profit, and private firm’s profit increase more than the public firm’s profits decrease, resulting in increased producer surplus under mixed duopoly.. 2.3 Effects of privatization. We have derived preprivatization and postprivatization equilibria, and the effects of privatization upon market equilibrium can be examined. The following propositions summarize our results. Proposition 2.1. (i) When the efficiency gap between preprivatization and postprivatization is large (small). As a result, environmental tax and abatement level are high (small) in the private duopoly than in the mixed duopoly. Define that Δt ≡ t MC − t PC , Δt curve describes the contour of the Δt = 0 along which the environmental tax and abatement level are identical between preprivatization and postprivatization.. 8 7 6 5 4 3 2 1. Δt. σ. Δt < 0 Δt > 0. σ=k. k 1. 2. 3. 4. 5. Figure 2.1 Illustration of Proposition 2.1. (i) (ii)The preprivatization and the postprivatization efficiency gap approach infinity which the producer surplus is identical. However, privatization is more likely to 15.

(24) improve producer surplus when efficiency gap is not large. Proof:. PS MC , PS PC 0.2. PS PC (k ). 0.15 0.1. PS MC (σ ). 0.05. σ,k. 0 1. 6. 11. 16. Figure 2.2 Illustration of Proposition 2.1. (ii). PS MC curve describes the contour of the PS MC / A2 and PS PC curve describes the contour of the PS PC / A2 . In figure 2.2, we can get PS PC > PS MC . If the efficiency gap between preprivatization and postprivatization closed to infinity, the producer surplus is identical. lim PS MC = lim PS PC = 0.108696 A2 g →∞. k →∞. (iii) When efficiency gap between preprivatization and postprivatization is large (small). As a result, consumer surplus is small (high) in the mixed duopoly than in the private duopoly, and the privatization is more likely to improve social welfare without environmental damage. Define that ΔW ≡ W MC − W PC , ΔW. curve describes the contour of the. ΔW = 0 along which the social welfare is identical between preprivatization and. postprivatization, ΔQ ≡ Q MC − Q PC , ΔQ curve describes the contour of the ΔQ = 0 along which the total output is indifferent between preprivatization and postprivatization, ΔCS ≡ CS MC − CS PC , ΔCS curve describes the contour of the ΔCS = 0 along which the consumer surplus is indifferent between preprivatization. and postprivatization, and ΔED ≡ ED MC − ED PC , ΔED curve describes the contour 16.

(25) of the ΔED = 0 along which the environmental damage is indifferent between preprivatization and postprivatization. In the ( σ ,k) space where it can be divided into two regions: I and II. In region I, privatization is more likely to improve consumer surplus and social welfare without environmental damage. In region II, owing to that Lemma 2.2, the producer surplus is higher in the private than in the mixed duopoly, the privatized firm is more likely to improve social welfare without increasing in environmental damage and losing in consumer surplus.. ΔCS. σ. 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1. ΔCS < 0, ΔW < 0, ΔED < 0 I. ΔCS > 0, ΔW < 0, ΔED < 0. σ =k. II. ΔW , ΔED. 1. 1.5. 2. 2.5. 3. 3.5. 4. 4.5. k 5. Figure 2.3 Illustration of Lemma 2 When the efficiency gap between preprivatization and postprivatization is large, it means that privatized firm has improved their production efficiency many times. In this situation, the output of industry is higher in the private duopoly than in the mixed duopoly, which leads to higher consumer surplus in the private than in the mixed duopoly. As a result, the higher output in the private duopoly induces higher abatement than mixed duopoly; hence, environmental tax is higher in the private than in the mixed duopoly. From the above the proposition, we can argue that due to privatization and no 17.

(26) welfare burden of a public firm, more (less) pollution abatement is devoted by all the firms coupled with high (less) environmental tax levied under privatization improve more (less) production inefficiency than mixed duopoly. On the other hand, the privatization improve more (less) that production inefficiency result in more (less) output, and the environment is more damage regardless of whether it improve more (less) the efficiency of privatization. When postprivatization improves more production inefficiency than preprivatization, social welfare improves accompanied with the path of privatization because the add of consumer surplus and producer surplus even if environmental is more damaged.. 2.4 Concluding Remark. Using the simple linear demand model, part of our findings are consistent with what has been show in Wang and Wang (2009), even though they consider all firms producing differentiated goods. Accompanied with the path of privatization result of loss consumer surplus and less pollution abatement is devoted by all the firms coupled with less environment levied by the government in a differentiated duopoly. In addition, we considered in a mixed duopoly market with a homogeneous good. We show that when the postprivatization improves more production efficiency, the raise of output resulted in the increase of consumer surplus and more pollution abatement is devoted by all the firms coupled with more environmental tax.. 18.

(27) CHAPTER Three: Governance, Environmental Taxes in a Mixed Duopoly. Bárcena-Ruiz and Garzón (2006), Wang and Wang (2009) considered the environmental tax chosen by government compels to pollution abatement and it also implies that firms reduce their output level. In this chapter, we consider better governance would reduce the marginal environmental damage of both firms by the different amount. It is shown that, better governance may not decrease the environmental damage unless it could sufficiently reduce marginal environmental damage. The effects of governance increases consumer surplus and social welfare. This chapter is organized as follows. Section 3.1 provides the basic model. Section 3.2 analyzes the effect of privatization and environmental tax. Section 3.3 analyzes the effect of better governance. Section 3.4 presents concluding.. 19.

