異質混合寡占市場技術研發投資，補貼與併購之策略分析

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(1)國立高雄大學經濟管理研究所碩士論文. 異質混合寡占市場技術研發投資，補貼與併購之策略分析 R&D INVESTMENT, SUBSIDIZATION AND MERGER IN A DIFFERENTIATED MIXED OLIGOPOLY. 研究生：楊苔琳撰指導教授：王鳳生博士. 中華民國九十七年六月.

(2) 異質混合寡占市場技術研發投資，補貼與併購之策略分析指導教授：王鳳生教授國立高雄大學應用經濟系學生：楊苔琳國立高雄大學經濟管理所. 摘要面對快速進步、競爭愈激烈的環境，廠商勢必要採取一些策略活動來維持其優勢地位以防止被對手淘汰，其可透過併購，合資，從事研發技術(R&D)或共同研發等方式來維持其競爭力。本研究主要在一個混合寡占市場廠商從事技術研發活動下，探討廠商併購決策，策略研發活動(獨自研發或合作研發)與政府補貼政策之分析。研究結果發現在混合同質寡占市場上廠商從事技術研發活動來降低其生產成本，公民營廠商承諾合作研發且兩方議價其所研發合作投資量的比重，當公營廠商有較高的議價能力時，對整體福利是有提升的作用。此外，技術研發合作可加速技術創新、降低生產成本與重複投資成本並可達到综效(synergy effect)使廠商有更高的誘因從事研發合作。在混合異質雙占市場，廠商從事技術研發活動降低其生產成本會進而降低其併購的誘因，但沒有從事技術研發活動之廠商的併購誘因會增加，研究發現，公民營廠商同時從事 R&D 會使總產量與社會福利最高，然而，一旦有一家廠商從事技術研發活動，廠商將不會有意願併購成一家多產品廠商(multi-product firm)。存在政府干預的情況下，正廠同時對對廠商採 R&D 與產量補貼的補貼額最高，其次是對產量補貼之政策，最低的補貼額是對 R&D 補貼之政策。政府補貼政策可以降低生產不足與過度生產的問題。若政府只採用一種補貼政策，產量補貼政策優於對 R&D 投資量的補貼政策。然而，政府同時對產量與 R&D 投資量補貼(mixed-subsidized policy)不但可以解決生產不足與過度生產的問題，並可以達到最佳配置(first-best )使成本極小以達社會最適境界。關鍵字：R&D、合作研發、併購、補貼政策、產品差異化、寡占競爭 I.

(3) R&D Investment, Subsidization and Merger in a Differentiated Mixed Oligopoly Advisor: Professor Leonard F.S. Wang Department of Applied Economics National University of Kaohsiung. Student: Tai-Lin Yang Institute of Economics and Management National University of Kaohsiung. ABSTRACT. Facing rapidly progress and more competitive environment, firms have to use some strategic ways to maintain their dominant positions prevent themselves from being eliminated by rivals; they can adopt strategic activities such as merger, joint venture, R&D or cooperative R&D to keep their competitiveness. The main purpose of this dissertation is to examine the merger decisions, strategic R&D behaviors (R&D competition and R&D cooperation) as well as government subsidization policies in the presence of process innovation activities under a mixed oligopolistic market. In the presence of cost-reducing R&D under a homogeneous mixed oligopoly market, if firms commit to cooperate on R&D where two parts of firm bargaining over the weight of their joint R&D, the overall welfare will enhance provided that public firm has higher bargaining power. Moreover, cooperation on innovation activity has many advantages such as accelerate technological innovations, reduce production cost and reinvestment cost, in addition, it can achieve an effect of synergy makes firm has more incentives to do so.. II.

(4) Under a differentiated mixed duopoly market, firm engages in cost-reducing R&D to reduce its production cost makes it has lower incentive to merge, whereas it increases merger incentive in the absence of innovation activity. We found that two firms engage in R&D have the highest aggregate production as well as overall social welfare; however, once one part of firm engages in R&D activity, they would not like to merge and set up a multi-product firm which is owned by two sectors. In the government intervention policies, the government grants the most output subsidy of mixed-subsidized scheme to encourage firms engage in R&D activity, then, output subsidization scheme is lie in the middle while the lowest is the R&D subsidy. Subsidization could reduce the problems of underproduction as well as overproduction. Besides, output subsidy is better than the R&D subsidy subject to the government only use a single subsidization policy. Furthermore, mix-subsidization policy could solve these problems and achieve the first-best allocation (i.e. the market price is equal to marginal cost) which minimize the total costs and boost the social welfare to the social optimum.. Keywords: R&D, Cooperative R&D, Merger, Subsidization Policy, Product Differentiation, Oligopolistic Competition. III.

