不完全競爭市場下環境議題之研究：工會，租稅與區位選擇

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(1)國立高雄大學應用經濟學系碩士論文. 不完全競爭市場下環境議題之研究: 工會，租稅與區位選擇 Essays on the Environment under Imperfect Competition: Unionization, Taxation and Plant Location. 研究生：王文宏撰指導教授：王鳳生博士. 中華民國一百零一年七月.

(2) 致謝時間飛逝，兩年的碩士生涯即將畫上句點了，這一路上有許多幫助過我的貴人，在此文宏真心地感謝您。首先，謝謝我的指導教授王鳳生老師，您總是用您那幽默風趣的口吻教導著艱澀難懂的經濟學，即使我有時無法了解那其中的經濟含意，但您仍一遍又一遍的耐心解釋給我聽，您是我心中最棒的教授，謝謝您這兩年來對文宏的教導。感謝兩位口試委員楊雅博老師和李仁耀老師，您們的建議使我的論文更為完備。再來，要感謝我研究所的好同學育維、俊儫、濬豪、嘉玲和文婷，可以跟你們分享生活中的點點滴滴真的很快樂，特別感謝育維，這兩年幸虧有你的陪伴與幫忙要不然我的碩士生涯會走得更加辛苦。還有一年前才加入應經大家庭的碩一學弟妹們，研究室有你們的加入也多了許多歡笑聲。最後，要感謝我的父親和母親從小到大對我的鼓勵和不放棄，我才能在這裡寫完這篇論文，這篇論文送給你們。要成為一個碩士生也許不困難但要栽培出一個碩士的兒子是相當不容易的，你們對我的付出在不久的將來會看到甜美的果實，未來我一定會好好孝順你們的。. 王文宏謹誌於國立高雄大學應用經濟學系中華民國一百零一年仲夏.

(3) 不完全競爭市場下環境議題之研究: 工會，租稅與區位選擇指導教授：王鳳生博士國立高雄大學應用經濟系. 學生：王文宏國立高雄大學應用經濟系. 摘要. 近年來，發展中的國家致力於保護環境和增進社會福利。本論文主要是在探討不完全競爭市場下環境政策的影響效果。文中將分別探討民營化，政府稅收偏好和環境政策對國內的產量、利潤、社會福利、環境與區位選擇之影響。在第二章中，當政府對有生產效率差與存在工會的廠商同時課徵排放稅和利潤稅時，我們發現:（i）在聯合工會之下，較低的利潤稅將導致較低的排放稅且廠商的產量會更高；（ii）當排放稅和利潤稅同時課徵時，聯合工會的工資將低於個別工會的工資，在聯合工會之下,它對環境的危害及廠商的利潤都將會高於個別工會情況。在第三章中，將政府對稅收的偏好加入具有工會之混寡市場中，我們發現: （i）在有工會的混寡且生產造成的污染時，當政府對稅收的偏好增加時，社會福利也會增加；然而，（ii）在有工會的民營化寡佔市場且生產會造成污染中，當政府對稅收的偏好減少時，社會福利將會增加;（iii）當政府的稅收偏好和廠 I.

(4) 商生產污染率都較高時，混寡之下的污染稅會高於純寡之下的污染稅。在第四章中，考慮污染稅之設計與廠房位置之距離相關時，我們發現:（i）如果生產函數為規模報酬遞減，較高的污染稅會使廠商的產出增加；（ii）不論生產函數為何種規模報酬類型，較高的污染稅會使廠房位置更遠離市區；（iii）當政府保護居民並對廠商課徵污染稅，將會提高居民的效用；（iv）無論規模報酬為何種類型，較高的污染稅會降低污染對市區的危害。. 關鍵字: 民營化、環境稅、利潤稅、工會、區位選擇. II.

(5) Essays on the Environment under Imperfect Competition: Unionization, Taxation and Plant Location. Advisor: Dr. Leonard F.S. Wang Department of Applied Economics National University of Kaohsiung. Student: WANG, WEN-HONG Department of Applied Economics National University of Kaohsiung. ABSTRACT. In recent years, developing countries endeavor to protect the environment and improve social welfare. This thesis mainly focus on the environment policy under imperfect competition. It explores how will privatization, government's preference of tax, and environmental policy respectively affect domestic output, profit, social welfare, environment and location. In chapter 2, when both emission and profit tax are imposed on the firms with productivity differentials and union, we find that (i) Under centralized union, lower profit tax will lead to a lower emission taxes and the output will be higher.; (ii) When emission and profit tax are imposed, the social welfare under centralized wage will be III.

(6) lower than the one under decentralized wages, while the environmental damage and firm’s profit under centralized wage will be higher than the one under decentralized wages. In chapter 3, the government’s tax preference is incorporated into unionized mixed. oligopoly,. we. find. that. (i). In. unionized. mixed. oligopoly with. production-caused emission, social welfare increases with an increase in government’s preference for tax revenues.; However, (ii) In unionized private oligopoly with production-caused pollution, social welfare increases with a decrease on government preference for tax revenues; (iii) When the government’s preference and pollution rate are higher, pollution tax under unionized mixed oligopoly is higher than the one under unionized privatize oligopoly.. In chapter 4 on the issue of plant location with distance-related pollution tax, we find that (i) The output level of the firm is higher as a result of a higher pollution tax, if the production function exhibits decreasing returns to scale.; (ii) The plant location of the firm is further away from the CBD as a result of a higher pollution tax, which is irrespective of the type of return to scale.; (iii) When the government protects the resident and implements pollution taxes, it will increase the utility of residents.(iv), regardless of the type of return to scale. A higher pollution tax will definitely decrease the pollution to the CBD regardless of the type of return to scale.. Keywords: Privatization, Environmental Tax, Profit Tax, Union, Location Selection. IV.

(7) CONTENTS CHAPTER ONE: AN INTRODUCTION………………………………..(1) 1.1 Research Background ........................................................................................ (1) 1.2 Literature Review............................................................................................... (1). CHAPTER TWO: Union Bargaining and Tax Coordination............(4) 2.1Basic Mode ......................................................................................................... (4) 2.2 Decentralized Union, Emission Tax and Profit Tax ........................................... (6) 2.3 Centralized Union, Emission Tax and Profit Tax............................................... (8) 2.4 Comparisons of the Centralized Union and Decentralized Union ..................... (11) 2.5 Conclusion ......................................................................................................... (13). CHAPTER THREE: Does Government's Tax Preference Matter? Emission Tax, Union and Privatization……………………………...(14) 3.1 Basic model ........................................................................................................ (14) 3.2 A unionized mixed oligopoly ............................................................................. (16) 3.3 A unionized privatized oligopoly ....................................................................... (20) 3.4 Comparisons ...................................................................................................... (22) 3.4 Concluding Remark ........................................................................................... (26). CHAPTER FOUR: The Effects of pollution Taxed on Urban Areas with an Endogenous Plant Location and Pollution Emitted …. (27) V.

(8) 4.1 Basic Model ................................................................................................... (27) 4.2 The Impact of the Resident Utility on Pollution Taxes .................................. (33) 4.3 Conclusion ..................................................................................................... (35). CHAPTER FIVE: CONCLUSIONS……………………………………(36) REFERENCES……………………………………………………………….(37) APPENDIX…………………………………………………………………….(38). VI.

(9) LIST OF FIGURE Figure 3.1 Illustration of Proposition 3 ................................................................... (23) Figure 3.2 Illustration of Corollary 1 ...................................................................... (24) Figure 3.3 Illustration of Corollary 2 ...................................................................... (25) Figure 3.4 Illustration of Corollary 3 ...................................................................... (26). VII.

(10) 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 decrease when public firms are privatized. As a result, it reduce the consumer surplus and increase 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. 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 oligopoly market, the affect of privatization on the environmental has become the focus of much attention and debate. In this paper, we focus on the effects of government's tax policy in an oligopoly competition: How will privatization, government's preference, location with environmental policy affect output, profit, social welfare and environment. 1.2 Literature Review In chapter two, there some literatures discuss on the environmental issue. Simpson (1995) derived the optimal pollution for a Cournot duopoly and found that if firms have different production costs, the optimal tax rate may exceed the marginal damage. There are many literature has been discussed environmental policy in oligopoly. Dragone., Lambertini and Palestini (2009) show that both profit taxation 1.

(11) and Pigouvian taxation are used, the former is no longer neutral and for any profit tax rate there exists a unique Pigouvian tax rate that entails the first best outcome as an equilibrium. The literature in wage bargaining union has focused mainly on two structures. In one, each firm negotiates with an independent union at firm level (decentralization) and in the other each firm bargains with an industry-wide union (centralization). Assuming simultaneous negotiations, Horn and Wolinsky (1988) and Davidson (1998) show that a centralized negotiation results in higher wages than a decentralized one since the bargaining strength of the workers is greater; therefore, workers prefer centralized bargaining while firms prefer decentralized bargaining. Some literature is extended to firm heterogeneity. Wang., Mukherjee and Hsu (2012) show that the higher emission tax imposed will lower the bargained wage and when an emission tax is imposed and the productivity spread between firms is wider, the union’s utility under centralized wage will be less than the sum of union utility under decentralized wages. In chapter three, there are some papers exploring the privatization issue and related government policy. Mujumdar and Pal (1988) showed that privatization can increase social welfare and tax revenue, where an increase in tax does not change the total output increase the output of the public firm and the tax revenues. Furthermore, Choi (2011) regardless of the government's preference for tax revenues and the number of private firms, the government and the public firm do not always have an incentive to privatize the public firm even if the government places lesser emphasis on the tax revenues than on social welfare. In chapter four, pollution control by governments by means of pollution taxation or pollution regulation has received a great deal of attention. More specifically, 2.

