混合寡占下之水平併購,外資進入與內生時間之課題研究

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(1)國立高雄大學應用經濟學系(研究所) 碩士論文. 混合寡占下之水平併購,外資進入與內生時間之課題研究 Horizontal merger, Foreign Penetration, and Endogenous Timing in Mixed Oligopoly. 研究生：王歆雅撰指導教授：王鳳生博士. 中華民國 101 年 08 月.

(2) 致謝在高雄大學二年的學習時光在此劃上句點，時光飛逝得真的很快。在論文撰寫和修改的過程中，首先我要感謝我的指導老師王鳳生，即使我的理解力和實力不夠，王老師還是能對我不厭其煩地一再教導，讓我在論文上就算遇到瓶頸時，也能夠迎刃而解。這些日子裡，我在王老師身上也學到了不侷制於學業範圍的知識。還有非常感謝辛苦的口試委員李仁耀老師與楊雅博老師給予我寶貴的建議，讓我在論文修改上能夠完整地呈現出來。再來就是要感謝我的同學們，佳志、俊儫、文宏、文婷、育維、濬豪和天使詩雅姐姐，不論是遇到什麼樣的困難，大家都能一起討論及解決，也使我在學習上有很大的幫助與激勵。接下來，也要感謝姿宇姐和珮瑜姐，不論是在研討會或是其他的雜事上給予幫助。還有要感謝之前學長姐和碩一的學弟妹們，在碩一時，有學長姐給予我們大家在課業上有問題時，給予我們大家協助，則在碩二時，有學弟妹們跟我們互相激勵，使我們能夠在研究所這二年時，一切都能順利完成，也期待學弟妹們在未來也能夠順利完成論文。最後，我要感謝我的家人，在這二年之中，你們的支持和鼓勵是我繼續下去的動力，也是我最大的精神支柱。在未來，我將會期許我自己能夠有所成就，並用與行動來回報你們。. 王歆雅謹誌於國立高雄大學中華民國一百年仲夏.

(3) 混合寡占下之水平併購,外資進入與內生時間之課題研究. 指導教授：王鳳生. 博士. 國立高雄大學應用經濟系. 學生：王歆雅國立高雄大學應用經濟系. 近年來，併購為現代企業在面臨國際化和自由化的衝擊下，所必須去面對的問題。由於併購熱潮的興盛，也引發了許多人對此類議題的研究。企業併購是現今企業家所要面臨成長挑戰時，不得不面對的議題，但需要注意的是，併購對企業整體策略為手段而非目標。第二章中，我們考慮在混合寡占市場裡有三個類型的廠商。假設廠商有個遞增性成本的規模經濟模型，每個廠商都是用相同的技術製造同質性商品。在未參與併購以前，民營廠商比國營廠商在生產上較具有成本效率性，相對來說，國營廠商的利潤也會比民營廠商的利潤還低。國營廠商和任何一間民營廠商進行併購時，就社會福祉來看，參與併購後的社會福祉會高於未參與併購前的社會福祉;社會福祉減少的缺口，是會增加國營廠商進行併購的誘因。此外,我們發現民營廠商之間進行併購時，併購後的社會福祉反而會下降。第三章中，在 Stackelberg 內生時間的併購後存在著三種情況下，包含了國營廠商和無外資進入的民營廠商進行併購、國營廠商和有外資進入的民營廠商進行併購,和民營廠商之間進行併購。在每一個情況中，我們發現都會存在著一個完 I.

(4) 美子賽局 Nash 均衡解(SPNE)。. 關鍵字：水平併購、內生時間、外資進入與混合寡占. II.

(5) Horizontal merger, Foreign Penetration, and Endogenous Timing in Mixed Oligopoly Adviser：Dr. Leonard F.S. Wang Department of Applied Economics National University of Kaohsiung. Student：Hsin-ya Wang Department of Applied Economics National University of Kaohsiung. ABSTRACT In recent years, the mergers and acquisitions have become the focal issue in the presence of internationalization and liberalization. The rise of merger wave has led many economists to concern about merger issues. It should be noted that the merger on the corporate overall strategy should be taken as a mean and it is not the final target. In the first chapter, we consider a mixed oligopoly market in which there are three types of firms in the industry. We postulate that firms have increasing marginal cost and each firm produces the good using identical technology. Under pre-merger, due to that private firm is more cost efficient than the public firm, we first find that the profit of public firm is lower than the profit of another private firm. We next analyze the decision made by the public and both private firms on possible merge in the first stage of the game. The post-merger social welfare is large than the pre-merger social welfare when III.

(6) the public firm decides to merger with another private firm. Since the gap of social welfare decreases, it enhances the public firm’s incentive to merge. In addition, we find that the merger between the private firms, the social welfare after merger is lower than the social welfare before merger. In the third chapter, there are three scenarios in endogenous timing framework of Stackelberg after the merger, which are (a) public firm and a private firm without foreign penetration, (b) merger involving public firm and a private firm without foreign penetration, and (c) merger involving no public firm. We find that on each case it has an optimal Subgame Perfect Nash Equilibrium (SPNE). Keywords: Horizontal merger, Endogenous Timing, Foreign Penetration, Mixed oligopoly. IV.

(7) Contents CHAPTER ONE: Introduction 1.1 Research Background………………………………………………………………01 1.2 Literature Review…………………………………………………………………..03 CHAPTER TWO: Horizontal merger, and Foreign Penetration in Mixed Oligopoly 2.1 Introduction………………………………………………………………………..04 2.2 Basic model………………………………………………………………………...04 2.3 A pre-merger equilibrium……………………………………………………….....07 2.4 Case 1: A post-merger involving public firm and a private firm without foreign penetration…………………………………………………………………08 2.5 Case 2: A post-merger involving public firm and a private firm with foreign penetration…………………………………………………………………10 2.6 Case 3: A post-merger involving no public firm…………………………………...12 2.7 Comparative Static’s Analysis……………………………………………………..14 2.8 Comparison effects of mergers………………………………………………….....16 2.8.1 Effect on total quantity………………………………………………………17 2.8.2 Effect on Profit……………………………………………………………….17 2.8.3 Welfare effects of a merger…………………………………………………..19 2.9 Concluding Remark………………………………………………………………..23 CHAPTER THREE: Mixed oligopoly, horizontal merger and foreign penetration in a endogenous timing framework 3.1 Introduction…………………………………………………………………….......25 3.1.2 Pre-merger……………………………………………………………………25 3.1.2 Post-merger………………………………………………………………......25 3.2 Merger Involving Public Firm and a Private Firm 1 of the Perfect Nash V.

(8) Equilibrium…………………………………………………………………………27 3.2.1 The merged firm as a Stackelberg leader…………………………………….27 3.2.2 The merged firm as a Stackelberg follower………………………………….28 3.3 Merger Involving Public Firm and a Private Firm 2 of the Perfect Nash Equilibrium…………………………………………………………………………28 3.3.1 The merged firm as a Stackelberg leader……………………………………..29 3.3.2 The merged firm as a Stackelberg follower…………………………………..29 3.4 A Merger Involving No Public Firm……………………….……………………….29 3.4.1 The merged firm as a Stackelberg leader……………………………………..30 3.4.2 The merged firm as a Stackelberg follower…………………………………..30 3.5 Comparative Static’s Analysis……………………………………………………...31 3.6 The analysis of profit and welfare in Stackelberg equilibrium……………………..32 3.7 Concluding Remark………………………………………………………………...37 CHAPTER FOUR: Conclusions……………………………………………………….38 References……………………………………………………………………………...39. VI.

(9) List of Figure Figure 1：The social welfare of endogenous timing for merger between the public firm and the private firm 1…………………………………………………….......33 Figure 2：The social welfare of endogenous timing for merger between the public firm and the private firm 2……………………………………………………......35 Figure 3：The social welfare of endogenous timing for merger between the both private firms………………………………………………………………………….36. VII.