(28) 3.1 Basic Model. We consider a single market made up of one semipublic firm (indexed by 0) and one foreign firm (indexed by 1) producing homogeneous good. However, firm 1 is serving the domestic market thorough FDI, it needs to set up its production plant in the host country, and therefore, needs to incur a fixed investment cost F. We assume that the production process generates pollution affected the worker’s health so that firm can hire the technical staff in order to lower their marginal environmental damage. We postulate that marginal environmental damage is θ = λ h ,. λ notes that one unit of the affected number of worker, and one unit of the needs production of h hours. As in Mukherjee and Maiti (2010), better governance reduces the marginal costs of firms. We assume that better governance reduces the output affected number of worker’s health by e , and better governance reduces the marginal environmental damage of firm 0 and 1 to. ( λ − ei ) h = θ − gi ≥ 0. ( i = 0,1 ), where. gi = ei h . Therefore, in this, we consider foreign firms do not concern about the production affected the worker’s health than domestic firm, where e0 ≥ e1 . If the firm i decides to hire the technical staff, the governance cost is wi . To simplify the exposition of the results, we use to governance gi substitute for effect of ei . The inverse demand function is given by p = A − Q , where Q = q0 + q1 is the total output of the market. Accordingly, total consumer surplus is CS = Q 2 / 2 . The cost function of firm i is c ( qi ) = qi2 / 2 ( i = 0,1 ). The. environmental. damage. is. measured. by. a. quadratic. form. ED = (θ − g 0 ) q02 / 2 + (θ − g1 ) q12 / 2 . Each firm has to pay an environmental tax per. unit of pollutant emitted, the profit of firms 1 and 2 are given by:. 20.

(29) π 0 = pq0 − q02 / 2 − tθ q0 − w0. (3.1). π 1 = pq1 − q12 / 2 − tθ q1 − w1 − F. (3.2). In accordance with Matsumura (1998), the objection of the semipublic firm is given by: V = απ 0 + (1 − α ) W. (3.3). Where α ∈ [0,1] notes the proportion of the share that is held by the producer’s owner. Note that α = 0 if the producer is a fully public-owned firm, and α = 1 if it is completely privatized-owned. Therefore, α is interpreted to represent the degree of privatization. The social welfare function considered by government comprises the consumer surplus, the profit of firm 0, and the tax revenues collected by the government, less the environmental damage ED . Thus, the social welfare can be expressed: W = CS + π 0 + tθ Q − ED. (3.4). The game is constructed by two-stage decision-making. During the first stage, the government simultaneously chooses the level of privatization and environmental tax. In the second stage, the foreign firm maximizes its own profits to choose its quantity, while the semipublic firm maximizes the objection V to choose its quantity. We use the method of backward induction and solve the equilibriums form the second stage.. 3.2 Privatization and Environmental tax Policy In the second stage, foreign firm maximizes its own profits to choose its quantity, while the semipublic firm maximizes the objective function V to choose its quantity simultaneously. Thus, the firms play Cournot games in a domestic market. Differentiating (3.2) and (3.3) with respect to q0 and q1 , we obtain the following 21.

(30) first-order conditions, ∂V = A − tαθ − ( 2 + α + (1 − α ) θ − (1 − α ) g 0 ) q0 − α q1 = 0 ∂q0. (3.5). ∂π 1 = A − tθ − q0 − 3q1 = 0 ∂q1. (3.6). Solving theses equations simultaneously, we get the following result, q0 =. ⎞ A ( 3 − α ) − 2tαθ 1⎛ , q1 = ⎜ A − tθ − ⎟ (3.7) ⎜ 3⎝ 2 ( 3 + α ) + 3 (1 − α )(θ − g 0 ) ⎟⎠ 2 ( 3 + α ) + 3 (1 − α )(θ − g 0 ). A ( 3 − α ) − 2tαθ. Doing comparative-static analysis, we get 6θ + 3 (1 − α ) (θ − g 0 )θ ∂q0 2αθ ∂q =− < 0, 1 = − < 0 (3.8) ∂t 2 ( 3 + α ) + 3 (1 − α )(θ − g 0 ) ∂t 6 ( 3 + α ) + 9 (1 − α )(θ − g 0 ) ⎞ θ⎛ 4α ∂Q = − ⎜1 + ⎟<0 3 ⎜⎝ 2 ( 3 − α ) + 3 (1 − α )(θ − g 0 ) ⎟⎠ ∂t. (3.9). The sign of (3.8) and (3.9) is the higher environmental tax decrease firm i’s and total market output. ⎞ ∂q0 6⎛ 4tθ = − ⎜ A − tθ + ⎟ ( 2 − θ + g0 ) ∂α H⎝ 2 − θ + g0 ⎠. (3.10). ⎞ ∂q1 2 ⎛ 4tθ = ⎜ A − tθ + ⎟ ( 2 − θ + g0 ) ∂α H ⎝ 2 − θ + g0 ⎠. (3.11). ∂Q 4 =− ∂α H. ⎛ ⎞ 4tθ ⎜ A − tθ + ⎟ ( 2 − θ + g0 ) 2 − θ + g0 ⎠ ⎝. (3.12). where H = ( 6 + 2α + 3 (1 − α )(θ − g 0 ) ) > 0 2. 3.3 Optimal Degree of Privatization and Environmental tax. In the first stage, the government simultaneously chooses the level of 22.