(12) Mathur (1976) has integrated space into the conventional theory of the firm in order to examine the effect of the pollution tax on waste disposal in heavily polluted areas as most urban areas are, and on different forms of abatement. Mai and Hwang (1992) this paper point out the case of monopoly, a positive shift in demand requires that a monopolist increase his output, but in the case of oligopoly, an increase in industry output may or may not increase output per firm because of the firms is not constant. Again tax rate into the model, Mai and Hwang (2004) it is shown that when the plant location is endogenous, as pollution taxes become higher, the firm moves its plant toward the CBD, causing higher pollution damage to the CBD residents, if the production function exhibits decreasing returns to scale.. 3.

(13) CHAPTER TWO: Union Bargaining and Tax Coordination We adopt the same framework in Wang, L.F.S., Mukherjee, A. and Hsu, C.C., (2012) to investigate, the design of environmental policy under the consideration of union bargaining and homogeneous firm in duopoly. We find that when emission and profit tax are imposed that the firms of two identical, the social welfare under centralized wage will be lower than the one under decentralized wages, while the environmental damage and firm’s profit under centralized wage will be higher than the one under decentralized wages. This chapter is organized as follows. Section 2.1 provides the basic model. In section 2.2 we set up a three-stage model in a decentralized union, emission tax and profit tax. In section 2.3 we set up a three-stage model in a centralized union, emission tax and profit tax. Section 2.4 analyzes the effect of the government the Government's policy. Section 2.5 presents concluding remarks.. 2.1 Basic Model Consider a Cournot duopoly with the linear demand function given as p(Q) = a-Q, where p is the market price, Q = 𝑞1 + 𝑞2 is the total combined output of two firms. The consumer surplus is defined as CS =. 𝑄 2� 2. Assuming that the cost structures of. both firms are C(𝑞𝑖 ) = 𝑤𝑖 𝑙𝑖 , 𝑖 = 1, 2 where 𝑙𝑖 is the amount of labors hired by each firm. The good produced by both firms will lead to pollution e𝑖 = τq 𝑖 , τ = 1,for both firms. Environmental damage is measured by the quadratic form ED = (∑2𝑖=1 𝑒𝑖 ). 2. , which is the government measure. Each firm has to pay an. environmental tax 𝑡. per unit of pollutant and let α ∈ [0,1] be the tax rate on 4.

(14) operative profits, indicating that T = α ∑2𝑖=1 𝜋𝑖 + t ∑2𝑖=1 𝑒𝑖 is the total taxes collected by the government. So that the net after-tax profits of firm are π𝑖 = (𝑝𝑞𝑖 − 𝑤𝑖 𝑙𝑖 )(1 − 𝛼) − 𝑡𝑒𝑖 , 𝑖 = 1,2. (2.1). The premise of homogeneous labors, it is assumed that the relations between the. labor input of firm, 𝑞𝑖 = ∅𝑙𝑖 .. Each firm has its own union and operate independently to negotiate with its. corresponding firm to decide the wage level. In these input-output relations, ∅ stands. for the average productivity. The reservation wage is set to be w . The utility functions of the unions are as Eq. (2.2). max𝑤𝑖 𝑢𝑖 = (𝑤𝑖 − 𝑤 �)𝜃 𝑙𝑖 , 𝑖 = 1,2. (2.2). In the utility functions, θ is the importance a union attaches to the wage.. However, following Booth (1995).Haucap and Wey (2004).Leahy and Montagna (2000).Lommerud et al. (2003), θ = 1 and w = 0 are assigned to exclude unnecessary influences from the analyses. The social welfare comprises consumer surplus, profit of firms, union utility, tax revenue and the emissions: SW = CS + ∑2𝑖=1 𝜋𝑖 + ∑2𝑖=1 𝑢𝑖 + 𝑇 − 𝐸𝐸. (2.3). The present game has a three-stage structure: in the first stage, the social planner chooses the taxation rate on profits 𝛼 and the taxation rate on the negative externality t produced by the industry in order to maximize social welfare. The second. stage decides the optimal wages through the bargaining between the firms and the unions. The final stage deals with the quantity competition to find out the output. With the Subgame Perfect Nash Equilibrium (SPNE), the backward induction is adopted to solve the game.. 5.

(15) 2 .2 Decentralized Union, Emission Tax and Profit Tax 2.2.1 The firms choose the output In the third stage, the firms maximize profit to choose the output. From Eq. (2.1), we have the following first-order conditions： ∂𝜋1 ∂𝑥1. ∂𝜋2 ∂𝑥2. 𝑤1. = �(𝑎 − 2𝑥1 − 𝑥2 ) −. ∅. 𝑤2. = �(𝑎 − 𝑥1 − 2𝑥2 ) −. ∅. � (1 − 𝛼) − 𝑡 = 0 � (1 − 𝛼) − 𝑡 = 0. (2.4) (2.5). Solving the first-order conditions Eqs. (4) and (5), we obtain that 1. 𝑡. 2𝑤2 −𝑤1. 1. 𝑡. 𝑤1 −2𝑤2. 𝑞1 = 3 (𝑎 + 𝛼−1 +. 𝑞2 = 3 (𝑎 + 𝛼−1 +. ∅. ). ∅. (2.6). ). (2.7). 2.2.2 The unions choose the wage In the second stage, each wage is set to maximize the union of the corresponding firm. Using Eq. (2), the union objective functions are 𝑢1 =. 𝑢2 =. 𝑤1 [𝑤2 +2𝑤1 (𝛼−1)−𝑤2 𝛼−(𝑡+𝑎(𝛼−1))∅]. (2.8). [𝑤1 −2𝑤2 )(𝑤2 (𝛼−1)+𝑤2 (𝑡+𝑎(𝛼−1))∅]. (2.9). 3∅2 (1−𝛼). 3∅2 (𝛼−1). The first-order conditions are the following ∂𝑢1. ∂𝑤1 ∂𝑢2. ∂𝑤2. 2𝑤. = − 3∅21 − =. 𝑤2 +2𝑤1 (𝛼−1)−𝑤2 𝛼−�𝑡+𝑎(𝛼−1)�∅ 3∅2 (1−𝛼). (𝑤1 −4𝑤2 )(𝛼−1)+�𝑡+𝑎(𝛼−1)�∅. Which lead to. 3∅2 (1−𝛼). 1. (𝑡+𝑎(𝛼−1))∅. 1. (𝑡+𝑎(𝛼−1))∅. 𝑤1 = 4 (𝑤2 + 𝑤2 = 4 (𝑤1 +. 𝛼−1 𝛼−1. =0. =0. (2.1) (2.2). ). (2.12). ). (2.13). 6.

(16) Lemma 2.1 When wage setting is decentralized, in equilibrium: 2. 𝑡. 𝑞1 = 𝑞2 = 9 (𝑎 + 𝛼−1) , 𝑤1 = 𝑤2 = T=. 4[𝑡+𝑎(𝛼−1)][2𝑎𝛼(𝛼−1)+𝑡(2𝛼−9)] 81(𝛼−1)2. ED = (𝑥1 + 𝑥2 )2 =. (𝑡+𝑎(𝛼−1))∅. ,. 16(𝑡+𝑎(𝛼−1))2. 3(𝛼−1). SW =. , 𝑢1 = 𝑢2 =. 2[𝑎(𝛼−1)+𝑡]2 27(𝛼−1)2. 4(−2𝑡+𝑎(𝛼−1))(𝑡+𝑎(𝛼−1)) 27(𝛼−1)2. (2.14). 81(𝛼−1)2. 2.2.3 The government decides the emission tax and profit tax The social welfare is computed as follows: SW =. 4(−2𝑡+𝑎(𝛼−1))(𝑡+𝑎(𝛼−1)). ∂SW. −4(4𝑡+𝑎(𝛼−1)). (2.15). 27(𝛼−1)2. The first-order and second-order conditions are ∂t. =. ∂2 SW ∂𝑡 2. 27(𝛼−1)2 −16. = 27(𝛼−1)2 < 0. =0. Hence, the optimal emission tax rate is 𝑎. t 𝑑 = 4 (1 − 𝛼). (2.16). However, following Dragone, Lambertini and Palestini (2009).This entails that, if. different authorities manoeuvre the two tax rates, they should coordinates in order to achieve the welfare maximization, in principle, is their common objective. In practice, the alternative between pollution taxing and subsiding firms in order to regulate the social welfare must be positive.. Proposition 2.1 Under decentralized union, the welfare-maximizing emission tax is 𝑎. t 𝑑 = 4 (1 − 𝛼). The corresponding equilibrium outcomes are the followings: 7.