(5) CONTENTS CHAPTER ONE: INTRODUCTION…………………………………………..…………1 1.1 Strategic R&D Activity………………………………………………………………..1 1.2 Merger………………………………………………………………………………....3 1.3 Government Policies: Privatization and Subsidization…………………………….….4 1.4 Structure of Thesis…………………………………………………………………….5 C H A P T E R T W O : B A R G A I N I N G O V E R C O O P E R AT I V E R & D A N D PRIVATIZATION IN A MIXED OLIGOPOLY ……………………………..7 2.1 The Basic Model……………………….…………………………………………....8 2.2 Oligopoly Market with Non-cooperative R&D Activity….…………………….…….10 2.2.1 Mixed Oligopoly with Non-cooperative R&D……………………………………...10 2.2.2 Privatized Oligopoly with Non-cooperative R&D…………………………………..11 2.3 Oligopoly Market with Cooperative R&D Activity………………………………….12 2.3.1 Mixed Oligopoly with Cooperative R&D…………………………………………...12 2.3.2 Privatized Oligopoly with Cooperative R&D……………………………………….15 2.4 Comparisons of Market Configuration ……………………………………………...16 2.4.1 R&D Investment ……………………………………………………………………16 2.4.2 Industrial Aggregate Output …………………………………………………...17 2.4.3 Industrial Profitability of Cooperation ………………………………………..19 2.4.3 Welfare Comparison ………………………………………………………………...22. 2.5 Concluding Remarks ………………………………………………………………...25 CHAPTER THREE：R&D, MERGER AND MULTI-PRODUCT FIRM IN A DIFFERENTIATED MIXED DUOPOLY……..………………..….26 3.1 The Basic Model…………………………………………………………………27 3.2 The Decisions of Firms to Merge and Engage in R&D Activity…………………….29 3.2.1 Both Firms Engage in R&D Activity………………………………………………..29 3.2.2 Only Public Firm Engages in R&D Activity………………………………………...35 3.2.3 Only Private Firm Engages in R&D Activity………………………………………..38 3.3 Comparison and Discussion of the Results…………………………………………..41 3.4 Concluding Remarks…………………………………………………………………43. V.

(6) C H A P T E R F O U R : C O S T- R E D U C I N G R & D I N V E S T M E N T A N D SUBSIDIZATION IN A DIFFERENTIATED MIXED DUOPOLY……………..45 4.1 The Basic Model ………………………………………………………………...45 4.1.1 Unsubsidized Regime……………………………………………………………….48 4.1.2 R&D Subsidized Regime……………………………………………………………49 4.1.3 Output Subsidized Regime…………………………………………………………..50 4.1.4 Both R&D and Output Subsidized Regime …………………………………………52 4.2 Product Differentiation and Social Optimum ………………………………………54 4.3 Policy Comparisons: Output, Profit, Welfare and Subsidization…………………….55 4.4 Concluding Remarks…………………………………………………………………57 CHAPTER FIVE: CONCLUSIONS……………………………………………………..58 REFERENCES…………………………………………………………………………….60 APPENDIX A……………………………………………………………………………...64 Appendix A.1………………………….....………………………………………………64 Appendix A.2……………………………………………………….……………………65 APPENDIX B……………………………………………………………………………...66 Appendix B.1…………………………….………………………………………………66 Appendix B.2…………………………….………………………………………………66 APPENDIX C……………………………………………………………………………...67 Appendix Appendix Appendix Appendix Appendix. C.1……………….……………………………………………………………67 C.2………………….…………………………………………………………67 C.3…………………….………………………………………………………68 C.4……………………….……………………………………………………69 C.5………………………….…………………………………………………70. VI.