(31) privatization of public firm and environmental tax with respect to α and t , which yields the following first-order condition: ∂q ∂q ∂W ∂Q ∂Q = Q + ( A − Q − tθ ) 0 − ( + θ + 0 )q0 ∂t  ∂t  ∂t ∂t ∂t. Δ consumer's surplus. Δsemipublicfirm's profit. ∂q0 ∂q ∂Q ⎞ ⎛ + θ ⎜Q + t + (θ − g1 ) q1 1 ] = 0 ⎟ − [(θ − g 0 ) q0 t ∂t ⎠  ∂ t ∂. ⎝  Δenvironmental tax. (3.13). Δ enviromental damage. ∂q ∂W ∂Q ∂Q ∂q0 = Q + ( A − Q − tθ ) 0 − ( + )q0 ∂α  ∂α ∂α ∂α α  . ∂ Δ consumer's surplus. +. Δsemipublicfirm's profit. ∂q ∂Q ∂q tθ − [(θ − g 0 ) q0 0 + (θ − g1 ) q1 1 ] = 0 ∂ α. α ∂α  ∂  . Δenvironmental tax. (3.14). Δ enviromental damage. By submitting (3.7)-(3.12) into (3.13) and (3.14), the first-condition can be solved for the optimal environmental tax and degree of privatization as follows:. α* =. A (1 + θ − g 0 )( 2 + θ − g1 ) 1 + θ − g0 , t* = θΦ 7 + θ + g 0 − 2 g1. (3.15). where Φ = 9 + ( 7θ − 5 g 0 − 2 g1 ) + (θ 2 + g 0 g1 − θ ( g 0 + g1 ) ) > 0 Substituting (3.15) into (3.10), (3.11) and (3.12), we get 6 A (13 + 3 g 0 − g1 ) ⎛ ⎞ ∂q0 4 =− 2 + θ − g0 − ⎟<0 2 ⎜ ∂α 13 + 3g 0 − 3g1 ⎠ Φ ( 6 + 2α + 3 (1 − α )(θ − g 0 ) ) ⎝. (3.16). 2 A (13 + 3g 0 − g1 ) ⎛ ⎞ ∂q1 4 = 2 + − − θ g ⎜ ⎟>0 0 ∂α Φ ( 6 + 2α + 3 (1 − α )(θ − g 0 ) )2 ⎝ 13 + 3g 0 − 3g1 ⎠. (3.17). 4 A (13 + 3g 0 − g1 ) ⎛ ⎞ ∂q0 4 =− 2 + θ − g0 − ⎟<0 2 ⎜ ∂α 13 + 3g 0 − 3g1 ⎠ Φ ( 6 + 2α + 3 (1 − α )(θ − g 0 ) ) ⎝. (3.18). Lemma 3.1.: Shows that raising the degree of privatization reduces the output level of ⎛ ∂q ⎞ ⎛ ∂Q ⎞ < 0 ⎟ , and raises the output semipublic firm ⎜ 0 < 0 ⎟ and total market output ⎜ ⎝ ∂α ⎠ ⎝ ∂α ⎠ 23.

(32) ⎛ ∂q ⎞ level of foreign firm ⎜ 1 > 0 ⎟ . ⎝ ∂α ⎠ The sign of (3.16), (3.17) and (3.18) is similar to Fujiwara (2007). The privatization makes the public firm’s market share lower and that of foreign firm higher.. 3.3.1 Effects of privatization. Lemma 3.2. (i): The optimal privatization policy is decreasing in g 0 , but increasing in g1 . (ii): The optimal environmental tax is decreasing in g 0 and g1 .. Proof:. 2 ( 4 + θ − g1 ) ∂α =− <0 2 ∂g 0 ( 7 + θ + g0 − 2 g1 ). (3.19). 2 (1 + θ − g 0 ) ∂α = >0 ∂g1 ( 7 + θ + g 0 − 2 g1 )2. (3.20). A ( 2 + θ − g1 )( 4 + θ − g1 ) ∂t =− <0 θ Φ2 ∂g 0. (3.21). A ( 5 + 3θ − 3 g 0 )(1 + θ − g 0 ) ∂t =− <0 θ Φ2 ∂g1. (3.22). When better governance reduces the marginal environmental damage of public (foreign) firm, better governance increases (decreases) the optimal degree of privatization of public firm. Intuitively, the better governance of public firm induced it produces more to increases the social welfare resulted in lower degree of privatization. In contrary, the efficiency governing on foreign firm resulted in public firm produces. 24.

(33) fewer to decreases environmental damage and the degree of privatization raise. If the marginal environmental damage increases induce public firm less production to avoid pollution result in higher degree of privatization. And better governance reduces the marginal environmental damage of both firms result in optimal environmental tax decreases. The sub-game perfect Nash equilibrium of the model is shown as follows:. q0 =. π0 = CS =. ED =. A ( 4 + θ − g1 ) Φ. , q1 =. A (1 + θ − g 0 ) Φ. A2 ( 4 + θ − g1 )( 3θ − 4 g 0 + g1 ) 2Φ 2 2 A2 ( 5 + 2θ − g 0 − g1 ) 2Φ 2. (. − w0 , π 1 =. 3 A2 (1 + θ − g 0 ). 2Φ 2 A2 ( 5 + 2θ − g 0 − g1 ) , W= − w0 2Φ. A2 (θ − g1 )(1 + θ − g0 ) + (θ − g0 )( 4 + θ − g1 ) 2. 2Φ. 2. 2. − w1 − F (3.23). ). 2. To see the effect of better governance of both firms on outputs, we have, A (1 + θ − g 0 ) ∂q0 A ( 4 + θ − g1 )( 5 + θ − g1 ) ∂q0 =− <0 = > 0, 2 ∂g1 Φ2 ∂g 0 Φ A ( 4 + θ − g1 ) ∂q1 ∂q1 A (1 + θ − g 0 )( 2 + θ − g 0 ) =− <0, = >0 2 ∂g 0 Φ ∂g1 Φ2. (3.24). ∂Q A ( 4 + θ − g1 ) ∂Q A (1 + θ − g 0 ) = >0 = >0, 2 ∂g1 Φ2 ∂g 0 Φ 2. 2. Better governance of public (foreign) firm will increase public (foreign) firm’s output but decrease foreign (public) firm’s output. This reason is result form Lemma 3.2, better governance of public (foreign) firm induces the public firm produces more (less) output to increases the social welfare result in foreign firm’s output decrease (increase) in Cournot competition. In addition, we obtain the following results:. 25.