(17) 𝑎. 𝑞1𝑑 = 𝑞2𝑑 = 6, w1𝑑 = w2𝑑 = 𝑎2. T 𝑑 = 36 (3 + 2𝛼),. 𝑎∅ 4. 𝑎2. ,. SW 𝑑 =. 𝑎2. 𝑢1𝑑 = 𝑢2𝑑 = 24. 6. ,. ED𝑑 =. 𝑎2. 𝑎2. 𝜋1𝑑 = 𝜋2𝑑 = 36 (1 − 𝛼). 9. (2.17). 2.3. Centralized Union, Emission Tax and Profit Tax We now consider that there is an industry-wide union. In the second stage, unions set wage simultaneously taking into account the equilibrium of the third stage. Union objective function is now specified as max𝑤 𝑈 = (𝑤 − 𝑤 �)𝜃 ∑2𝑖=1 𝑙𝑖. (2.18). where w is the centralized wage.. 2.3.1 The firms choose the output In the third stage, the firms maximize profit to choose the output. we have the following first-order conditions： ∂𝜋1 ∂𝑞1. ∂𝜋2 ∂𝑞2. 𝑤. (2.19). 𝑤. (2.20). = �(𝑎 − 2𝑥1 − 𝑥2 ) − ∅ � (1 − 𝛼) − 𝑡 = 0 = �(𝑎 − 𝑥1 − 2𝑥2 ) − ∅ � (1 − 𝛼) − 𝑡 = 0. Solving the first-order condition (19) and (20), we obtain 1. 𝑡. 𝑤. q1 = 3 (𝑎 + 𝛼−1 − 𝜙 ) 1. 𝑡. (2.21). 𝑤. q 2 = 3 (𝑎 + 𝛼−1 − 𝜙 ). (2.22). 2.3.2 The union chooses the wage In the second stage, the union objective function is U=. 2𝑤[𝑤−𝑤𝑤+(𝑡+𝑎(𝛼−1))∅]. (2.23). 3∅2 (𝛼−1). The first-order and second-order conditions are the following:. 8.

(18) ∂U. 2[−2𝑤(𝛼−1+(𝑡+𝑎(𝛼−1))∅]. = ∂w ∂2 U. ∂w2. =0. 3∅2 (𝛼−1). −4. = 3∅2 < 0. Which leads to w𝑐 =. ∅(𝑡+𝑎(𝛼−1)). (2.24). 2(𝛼−1). Lemma2.2: When wage setting is centralized, in the equilibrium 1. 𝑡. 𝑞1 = 𝑞2 = 6 (𝑎 + 𝛼−1) , w = T=. ∅(𝑡+𝑎(𝛼−1)). �𝑡+𝑎(𝛼−1)�[𝑡(6−15𝛼)+5𝑎(𝛼−1)𝛼]. SW =. 18(𝛼−1)2. 2(𝛼−1). [𝑡+𝑎(𝛼−1)][𝑡(5−12𝛼)+7𝑎(𝛼−1)]. U=. ,. , ED =. (𝑡+𝑎(𝛼−1))2 6(𝛼−1)2. [𝑡+𝑎(𝛼−1)]2 9(𝛼−1)2. ,. 18(𝛼−1)2. (2.25). 2.3.3 The government decides the emission tax and profit tax The social welfare is computed as follows: SW =. [𝑡+𝑎(𝛼−1)][𝑡(5−12𝛼)+7𝑎(𝛼−1)] 18(𝛼−1)2. The first-order and second-order conditions are dSW 𝑡(5 − 12𝛼) − 6𝑎(𝛼 − 1)2 = =0 9(𝛼 − 1)2 dt. d2 SW 5 − 12𝛼 = <0 dt 2 9(𝛼 − 1)2. Hence, the optimal emission tax rate is t𝑐 =. 6𝑎(𝛼−1)2 5−12𝛼. <0. (2.26). However, following Dragone, Lambertini and Palestini (2009).This entails that, if different authorities manoeuvre the two tax rates, they should coordinates in order to achieve the welfare maximization, in principle, is their common objective. In practice, 9.

(19) the alternative between taxing and subsiding firms in order to regulate the social welfare must be positive.. Proposition 2.2 Under centralized union, the welfare-maximizing emission tax is t𝑐 =. 6𝑎(𝛼 − 1)2 5 − 12𝛼. The corresponding equilibrium outcomes are the followings: 𝑎+6𝑎𝑎. 𝑞1 𝑐 = 𝑞2 𝑐 = 72𝛼−30 , T𝑐 =. 𝑎2 (1+6𝑎)(36+𝛼(150𝛼−151)). SW 𝑐 = dt𝑐 dα. w𝑐 =. 𝑎. 18(5−12)2. (𝑎+6𝑎𝑎)2 216𝛼−90 49. (𝑎+6𝑎𝑎)∅ 24𝛼−10. (𝑎+6𝑎𝑎)2. , ED𝑐 = 9(5−12𝛼)2 , (𝑎+6𝑎𝑎)2. 𝜋1𝑐 = 𝜋2𝑐 = 36(5−12𝛼)2. = 2 �(5−12𝛼)2 − 1� > 0. (𝑎+6𝑎𝑎)2. U = 6(5−12𝛼)2. ,. 𝑖𝑖. 5. 12. (2.27). <𝛼<1. (2.28). The government to ensure that social welfare is positive, the range must be set the profit tax,. 5. 12. < 𝛼 < 1. Therefore, the original emission taxes become a pollution. subsidy, t will become negative, t 𝑐 =. 6𝑎(𝛼−1)2 5−12𝛼. < 0. Its interpretation as follows:. The social welfare comprises consumer surplus, profit of firms, union utility, tax. revenue and the emissions. In between these objective function, there is a trade-off. The government in order to increase CS, ∑2𝑖=1 𝜋𝑖 and ∑2𝑖=1 𝑢𝑖 utility of the objective. functions, the output will increase when the government makes t become a pollution. subsidy. However, taxes become subsidy is accompanied from the taxation reduction and. pollution will increase. Since the Government is concerned about social welfare,. as long as ∆CS + ∆π + ∆U + ∆T will be higher than ∆ED, the social welfare will continue to increase.. 10.

(20) 1. 𝑡. 𝑞1 𝑐 = 𝑞2 𝑐 = 6 �𝑎 + 𝛼−1� and Eq.(2.28). Form Eq.(2.27). dt𝑐 dα. >0. 𝑖𝑖. 5. 12. <𝛼<1. We can find lower profit tax will lead to emission taxes will be lower(subsidies increase) and the output will be higher. Form 1 express the above results. Output. Increase. Consumer. Profit of. Surplus. Firms. increase. increase. Union Utility. Tax Revenue Environmental Damage. increase. decrease. increase. Form 1. The lower profit tax will lead to emission taxes will be lower (subsidies increase). If. ∆CS + ∆π + ∆U + ∆T > ∆𝐸𝐸. (2.29). ∆SW = ∆CS + ∆π + ∆U + ∆T + ∆ED > 0. (2.30). We can know the Social welfare will increase. Therefore, the government will take the pollution subsidies and lower profit tax.. 2.4. Comparisons of the Centralized Union and Decentralized Union In this section we are going to compare the results obtained in the section 3 and 4 From Eq. (2.16),(2.26), we compare emission tax under centralized union and under decentralized, 𝑡𝑐 − 𝑡𝑑 =. 𝑎(𝛼−1)(12𝛼−19) 20−48𝛼. <0. 𝑖𝑖. 5. 12. <𝛼<1. (2.31). From Eq. (2.17), (2.27), we compare social welfare under centralized union and under decentralized SW 𝑐 − SW 𝑑 =. 𝑎�15−36𝛼+𝑎(1+6𝛼)2 � 90−216𝛼. <0. 𝑖𝑖. 5. 12. <𝛼<1. (2.32). we compare environmental damage under centralized union and under decentralized ED𝑐 − 𝐸𝐸𝑑 =. −4𝑎2 (𝛼−1)(9𝛼−2) 3(5−12𝛼)2. >0. 𝑖𝑖. 5. 12. <𝛼<1. we compare wage under centralized union and under decentralized 11. (2.33).

(21) 7𝑎𝑎. 𝑤 𝑐 − 𝑤 𝑑 = 48𝛼−20 > 0. 𝑖𝑖. 5. 12. <𝛼<1. (2.34). we compare profit under centralized union and under decentralized 𝜋𝑐 − 𝜋𝑑 =. 2𝑎2 �𝛼�2+96𝛼−81𝛼2 �−17� 9(5−12𝛼)2. >0. 5. 𝑖𝑖. < 12. 1. 54. �5 + 7√13� < 𝛼 < 1. (2.36). Proposition 2.3 When emission and profit tax are imposed, the social welfare under centralized wage will be lower than the one under decentralized wages, while the environmental damage and firm’s profit under centralized wage will be higher than the one under decentralized wages. The paradoxical result is coming from the following reasoning. In general, when the existence of the industry-wide union, the centralized union will be to the greater bargaining power than the decentralized with firms talk about wages. In other words, the firm’s profit under centralized wage will be lower than the one under decentralized wages. In this paper, we can find that the firms will prefer centralize union than decentralized union, the firm's profit under centralized wage will be higher than the one under decentralized wages. This causes increased output when the government's policy is pollution subsidies and decrease profits tax under centralized union. Due to increased output, the wages and pollution will follow increased under centralized union. Q𝐶 − 𝑄 𝐷 =. U𝐶 − 𝑈𝐷 =. 𝑎(1−𝛼) 12𝛼−5. >0. 𝑎2 �−23−72𝛼(𝛼−2)� 12(5−12)2. >0. 𝑖𝑖. 𝑖𝑖. 5. 12 5. 12. <𝛼<1. <𝛼<1. (2.36) (2.37). Accordingly, if the wage is setting centralized, the union’s utility is higher than the one when the wage is setting decentralized, the environmental damage is higher 12.