(10) List of table Table 1: Endogenous Timing of merged firm and another firm……………………….26 Table 2: Endogenous Timing equilibrium of merger between the public firm and the private firm 1………………………………………………………………….32 Table 3: Endogenous Timing equilibrium of merger between the public firm and the private firm 2………………………………………………………………….34 Table 4: Endogenous Timing equilibrium of merger between both private firms….....36. VIII.

(11) CHAPTER ONE: Introduction. 1.1 Research Background. Accompanied with the rapid progress of economic development, and the rapid transformation of investment environment.In recent years, many mergers cased often caused by a high degree of societal attention from domestic and foreign, whether in order to expand the territory of enterprise, the consolidation of market share, and the improve performance of enterprise, or the pursue of enterprises have grown rapidly and the purpose of mergers or not. There is no doubt that mergers and acquisitions have become in the face of the impact of internationalization and liberalization, it must need to face the problem. In the past, the Taiwan businessmen continue to tried various methods to reduce costs, for example, the manufacturing industries moved out in china, expand the economies of scale, and enhance the flexibility and speed of various methods, indeed, only the cost reduction has been insufficient to maintain a sustainable competitive, the enterprises in addition to have the cost of thinking, and more importantly have the value of thinking, but merger is only a means that it is not for the purpose. For example, in recent years, the Taiwan Mechanical Ship-building Business continued to acquisition of the other private firm in Taiwan. Due to the trend of liberalization and internationalization, and perhaps unbearable sustained the loss of pressure, finally, the Taiwan Mechanical Ship-building Business has been included the list of the first wave of privatization, but has accumulated the huge losses, and a heavy financial burden, that had planned to shift to layoffs substantially and factory sold to reach transfer of the privatization target. From the end of 1992, the company is fully privatized. In 1996, the. １.

(12) merger between the Taiwan Mechanical Ship-building Businesses’s Steel Products Factory and the Uni-President Enterprises Corporation. In 1997, the merger between the Taiwan Mechanical Ship-building Businesses Ships Factory and the Southeast Cement Corporation, and the merger between the Taiwan Mechanical Ship-building Businesses Alloy steel plant and the Lon Chen Fa Iron-Works Co., Ltd. The entire example above, we examine what economic theory can tell us about the rationale for merger.. 1.2 Literature Review. Due to the rise of mergers wave, lead to many people studies on such issues. Kenji Fujiwara (2010) has two papers of Horizontal Mergers and Partial Privatization in a Mixed Oligopoly I &II. Our theoretical literature on horizontal merger views Kenji Fujiwara (2010) as a point of departure. They assume that simplifying model including linear demand, constant marginal cost, a homogenous product and Cournot-Nash competition. Kenji Fujiwara (2010) I show that the merger with a sufficiently large share can be unprofitable if the degree of privatization is small enough, so the merger increases outsiders` profit and welfare-deteriorating. Kenji Fujiwara (2010) II show that a public firm is profitable if the public firm is insufficiently privatized, that the merger unambiguously raises the outsider’s profit and welfare losses. Our paper is along the line of Kenji Fujiwara’s research, but its purpose is clearly different from the predecessors. Yasuhiko Nakamura and Tomohiro Inoue (2007) assume that merged firm has two plants. They show that both owners of a public firm and a private firm want to merger by coordinating their shareholding ratio. The foreign entry into a market that have three types: foreign direct investment (FDI), exports, and foreign penetration by multinational enterprises. The idea of foreign ２.

(13) penetration to look back at Leonard F.S. Wang and Tai-Liang Chen(2011). Consider that α represents the extent of domestic ownership of multinational firm. They show that an increases in domestic ownership of multinational firm, and that raise all domestic private firm’s profit and social welfare, while if may either increase or decrease public firm’s profit. However, most of precedent theoretical literature in mixed oligopoly focused on endogenous timing that firms make quantity or price choices simultaneously or sequentially. José Méndez Naya (2011) discusses endogenous timing in a mixed oligopoly model. They show that a merger between the two private firms does not change the timing of the game, which a merger between the public firm and the private firm into a mixed firm could change the market structure from Stackelberg to Cournot competition. This thesis show that a merger between both two private firms, and a public firm and another private firm, that could improve the social welfare of no firms merge. The whole social welfare after post-merger, the social welfare of pre-merger is large than the social welfare of post-merger. The merger between the public and a private, and that the both private firm decide to merge, that the merger will change market competition from Stackelberg to Cournot competition. Under endogenous timing of post-merger, the merger could change the equilibrium of the game. The thesis is organized as follows and has four sections. Building a basic model, Chapter 2 sets up the model. We refer to Kenji Fujiwara (2010) for the cost function of the merged firm. We explore the result of the merger. In Chapter 3, we analyze the endogenous timing before and after the merger. In Chapter 4, we provide the conclusion.. ３.

(14) CHATPER Two: Horizontal Merger, and Foreign Penetration in Mixed Oligopoly 2.1 Introduction A firm desire to grow and to reorganize corporate activity via merger is ever present. One possible motivation for merging is to scale economies, and could by eliminating wasteful duplication or by improving cost inefficiency within the merged organization. However, mergers between both private firms can also be an attempt to create legal cartels. By way of introduction, it is useful to recognize that merging firm prior to their combination. In this chapter, we focus on horizontal merger. Since these reflect combinations of two or more firms in the same industry, so far as merger are concerned, market substitute products. The horizontal mergers replace two or more former competitors with a single firm. The merger of two firms in a three firm market changes the industry to a duopoly. We assume that there are a public firm and two private firms in the market. The public firms are more cost inefficient than the private firm. The public firm wants to merge with the effect of improving the productivity of the merged firm. In this chapter, we examine what economic theory can tell us about the rationale for merger. 2.2 Basic Model Consider a mixed market in which four types of firms in the industry. One of the firm is a welfare-maximizing public firm (indexed by firm 0 ), and the others are symmetric profit-maximizing private firms (indexed by firm 1 and firm 2 ). We postulate one private firm (firm1) with whole domestic stockholder and one other private firm (firm 2) with domestic and foreign stockholders. The inverse demand ４.

(15) function for the product in the domestic country is given by P = a − Q = a − (q 0 + q1 + q 2 ) ,. a>0. Where P is market price, Q is total output, q0 is the output of the domestic, q1 is the output of the private firm with whole domestic stockholder, and q 2 is the output of the private firm with domestic and foreign stockholders. Following the literature by Kenji Fujiwara (2010) consider an oligopolistic model with linear demand and constant marginal cost. We postulate that firms have increasing marginal cost represented by the quadratic function. Each firm produces the good using identical technology, represented by public firm cost function: C( q0 )= gq 02 where g≧1 is inefficiency and constant. The idea of foreign penetration to look back at Leonard F.S. Wang , Ya-Chin Wang and Lihong Zhao(2009) .Indicates that there is an efficiency gap between the public firm and private firm competitors, and the private firms are more cost efficient than the public firm. Furthermore, we allow that privatization improves the public firm’s efficiency to that of private firm’. All the private firms select their outputs to maximize their own profits which are given by C( qi )=F+ qi2 , i=1,2 Where the fixed cost F is assumed to be zero for no loss of generality. Therefore, the profit function of firm is given by:. π 0 = Pq0 − C (q0 ) = [a − (q0 + q1 + q2 )]q 0 − gq02 π i = Pqi − C (qi ) = [a − (q 0 + q1 + q 2 )]q i −qi2 ,i=1,2………………………………...(2.1) In mixed oligopoly models, it is assumed that private firms decide quantities, q1 and q 2 to maximize profits given by (2.1).. ５.