(34) 2 2 ∂π 0 A ( 4 + θ − g1 ) (θ + θ + ( 9 − g1 ) g1 − 2 ( 5 + θ − g1 ) g 0 − 18 ) = ∂g 0 Φ3. 3 A2 (1 + θ − g 0 )( 4 + θ − g1 ) ∂π 1 =− <0 ∂g 0 Φ3 2 ∂CS A ( 4 + θ − g1 ) ( 5 + 2θ − g 0 − g1 ) = >0 ∂g 0 Φ3 2. 2 ∂W A ( 4 + θ − g1 ) = >0 2Φ 2 ∂g 0 2. (. ). 2 2 ∂π 0 A (1 + θ − g 0 ) 18 + (11θ − 6 g 0 − 5 g1 ) + 2 (θ + g 0 g1 − θ ( g 0 + g1 ) ) = >0 ∂g1 Φ3 2 ∂π 1 3 A (1 + θ − g 0 ) ( 2 + θ − g 0 ) = >0 ∂g1 Φ3 2. 2 ∂CS A (1 + θ − g 0 ) ( 5 + 2θ − g 0 − g1 ) = >0 ∂g1 Φ3 2. 2 ∂W A (1 + θ − g 0 ) = >0 2Φ 2 ∂g1 2. Better governance of public firm will decrease foreign firm’s profit but increase consumer surplus, and the effect on public firm’s profit is ambiguous. However better governance of foreign firm will increase firm’s profits, consumer surplus and social welfare. On one hand, better governance of foreign firm could earn more profit with public firm reduce their output. On the other hand, it increases the optimal degree of privatization of public firm. As a result, the public firm’s profit increases. Proposition 3.1: If better governance reduces environmental damage of both firms by different amount, better public firm’s governance increases the social welfare than foreign firm’s governance. Proof: 26.

(35) 2 ∂W ∂W A [( 4 + θ − g1 ) − (1 + θ − g 0 ) ] − = >0 2Φ 2 ∂g 0 ∂g1 2. 2. Lemma 3.3.(i): If better governance reduces the marginal environmental damage of public firm, better governance decreases the environmental damage if g 0 > g a , but it may increase the environmental damage for g 0 < g a . (ii): If better governance reduces the marginal environmental damage of foreign firm, better governance decreases the environmental damage if g1 > gb , but it may increases the environmental damage for g1 < gb . Proof: ∂ED = ∂g 0. ∂q0 q02 − + ∂g 0 2 ( +)  . (θ − g0 ) q0. Δ Public firm's enviromental damage. ∂q1 ∂g 0 (−)  . (θ − g1 ) q1. Δ foreign firm's enviromental damage. A2 ( 4 + θ − g1 ) ⎛ Φ (θ − g1 )(1 + θ − g 0 ) ⎞ < ⎜ (θ − g 0 ) ( 5 + θ − g1 ) − − ⎟ 0 3 θ 2 4 g − Φ + 1 ⎝ ⎠> > 4 − 5θ + 5 g1 if g 0 θ + − 2 ≡ ga < 20 + θ ( 7 + θ ) − g1 ( 7 + 2θ − g1 ) 2. =. ∂ED = ∂g1. ∂q0 + ∂g1 ( −)  . (θ − g0 ) q0. Δ Public firm's enviromental damage. ∂q1 q12 − ∂g1 2 (+)  . (θ − g1 ) q1. Δ foreign firm's enviromental damage. A2 (1 + θ − g 0 ) ⎛ (θ − g 0 ) ( 4 + θ − g1 ) Φ⎞< + (θ − g1 )( 2 + θ − g 0 ) − ⎟ 0 ⎜⎜ − 3 Φ 2 ⎟⎠ > (1 + θ − g0 ) ⎝ 1 − 17θ + 17 g 0 > if g1 θ + − 5 ≡ gb < 2 + θ + θ 2 − g 0 (1 + 2θ − g 0 ) 2. =. Better governance of public (foreign) firm reduces the rival firm’s output and increases it output. As a result, it will help decrease rival firm’s environmental damage but it environmental damage is ambiguous with it raises output. Because better governance of public (foreign) firm induce it produce more output, if firms governance have not enough efficiency to low the produce pollution for g 0 < g a ( g1 < gb ) , it will resulted in environmental damage increasing. However, 27.