(22) due to the higher output is produced by pollution subsidies and raise profits tax under centralized union.. 2.5. Conclusion In this paper, we explored the design of environmental policy under the consideration of union bargaining and homogeneous firm in duopoly. The results obtained are the following. Firstly, under decentralized union, the government's tax policy will only affect the firm's profit and tax revenue. Secondly, under centralized union, in correspondence of the welfare-maximizing, emission tax and profit tax strategic complementary. When the government has decided to profit tax must ensure that social welfare must be positive. Lastly, when emission and profit tax are imposed that the firms of two identical, the social welfare under centralized wage will be lower than the one under decentralized wages, while the environmental damage and firm’s profit under centralized wage will be higher than the one under decentralized wages.. 13.

(23) CHAPTER THREE: Does Government's Tax Preference Matter? Emission Tax, Union and Privatization Choi (2011) considered the government's preference for tax revenues into mixed oligopoly and privatization. In this paper, we consider the good produced by firms will lead to pollution and the difference of productivity between public firm and private firms. It is shown that, in the mixed oligopoly, firm production will cause pollution, social welfare increase with an increase government preference for tax revenues. Even if the Government favored tax, the output of the entire market will not decreased instead also increase of total output and social welfare will also increase. This chapter is organized as follows. Section 3.1 provides the basic model. 3.2 analyzes the effect of mixed oligopoly and environmental tax. Section 3.3 analyzes the effect of privatization and privatization and environmental tax. Section 3.4 compare policy and welfare of mixed and privatization oligopoly. Section 3.5 present concluding.. 3.1 Basic model We consider a mix-oligopoly situation for a homogeneous good that is supplied by a public firm and n(≥ 1) private firms. Firm i (i =1,2...n) is a profit-maximizing. private firm and firm 0 is a public firm that maximizes the social welfare. Assume that the inverse demand is given by p = 1 − 𝑥0 − ∑𝑛𝑖=1 𝑞𝑖. (3.1). where p is the price of the good 𝑥0 is the output level of the public firm and 𝑥𝑖 is the output level of the 𝑖 𝑡ℎ private firm. On the demand side of the market, the representative consumer surplus is. 14.

(24) 1. CS = 2 (𝑥0 + ∑𝑛𝑖=1 𝑞𝑖 )2 𝑙𝑗. (3.2). Assuming that the cost structures of firms are C�𝑞𝑗 � = 𝑤𝑗 𝑙𝑗 , 𝑗 = 0,1, … 𝑛 where. is the amount of labors hired by each firm, and 𝑤𝑗 are the wages bargained. between each union and its corresponding firm. We assume the good produced by firms will lead to pollution 𝑒𝑗 = 𝜏𝑙𝑗 , τ ≤ 1 , for each firms. Environmental damage is. measured by the quadratic form ED = 2 ∑𝑛𝑗=1 𝑒𝑗 , which is the government measure.. In what follows, we assume that an environmental tax rate t is imposed on the public and private firms. The price of labor (i.e., wage) that firm j has to pay is denoted by w𝑗 = 0,1, … 𝑛. Each firm profit follows the function. 𝜋𝑗 = 𝑝𝑞𝑗 − 𝑤𝑗 𝑙𝑗 − t𝑒𝑗 , j = 0,1, … n. (3.3). To explicitly depict the difference of productivity but under the premise of. homogeneous labors, it is assumed that the relations between the labor input and the output of a less efficient firm and an efficient firm are 𝑥0 = (1 − 𝑠)𝑙0 and. 𝑞𝑖 = (1 + 𝑠)𝑙𝑖 , respectively. In these input-output relations, 0 < s < 1 brings out the productivity differences between firms, which results in that the less efficient public. firm needs to hire more employers to achieve the same level of output that can be produced with fewer workers by the private firms. Each firm has its own union and the unions operate independently to negotiate with its corresponding firm to decide the wage level. The reservation wage is set to be w . The utility functions of the unions are as. max𝑤𝑗 𝑢𝑗 = (𝑤𝑗 − 𝑤 �)𝜃 𝑙𝑗 , 𝑗 = 0,1, … , 𝑛. (3.4). In the utility functions, θ is the importance a union attaches to the wage. However, following Booth (1995).Haucap and Wey (2004).Leahy and Montagna (2000).Lommerud et al. (2003), θ = 1 and w = 0 are assigned to exclude 15.

(25) unnecessary influences from the analyses. It is also assumed that f = 0 . The social welfare comprises consumer surplus, profit of firms, union utility, tax revenue and the emissions: SW = CS + ∑𝑛𝑗=0(𝜋𝑗 + 𝑢𝑗 ) + 𝑇 − 𝐸𝐸. (3.5). In the manner of Kato (2008), we also assume that the government objective is. tax-inclusive social welfare (again, hereafter called government payoff) as follows: G = SW + αT. (3.6). Where α is the parameter that represents the weight of the government. preference for tax revenues. Here, the government values the tax revenues, T, more than social welfare, SW, when α > 1. Otherwise, the government values the tax. revenues less social welfare when 0 < 𝛼 < 1. Finally, a three-stage game is conducted. The timing of the game is as follows. In. the first stage, the government sets the environmental rate. The second stage decides the optimal wage through the bargaining between the firms and the unions. The final stage deals with the quantity competition to find out the output. With the Subgame Perfect Nash Equilibrium (SPNE), the backward induction is adopted to solve the game. 3.2 A unionized mixed oligopoly In this case, the public firm objective is to maximize social welfare. Thus , given t and 𝑤𝑗 for each firm j(j=0,1,….,n), the public firm maximization problem is as. follow:. max𝑞0 𝑆𝑆 = CS + ∑𝑛𝑗=0(𝜋𝑗 + 𝑢𝑗 ) + 𝑇 − 𝐸𝐸. Difference with respect to 𝑥0 for social welfare, we have ∂SW ∂𝑞0. 𝑤. 0 = 1 − q 0 − 𝑛q 0 − 1−𝑠 − 𝑡𝑡 = 0. 16. (3.7). (3.8).

(26) On the other hand, the optimal output for a private firm is givens by ∂𝜋𝑖 ∂q𝑖. 𝑤. = 1 − 𝑞0 − 𝑛𝑞𝑖 − 𝑞𝑖 − 1+𝑠𝑖 − 𝑡𝑡 = 0. (3.9). From the above first-order conditions, we obtain the results 𝑛𝑤. 𝑞0 = 1 + 1+𝑠𝑖 + 𝑤. (1+𝑛)𝑤0. 𝑤. 0 𝑞𝑖 = 1−𝑠 − 1+𝑠𝑖. 𝑠−1. − 𝑡𝑡. (3.10) (3.11). Using Eqs.(3.10) and (3.11). The problems for unions i=1,…,n and union 0 are defined as max 𝑢𝑜 = 𝑤0 𝑙𝑜 = 𝑤0. 𝑤0 (1 − 𝑤0 − 𝑛𝑤0 + 𝑛𝑤𝑖 − 𝑠(𝑤0 + 𝑛𝑤0 + 𝑤𝑖 )𝑡𝑡 + 𝑠 2 (1 − 𝑡𝑡)) (1 + 𝑠)(𝑠 − 1)2 𝑤. 𝑤. 0 𝑖 max𝑤𝑖 𝑢𝑖 = 𝑤𝑖 𝑙𝑖 = 𝑤𝑖 ((1+𝑠) 2 − 𝑠2 −1). (3.12). respectively. Straightforward computation yields each firm reaction function as follows: 𝑤0 =. 2(1−𝑠)(1−𝑡𝑡) 4+3𝑛. , 𝑤𝑖 =. (1+𝑠)(𝑡𝑡−1). (3.13). 4+3𝑛. Then, the equilibrium wages, which are denoted as wjm , j = 0,1 … , n are. obtained by solving Eq. (3.13); the substitution of each equation in Eq. (3.13) into Eqs. (3.10) and (3.11) yields the respective equilibrium outputs, 𝑞𝑗𝑚 . The equilibrium. wages and outputs, 𝑤𝑗𝑚 and 𝑞𝑗𝑚 , respectively, can be obtained as follows: 𝑤0𝑚 = 𝑞0𝑚 =. 𝑤0𝑚 = 𝑢0𝑚 =. T𝑚 =. 2(𝑠−1)(𝑡𝑡−1) 4+3𝑛. 2(1+𝑛)(1−𝑡𝑡) 4+3𝑛. 2(𝑠−1)(𝑡𝑡−1) 4+3𝑛. 4(1+𝑛)(𝑡𝑡−1)2 (4+3𝑛)2. , 𝑤𝑖𝑚 = , 𝑞𝑖𝑚 =. 4+3𝑛. (1−𝑡𝑡). , 𝑤𝑖𝑚 =. 4+3𝑛. 2(𝑠−1)(𝑡𝑡−1) 4+3𝑛. (𝑡𝑡−1)2. , 𝑢𝑖𝑚 = (4+3𝑛)2. (2+3𝑛)(1−𝑡𝑡)𝑡𝑡 (4+3𝑛). 2(𝑠−1)(𝑡𝑡−1). ,. ED𝑚 =. 2(2+3𝑛)(1−𝑡𝑡)𝜏 4+3𝑛. 17.