(7) LIST OF FIGURES AND TABLE Figure 1.1. The Structure of Thesis………………………………………………………...6. Figure 2.1. Game Structure of R&D Activity and Privatization..……………………….9. Figure 2.2. R&D Comparisons between Cooperative and Non-cooperative Regime in a Mixed Oligopoly Market…………………………..........………………...16. Figure 2.3. Output Comparisons between Cooperative and Non-cooperative R&D in a Mixed Oligopoly Market…………………………………………………….17. Figure 2.4 Output Comparisons between Privatized Competitive R&D and Mixed Non-cooperative Regime…………………………………………………….18 Figure 2.5. Profit Comparisons between Cooperative and Non-cooperative R&D in a Mixed Oligopoly Market…………………………..........………………...20. Figure 2.6. Profit Comparisons between Cooperative Mixed Market and Non-cooperative Privatized Market……………………………………………………………21. Figure 2.7. Welfare Comparisons between Cooperative and Non-cooperative R&D in a Mixed Oligopoly Market……………………………………………….22. Figure 2.8. The Dynamic Game of R&D Strategic Decision……….……………………24. Figure 3.1. Game Structure of Merger and R&D Activity………………………………..29. Figure 3.2. Illustration of Lemma 3.1…………………………………………………….32. Figure 3.3. Illustration of Lemma 3.2…………………………………………………….34. Figure 3.4. Illustration of Lemma 3.3…………………………………………………….35. Figure 3.5. Illustration of Lemma 3.4…………………………………………………….37. Figure 3.6 Illustration of Lemma 3.5…………………………………………………….40 Figure 4.1. Game Structure of Government Subsidization and R&D Activity…………...47. Figure A.1 Comparative Static Results of Bargaining Power under Cooperative R&D In a Mixed Oligopoly Market………………….…………………………….64 Figure A.2 Comparisons of Cooperative R&D between Mixed Oligopoly and. Privatized Oligopoly Market………………………………………..………65. VII.

(8) Figure C.1 Comparative Static Results of Product Differentiation with Output Subsidization………………………………………………………………68. Table 3.1. Comparative Static Results of Non-merger Scheme…………………...…...43. VIII.

(9) CHAPTER ONE: INTRODICTION When facing the pressures of liberalization and internationalization push rapidly, firms have to rapidly exalt his own competitiveness. Facing this more and more competitive environments, firms may use some strategic activities to maintain its dominant position in order to prevent themselves from being eliminated by rivals. Firms can via merger, joint venture or strategic alliance to enlarge the market scope or gain high market share. In recent years, many firms adopt research and develop activities (abbreviate R&D or process innovation) to foster technological change and improve productivity that will reduce the production costs as well as promote their competitiveness. However, a proactively technological innovation takes a tremendous of time to develop; furthermore, it is also accompanied with high risk and uncertainty. Thus, fewer firms are willing to take such a risky task unless they were be supported or granted patents by the government. Hence, government plays an important role to encourage firms engage in process innovation activities. Besides, firms could use cooperative R&D activities to reduce the reinvestment cost and maximize the innovative efficiency is also an attainable method.. 1.1 Strategic R&D Activity There are two types of innovation activities, one is process innovation and the other is product innovation. Process innovation is mean that firms can use lower production cost to produce the original products, however, product innovation is imply that firms can introduce new products or make more efforts to improve the products’ utility efficiently, thereby to increase the demand. In this dissertation, we focus on the former issue, cost-reducing process innovation.. 1.

(10) The literature on R&D1 has widely handled with the issues of cost-reducing R&D in the presence of spillovers. Gersbach and Schmutzler (2003) and Akgün and Chioveanu (2006) compared Cournot and Bertrand equilibriums in a differentiated industry and investigated how the incentives for the cost reduction depend on the degree of product substitutability and the degree of spillovers. However, Cellini and Lambertini (2004) focused on the relationship between R&D intensity and market structure, and found that the industry R&D investment monotonically increases in the number of firms. Besides, Strategic behavior of cooperative R&D had initial discussed by the seminar paper of d’Aspremont and Jacquemin (1988), who compared the cooperative R&D with R&D competition and obtained that cooperative behavior played a positive role with a few firms and characterizes by R&D activities generating spillover effects. Then, Hinloopen (2000) and Atallah (2005-1; 2005-2) analyzed R&D cooperation with spillovers, where the types of R&D cooperation are divided into R&D cartelization and RJV cartelization. Note that the only difference between two scenarios is that RJV cartelization involves information sharing, while R&D cartelization does not. They showed that the equilibrium configuration is RJV cartelization for low spillover asymmetries, R&D competition for intermediate asymmetries, and R&D cartelization for high asymmetries. Moreover, cooperation is always beneficial to firms with symmetric spillovers, whereas with asymmetric spillovers only a very limited range of spillovers make firms prefer cooperation. Above literatures all followed d’Aspremont and Jacquemin’s model (i.e. AJ model), whereas Lambertini and Roossini (2004) designed a concave R&D technology with linear cost as compared to competition such that no corner solution emerged and cooperative either in the form of a cartel or a joint venture. They found the corresponding results with aforementioned literatures. 1. Haaland and Kind (2008) and Liao (2008) extended the issue of R&D to explore the relationship between trade policy and R&D investment.. 2.