(16) The public firm chooses output level, q 0 , which aggregate domestic social welfare, which is assumed to be given by the sum of consumer’s surplus and producer’s surplus, and can be represented as follow: SW = CS + π 0 + π 1 + απ 2 where CS =. α ∈ [0,1] ………………………………………………..(2.2). 1 (q 0 + q1 + q 2 ) 2 ,and α represent the extent of domestic ownership of the 2. private firm 2. The (1-α) represent extent of foreign penetration of the private firm 2. α=1,foreign penetration are not allowed so that the private firm 2 in the market are owned by domestic stockholder. α=0, the case in which this is foreign penetration by FDI. Assume that if the public firm and one private firm decide to merger, while the public firm wants to merger with the effect of improving the productivity of the merged firm, the cost function of the merged firm is given by: 1 C M (q M ) = q M2 2. M=0,1、0,2 and 1,2. Following Yasuhiko Nakamura and Tomohiro Inoue (2007), it assume that the public firm and one of the private firms decide whether to merge and set up a multilane firm whose ownership is shared by the owners of the public and private firms. Therefore, we considering that private owners own θ percent of the shares in the merger firm, the objective function of the mixed firm is given by: V = θπ M + (1 − θ ) SW. M=0,1、0,2 and 1,2………………………………………..(2.3). We need to note that manager of fully privatized firm (θ=1) seeks the public firm’s profit, while the manager of a fully nationalized firm (θ=0) maximizes social welfare. ６.

(17) However, both private firms decide to merger that the objective function of the merged firm, the resulting from adding together both firms’ profits, it is given by: Π = π1 + π 2. (2.4). First, the firms do not merge, resulting in the competition between one public and two private firms. We denote this no merger case as N, Second, the firms this merger case is denoted as M.. 2.3 A pre-merger equilibrium. To develop the analysis, a two-stage game is stated. First examine the second stage of the game in case N. The public firm chooses q0 to maximize (2.2), Solving these maximization problems simultaneously, we obtain the Nash equilibrium in the second stage: q0N =. α (4 − α ) >0 4 + 10 g − α. q1N = q2N =. π 0N =. 2αg >0 4 + 10 g − α. α 2 g (4 − α )(2 + α ) >0 (4 + 10 g − α ) 2. π 1N = π 2N =. 8α 2 g 2 >0 (4 + 10 g − α ) 2. CS N =. α 2 [4(1 + g ) − α ]2 >0 2(4 + 10 g − α ) 2. SW N =. α 2 (4 + 8 g − α )(11 + 20 g − 3α ) >0 2(4 + 10 g − α ) 2. As a result of we assume that private firm are more cost efficient than the public firm, the profit of each private firm is larger than the profit of the public firm. Following José Méndez Naya (2011) discusses that the comprising on public firm and two private firms in a mixed oligopoly model. We assume that the decision by firms. ７.

(18) to merger in market that have three types: the merger between public firm and a private firm without foreign penetration, that the merger between public firm and a private firm with foreign penetration, and that the merger involving no public.. Proposition 2.1 Under private firm is more cost efficient than the public firm, the public firm’s profit always lower than each private firm’s profit.. Next, we analyze both the public and private firm is incentives to merge in the first stage of the game.. 2.4 Case 1: a post-merger involving the Public Firm and the Private Firm 1. This section moves on to the situation in which the public firm and a private firm without foreign penetration. Therefore, the profit function of firm is given by 1 2. π 0NF q02,1 …………………………………..(2.5) ,1 = Pq0 ,1 − C ( q0 ,1 ) = [ a − ( q0 ,1 + q 2 )]q 0 ,1 −. π 2NF = Pq2 − C (q2 ) = [a − (q0,1 + q2 )]q 2 −q22 ………………………………………….(2.6) This is assumed to be given by the sum of consumer’s surplus and producer’s surplus, and can be represented as follow: NF NF SW0NF ,1 = CS + π 0 ,1 + απ 2. α ∈ [0,1] ……………………………………………….(2.7). The aggregate domestic social welfare, which is assumed to be given by the sum of the consumer surplus, the producer surplus, and that can be represented as follow： NF NF V0NF ,1 = θπ 0 ,1 + (1 − θ ) SW0 ,1 …………………………………………………………..(2.8). ８.

(19) NF The merged firm chooses q0NF to ,1 to maximize (2.8), the private firm chooses q2. maximize (2.6). Solving these maximization problems simultaneously, we obtain the Nash equilibrium: θ0NF ,1 =. α [4 − α (1 − θ ) − θ ] >0 8 − α (1 − θ ) − 5θ. θ2NF =. α (1 − θ ) >0 8 − α (1 − θ ) − 5θ. π 0NF ,1 =. α 2 [4 − α (1 − θ ) − θ ][2 + α (1 − θ ) − 5θ ] >0 2[8 − α (1 − θ ) − 5θ ]2. π 2NF =. 2α 2 (1 − θ ) 2 >0 [8 − α (1 − θ ) − 5θ ]2. CS 0NF ,1 =. α 2 [5 − α (1 − θ ) − 2θ ]2 >0 2 [8 − α (1 − θ ) − 5θ ]2. Substituting the equation (2.5), and (2.6) into the equation (2.7) α 2 [33 − 4α (1 − θ ) − 9θ ](1 − θ ) >0 2[8 − α (1 − θ ) − 5θ ]2. SW0NF ,1 =. Where the superscript NF stands for the post-merger involving the public firm and the private firm without foreign penetration, and that the subscript 0,1 stands for the post-merger between the public firm and the private firm 1, and that the subscript 2 stands for the private firm 2. ∂SW0NF ,1 ∂θ. =. − 3α 2 (11θ + 1) =0 [8 − α (1 − θ ) − 5θ ]3. We obtain the optimal degree of privatization as：. θ ∗NF = 0. The manager of a fully nationalized firm ( θ ∗ NF =0) maximizes social welfare. We see that how the equity affects the degree of privatization and the proportion of domestic stockholding, the following expression. ９.

(20) ∂θ ∗ NF =0 ∂α. For 0 < θ ∗NF < 1 and 0 < α < 1 . The proportion of domestic stockholding unchanged as a higher degree of privatization for public firm.. Proposition 2.2 Under a merger between the public firm and the private firm 1, along with the proportion of domestic stockholding unchanged, when the public firm increase the degree of privatization.. 2.5 Case 2: a post-merger involving the Public Firm and a Private Firm 2. This section moves on to the situation in which the public firm and a private firm with foreign penetration. Therefore, the profit function of firm is given by 1 2. π 0F, 2 = Pq0, 2 − C (q0, 2 ) = [a − (q0, 2 + q1 )]q 0, 2 − q02, 2 ………………………………… (2.9). π 1F = Pq1 − C (q1 ) = [a − (q0, 2 + q1 )]q1 −q12 …………………………………………..(2.10) This is assumed to be given by the sum of consumer’s surplus and producer’s surplus, and can be represented as follow:. SW0F, 2 = CS 0F, 2 + π 1F + απ 0F, 2. α ∈ [0,1] ……………………………………………..(2.11). The aggregate domestic social welfare, which is assumed to be given by the sum of the consumer surplus, the producer surplus, and that can be represented as follow：. V0F, 2 = θπ 0F, 2 + (1 − θ ) SW0F, 2 …………………………………………………………..(2.12) The merged firm chooses q0F, 2 to maximize (2.12), the private firm chooses q1F to maximize (2.10). Solving these maximization problems simultaneously, we obtain the １０.