(27) SW 𝑚 =. (2+3𝑛)(1−𝑡𝑡)(6+2(−8+𝑡)𝜏+3𝑛(1+(𝑡−4)𝜏)). (3.14). 2(4+3𝑛)2. We can find that 𝜋0𝑚 = 0, because the public firm's profit will be taken away by. the public union. Therefore, the utility of the public union will be higher than the utility of the private union, 𝑢0𝑚 > 𝑢𝑖𝑚 .. In the first stage, the government's payoff, 𝐺 𝑚 , in the unionized mixed oligopoly. can be rewritten as: max𝑡 𝐺 𝑚 =. (2+3𝑛)(1−𝑡𝑡)(−3(2+𝑛)+16�𝑡(−2+8𝛼)+3𝑛�4+𝑡(−1+2𝛼)��𝜏) 2(4+3𝑛)2. (3.15). and differentiating it with respect to t, we obtain the optimal environmental tax, 2+(4+3𝑛)(𝛼−2𝑡). t = (8𝛼−1+𝑛(6𝛼−3))𝑡. (3.16). If the weight of the government's preference for tax revenues is sufficiently large 2. in the case of α > 2𝜏 − 4+3𝑛, the optimal tax rate becomes positive. Conversely, 2. when it is small in the case ofα > 2𝜏 − 4+3𝑛, the optimal tax rate becomes negative, 2. and in the case of α = 2τ − 4+3𝑛, the optimal tax rate is zero. We find that the greater. the weight of the government's preference for tax revenues, the higher will be the tax rate that the government imposes. we get the Cournot-Nash equilibrium outcomes. In market equilibrium, the equilibrium wages and output levels under a unionized mixed oligopoly are given by 𝑞0𝑚 =. 𝑤0𝑚 =. 2(1+𝑛)(−1+𝛼+2𝑡) 8𝛼−2+𝑛(6𝛼−3). ,. 2(1 − 𝑠)(−1 + 𝛼 + 2𝜏) , 8𝛼 − 2 + 𝑛(6𝛼 − 3). 𝑞𝑖𝑚 =. (−1+𝛼+2𝑡). 8𝛼−2+𝑛(6𝛼−3). 𝑤𝑖𝑚 = 18. (1 + 𝑠)(−1 + 𝛼 + 2𝜏) 8𝛼 − 2 + 𝑛(6𝛼 − 3).

(28) 𝑢0𝑚. (1 + 𝑛)(−1 + 𝛼 + 2𝜏)2 = , (8𝛼 − 2 + 𝑛(6𝛼 − 3))2 (−1+𝛼+2𝑡)2. 𝜋𝑖𝑚 = (8𝛼−2+𝑛(6𝛼−3))2 T𝑚 =. (−1 + 𝛼 + 2𝜏)2 = (8𝛼 − 2 + 𝑛(6𝛼 − 3))2. (2+3𝑛)(−1+𝛼+2𝑡)(2+(3𝑛+4)(𝛼−2𝑡)). ED𝑚 =. (8𝛼−2+𝑛(6𝛼−3))2. 2𝑡(2+3𝑛)(−1+𝛼+2𝑡). 𝑆𝑆 𝑚 = 𝐺𝑚 =. 𝑢0𝑚. 8𝛼−2+𝑛(6𝛼−3). (2+3𝑛)(−1+𝛼+2𝑡)(2−4𝑡+2𝛼(−7+16𝛼)+37(1−2𝑡+𝛼(−3+8𝑡))). (2+3𝑛)(−1+𝛼+2𝑡)2. (8𝛼−2+𝑛(6𝛼−3))2. (3.17). 2(8𝛼−2+𝑛(6𝛼−3)). As can be seen, all equilibrium outcomes depend on α、n and τ. Thus, we now. obtain how social welfare varies with the number of firms and the government’s preference and pollution rate for tax in a unionized mixed oligopoly as follows.. Lemma 3.1 (Choi,2011) In the case of a unionized mixed oligopoly, social welfare increases with decreases in the government preference for tax revenues regardless of the number of firm, n.. Proposition 3.1 In unionized mixed oligopoly with production-caused emission, social welfare increases with an increase in government’s preference for tax revenues.. Proof. Differentiating Eq.(3.17) with respect to n、α、τ, we obtain ∂SW ∂α. =. 𝛼(2+3𝑛)(3(2+𝑛)−4𝑡(4+3𝑛))2 (8𝛼−2+𝑛(6𝛼−3))3. We know from where 𝐺 𝑚 =. >0. (3.18). (2+3𝑛)(−1+𝛼+2𝑡)2 2(8𝛼−2+𝑛(6𝛼−3)). must be positive, that. 2(8𝛼 − 2 + 𝑛(6𝛼 − 3)) would also be positive.. When the government the more favored tax revenue, the government will expect 19.

(29) that the increase in production in order to increase tax revenue. However, imposed pollution tax will make private firms have an incentive to reduce production. Therefore, the unions are bargaining with firms lower employee wages in order to production will not reduce too much. The public firm’s objective is to maximize social welfare. More production yield will consumer surplus increases, but can cause the increase of the environment 1. pollution. Since CS = 2 𝑋 2 > 𝐸𝐸 = 2𝜏𝜏, change in consumer surplus per unit of. production higher than the changes in environmental damage, ∆CS > ∆𝐸𝐸. Public firm will produce more to achieve maximize social welfare. Even if the Government. favored tax, the output of the entire market will not decreased instead also increase of total output and social welfare will also increase. 3.3 A unionized privatized oligopoly This subsection compares the equilibrium of a unionized mixed oligopoly with the equilibrium that would be established in the case of a unionized privatized oligopoly. As discussed in the basic model, consider the situation of a unionized privatized oligopoly for a homogeneous good that is supplied by firm (k=1,…,n+1), which is a profit-maximizing private firm. In the third stage, given 𝑤𝑘 、𝑡 and τ, the firm k's profit-maximization is to maximize 𝜋𝑘 = p𝑝 𝑞𝑘 − 𝑤𝑘 𝑙𝑘 − t𝑒𝑘 , k =. 1, … n, n + 1 where 𝑝𝑝 = ∑𝑛+1 𝑘=1 𝑞𝑘 , 𝑛 ≥ 1 Hence, solving across the n+1 first-order conditions, the n+1best response functions can be rewritten as follows:. ∂𝜋𝑘 ∂q𝑘. 𝑤. 𝑘 = 1 − (𝑛 + 1)q 𝑘 − q 𝑘 − 1+𝑠 − 𝑡𝑡 = 0. (3.19). From the above first-order conditions, we obtain the results 𝑞𝑘 =. 1+𝑠−𝑤𝑘 −(1+𝑠)𝑡𝑡. (3.20). (𝑛+2)(1+𝑠). In the second stage, given the output as a function of wage rates, each union at 20.

(30) each private firm sets the wage 𝑤𝑘 , that maximizes union utility,𝑢𝑘 max𝑤𝑘 𝑢𝑘 = 𝑤𝑘 𝑙𝑘 =. 𝑤𝑘 (1+𝑠−𝑤−(1+𝑠)𝑡𝑡) (𝑛+2)(1+𝑠)2. (3.21). Solving this problem, we obtain the following result: 1. 𝑤𝑘 = 2 (1 + 𝑠)(1 − 𝑡𝑡). 1−𝑡𝑡. 𝑝. 𝑞𝑘 = 2(2+𝑛). (3.22). When wage setting is under unionized privatized oligopoly, in equilibrium: 1−𝑡𝑡. 𝑝. 𝑝. 𝑞𝑘 = 2(2+𝑛) 𝑝. 𝑢𝑘 =. 𝑇𝑝 =. 𝑤(1+𝑠−𝑤−(1+𝑠)𝑡𝑡) (𝑛+2)(1+𝑠)2. 𝐶𝐶 𝑃 =. (1+𝑛)(1−𝑡𝑡)𝑡𝑡. SW 𝑝 =. 1. 𝑤𝑘 = 2 (1 + 𝑠)(1 − 𝑡𝑡). ED𝑝 =. 2(2+𝑛). (1+𝑛)2 (𝑡𝑡−1)2 8(2+𝑛)2. (1+𝑛)(1−𝑡𝑡)𝜏 2+𝑛. (1+𝑛)(1−𝑡𝑡)(7+3𝑛+(−16+𝑛(−8+𝑡)+𝑡)𝜏). (3.23). 8(2+𝑛)2. In the first stage, the government's payoff, 𝐺 𝑚 , in the unionized mixed oligopoly can. be rewritten as: max𝑡 𝐺 𝑚 =. (1+𝑛)(1−𝑡𝑡)(7+3𝑛+(−16+𝑛(−8+𝑡)+𝑡+4(2+𝑛)𝑡𝑡)𝜏) 8(2+𝑛)2. (3.24). and differentiating it with respect to t, we obtain the optimal environmental tax, t=. 4𝛼−3+8𝑡+𝑛(−1+2𝛼+4𝑡). (3.25). (1+𝑛+4(2+𝑛)𝛼)𝑡. If the weight of the government's preference for tax revenues is sufficiently large 3+𝑛. in the case of α > 4+2𝑛 − 2τ, the optimal tax rate becomes positive. Conversely, 3+𝑛. when it is small in the case of α < 4+2𝑛 − 2τ, the optimal tax rate becomes negative, 3+𝑛. and in the case of α = 4+2𝑛 − 2τ, the optimal tax rate is zero. We find that the greater the weight of the government's preference for tax revenues, the higher will be the tax rate that the government imposes. In market equilibrium, the equilibrium wages and output levels under a unionized privatized oligopoly are given by 21.