(11) 1.2 Merger The literature on horizontal mergers had resulted in a curious result. In quantity setting games without cost synergies, mergers are not typically beneficial for the merging parties unless they include the vast majority of industry participants (Salant et. al; 1983). The phenomenon is called “merger paradox”. However, Bárcena-Ruiz and Garzón (2003) considered the decision whether to merge by a private firm and a public firm in a differentiated market and set up a multi-product firm which the government owns an exogenous percentage of shares and showed that the decision to merge by firms depends on the degree of product differentiation and the percentage of the shares owned by the government. However, Nakamura and Inoue (2007) extended Bárcena-Ruiz and Garzon’s model from duopoly to oligopoly and showed that both owners of a public firm and a private firm want to merge by coordinating their shareholding ratios in the merged firm, whenever the number of the private firm is larger than a critical value, while the public firm does not want to merge without the effect of improving the productivity of the merged firm. Mukherjee (2006) assumed that there are one domestic and q foreign firm in a homogeneous market and considered the welfare effect of cross-border merger in the presence of international R&D competition. He showed that cross-border merger increases domestic welfare if the bargaining power of the foreign firm and the slope of the marginal cost of R&D are sufficiently low. Moreover, Heywood and McGinty (2008) examined a Stackelberg leader merger with followers when cost were convex and showed that such type of merger were always profitable for the participants, besides, the followers did better merging than excluded rivals. Naya (2008) analyzed merger profitability in a mixed oligopoly model and showed that there were profitable gains for the firms participating in a horizontal merger that was not a merger. 3.

(12) to a monopoly. Above works controvert the view of merger paradox and obtained the profit enhancing effect.. 1.3 Government Policies: Privatization and Subsidization It is commonly know that government intervention is inferior to the society, however, if there are some distortions or externalities in the market, government intervention is indispensable. In mixed oligopoly literature, DeFraja and Delbono (1990) modeled that the private firms maximize their profit functions while competing with a public firm that maximizes social welfare. To see the desirability of government subsidy, White (1996) founded that the optimal subsidy was the same both in the mixed oligopoly and the private oligopoly. Poyago-Theotoky (2001), Myles (2002), Tomaru (2006) and Hashimzade (2007) respectively extended White’s model from simutaneous-move to sequential-move, general setting of demand and cost function, partial privatization and heterogeneous product with price as the strategic variable and reached a surprising irrelevance result. That is, whether a public firm moved simultaneously with many private firms or it acted as a Stackelberg leader or all firms (public and privates) behave as profit−maximizers, the optimal subsidy, output, profit as well as social welfare were identical. Moreover, Kato and Tomaru (2007) showed the robustness of results in the earlier literatures for a subsidy policy in a mixed oligopoly even private firms maximize the weighted average of its own profit and other factors However, Zikos (2007-2) allowed asymmetric subsidies and got a welfare-enhancing effect; Fjell and Heywood (2003) assumed that if a private firm becomes a leader, the optimal subsidy, output and welfare were all reduced which reversed the previous irrelevance result. There had few literatures put the view on the interaction between R&D activity and. 4.