(36) if better governance for g 0 > g a ( g1 > gb ) , environmental damage will decreasing.. ED. ED. Figure 3.1. ga. g0 Figure 3.2. gb. g1. Figure 3.1. : The effect of public firm’s governance 3.2: The effect of foreign firm’s governance Figure 3.1, show that environmental damage following better governance, if better governance induces firm 0 to increases output. Since firm 0 decides to increase output for g 0 < g a result in environmental damage increasing. However, if the level of governance increases for g 0 > g a , better governance reduces environmental damage. Figure 3.2, similar to 3.1, if the level of governance increases for g1 > gb , better governance reduces environmental damage.. 3.4 Conclusion. We considered in a duopoly market with a homogeneous good, one partially privatized domestic public firm competes with foreign private firm. Better governance reduces the marginal environmental damage of both firms, and public firm’s governance better than foreign firm. We show that the effects on governance increases consumer surplus and social welfare. And public firm’s governance would increase the degree of privatization, but foreign firm’s governance will decrease it. Further, 28.

(37) better governance may not decrease the environmental damage unless it could sufficiently lower marginal environmental damage. Comparing with Bárcena-Ruiz and Garzón (2006), the government compels firms to abate emissions but it also implies that firms reduce their output level. In this section, we found that better governance increase total output level. When foreign firm’s governance increase induce public firm will increase the degree of privatization in a duopoly market.. 29.

(38) CHAPTER FOUR: Entry Mode, Pollution and Host Country Welfare in Mixed Oligopoly. This chapter considers a domestic mixed oligopoly market where there exists one domestic public firm, one domestic private firm and one foreign private firm in a domestic country. A foreign firm has two options for entering the domestic market: direct entry or acquisition of domestic private firm. We extend Bárcena-Ruiz (2006) by entry mode of foreign firm. We will examine how production advantage, environmental tax and abatement level affect the choice of foreign entry and the host country’s welfare. We consider two cases: Case I, the government dose not set an environment tax to control pollution and firms do not abate emissions. Case II, the government set an environment tax to protect the environment. From case I, foreign firm will choose to acquire a domestic private firm with foreign firm has enough high production advantage. Case II, foreign firm never chooses to acquire. The chapter is organized as follow. Section 4.1 present the models. Section 4.2 analyses the foreign firm chooses to entry mode with government not set environmental policy. Section 4.3 analyses the foreign firm chooses to entry mode with government set environmental policy. Section 4.4 summarizes our main conclusions.. 30.

(39) 4.1 Basic Model. We depict a single market made up of one public firm (indexed by 1), one domestic private firm (indexed by 2) and one foreign private firm (indexed by 0) producing a homogeneous good. A foreign firm, firm 0, has two options for entering the domestic market: Greenfield investment (direct entry) where it establishes a new wholly owned subsidiary, or it select for M&A (acquisition) of domestic private firm. The inverse demand function is given by p = A − Q , where p is the market price, Q is the industry output (or domestic consumption). Accordingly, total consumer surplus is CS = Q 2 / 2 . Domestic firms have same technology represented by the following production cost function c ( qi ) = cqi2 / 2 , i = 1, 2 . Foreign firm have advantage technology represented by the following production cost function c ( q0 ) = k q02 / 2 and c ≥ k .. We assume that a pollutant is associated with the production of the good and each unit of good produced gives rise to one unit of pollution. However, each firm can prevent pollution by undertaking abatement measures. If firm i choose pollution abatement level ai , pollutant emissions by firm i are ei = qi − ai i = 0,1, 2 . As in Bárcena-Ruiz (2006) and Wang and Wang (2009), the environmental damage is. (. measured by a quadratic form ED = e0 + ∑ ei. ). 2. / 2 , and the total cost of pollution. abatement of firm i is ai2 / 2 . Each firm has to pay an environmental tax per unit of pollutant emitted, the profit functions are written as. π 0 = pq0 − k. q02 a2 − te0 − 0 2 2. (4.1). 31.

(40) π i = pqi − c. qi2 a2 − tei − i , 2 2. direct entry:i = 1, 2 acquisition:i = 1. (4.2). To simplify the exposition of the results, we shall that c = 1 and k ∈ ( 0,1) . From an environmental governance perspective, the enforcement of pollution abatement requisites associated with governance has been either weak or non-existent, many state-owned firms, therefore, have operated without paying attention to long run sustainability. In addition, the authority of the public firm and tax-collecting administration are not the same, the objective function of the public firm and tax-collecting administration are not the same, the objective function of the public firm is most likely diverges from the “social welfare” as its objective, and for the partially privatized firm who is considering its own profit as a weighted part of the objective, and for the partially privatized firm who is considering its own profit as a weighted part of the objective, Beladi and Chao (2006) in privatized public monopoly model specified the sum of consumer surplus and the firm’s profit as the firm’s objective. We observed the weak governance and recognized the possible diverged interests between the government authority and the public firm, as in Beladi and Chao (2006), Ohori (2006) and Wang and Wang (2009), the public firms’ objective functions is defined as the sum of consumer surplus and firm’s profit, given as G = CS + π 1. (4.3). The social welfare function considered by government comprises the comprises the consumer surplus, the producer surplus, and the tax revenues collected by the government are T = t (e0 + ∑ ei ) , less the environmental damage ED . Thus, the social welfare can be expressed: W = CS + ∑ π i + T − ED ,. direct entry:i = 1, 2 acquisition:i = 1. (4.4). We consider three-stage game with the following timing. In the first stage, the 32.