(31) 1+𝛼−2𝜏. 𝑝. 𝑝. 𝑞𝑘 = 1+𝑛+4(2+𝑛)α 𝑝. 𝑤𝑘 =. (2+𝑛)(1+𝛼−2𝜏)2. 𝑝. 𝑢𝑘 = (1+𝑛+4(2+𝑛)𝛼)2. T𝑃 =. (2+𝑛)(1+𝑠)(1+𝛼−2𝜏) 1+𝑛+4(2+𝑛)𝛼. (2+𝑛)(1+𝛼−2𝜏)2. 𝜋𝑘 = (1+𝑛+4(2+𝑛)𝛼)2. (1+𝑛)(1+𝛼−2𝜏)(−3+4𝛼+8𝜏+𝑛(−1+2𝛼+4𝜏)) (1+𝑛+4(2+𝑛)𝛼)2. (1+𝛼−2𝜏)2. ED𝑝 = (1+𝑛+4(2+𝑛)𝛼)2. SW𝑃 =. (1+𝑛)(1+𝛼−2𝜏)(1+𝑛+15𝛼+7𝑛𝑛−2(1+𝑛+8(2+𝑛)𝛼)𝜏) 2(1+𝑛+4(2+𝑛)𝛼)2. (3.26). Proposition 3.2 In unionized private oligopoly with production-caused pollution, social welfare increases with a decrease on government preference for tax revenues. Proof. Differentiating Eq.(3.27) , we obtain ∂SW𝑝 ∂α. =. −𝛼(1+𝑛)(7+3𝑛+8(2+𝑛)𝜏) (1+𝑛+4(2+𝑛)𝛼)2. <0. (3.27). (1+𝑛)(1+𝛼−2𝑡)2. We know from where 𝐺 𝑝 = 2(1+𝑛+4(2+𝑛)𝛼) must be positive, because the. government's payoff can not be negative, that (1 + 𝑛 + 4(2 + 𝑛)𝛼) would also be. positive.. In this case does not exist public firms, a higher government's preference for tax revenue force the union to be less aggressive in wage bargaining. Lower wages will make firm’s produce more output. Because not exist public firms will produce more to achieve maximize social welfare, an increase in α works to tax revenues by decreasing social welfare, lowering the total output and wages.. 3.4 Comparisons Once the equilibria for all firms and the government are derived as discussed in 22.

(32) previous. We have derived mixed and private oligopoly, and we assume that the number of firms can be observed, if n = 10. Proposition 3.3 When the government’s preference and pollution rate are higher, pollution tax under unionized mixed oligopoly is higher than the one under unionized privatize oligopoly.. Thus, the differences in the optimal tax, Define that ∆t ≡ 𝑡 𝑚 − 𝑡 𝑝 , ∆t courve. describes the contour of the ∆t = 0 along which the productivity and firm's objective function are identical between mixed and private oligopoly.. Figure 3.1 Illustration of Proposition 3.3. By the diagram above, the less pollution ratio that pollution tax paid by the firms are also relatively small. Privatization firms production to maximize profits so that the output will increase. Therefore, the higher the government preference will make the privatization of the manufacturers of higher pollution tax. 23.

(33) When the degree of pollution is high, the government preference is higher will make pollution tax under mixed oligopoly are higher than privatized oligopoly. Because in the mixed oligopoly, the production higher cause of social welfare the higher, even if the government levied a higher pollution tax does not reduce social welfare. Therefore, pollution tax under mixed oligopoly are higher than privatized oligopoly.. Corollary 1 When the government preference and pollution ratio the higher, social welfare under mixed oligopoly are higher than privatized oligopoly.. Thus, the differences in the optimal tax, Define that. ∆SW ≡ 𝑆𝑆 𝑚 − 𝑆𝑆 𝑝 , ∆t. courve describes the contour of the ∆SW = 0 along the productivity and the output are identical between mixed and private oligopoly.. Figure 3.2 Illustration of Corollary1. 24.

(34) Corollary 2 When the government preference and pollution ratio the higher, consumer surplus under mixed oligopoly are higher than privatized oligopoly.. Thus, the differences in the optimal tax, Define that. ∆CS ≡ 𝐶𝑆 𝑚 − 𝐶𝑆 𝑝 , ∆t. courve describes the contour of the ∆CS = 0 along which the productivity and firm's objective function are identical between mixed and private oligopoly.. Figure 3.3 Illustration of Corollary 2. Corollary 3 When the government preference and pollution ratio the higher, environmental damage under mixed oligopoly are higher than privatized oligopoly.. Thus, the differences in the optimal tax, Define that. ∆ED ≡ 𝐸𝐸𝑚 − 𝐸𝐸𝑝 , ∆t. courve describes the contour of the ∆ED = 0 along which the productivity and firm's objective function are identical between mixed and private oligopoly.. 25.

(35) Figure 3.4 Illustration of Corollary 3. 3.5 Concluding Remark We consider a mix-oligopoly situation for a homogeneous good that is supplied by a public firm and n(≥ 1), private firms and the good produced by each firms will lead to pollution. This section analyses that the impact of government preference for tax on social welfare. The results obtained are the following. Firstly, in the mixed oligopoly, firm production will cause pollution, social welfare increase with an increase government preference for tax revenues. Secondly, a unionized private oligopoly that there are production will cause pollution, social welfare increase with an decrease government preference for tax revenues. Lastly, when the government preference and pollution ratio are higher, social welfare, consumer surplus and environmental damage under mixed oligopoly are higher than privatized oligopoly.. 26.

(36) CHAPTER FOUR: The Effects of Pollution Taxes on Urban Areas with an Endogenous Plant Location and Pollution Emitted. This result is different from Hwang and Mai (2004) who indicate that the tax revenue is independent of a change in the distance between plant and CBD case. In this paper, we show that the pollution tax revenue has positive correlation with the distance between plant and CBD. We find that government makes upgrade the resident utility if a higher pollution tax may lead a lower level of pollution measured at CBD. Further to say, a stricter pollution policy such as a higher pollution tax lead to lower pollution damage to the CBD irrespective of the type of Return to scale. Although the paper assumes the markets to be of monopoly, the intuition derived in this paper is robust in other market structures, such as oligopoly or perfect competition.. 4.1 Basic Model. Figure 4.1. Locational triangle.. 27.

(37) The analysis is based on the following assumptions: (a) There is a monopoly industry in which firm produce homogeneous output. (b) The firm uses two transportable inputs 𝑀1 and 𝑀2 , which are available at A and. B, respectively ,in the production of output q , which it supplies to the consumption center C, as illustrated in Figure4.1. The firm is interested in finding the optimum production location E. In figure4.1, the distance a and b and the angle 𝛽 are known; h. is the distance between the plant location E and the CBD(C);𝑧1 and 𝑧2 are the distance of plant E from A and B, respectly;θ. (c)The production function of the firm can be specified as:. ∂q. ∂q. q = f(𝑀1 , 𝑀2 ). ∂2 q. ∂2 q. with 𝑓𝑀1 ≡ ∂M1 > 0, 𝑓𝑀2 ≡ ∂𝑀 > 0, 𝑓𝑀1 𝑀1 ≡ ∂M12 < 0, 𝑓𝑀2 𝑀2 ≡ ∂M22 < 0 2. (4.1). (d)To simplify our analysis, we first derive the total cost function by minimizing total cost subject to a given output level. That is Min s.t.. (𝑤1 + 𝑟1 𝑧1 )𝑀1 + (𝑤2 + 𝑟2 𝑧2 )𝑀2 q = f(𝑀1 , 𝑀2 ). (4.2). where 𝑤1 and 𝑤2 are the base price of 𝑀1 and 𝑀2 at A and B ,respectively,. which are assumed to be constant; 𝑟1and 𝑟2 are constant transport rates of 𝑀1 and. 𝑀2 respectively; and 𝑧1 and 𝑧2 may be defined by the low of cosines as follows: 𝑧1 = √𝑎2 + ℎ2 − 2𝑎ℎ cos 𝑑. (4.3). 𝑧2 = �𝑏 2 + ℎ2 − 2𝑏ℎ cos( 𝛽 − 𝑑). (4.4). 28.