(21) Nash equilibrium: θ0F, 2 =. 3α [α (1 − θ ) + θ ] >0 15θ + 11α (1 − θ ) − 4. θ1F =. α [2α (1 − θ ) + 3θ − 1] >0 15θ + 11α (1 − θ ) − 4. π. F 0, 2. 9α 2 [5θ + 3α (1 − θ ) − 2][α (1 − θ ) + θ ] >0 = [15θ + 11α (1 − θ ) − 4]2. 2α 2 [1 − 2α (1 − θ ) − 3θ ]2 >0 π = [15θ + 11α (1 − θ ) − 4]2 F 1. CS. F 0, 2. α 2 [1 − 5α (1 − θ ) − 6θ ]2 >0 = 2[15θ + 11α (1 − θ ) − 4]2. Substituting the equation (2.9), and (2.10) into the equation (2.11) F 0, 2. SW. α 2 [5 + 27α 3 (1 − θ ) 2 + 36(2θ − 1) + α ((116 − 63θ )θ − 26) + α 2 (23 + (8 − 31θ )θ )] = 2[15θ + 11α (1 − θ ) − 4]2. Where the superscript F stands for the post-merger involving the public Firm and the private Firm with foreign penetration. The subscript 0,2 stand for the merger between the public firm and the private firm 2, and the subscript 1 stand for the private firm 1. The quantity of all firm may be positive, that may also be negative. We find that the quantity of all firm be positive if 0 ≤ α <. 1 4 and < θ < 1. 2 15. We then obtain the optimal degree of privatizations as：. θ ∗F =. 107 + 71α − 3α 2 180 + 74α − 3α 2. To see how the properties command that affects the degree of privatization and the proportion of domestic stockholding, we have the following expression.. ∂θ ∗F 4862 − 3α (146 + 3α ) >0 = ∂α [180 + α (74 − 3α )]2 １１.

(22) For 0 < θ ∗F < 1 and 0 < α < 1 . An increasing proportion of domestic stockholding when a high degree of privatization for public firm.. Proposition 2.3 Under a merger between the public firm and the private firm 2, along of an increasing proportion of domestic stockholding, the public firm should increase the degree of privatization.. 2.6 Case 3: a Post-Merger Involving No Public Firm. This case moves on to the situation in which the public firm and a private firm with foreign penetration. Therefore, the profit function of firm is given by. Π = π 1 + π 2 = 2[(a − (q1, 2 + q0 ))q1, 2 −q12, 2 ] …………………………………...……..(2.13). π 0 = Pq0 − C (q0 ) = [a − (q1, 2 + q0 )]q 0 − gq02 …………………………………………(2.14) This is assumed to be given by the sum of consumer’s surplus and producer’s surplus, and can be represented as follow: SW NΠ = CS + π 0 + αΠ α ∈ [0,1] ………………………………………………….(2.15). The aggregate domestic social welfare, which is assumed to be given by the sum of the consumer surplus, the producer surplus, and that can be represented as follow： NP NP V1,NP 2 = θπ 0 + (1 − θ ) SW1, 2 ………………………………………………………….(2.16). NP The merged firm chooses q1NP to , 2 to maximize (2.13), the public firm chooses q 0. maximize (2.16). Solving these maximization problems simultaneously, we obtain the Nash equilibrium: １２.

(23) θ0NP =. α [4 − 2α (1 − θ ) − θ ] >0 4 − 2α (1 − θ ) + 3θ. θ1NP ,2 =. αθ >0 4 − 2α (1 − θ ) + 3θ. π 0NP =. − α [αθ + α ( g (4 − 2α (1 − θ ) − θ ) − 4θ )][4 − 2α (1 − θ ) − θ ] <0 [4 − 2α (1 − θ ) + 3θ ]2. π 1NP ,2 =. 4α 2θ 2 >0 [4 − 2α (1 − θ ) + 3θ ]2. CS1NP ,2 =. [αθ + α (4 − 2α (1 − θ ) − θ )]2 >0 2[4 − 2α (1 − θ ) + 3θ ]2. Substituting the equation (2.13), and (2.14) into the equation (2.15). SW1,NP 2 =. αθ 2 (1 − 8α ) + 16α 2θ 2α − α 2 [4 − 2α (1 − θ ) − θ ][2α + g (8 − 4α (1 − θ ) − 2θ ) − 4 − (7 + 2α )θ ] >0 2[4 − 2α (1 − θ ) + 3θ ] 2. Where the superscript NP stands for the post-merger involving the both private firms. The subscript 1,2 stand for the merger between the both private firms, and the subscript 0 stand for the public firm. We then obtain the optimal degree of privatizations as：. θ ∗NP =. 32α 2 g (2 − α ) 2 + αθ 2 (3 + 2α )(8α − 1) 16α 2 (2 − α )[2 + g − 2(1 + g )α ]. To see how the properties command that affects the degree of privatization and the proportion of domestic stockholding, we have the following expression.. ∂θ ∗ NP 32α 2 g (2 + 3 g )(2 − α ) 2 + αθ 2 [ g (29 + (19 − 31α )α ) + 70(1 + 2(1 − α )α )] >0 = ∂α 16α 2 (2 − α ) 2 [2 + g − 2 (1 + g )α ]2. For 0 < θ ∗NP < 1 and 0 < α < 1 . The proportion of domestic stockholding increases as a higher degree of privatization for public firm. １３.

(24) Proposition 2.4 Under a merger between the both private firms, along with the proportion of domestic stockholding, the governments should increase the degree of privatization.. 2.7Comparative Static’s Analysis. In the pre-merger, we first check the case that the degree of domestic stockholding. ∂q0N − 10ag <0 = ∂a (a − 10 g − 4) 2 ∂q1N ∂q2N 2ag >0 = = ∂a ∂a (a − 10 g − 4) 2 ∂π 0N 2α 2 g[3(4 − α ) + 10 g (1 − α )] >0 = ∂α (4 + 10 g − α ) 3 ∂π 1N ∂π 2N 16α 2 g 2 >0 = = ∂α ∂α (4 + 10 g − α ) 3 ∂CS N − 6α 2 g[(1 + g ) − α ] <0 = ∂α (4 + 10 g − α ) 3 ∂SW N 4α 2 g 2 (11 + 20 g − 3α ) >0 = ∂α 2(4 + 10 g − α ) 3. For a given of parameter θ, when parameter α is sufficiently high, the output of the public firm and the consumer surplus decrease as α increase, while profit of all the firms, the output of all the private firms, and social welfare increase as α increase. Although the productivity improving merger enhances social welfare within the bounds of high α.. In the post-merger between the public firm and the private firm 1, we first check the case that the degree of domestic stockholding sets up the merger. １４.

(25) ∂θ0NF ,1 ∂α. =. − 4α (1 − θ ) 2 <0 [8 − α (1 − θ ) − 5θ ]2. ∂θ2NF α (1 − θ ) 2 >0 = ∂α [8 − α (1 − θ ) − 5θ ]2 ∂π 0NF ,1 ∂α. =. α (1 − θ ) 2 [16 − 7α (1 − θ ) + 5θ ] >0 [8 − α (1 − θ ) − 5θ ]3. ∂π 2NF − 4α 3 (θ − 1)3 >0 = ∂α [8 − α (1 − θ ) − 5θ ]3 ∂CS NF − 3α 2 [5 − α (1 − θ ) − 2θ ](θ − 1) 2 <0 = ∂α [8 − α (1 − θ ) − 5θ ]3 ∂SW NF α 2 (1 − θ ) 2 [17 − 2α (1 − θ ) + θ ] >0 = ∂α [8 − α (1 − θ ) − 5θ ]3. For a given of parameter θ, the output of the merged firm, and consumer surplus decreases as α increase when the value of α is sufficiently high, that the output and profit of the private firm 2, the profit of merged firm, and social welfare increases as α increase. Although the productivity improving merger enhances social welfare within the bounds of high α.. In the post-merger between the public firm and the private firm 2, we first check the case that the degree of domestic stockholding sets up the merger. ∂θ0F, 2 ∂α. =. − 12α (1 − θ ) 2 <0 [11α (1 − θ ) + 15θ − 4]2. ∂θ1F 3α (1 − θ ) 2 >0 = ∂α [11α (1 − θ ) + 15θ − 4]2 ∂π 0F, 2 ∂α. =. 9α 2 [4 − α (1 − θ ) − 5θ ](1 − θ ) 2 >0 [11α (1 − θ ) + 15θ − 4]3. ∂π 1F 12α 2 [3θ + 2α (1 − θ ) − 1](1 − θ ) 2 >0 = ∂α [11α (1 − θ ) + 15θ − 4]3 ∂CS F 9α 2 [1 − 5α (1 − θ ) − 6θ ](1 − θ ) 2 <0 = ∂α [11α (1 − θ ) + 15θ − 4]3 ∂SW F 3α 2 [−2 + 99α 3 (1 − θ ) 3 + 27α 2 (1 − θ ) 2 (4 − 15θ ) + θ (16 − (128 − 213θ )θ ) − α (1 − θ )(34 − θ (278 − 541θ ))] >0 = ∂α [11α (1 − θ ) + 15θ − 4]3. １５.