(41) foreign firm choose the mode of entry by either direct entry (denoted by E ) or acquisition (denoted by M ). If foreign firm decides to enter directly, we denote the subsidiary by firm 0. If foreign firm decides to acquire a domestic private firm, it offers a proper and acceptable transaction price ν to its target domestic private firm and forms a new firm which is also owned by foreign firm 0. In the second stage, the government set the environmental tax. In the third stage, the domestic firms and foreign firm complete in the market by choosing output and abatement level. To find a sub-game perfect Nash equilibrium (SPNE), the game is solved by backward induction. We consider two cases. Case I, the government dose not set an environment tax to control pollution and firms do not abate emissions. Case II, the government set an environment tax to protect the environment. To find a sub-game perfect Nash equilibrium (SPNE), the game is solved by backward induction. 4.2Case I: No environmental policy We consider now that the social welfare includes the environmental damage generated by the production process. However, the government dose not set an environmental tax to control pollution and firms do not abate emissions ( ai = t = 0 ). By comparing the results obtained the foreign firm undertake FDI and M&A in the mixed oligopolies. The backward induction method is used for finding Subgame Perfect Nash Equilibrium (SPNE). In the second stage, the domestic firms and foreign firm complete in the market by choosing output and abatement level. In the first stage, the foreign firm chooses the mode of entry by either direct entry or acquisition.. 4.2.1. Foreign firm chooses to FDI In the two stage, the domestic firms and foreign firm complete in the market by choosing output and abatement level, qi ( i = 0,1, 2 ), simultaneously. Differentiating 33.

(42) (4.1), (4.2) and (4.3) with respect to qi , we obtain the following first-order conditions, ∂G = A − 2q1 = 0 ∂q1 ∂π 0 = A − 2q0 − kq0 − q1 − q2 = 0 ∂q0. (4.5). ∂π 2 = π − q0 − q1 − 3q2 = 0 ∂q2 Solving these equations simultaneously, we get the following results, q0E =. π = E 0. A (1 + k ) E 2 A ( 2 + k ) A A ,Q = , q1E = , q2E = 10 + 6k 5 + 3k 5 + 3k 2 A2 ( 2 + k ) 2 ( 5 + 3k ). CS = E. 2. A2 ( −1 + k ) 3 A2 (1 + k ) , π = , π 2E = 2 8 ( 5 + 3k ) 8 ( 5 + 3k ). 2. E 1. 2 A2 ( 2 + k ). ( 5 + 3k ). 2. 2. , ED = E. 2 A2 ( 2 + k ). ( 5 + 3k ). 2. 2. , W = E. A2 ( −1 + k ( 4 + 3k ) ) 4 ( 5 + 3k ). 2. where the superscript E denotes FDI.. 4.2.2. Foreign firm chooses to M&A If foreign firm decides to acquire firm 2 in domestic, it offers a proper and acceptable transaction price ν * to firm 2 and forms a new firm which is also owned by foreign firm 0. In the two stage, the domestic firms and foreign firm complete in the market by choosing output and abatement level, qi ( i = 0,1 ), simultaneously. Differentiating (4.1), (4.2) and (4.3) with respect to qi , we obtain the following first-order conditions, ∂G = A − 2q1 = 0 ∂q1. (4.6). ∂π 0 = A − 2q0 − kq0 − q1 = 0 ∂q0 34.

(43) Solving these equations simultaneously, we get the following results, Under M&A, the foreign firm offers a proper and acceptable transaction price. ν * to its target domestic private firm and forms a new firm which is also owned by foreign firm. The foreign firm have the full bargaining power of determining the transaction price, we have ν * = π 2E . q0M =. π. M 0. A (3 + k ) A A , q1M = , Q M = 2(2 + k ) 4 + 2k 2. A2 A2 k * M = −ν , π 1 = , 16 + 8k 16 + 8k. CS M =. W. M. A2 ( 3 + k ) 8(2 + k ). 2. 2. , ED M =. A2 ( 3 + k ) 8(2 + k ). 2. 2. ,. A2 ( 3 + 2k ) (1 + 3k ( 2 + k ) ) A2 k * = +ν = 2 16 + 8k 4 ( 2 + k )( 5 + 3k ). where the superscript M denotes M&A. 4.2.3 Foreign firm’s preferred mode of entry By comparing the results obtained the foreign firm undertake FDI and M&A in the mixed oligopolies we find that W E < W M and ED E > ED M . Proposition 4.1. In case I , in equilibrium. (i) π 0E. ≥ M ≥ π 0 if and only if k 0.5352 . < <. (ii) ED E > ED M (iii) W E < W M Proof: A (1 + k ) Q −Q = >0 20 + 22k + 6k 2 2. E. M. 35.

(44) A2 (1 + k ) ( 31 + k ( 30 + 7k ) ) 2. ED − ED = E. M. π 0E − π 0M =. 8 ( 2 + k ) ( 5 + 3k ) 2. A2 ( 3 − k − 7k 2 − 3k 3 ) ≥ 8 ( 2 + k )( 5 + 3k ). 2. <. 2. >0. 0 if and only if k. ≥ 0.5352 = ka <. A2 (1 + k ) =− <0 4 ( 2 + k )( 5 + 3k ) 2. W −W E. M. W. 10. WM. 8 6 4 WE. 2 0 0.1 -2. 0.2. 0.3. 0.4. 0.5. ka. k 0.6. 0.7. 0.8. 0.9. 1. Illustration of Proposition 4.1. The domestic welfare decrease result of foreign firm’s profit increase. Under FDI, if k < 0.2153 result in domestic welfare is negative, but foreign will choose acquisition with k < 0.5352 result in domestic welfare must be positive. The proposition shows that the foreign firm chooses to acquire a domestic private firm with foreign firm have enough high production advantage. When foreign firm chooses to M&A entering the domestic market result in environmental damage reduce and host country’s welfare raise. 4.3 Case II: The government implements an environmental policy 4.3.1. Foreign firm chooses to FDI In the third stage of the game, each firms choose output and abatement level 36.