(38) (e)For homothetic production function, the cost function can be written as the product of two functions of factor prices only. We have:. C(q) = c(𝑤1 + 𝑟1 𝑧1 , 𝑤2 + 𝑟2 𝑧2 )H(q). (4.5). Hence, the average cost and marginal cost can be written as: AC =. 𝐶(𝑞) 𝑞. =. 𝑐𝐻. (4.6). 𝑞. MC=𝐶𝑞 = 𝐶𝐻𝑞. (4.7). Following Hanoch (1975), form(4.6)and(4.7), we obtain the following relation: 𝐻 𝑞. > (=, <)𝐻𝑞. (4.8). if the production function is increasing (constant, decreasing) returns to scale,i.e.,IRS(CRS,DRS).. (f) The industry inverse demand function for output is given by P = P(q), 𝑃𝑞 < 0. (4.9). (g)The prices of inputs and output are evaluated at the plant location E. The cost of purchasing inputs in the price of input at the source plus the freight cost, and the price of output is the market price minus the freight cost. (h) Transportation rates are constant. (i)The pollution tax revenue function G(q) is specified as follows: G(q) = em(h)y(q). (4.10). where e is the pollution tax, m(h) is the relationship between the pollution level at CBD and y(q) is the a mount of pollution generated by the production process which depends on the amount of output produced.. 29.

(39) where G(q) = em(h)y(q) and t is the constant transport rate of shipping one unit of the output to the CBD.. We assume throughout the paper that emission rises linearly with output(i.e.,𝑒𝑞 > 0 and 𝑒𝑞𝑞 = 0). Given this assumption, we can immediately derive that 𝐺𝑞 =. 𝑒𝑚𝑒𝑞 > 0, 𝐺𝑞𝑞 = 𝑒𝑞 > 0and 𝐺𝑞 > 0. Moreover, an increase in e indicates that the government adopts a stricter pollution policy.. With these assumptions, the profit maximizing location problem of the representative firm is given by Max π=[P(q)-th]q-c(θ,h)H(q)-G(q). (4.11). q, θ,h The first-order conditions for profit maximization are: 𝜋𝑞 = (𝑃 − 𝑡ℎ) + 𝑃𝑞 𝑞 − 𝑐𝐻𝑞 − 𝐺𝑞 = 0 𝜋𝜃 = −𝐶𝜃 H = 0 𝜋ℎ = −𝑡𝑡 − 𝐶ℎ 𝐻 − 𝑒𝑒𝑚ℎ = 0. Moreover, taking the total different and using Cramer , s rule, we can examine the effects of a change in the demand function on the optimum location: 𝜋𝑞𝑞 �𝜋𝜃𝜃 𝜋ℎ𝑞. 𝜋𝑞𝑞 𝜋𝜃𝜃 𝜋ℎ𝜃. 𝜋𝑞ℎ 𝑑𝑑 𝜋𝑞𝑞 𝜋𝜃ℎ � �𝑑𝑑� = − �𝜋𝜃𝜃 � 𝑑𝑑 𝜋ℎℎ 𝑑ℎ 𝜋ℎ𝑒. (4.12). where 𝜋𝑞𝑞 = 2𝑝𝑞 + 𝑝𝑞𝑞 𝑞 − 𝐶𝐻𝑞𝑞 < 0 𝜋𝑞𝑞 = 𝜋𝜃𝜃 = −𝐶𝜃 𝐻𝑞 = 0. 𝐻 𝜋𝑞ℎ = 𝜋ℎ𝑞 = −𝑡 − 𝐶ℎ 𝐻𝑞 = 𝐶ℎ � − 𝐻𝐻� 𝑞. 𝜋𝜃𝜃 = −𝐶𝜃𝜃 < 0 𝜋ℎℎ = −𝐶ℎℎ 𝐻 − 𝑒𝑒𝑚ℎℎ < 0 𝜋𝑞𝑞 = −𝑚𝑦𝑞 < 0 𝜋ℎ𝑒 = −𝑦𝑚ℎ > 0. 30.

(40) We can derive the effects of an increase in the pollution tax on and q、h and θ respectively, as 𝑑𝑑 𝑑𝑑. 𝑑ℎ 𝑑𝑑. 𝑑𝑑 𝑑𝑑. 1. 𝐻. (4.13). 1. 𝐻. (4.14). = 𝐷 [𝜋ℎ𝑒 𝜋𝜃𝜃 𝐶ℎ � 𝑞 − 𝐻𝑞 � − 𝜋𝑞𝑞 𝐷2 ] 3. = 𝐷 �𝜋𝑞𝑞 𝜋𝜃𝜃 𝐶ℎ � 𝑞 − 𝐻𝑞 � − 𝜋𝑞𝑞 𝜋𝜃𝜃 𝜋ℎ𝑒 � =. 3. 𝐶𝜃ℎ 𝐻 𝐷3. 𝐻. �𝜋𝑞𝑞 𝐶ℎ � 𝑞 − 𝐻𝑞 � − 𝜋𝑞𝑞 𝜋ℎ𝑒 �. (4.15). 2 where 𝐷3 is the relevant Hessian determinant; 𝐷3 < 0, 𝐷2 = 𝜋𝜃𝜃 𝜋ℎℎ − 𝜋ℎ𝜃 > 0 ,and 𝜋𝜃𝜃 < 0 by the second-order conditions, and 𝐶ℎ < 0.. Since the effect of a change in the pollution standard on production is important in understanding the economic forces controlling the optimal plant location and. the measurement of pollution emission, we shall address this issue first. It follows immediately from Equation (4.13) that: 𝑑𝑞 𝑑𝑞. 𝑑𝑞 𝑑𝑞. 𝑑𝑞 𝑑𝑞. <0 <0 ⋛0. 𝑖𝑖. 𝑖𝑖 𝑖𝑖. 𝐻 𝑞. 𝐻 𝑞. 𝐻 𝑞. > 𝐻𝑞. = 𝐻𝑞. < 𝐻𝑞. (4.16). When the production is DRS then exhibits three outcomes, a higher pollution. taxes may leads to a lower, invariant or higher output level. We now turn to the effect on locational choice. It follows from Equation (4.14) that: 𝑑ℎ 𝑑𝑑. 𝑑ℎ 𝑑𝑑. 𝑑ℎ 𝑑𝑑. >0 >0. ⋛0. 𝑖𝑖. 𝑖𝑖 𝑖𝑖. 𝐻 𝑞. 𝐻 𝑞. 𝐻 𝑞. > 𝐻𝑞. = 𝐻𝑞. < 𝐻𝑞. (4.17). When the production is DRS then exhibits three outcomes, a higher pollution tax. may leads closer to, invariant or farther away from the CBD. 31.

(41) According to Equations (4.8) and (4.17), we can derive:. Proposition 4.1 The output level of the firm is higher as a result of a higher pollution tax, if the production function exhibits decreasing returns to scale. The effect of pollution tax on the optimum output level is, perhaps, surprising. According to HM (2004), tax revenue is independent of a change in the distance between plant and CBD, an increase in the pollution tax rate will decrease the output level. But the above result shows at HM ， s result can not apply to the this case. The economic interpretation behind Proposition 1 is given as follows.. In this paper, the first-order condition for profit maximization of location is 𝜋ℎ = −𝑡𝑡 − 𝐶ℎ 𝐻 − 𝑒𝑒𝑚ℎ . The relationship between the firm determining the. location and the pollution level at CBD is negative correlation (𝑚ℎ < 0). In other words, the pollution tax revenue not only about output level but also have relationship the distance which between the plant location E and the CBD. As a result, it will make the output level of the firm will increase as the pollution tax rate increase if the production function is decreasing returns to scale. In Hwang and Mai (2004), is not consider space factor of the pollution tax. In other words, the pollution tax revenue is unrelated the distance h that between the plant location E and the CBD.. Lemma 4.1 (Hwang-Mai 2004): The plant location of the firms is invariant with respect to a change in the pollution functions is CRS. Nevertheless, the plant location moves closer to (farther away from) the CBD as a result of a higher pollution tax if production is DRS (IRS). 32.

(42) Proposition 4.2 The plant location of the firm is further away from the CBD as a result of a higher pollution tax, which is irrespective of the type of return to scale. The logic behind this proposition is straightforward. In Hwang and Mai (2004) , the location determine is independent with pollution tax(𝜋ℎ𝑒 = 0). In this paper, the. firm choice the location that in order to maximum profit and pollution tax are positive correlation (𝜋ℎ𝑒 > 0). We know that the plant location moves closer to the CBD can. decrease transport cost, but the distance of plant E from CBD more closer that the. amount of pollution is more higher. As a result, the effect on location choice that not only determine production function but also to depend on the relation between distance and pollution rate.. 4.2 The Impact of the Resident Utility on Pollution Taxes Next, we examine the impact of pollution taxes on the pollution level at the CBD. The pollution level measured at the CBD is lower than at the plant location and is affected by the distance between the plant location the CBD. Following Hwang and Mai (2004), the pollution level at CBD is specifies as: 𝑋 ∗ = 𝑚(ℎ)𝑋. (4.18). where X= total pollution measured at E, 𝑋 ∗ =total pollution measure at C, m(h)=relationship between the pollution at CBD and the plant location.. With. 𝑚ℎ < 0 and 𝑚ℎℎ > 0,implying that as the distance between CBD and the plant goes. up, the pollution measured at C not only declines but also declines at a decreasing rate. Then, the impact of a higher pollution tax (i.e., an increase of e) on 𝑋 ∗ is. derivable as follows: ∂𝑋 ∗ ∂e. = 𝑚𝑦𝑞 𝑞𝑒 + 𝑚ℎ ℎ𝑒 𝑦 = output effect + location effect 33. (4.19).