(26) For a given of parameter θ, when parameter α is sufficiently high, the output of the merged firm and the consumer surplus decrease as α increase, while the output and profit of the private firm 1, the profit of the merged firm, and social welfare increase as α increase. Although the productivity improving merger enhances social welfare within the bounds of high α.. In the post-merger between no public firms, we first check the case that the degree of foreign penetration sets up the merger. ∂θ0NP − 8α θ (1 − θ ) <0 = ∂α [4 − 2α (1 − θ ) + 3θ ]2 ∂θ1NP ,2 ∂α. =. 2α θ (1 − θ ) >0 [4 − 2α (1 − θ ) + 3θ ]2. ∂π 0NP 2α (1 − θ )[4α(4 + g (8 − 4α (1 − θ ) − 2θ ) − 2α (1 − θ ) − 5θ )θ + αθ (−4 + 2α (1 − θ ) + 5θ )] >0 = ∂α [4 − 2α (1 − θ ) + 3θ ]3. ∂π 1NP ,2. =. ∂α ∂CS NP ∂α ∂SW NP ∂α. 16α 2 θ (1 − θ ) >0 [4 − 2α (1 − θ ) + 3θ ]3 =. =. − 6αθ [θ (α − 1) + α (4 − 2α (1 − θ ) − θ )](1 − θ ) <0 [4 − 2α (1 − θ ) + 3θ ]3 − 2[αθ 2 (7(1 + θ ) + 4α (1 − θ )) − 4α 2θ (2 g (4 − 2α (1 − θ ) − θ )(1 − θ ) − (2α (1 − θ ) + 7θ )θ )] > 0 [4 − 2α (1 − θ ) + 3θ ]3. For a given of parameter θ, the output of the public firm, and consumer surplus decreases as α increase when the value of α is sufficiently high, that the output of the merged firm , the profit of the all firms and social welfare increases as α increase. Although the productivity improving merger enhances social welfare within the bounds of high α.. 2.8 Comparison Effects of Mergers １６.

(27) 2.8.1 Effect on total quantity Case 1：Comparison the total quantity of the post-merger between the public firm and the private firm 1 and the pre-merger Q NF − Q N =. 3α [2 g (3 − α (1 − θ )) − (4 − α )(1 − θ )] >0 (4 + 10 g − α )[8 − α (1 − θ ) − 5θ ]. Case 2：Comparison the total quantity of the post-merger between the public firm and the private firm 2 and the pre-merger QF − QN =. 3α [2 g (1 + α (1 − θ )) − (4 − α )(1 − 2α (1 − θ ) − 3θ ] >0 (4 + 10 g − α )[15θ + 11α (1 − θ ) − 4]. Case 3：Comparison the total quantity of the post-merger between the both private firms and the pre-merger Q NP − Q N =. 3α [4 g (2 − α (1 − θ ) − θ ) − (4 − α )θ ] >0 (4 + 10 g − α )[4 − 2α (1 − θ ) + 3θ ]. In the three cases, the total quantity and the consumer surplus are positive correlation. There have three merger approach, the total quantity of the all post-merger is large than the total quantity of the pre-merger.. 2.8.2 Effect on Profit. Case 1：Comparison effects of the profit of the merger between the public firm and the private firm 1 and the profit of the public firm before merger.. α 2 [(100 g 2 + (4 − α ) 2 )(2 + α (1 − θ ) − 5θ )(4 − α (1 − θ ) − θ ) − 2 g (4 − α ). π. NF 0 ,1. −π. N 0. (48 + 60θ + α (12 + α 2 (1 − θ ) 2 − 48θ + 45θ 2 − 2α (2 − θ − θ 2 )))] = 2(α − 10 g − 4) 2 [8 − α (1 − θ ) − 5θ ] 2. １７. >0.

(28) N Therefore, π 0NF ,1 > π 0 for any α ∈ [0 , 1 ) and θ ∈ [0 , 1 ). The public firm and the private firm 1 decide to merge, the profit of post-merger is large than the profit of public firm. The profit increases, that which enhance the public firm incentive to merge.. Case 2：Comparison effects of the profit of the merger between the public firm and the private firm 2 and the profit of the public firm before merger.. α 2 [9 (100 g 2 + (4 − α ) 2 )(5θ + 3α (1 − θ ) − 2)(α (1 − θ ) + θ ) − 2 g (4 − α ). π 0F, 2 − π 0N =. (32 − 60θ + α (20 + 121α 2 (1 − θ ) 2 − 2α (1 − θ )(58 − 179θ ) − θ (184 − 285θ )))] >0 2(α − 10 g − 4) 2 [4 − 11α (1 − θ ) − 15θ ] 2. Therefore, π 0F, 2 > π N for any α ∈ [0 ,1 ) and θ ∈ [0 ,1 ). The public firm and the private firm 2 decide to merge, the profit after the merger is large than the profit before the merger. The profit increases, that which enhance the public firm incentive to merge.. Case 3：Comparison effects of the profit of the merger between the public firm and the private firm 1 and the profit of the merger between the public firm and the private firm 2.. α [64 + 47α 4 (1 − θ ) 4 − 80θ + 50(2 − 15θ )θ 2 + 7α 3 (1 − θ ) 3 (51θ − 26) −. π. NF 0 ,1. −π. F 0, 2. α 2 (1 − θ ) 2 (252 + 890θ − 685θ 2 ) + α (1 − θ )(176 − θ (472 + 5θ (266 − 75θ )))] >0 = [4 − 11α (1 − θ ) − 15θ ] 2 [8 − α (1 − θ ) − 5θ ] 2. F Therefore, π 0NF ,1 > π 0 , 2 for any α ∈ [0 , 1 ) and θ ∈ [0 , 1 ). １８.

(29) The profit of the public firm and the private 1 decide to merge, that is large than the profit of the public firm and the private 2 decide to merge since the proportion of foreign penetration 1-α were taken away. We analyze the public firm and the private firm 1 incentive to merge.. Case 4：Comparison effects of the profit of the public firm after the both private firm decide to merge, that and the profit of the public firm before merger.. α [−αθ (α − 10 g − 4) 2 (4 − 2α (1 − θ ) − θ ) − 2α (2(−(4 − α ) 2 (4 − 2α (1 − θ ) − θ )θ + 25 g 3 (4 − 2α (1 − θ ) − θ ) 2 − 5 g 2 (4 − 2α (1 − θ ) − θ )(−(4 − α )(2 − α ) + (24 − α (9 − 2α ))θ )). π 0NP − π 0N =. + g (4 − α )(12 (2 − α ) 2 − 4 (2 − α )(19 − 8α )θ + (51 − 4α (18 − 5α ))θ 2 ))] (α − 10 g − 4) 2 [4 − 2α (1 − θ ) + 3θ ]2. <0. π 0NP < π 0N for any α ∈ [0 ,1 ) and θ ∈ [0 ,1 ). The profit of both private firm decide to merge, that the profit of the public firm after the merger is large the profit of the public firm before the merger. Next, we analyze the public firm and another private firm incentive to merger in the first stage of the game.. Proposition 2.5 By way of merge that public firm improves cost efficiency, and the public firm and another private firm decide to merge that is profitable.. 2.8.3 Welfare effects of a merger. Case 1: Comparison effects of the post-merger Involving Public Firm and the Private Firm 1. １９.