(45) simultaneously. Differencing (4.1) with respect to q0 and a0 for foreign firm, we have ∂π 0 = A − t − ( 2 + k ) q0 − q1 − q2 = 0 ∂q0. (4.7). ∂π 0 = t − a0 = 0 ∂a0 Differencing (4.3) with respect to q1 and a1 for public firm, we have ∂G = A − t − 2q1 = 0 ∂q1. (4.8). ∂G = t − a1 = 0 ∂a1. Turning to the domestic private firm, we differencing (4.2) with respect to q2 and a2 , and obtain that ∂π 2 = A − t − q0 − q1 − 3q2 = 0 ∂q2. (4.9). ∂π 2 = t − a2 = 0 ∂a2 From the above first-order conditions, we obtain the results q0 =. (1 + k )( A − t ) ; a = a = a = t A−t A−t ; q1 = ; q2 = 0 1 2 10 + 6k 5 + 3k 2. (4.10). In the two stage, the government sets the environmental tax to maximize the social welfare. We substitute (4.10) into (4.4), and thus social welfare is given by: W=. (. ). A2 k ( 4 + 3k ) + 2 A (161 + k (172 + 45k ) ) t − ( 971 + 3k ( 376 + 109k ) ) − 1 t 2 4 ( 5 + 3k ). 2. ,. and differentiating it with respect to t, we obtain the optimal environmental tax, a0E = a1E = a2E = t E =. A (161 + k (172 + 45k ) ) 971 + 3k ( 376 + 109k ). where the superscript E denotes FDI. Substituting t E back to qi , we get the following SPNE outcomes as follows: 37. (4.11).

(46) q0E =. 2 A ( 81 + 47k ) 971 + 3k ( 376 + 109k ). q1E =. A ( 5 + 3k )( 81 + 47 k ) 971 + 3k ( 376 + 109k ). q2E =. A (1 + k )( 81 + 47k ) 971 + 3k ( 376 + 109k ). (4.12). Substituting (4.11) and (4.12) in profit function (4.1) and (4.2), we have. π 0E =. π 1E =. π 2E =. (. A2 4 ( 2 + k )( 81 + 47 k ) + (161 + 172k + 45k 2 ) 2. 2 ( 971 + 3k ( 376 + 109k ) ). (. 2. ). 2. A2 (161 + 172k + 45k 2 ) − (1 − k )( 5 + 3k )( 81 + 47 k ) 2. ( 971 + 3k ( 376 + 109k ) ). (. 2. 2 A2 3 (1 + k ) ( 81 + 47 k ) + (161 + 172k + 45k 2 ) 2. 2. ( 971 + 3k ( 376 + 109k ) ). 2. 2. ). (4.13). ). 2. We can obtain consumer surplus, environmental damage and social welfare as follows: 8 A2 ( 2 + k ) ( 81 + 47 k ) 2. CS = E. ( 971 + 3k ( 376 + 109k ) ). ED = E. W = E. 2. ,. 2. A2 (165 + k (184 + 53k ) ). 2. 2 ( 971 + 3k ( 376 + 109k ) ). A2 ( 499 + k ( 564 + 167k ) ) 1942 + 6k ( 376 + 109k ). 2. ,. (4.14). .. 4.3.2. Foreign firm chooses to M&A. If foreign firm decides to acquire firm 2 in domestic, it offers a proper and 38.

(47) acceptable transaction price ν to firm 2 and forms a new firm which is also owned by foreign firm 0. In the third stage of the game, both firms choose output and abatement level simultaneously. Differencing (4.1) with respect to q0 and a0 for foreign firm, we have ∂π 0 = A − t − ( 2 + k ) q0 − q1 = 0 ∂q0. (4.15). ∂π 0 = t − a0 = 0 ∂a0. Turning to the domestic public firm, we differencing (4.3) with respect to q1 and a1 , and obtain that ∂G = A − t − 2q1 = 0 ∂q1. (4.16). ∂G = t − a1 = 0 ∂a1 From the above first-order conditions, we obtain the results q0 =. A−t A−t ; q1 = ; a0 = a1 = t 4 + 2k 2. (4.17). In the two stage, the government sets the environmental tax to maximize the social welfare. We substitute (4.17) into (4.4), and thus social welfare is given by: W=. A2 k + 2 A (18 + 5k ) t − ( 92 + 39k ) t 2 8(2 + k ). +ν ,. and differentiating it with respect to t, we obtain the optimal environmental tax, tM =. A (18 + 5k ) 92 + 39k. (4.18). where the superscript M denotes M&A Substituting t M back to qi , we get the following SPNE outcomes as follows:. 39.