(43) when. 𝜕𝑋 ∗ 𝜕𝜕. < 0, there are three situations can be increase in e may lead to a lower. level of pollution measured at CBD ℎ𝑒 > 0, 𝑞𝑒 < 0. ⇨. the production function is (ALL, ALL). iii. ℎ𝑒 < 0, 𝑞𝑒 < 0. ⇨. the production function is (DRS, ALL). i.. ii. ℎ𝑒 > 0, 𝑞𝑒 < 0. ⇨. the production function is (ALL, DRS). which ℎ𝑒 > 0, 𝑞𝑒 < 0 is necessary condition can be sure be increase in e lead to a. lower level of pollution measured at CBD.. Now, we can set a function to measure the resident utility at C in Figure4. 1, is given by: G(𝑋 ∗ ) = U(𝑋 ∗ ) + se𝑋 ∗ ,. 𝑈𝑋 ∗ < 0. Where U is resident utility at CBD, and s > 0 is percent rate of the government subsidies to residents. We take partial derivative of G with respect of e to obtain. ∂G ∂e. = [𝑈𝑋 ∗ + 𝑠𝑠]. 𝜕𝑋 ∗ 𝜕𝜕. + 𝑠𝑋 ∗. (4.20). we can show 𝑈𝑋 ∗ + 𝑠𝑠 < 0,and 𝑠𝑋 ∗ > 0,. Thus, we can conclude that. Lemma 4.2 (Huang-Mai 2004): If the production function is DRS, then a higher pollution tax may increase the pollution damage to CBD residents.. Proposition 4.3 When the government protects the resident and implements pollution taxes, it will increase the utility of residents. Moreover, if the production function of plant is irrespective of the type of return to scale , than a higher pollution tax will definitely decrease the pollution to the CBD. If the Government takes pollution taxes, would increase the utility of 34.

(44) ∂G. residents� ∂e > 0�, than the pollution taxes and total pollution measure at CBD must ∂𝑋 ∗. be negatively correlated � ∂e < 0� . Form. ∂𝑋 ∗ ∂e. < 0 , we can know the necessary. condition is ℎ𝑒 > 0 and 𝑞𝑒 < 0, regardless of the plant is IRS, CRS or DRS. 4.3 Concluding Remarks. This result is quite different from Hwang and Mai (2004) who indicate that the tax revenue is independent of a change in the distance between plant and CBD case. In this paper, we show that the pollution tax revenue has positive correlation with the distance between plant and CBD. In Hwang and Mai (2004) conclusion ”Our paper has show that a stricter pollution policy such as a higher pollution tax may lead to higher pollution damage to CBD residents when the plant location is endogenous and the production technology of the firm exhibits DRS .” This statement may not hold true in our spatial model. Instead of, the government makes upgrade the resident utility if a higher pollution tax may lead a lower level of pollution measured at CBD (I.e., From (4.19), we know. 𝑑𝑞 𝑑𝑞. < 0 and. 𝑑ℎ 𝑑𝑑. ∂𝑋 ∗ ∂e. < 0) .. > 0 are necessary conditions if a. tougher pollution control usually results in less pollution damage. Further to say, a stricter pollution policy such as a higher pollution tax lead to lower pollution damage to the CBD irrespective of the type of Return to scale. Although the paper assumes the markets to be of monopoly, the intuition derived in this paper is robust in other market structures, such as oligopoly or perfect competition.. 35.

(45) CHAPTER FIVE:CONCLUSION In chapter 2, we explored the design of environmental policy under the consideration of union bargaining and homogeneous firm in duopoly. We find that emission and profit tax are imposed that the firms of two identical, the social welfare under centralized wage will be lower than the one under decentralized wages, while the environmental damage and firm’s profit under centralized wage will be higher than the one under decentralized wages. In chapter 3, we consider a mix-oligopoly situation for a homogeneous good that is supplied by a public firm and private firms and the good produced by each firms will lead to pollution. We found that even if the Government favored tax, the output of the entire market will not decreased instead also increase of total output and social welfare will also increase. In chapter 4, we consider space into the effect of a direct pollution control on the pollution damage and the pollution tax will change with location. We find that the government make upgrade the resident utility if an higher pollution tax may lead a lower level of pollution measured at CBD. Further to say, a stricter pollution policy such as a higher pollution tax lead to lower pollution damage to the CBD irrespective of the type of return to scale.. 36.

(46) REFERENCES Choi, K., (2011) “Unions, government's preference, and privatization.” Economic Modelling , 28, 2502-2508. Dragone, D., Lambertini, L. and Palestini, A., (2009). “On the non-neutrality of profit taxation in a Cournot oligopoly with environmental effects.” Unpublished paper. Mai, C.C., and Hwang, H.,(1992). “Production-Location Decision and Free Entry Oligopoly.” Journal of Urban Economics, 31, 252-271. Mai, C.C., and Hwang, H.,(2004). “The Effects of Pollution Taxes on Urban Areas with an Endogenous Plant Location.’’ Environment & Resource Economics, 29, 57-65. Mathur, V.K., (1976). “Spatial Economics Theory of Pollution Control.” Journal of Environmental Economics and Management, 3, 16-28. Mujumdar, S., Pal, D., (1998). “Effects of indirect taxation in a mixed oligopoly. ” Economics Letters, 58, 199–204. Mukherjee, A., (2010). “Product Market Cooperation, Profits and Welfare in the Presence of Labor Union. ” Journal of Competition Industry and Trade, 10, 151-160. Wang, L.F.S., Mukherjee, A. and Hsu, C.C., (2012). “To Be Unionized or Not to Be? A Case for Environment Concern and Firm Heterogeneity. ” Unpublished paper. Wang, L.F.S., and Hsu, C.C., (2012). “Environmental Taxes in Free Entry Oligopoly with Upstream Pollution Abatement .” Unpublished paper. Simpson, R.D.,(1995). “Optimal Pollution Taxation in a Cournot Duopoly.” Environment and Resource Economics, 6, 359-369. 37.

(47) APPENDIX 𝑡𝑚 − 𝑡𝑝 =. −4 + 52𝛼 + 3𝑛(−3 + 19𝛼 + 𝑛(−1 + 5𝛼)) + 8𝜏 − 2(−3𝑛(3 + 𝑛) + 8(2 + 𝑛)(4 + 3𝑛)𝛼)𝜏 (1 + 𝑛 + 4(2 + 𝑛)𝛼)(−2 + 8𝛼 + 𝑛(−3 + 6𝛼))𝜏. 𝑆𝑆 𝑚 − 𝑆𝑆 𝑝 = (−(2𝛼 2 2 (−10 + 3𝑛(3 + 𝑛)(−2 + 𝛼) + 4𝛼 + 24𝜏 + 2𝑛(23 +. 9𝑛)𝜏)(4 − 52𝛼 + 3𝑛(3 + 𝑛 − 19𝛼 − 5𝑛𝛼) − 8𝜏 + 2(−3𝑛(3 + 𝑛) + 8(2 + 𝑛)(4 + 3𝑛)𝛼)𝜏)))/(1 + 𝑛 + 4(2 + 𝑛)𝛼)2 (−2 + 8𝛼 + 𝑛(−3 + 6𝛼))2. 𝐶𝑆 𝑚 − 𝐶𝑆 𝑝 = 2(−2𝑛𝜏 − 3𝑛2 2 𝜏 − 20𝛼𝜏 − 30𝑛𝛼𝜏 − 9𝑛2 2 𝛼𝜏 + 8𝛼 2 2 𝜏. +26𝑛𝛼 2 2 𝜏 + 12𝑛2 2 𝛼 2 2 𝜏 + 4𝑛𝜏 2 2 + 6𝑛2 2 𝜏 2 2 + 48𝛼𝜏 2 2 + 76𝑛𝛼𝜏 2 2 +24𝑛2 2 𝛼𝜏 2 2) ⁄ (1 + 𝑛 + 8𝛼 + 4𝑛𝛼)(−2 − 3𝑛 + 8𝛼 + 6𝑛𝛼). 𝐸𝐸𝑚 − 𝐸𝐸𝑝 = (((−4 − 8𝛼 + 8𝜏 + 3𝑛2 (1 + 4𝛼)(−1 + 𝛼 + 2𝜏) + 8𝛼(3𝛼 + 2𝜏). +2𝑛(−4 + 8𝜏 + 𝛼(−12 + 19𝛼 + 26𝜏)))(3𝑛2 (1 + 4𝛼)(−1 + 𝛼 + 2𝜏) + 4𝛼(−5. +2𝛼 + 12𝜏) + 𝑛(−2 + 4𝜏 + 2𝛼(−15 + 13𝛼 + 38𝜏))))) ⁄ ((2(1 + 𝑛 + 4(2 + 𝑛)𝛼)2 (−2 + 8𝛼 + 𝑛(−3 + 6𝛼))2 )). 38.

(48)