(30) N SW0NF = ,1 − SW. α 2 [−20 g 2 (347 + 8α 2 (1 − θ ) 2 − 12α (1 − θ )(9 − 5θ ) − 5θ (86 − 31θ )) + (4 − α )(−572 + 3α 2 (1 − θ ) 2 + (712 − 239θ )θ + α (11 − 8θ )(29 − 20θ )α 2 (1 − θ )(55 − 37θ )) + 4 g. >0. (11α 3 (1 − θ ) 2 − 66α 2 (1 − θ )(3 − 2θ ) − 6(338 − 5θ (84 − 29θ )) + 3α(377 − 2θ ] 2(α − 10 g − 4) 2 [8 − α (1 − θ ) − 5θ ]2 N Therefore, SW0NF for any α ∈ ( 0 ,1) . ,1 < SW. We examine that the public firm decide to merge with the private firm 1. Since the public firm maximizing social welfare, it does not has an incentive to merge if N . Let θ1∗ and θ1∗∗ denote the values of parameter θ such that SW0NF ,1 > SW. N . SW0NF ,1 = SW. 20 g 2 (215 − 84α + 8α 2 ) + α (1260 − α (410 − (58 − 3α )α )) + g (5040 − 4α (801 − 11 (15 − α )α )) −. θ1∗ =. 144000 g 4 (4α − 21) − 9(4 − α ) 3 [277 − α (121 − 12α )] − 3600 g 3 [1654 − α (725 − 76α )] + 4 g (4 − α )[−1879452 + α (233819 − 2α (601977 − 2α (82066 − α (12479 − 11α (91 − 3α ))))) + 5 g (−360025 + α (337529 − 4α (32325 − α (6317 − 4α (155 − 6α )))))] 20 g 2 (155 − 60α + 8α 2 ) + 4 g[870 − α (570 − 11(12 − α )α )] + (4 − α )[239 − α (160 − α (37 − 3α ))]. 20 g 2 (215 − 84α + 8α 2 ) + α (1260 − α (410 − (58 − 3α )α )) + g (5040 − 4α (801 − 11 (15 − α )α )) +. θ1∗∗ =. 144000 g 4 (4α − 21) − 9(4 − α ) 3 [277 − α (121 − 12α )] − 3600 g 3 [1654 − α (725 − 76α )] + 4 g (4 − α )[−1879452 + α (233819 − 2α (601977 − 2α (82066 − α (12479 − 11α (91 − 3α ))))) + 5 g (−360025 + α (337529 − 4α (32325 − α (6317 − 4α (155 − 6α )))))] 20 g 2 (155 − 60α + 8α 2 ) + 4 g[870 − α (570 − 11(12 − α )α )] + (4 − α )[239 − α (160 − α (37 − 3α ))]. N ∂ ( SW0NF ,1 − SW ). ∂θ. =. − 3α 2 (1 + 11θ ) <0 [8 − α (1 − θ ) − 5θ ]3. N Proposition 2.6 SW0NF if and only θ1∗ < θ < θ1∗∗ ,1 > SW. ２０.

(31) Case 2: Comparison effects of the post-merger involving public firm and the private firm 2 SW0F, 2 − SW N = − α [ −(4 − α )(27α 4 (1 − θ ) 2 − 2α 3 (1 − θ )(224 − 251θ ) − α (943 − 4566θ − 4053θ 2 ) +. α 2 (1477 − 3832θ + 2382θ 2 ) + 3(100 − θ (536 − 825θ ))) + 20 g 2 (−283 + 135α 2 (1 − θ ) 2 +. >0. 120(11 − 15θ )θ − α (1 − θ )(853 − 1123θ ) + α (574 + θ (−2764 + 2325θ ))) + 4 g (−1292 − 135α (1 − θ ) 2. 4. 2. + 270(24 − 35θ )θ − 2α 3 (1 − θ )(878 − 1013θ ) + α 2 (−5460 + 71(202 − 127θ )θ )) + α (3507 + θ (−16916 + 15075θ )))] 2(α − 10 g − 4) 2 [4 − 11α (1 − θ ) − 15θ ] 2. Therefore, SW0F, 2 > SW N for any θ ∈ ( 0 ,1 ) and α ∈ ( 0 ,1 ) .. We determine that the private firm wants to merge with the private firm 2 in the mixed oligopoly, let θ 2∗ and θ 2∗∗ denote the values of parameter θ such that SW0F, 2 = SW N .. − 48 [67 + 5 g (54 + 55 g )] + 8 [1242 + g (4229 + 3455 g )]α − [9947 + 4 g (7171 + 4940 g )]α 2 + 4 [954 + g (1891 + 675 g )]α 3 − (583 + 540 g )α 4 + 27α 5 − 3. θ 2∗ =. (α − 10 g − 4) 2 [20 g 2 (−1640 + α (−2957 + 585α 2 )) − (4 − α )(2669 + α (4035 − α (1793 − 117α )) − 4 g (9510 + α (14543 − α (6869 − 585α )))]. 20 g 2 [−1800 + α (2325 − α (1123 − 135α ))] − (4 − α )[2475 − α (4053 − α (2382 − α (502 − 27α )))] − 4 g [9450 − α (15075 − α (9017 − α (2026 − 135α ))))]. − 48 [67 + 5 g (54 + 55 g )] + 8 [1242 + g (4229 + 3455 g )]α − [9947 + 4 g (7171 + 4940 g )]α 2 + 4 [954 + g (1891 + 675 g )]α 3 − (583 + 540 g )α 4 + 27α 5 + 3. θ 2∗∗ =. (α − 10 g − 4) 2 [20 g 2 (−1640 + α (−2957 + 585α 2 )) − (4 − α )(2669 + α (4035 − α (1793 − 117α )) − 4 g (9510 + α (14543 − α (6869 − 585α )))]. 20 g 2 [−1800 + α (2325 − α (1123 − 135α ))] − (4 − α )[2475 − α (4053 − α (2382 − α (502 − 27α )))] − 4 g [9450 − α (15075 − α (9017 − α (2026 − 135α ))))]. ∂ ( SW0F, 2 − SW N ) ∂θ. =. 3α 2 [107 − 180θ + α (71 − 3α (1 − θ ) − 74θ )] <0 [15θ + 11α (1 − θ ) − 4]3. Proposition 2.7 SW0F, 2 > SW N if and only θ 2∗ < θ < θ 2∗∗. ２１.

(32) Case 3: Comparison effects of the post-merger involving no public firm. N SW1,NP = 2 − SW. − α 2 [−100 g 3 (8 − α (1 − θ ) − 2θ )(4 − 2α (1 − θ ) − θ ) − (4 − α )(4(2 − α ) 2 (−7 + 2α ) − (164 + α (13 + 8α (−9 + 2α )))θ + (−127 + 2α (7 + 2α (−5 + 2α )))θ 2 ) + 20 g 2 (−176 + 2α 3 (1 − θ ) 2 − 5α 2 (1 − θ )(8 − 5θ ) − θ (3 + 115θ ) + 2α (80 − 84θ + 33θ 2 )) + g (−2α 4 (1 − θ ) 2 + 3α 3 (1 − θ )(44 − 39θ ) + 4α (592 − θ (241 − 21θ )) − 2α 2 (480 + θ (−620 + 229θ )) =. − 8(240 + θ (222 + 263θ )))] 2(α − 10 g − 4) 2 [4 − 2α (1 − θ ) + 3θ ] 2. Therefore, θ ∈ ( 0 ,1 ) and α ∈ ( 0 ,1 ) .. N Let θ 3∗ and θ 3∗∗ denote the values of parameter θ such that SW0NF . ,1 = SW. 2α (2 − α )[(11 + 20 g − 3α )(4 + 8 g − α )(3 + 2α ) − α (α − 10 g − 4) 2 (3 + 2α + g (2 − 4α ))] − 2. θ 3∗ =. α (2 − α ) 2 (α − 10 g − 4) 2 [−(11 + 20 g − 3α )(4 + 8 g − α )(16α 2 (1 + 2 g − α ) + 8α − 1) + (α − 10 g − 4) 2 (16α 2 + 2 g + 8 (2α 2 − 1)(2 g − 1)α − 1). α (11 + 20 g − 3α )(4 + 8 g − α )(3 + 2α ) 2 − (α − 10 g − 4) 2 [8α − 1 + α 2 (7 + 2 g (1 − 2α ) 2 − 4α (7 + α ))]. 2α (2 − α )[(11 + 20 g − 3α )(4 + 8 g − α )(3 + 2α ) − α (α − 10 g − 4) 2 (3 + 2α + g (2 − 4α ))] + 2. θ 3∗∗ =. α (2 − α ) 2 (α − 10 g − 4) 2 [−(11 + 20 g − 3α )(4 + 8 g − α )(16α 2 (1 + 2 g − α ) + 8α − 1) + (α − 10 g − 4) 2 (16α 2 + 2 g + 8 (2α 2 − 1)(2 g − 1)α − 1). α (11 + 20 g − 3α )(4 + 8 g − α )(3 + 2α ) 2 − (α − 10 g − 4) 2 [8α − 1 + α 2 (7 + 2 g (1 − 2α ) 2 − 4α (7 + α ))]. Due to the merger involving the both private firms, the social welfare of merger is deteriorating, and that the profit of public firm is negative. Most of the market share taken away by the merged firm, the public firm is the commitment for the social welfare. Since the aims of the public firm maximizing social welfare, it has an incentive to merger with another private firm.. ２２.