(48) A ( 37 + 17 k ) ( 2 + k )( 92 + 39k ). q0M =. (4.19). A ( 37 + 17k ) 92 + 39k. q1M =. If foreign firm chooses to enter thorough acquisition, it makes a take-it-or-leave-it offer to the target firm 2. A domestic target firm 2 will accept the foreign firm’s offer acquisition price can compensate the domestic firm’s gain under direct entry at least, i.e. ν ≥ π 2E . Because the foreign firm have the full bargaining power of determining the transaction price, we have ν * = π 2E . Substituting (4.18) and (4.19) in profit function (4.1) and (4.2), we have. π. (. A2 2017 + k (1942 + k ( 519 + 25k ) ). =. M 0. 2 ( 2 + k )( 92 + 39k ). 2. (. ) −ν. A 648 + k ( 2053 + 2k ( 744 + 157 k ) ) 2. π 1M =. 2 ( 2 + k )( 92 + 39k ). 2. *. , π 2M = ν * = π 2E ,. );. (4.20). where π 2M is payoff of the domestic target of private firm. Now, we can obtain consumer surplus, environmental damage and social welfare as follows: A2 ( 3 + k ) ( 37 + 17k ) 2. CS. =. M. 2 ( 2 + k ) ( 92 + 39k ) 2. ED = M. W. M. =. 2. A2 ( 39 + k ( 32 + 7 k ) ) 2 ( 2 + k ) ( 92 + 39k ) 2. A2 ( 81 + 4k (17 + 4k ) ) 2 ( 2 + k )( 92 + 39k ). 2. ,. 2. 2. ,. (4.21). +ν * .. 40.

(49) 4.3.3 Effects of Entry Mode. Proposition 4.2. In case II . When the government implements an environmental policy, in equilibrium. (i). q1E > q1M > q0M > q0E ≥ q2E if 0 < k ≤ 1. (ii) π 0E > π 2E > π 1E and π 0E > π 0M (iii) Q E > Q M and CS E > CS M Proof: See Appendix B.2. Given that the public firm is more aggressive in the product market than the privates, the public firm has the highest level output level. When the foreign firm has advantage cost technology, the foreign firm’s output more than the domestic private firm but less than the domestic public firm. Along with the foreign firm decides to acquisition, the foreign firm could get more market share result in their output raise ( q0M > q0E ) and public firm’s output lower ( q1E > q1M ). In the FDI case, the higher output level of the public firm offsets the lower output level of the domestic private firm and foreign private firm, as a result, the output of industry is higher in the FDI case than in the M&A case ( Q E > Q M ). On the other hand, as the consumer surplus depends positively on the out of industry, the greatest consumer surplus is obtained with the foreign firm decides to FDI in the domestic markets. Although the foreign private firm choose acquisition will increase it’s output, but acquiring firm has to offer the target firm acquisition price can compensate the domestic firm’s gain under direct entry result in acquiring firm’s profit less than the foreign firm decides to FDI ( π 0E > π 0M ). Thus, the foreign firm will direct investments in the domestic markets. Proposition 4.3. In case II . When the government implements an environmental 41.

(50) policy, in equilibrium. (i) a0E = a1E = a2E = t E < t M = a0M = a1M , and. ∑. 2 i =0. aiE > ∑ i =0 aiM 1. (ii) ED E < ED M (iii) W E > W M Proof: See Appendix B.3.. From proposition 4.3. (i) we define a variable: ℑ( k ) = QE − QM ℜ(k ) = t − t E. (4.22) M. We evaluate ∂ℑ / ∂k and ∂ℜ / ∂k : 2 2 ∂ℑ A ⎛ 3 ( 92 + 39k ) + 3025 ( 2 + k ) ⎞ 92 A ( 557 + k ( 638 + 183k ) ) = ⎜ >0 ⎟− 2 2 ⎟ ( 971 + 3k ( 376 + 109k ) )2 ∂k 14 ⎜⎝ ( 2 + k ) ( 92 + 39k ) ⎠. ∂ℜ 242 A ( 971 + 3k ( 376 + 109k ) ) − 4 A ( 92 + 39k ) ( 3649 + 3k (1492 + 457 k ) ) = >0 2 2 ∂k ( 92 + 39k ) ( 971 + 3k ( 376 + 109k ) ) 2. 2. We find that ∂ℑ / ∂k and ∂ℜ / ∂k are definitely positive. The degree of the cost advantage possessed by foreign firm increase, the domestic total output raises in the M&A case than FDI case. Similarly, The degree of the cost advantage possessed by foreign firm increase, the domestic environmental tax raises in the M&A case than FDI case. Thus, the government set a lower environmental tax in the FDI case than M &A case ( t E < t M ). Hence, as the environmental tax is the higher in the M&A case,. their abatement levels are also the higher ( aiE < aiM ). Although the greater abatement level and lower output level under M&A but it’s the total number of firms less than FDI. As a result, the total abatement level under M & A lower than FDI (. ∑. 2 i =0. aiE > ∑ i =0 aiM ) and the total emissions under M & A higher than FDI 1. 42.

(51) ( ∑ i =0 eiE < ∑ i =0 eiM ). As environmental damage depends positively on total emissions, 2. 1. the greatest environmental damage is obtained under M&A ( ED E < ED M ). Since the greater consumer surplus and lower environmental damage under FDI, we can get the higher social welfare under FDI than M&A. 4.4. Conclusion. This section analyses the decision by foreign firm’s entry mode. In order to study this question we consider two cases. First, the social welfare function includes environmental damage but there is no environmental policy (case I). Second, the government sets an environmental tax and firms decide their emission abatement level (case II). From case I, we find that the foreign firm chooses to acquire a domestic private firm with foreign firm have enough high production advantage, as result of the environmental damage reduce and host country’s social welfare raise under M&A. This result difference from case II, the foreign never choose to acquire a domestic private firm, the environmental damage reduces and host country’s social welfare raise under FDI.. 43.

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