(33) N ∂ ( SW1,NP 2 − SW ). ∂θ. =. α 2 [2(2 − α )(1 − 8α + g (64 + α )) − (131 + 64 g − (214 + 91g )α − 2(24 − g )α 2 )θ ] < 0 [4 − 2α (1 − θ ) + 3θ ]3. Proposition 2.8 Due to the profit of the public firm is negative; the social welfare of the N merger between the both private firms may be deteriorating. SW1,NP if and only 2 < SW. θ 3∗ < θ < θ 3∗∗. Case 4: Comparison welfare effects of the merger between the public firm and the private firm 1, and that the merger between the public firm and the private firm 2 F SW0NF ,1 − SW0 , 2 =. α 2 [2512 − 27α 5 (1 − θ ) 4 + α 4 (1 − θ ) 3 (409 − 301θ ) − 2α 3 (1 − θ ) 2 (909 − θ (1639 − 703θ )) − θ (11720 − θ (19144 − 45θ (274 − 45θ ))) + 2α 2 (1 − θ )(1244 − θ (4615 − θ (4486 − 1277θ ))) − α (1800 − θ (10552 − θ (19832 − 17(746 − 135θ )))] = 2(α − 10 g − 4) 2 [4 − 2α (1 − θ ) + 3θ ] 2. >0. The social welfare of the merger between the public firm and the private firm without foreign penetration is large than the social welfare of the merger between the public firm and the private firm with foreign penetration. Due to the foreign penetration 1-α taken away, the public firm choose to merger with the private firm 1, it may be profitable, and that is best strategy.. Proposition 2.9 The merger between the public firm and the private firm without foreign penetration, and is the best strategy of the public firm.. 2.9 Concluding Remark. In the chapter, we see that the effects of the post-merger equilibrium. Under the ２３.

(34) equilibriums of the post-merger, the public firm decides to merge with another the private firm, the profit after the merger is large than the profit before the merger. The public firm will have incentives to merge, if the profit and social welfare increases after the merger. An increase in the degree of privatization and the proportion of domestic stockholding, the social welfare of post-merger is large than the social welfare of pre-merger, due to the market price decrease, the market quantity increase, and the consumer surplus increase. When the both private firms decide to merge, the profit of the public firm is negative. In the light, the social welfare after merger is lower than the social welfare before merger. There exists a traditional merger paradox in the mixed oligopoly model since the market price increase, the market quantity increase.. ２４.

(35) CHAPTER THREE: Mixed Oligopoly, Horizontal Merger and Foreign Penetration In a Endogenous Timing Framework 3.1 Introduction 3.1.2 Pre-merger 1) There have three firms decide their quantity simultaneously. 2) The public firm as a Stackelberg leader. The public firm decides their quantity in stage 1, two firms decide their quantity in stage 2. 3) The private firm 1 as Stackelberg leader. The private firm 1 decides their quantity in sage 1, the public firm and the private firm 2 decides their quantity in stage2. 4) The private firm 2 as Stackelberg leader. The private firm 2 decides their quantity in sage 1, the public firm and the private firm 1 decides their quantity in stage2. This literature of endogenous timing in mixed oligopoly, this result from we see Naya (2009), can state that the most existing literature on mixed oligopoly, they consider that their firms make their decisions simultaneously, such a situation is not the equilibrium. In literature of Naya (2009), for example of simultaneous and sequential equilibrium, Pal (1998), there are two subgame perfect Nash equilibrium, which the private firm decides their quantity simultaneously in stage 1, and the public firm decides their quantity in other stage. 3.1.2 Post-merger In this chapter, there are three situations in Endogenous Timing of Stackelberg after the merge. In this case, three different alternative scenarios are considered: merger involving public firm and the private firm 1, merger involving public firm and the private firm 2, and merger involving no public firm.. ２５.

(36) In this context, seven alternatives scenarios should be stated to determine endogenous timing: 1) This simultaneous movement, there have two post-merger firms decide their quantity in the same stage. 2) Merged between public firm and the private firm 1 as Stackelberg leader. In this case, the private firm’s reaction functions (firm 1) are derived in stage 2, and taking into account the said reaction functions, the merged firm optimizes in stage 1. 3) Merged between public firm and the private firm 1 as Stackelberg follower. 4) Merged between public firm and the private firm 2 as Stackelberg leader. In this case, a private firm’s reaction functions (firm 2) are derived in stage 2, and taking into account the said reaction functions, the merged firm optimizes in stage 1. 5) Merged between public firm and a private firm 2 as Stackelberg follower. 6) Merged between both private firms as Stackelberg leader. Both private firms decide their quantity in stage 1, and the public firm makes its decision in stage 2. 7) Merged between both private firms as Stackelberg follower.. Table 1: Endogenous Timing of merged firm and another firm. qM qi. Leader (L). Follower (F). Case 2 Leader (L). Cournot Stackelberg Case 1. Follower (F). Cournot Stackelberg. ２６.

(37) Table 1 summarizes three cases situation with simultaneous play (LL and FF), sequential play with merged firm as leadership (LF) and sequential play with other firm as leadership (FL). In the chapter, there are two variables that play a very important role in determining the endogenous timing of the game in the stated model: the degree of foreign penetration and the degree of privatization of the mixed firm. There are six subgame perfect Nash equilibrium of the game under endogenous timing of post-merger are: the merged firm as a Stackelberg leader, and another firm as Stackelberg follower.. From the analysis of the subgame perfect Nash equilibrium in the seven scenarios, the follow result is obtained:. 3.2 Merger Involving Public Firm and a Private Firm 1 of the Perfect Nash Equilibrium. In this case, we assume that the public firm and the private firm 1 without foreign penetration decide to merger in the existing market structure, that it is a duopoly composed of a mixed firm after the merger. We have two alternative scenarios: the merged firm as a Stackelberg leader and another firm as Stackelberg leader, denoted by the superscripts NF, in equilibrium, the output level of the firms, the consumer, the profits of the firms and the social welfare are, respectively:. 3.2.1 The merged firm as a Stackelberg leader θ LNF0,1 =. α [3(5 − θ ) − 4α (1 − θ )] 31 − 4α (1 − θ ) + 9θ. θ FNF2 =. α [4 + (α − α )(1 − θ ) + 3θ ] >0 31 − 4α (1 − θ ) + 9θ ２７.

(38) π LNF0,1 =. α 2 [3(5 − θ ) − 4α (1 − θ )][10α (1 − θ ) + 3(3 − 2α (1 − θ ) + 7θ )] 2[31 − 4α (1 − θ ) + 9θ ]2. π FNF2 =. 2α 2 [4 + (α − α )(1 − θ ) + 3θ ]2 >0 [31 − 4α (1 − θ ) + 9θ ]2. CS LNF0,1 =. α 2 [19 − (3α + α )(1 − θ )]2 >0 2[31 − 4α (1 − θ ) + 9θ ]2. SWLNF 0 ,1 =. α 2 [(α − α )(1 − θ ) − 3θ − 4][−124 + α (31 − 4α )(1 − θ ) + 21θ + α (15 − 4α (1 − θ ) + 13θ )] 2 [31 − 4α (1 − θ ) + 9θ ]2. 3.2.2 The merged firm as a Stackelberg follower θ FNF0,1 =. α [8 − α (3 − θ )(1 − θ ) − (7 − θ )θ ] >0 2[4 − α (1 − θ ) − 3θ ](2 − θ ). θ LNF2 =. α (1 − θ ) >0 2[4 − α (1 − θ ) − 3θ ]. π FNF0,1 =. α 2 [8 − α (3 − θ )(1 − θ ) − (7 − θ )θ ][4 + α − 13θ + (7 − α )θ 2 ] 8(2 − θ ) 2 [4 − α (1 − θ ) − 3θ ]2. π LNF2 =. α 2 (1 − θ ) 2 4(2 − θ )[4 − α (1 − θ ) − 3θ ]. CS LNF2 =. α 2 [α (3 − θ )(1 − θ ) − 2(5 − (5 − θ )θ )] 2 >0 8(2 − θ ) 2 [4 − α (1 − θ ) − 3θ ]2. SWLNF 2 =. α 2 (1 − θ )[132 + 2α 2 (1 − θ ) 2 − θ (200 − (99 − 11θ )θ ) − 2α (1 − θ )(24 − θ (20 − 3θ ))] 8(2 − θ ) 2 [4 − α (1 − θ ) − 3θ ]2. 3.3 Merger Involving Public Firm and a Private Firm 2 of the Perfect Nash Equilibrium. In this case, we assume that the public firm and the private firm 2 with foreign penetration decide to merger in the existing market structure, that it is a duopoly composed of a mixed firm after the merger. We have two alternative scenarios: the merged firm as a Stackelberg leader and another firm as Stackelberg leader, denoted by the superscripts, F, in equilibrium, the output level of the firms, the consumer, the. ２８.

(39) profits of the firms and the social welfare are, respectively: 3.3.1 The merged firm as a Stackelberg leader α [12α (1 − θ ) + 13θ − 1] >0 40α (1 − θ ) + 53θ − 13. θ LF0, 2 = θ FF1 =. α [7α (1 − θ ) + 10θ − 3] >0 40α (1 − θ ) + 53θ − 13. π. F L 0, 2. α 2[17 − 30α (1 − θ ) − 47θ ][1 − 12α (1 − θ ) − 13θ ] >0 = 2[40α (1 − θ ) + 53θ − 13]2. π. F F1. CS. 2α 2[3 − 7α (1 − θ ) − 10θ ]2 >0 = [40α (1 − θ ) + 53θ − 13]2. F L 0, 2. α 2[4 − 19α (1 − θ ) − 23θ ]2 >0 = 2[40α (1 − θ ) + 53θ − 13]2. SWLF0, 2 =. α 2[52 + 360α 3 (1 − θ ) 2 + α 2 (1 − θ )(323 + 397θ ) − θ (424 − 929θ ) − α (303 − (1486 − 823θ )θ )] > 2[40α (1 − θ ) + 53θ − 13] 2. 0. 3.3.2 The merged firm as a Stackelberg follower θ FF 0, 2 =. α [8α (1 − θ ) + 11θ − 3][α (1 − θ ) + θ ] >0 2[5α (1 − θ ) + 7θ − 2][3α (1 − θ ) + 4θ − 1]. θ LF1 =. α [2α (1 − θ ) + 3θ − 1] >0 2[5α (1 − θ ) + 7θ − 2]. π. F F 0, 2. α 2 [3 − 8α (1 − θ ) − 11θ ]2 [3α (1 − θ ) + 5θ − 2][α (1 − θ ) + θ ] >0 = 8[5α (1 − θ ) + 7θ − 2]2 [3α (1 − θ ) + 4θ − 1]2. π. F L1. α 2 [2α (1 − θ ) + 3θ − 1]2 >0 = 4[5α (1 − θ ) + 7θ − 2]2 [3α (1 − θ ) + 4θ − 1]2. α 2 [1 + 14α 2 (1 − θ ) 2 + 4α (1 − θ )(9θ − 2) + θ (23θ − 10)]2 >0 CS = 8[5α (1 − θ ) + 7θ − 2]2 [3α (1 − θ ) + 4θ − 1]2 F L1. α 2 [5 + 192α 5 (1 − θ ) 4 + 4α 4 (1 − θ ) 3 (11 + 181θ ) − α 3 (1 − θ ) 2 (309 − θ (1066 + 359θ )) + 2α 2 (1 − θ )(104 − θ (837 − θ (1902 − 785θ ))) − θ (74 − θ (418 − θ (1066 − 1033θ ))) − α (54 − θ (650 − θ (2799 − (4856 − 2461θ )θ )))] >0 SWLF1 = 8[5α (1 − θ ) + 7θ − 2]2 [3α (1 − θ ) + 4θ − 1]2. 3.4 A Merger Involving No Public Firm In this case, we assume that the both private firm decide to merger in the existing market structure, that it is a duopoly composed of a mixed firm in the post-merger. We ２９.

(40) have two alternative scenarios: the merged firm as a Stackelberg leader and public firm as Stackelberg leader, denoted by the superscripts, NP, in equilibrium, the output level of the firms, the consumer, the profits of the firms and the social welfare are, respectively:. Case1: The merged firm as a Stackelberg leader α [2 − 2(1 − θ 2 )α + (1 − θ )θ ] >0 [2 − 2α (1 − θ ) + θ ](1 + θ ) αθ >0 = 2[2 − 2α (1 − θ ) + θ ]. θ FNP0 = θ LNP1, 2. π FNP0 =. α 2 [2 g (2 − 2α (1 − θ ) − θ ) − 3θ ][2 − 2α (1 − θ ) − θ ] >0 2[2 − 2α (1 − θ ) + θ ]2. π LNP1, 2 =. α 2θ 2 >0 [2 − 2α (1 − θ ) + θ ]2. CS LNP 1, 2 =. α 2 [4 − 4α (1 − θ ) − θ ]2 >0 8[2 − 2α (1 − θ ) + θ ]2. SWLNP 1, 2 =. α 2 [16(1 − α ) 2 − 8 (1 − α )(7 − 4α )θ + (25 − 16 (3 − α )α )θ 2 + 16 g (2 − 2α (1 − θ ) − θ ) 2 ] >0 8[2 − 2α (1 − θ ) + θ ]2. Case2: The merged firm as a Stackelberg follower θ LNP0 =. α [3(5 − θ ) − 8α (1 − θ )] >0 15 − 8α (1 − θ ) + 9θ. θ FNP1, 2 =. 3αθ >0 15 − 8α (1 − θ ) + 9θ. π LNP0 =. − α 2 [3(5 − θ ) − 8α (1 − θ )][ g (3(5 − θ ) − 8α (1 − θ )) − 9θ ] <0 [15 − 8α (1 − θ ) + 9θ ]2. π FNP1, 2 =. 18α 2θ 2 >0 [15 − 8α (1 − θ ) + 9θ ]2. CS LNP0 =. α 2 [15 − 8α (1 − θ )]2 >0 [15 − 8α (1 − θ ) + 9θ ]2 α 2 [64α 2 (1 − θ ) 2 + 9(25 + 6(5 − θ )θ ) − 12α (20 − θ (8 + 15θ )) − 2 g. SW. NP L0. (3(5 − θ ) − 8α (1 − θ )) 2 ] = 2[15 − 8α (1 − θ ) + 9θ ]2. ３０. >0.