(13) subsidization policy in a mixed oligopoly market 2 , Zikos(2006) introduced R&D subsidization and the effect of privatization on welfare in mixed oligopoly and showed that if R&D subsidies are employed, privatization is welfare R&D promoting while the number of firms was sufficiently large. Then, Zikos (2007-1) investigated the sequence of the R&D moves between Cournot and Stackelberg models of fixed timing by using the observable delay game and found that public firm should carry out its investment as a Stackelberg follow rather than a leader. Gil-Moltó et. al. (2006-1) investigated a homogeneous duopoly market used of subsidies to R&D, both in a mixed and private duopoly and found that private firms should be subsidized less than mixed. Then, they (Gil-Moltó et. al. ;2006-2) extended their model to oligopoly without presence of spillovers and showed that privatization could promote welfare and R&D investments if the number of competitors was sufficiently large.. 1.4 Structure of Thesis Firms engage in R&D activity to reduce its production cost is a better way to maintain its position, however, developing a new product or technology takes a lot of time; furthermore, it is also accompanied with high risk and uncertainty. Thus, fewer firms are willing to take such a risky assignment unless they were be supported by the government or firms do some internal efforts to accrue its competitiveness. Therefore, the thesis of this dissertation is divided into two ways to discuss, one is via internal strategic behaviors of firms (e.g. merger, joint venture, cooperative R&D and so on), and the other is by means of external government intervention. That is, these compose of the issues of merger decision between public and private firm, government allowance among different regimes in the presence of cost-reducing R&D activity, and strategic cooperative R&D behaviors under a mixed oligopoly market. 2. Ishibashi and Matsumura (2005) investigated a mixed market on competitive R&D by using a standard model where each firm chooses both its innovation size and R&D expenditure. 5.

(14) The rest of chapters are organized as follows (See Figure 1.1). In Chapter 2, we evaluate the strategic cooperative R&D behaviors as well as privatization policy in a mixed oligopoly market. Chapter 3, we investigate the incentives of the merger and set up a multi-product firm provided that both public and private firm engage in cost-reducing R&D or only one part of firm engages in it. Moreover, Chapter 4 introduces the government intervention and builds up the distinct subsidized policies, which are R&D subsidy, output subsidy and mix- subsidization policies, to assess which type of grant scheme is beneficial to the overall society and conclude in Chapter 5.. Process Innovation Activity. Chapter 2. Strategic R&D Behaviors. Chapter 3. Merger Decisions. Chapter 5. Conclusions. Figure 1.1 The Structure of Thesis 6. Chapter 4. Subsidization Policies.

(15) CHAPTER TWO: BARGAINING OVER COOPERATIVE R&D AND PRIVATIZATION IN A MIXED OLIGOPOLY In recent years, Taiwan has been becoming one of the most important countries to produce or invent products such as advanced technologies, chips of semiconductor, information products and so on, who plays an irreplaceable role in highly technological industries. But how to maintain this dominant position to invent new technologies or product innovations under the more and more competitive environment is a significant issue. However, innovating on new products as well as technologies are undoubtedly spend much money, time and accompanied with highly risk. Hence, firms could use cooperative R&D activities to reduce the reinvestment cost and maximize the innovative efficiency is an attainable method.. Few studies considered the interaction between market structure with cooperative R&D. Therefore, we allow one welfare-maximizing public firm and n profit-maximizing private firms in the industry. Even if public firm plays an important role in the process of economic development, but public enterprise is prone to monopoly who is be supposed to have excess profit and doesn’t pay much attention on consumer demand than private firms. Hence, public firm gradually full privatize3 or partial privatize to evaluate industries’ efficiency. We evaluate privatization policies (privatize and non-privatize) as well as R&D strategic behaviors (cooperative R&D and competitive R&D) that we divide into four regimes to analyze the amounts of R&D investment, firms’ profitability and overall social welfare. We demonstrate that in the presence of cooperative R&D activity where two parts of firm bargaining over the weight of their joint R&D, if public firm has higher bargaining 3. Matsumura (1998) investigated a Cournot competition in mixed oligopoly and found that neither full privatization nor full nationalization was optimal under moderate conditions. Besides, Matsumura and Shimizu (2005) investigated mixed economy where public enterprises compete against private’s and examined sequential privatization of public enterprises and found that privatization increased the welfare gains of the subsequent privatizations and Fujiwara (2007) analytically derived the optimal degree of partial privatization not only in the short run with restricted entry but also in the long run with free entry.. 7.

(16) power, the overall welfare will enhance. Moreover, cooperation on innovation activity has many advantages make firms have more incentives to do so, hence, facing this rapidly progress and strongly competitive environment, firms adopt strategic cooperative R&D to maintain its position is an acceptable and feasible way. The rest of this chapter is organized as follows. Section 2.1 presents a general framework in mixed oligopoly and privatized oligopoly market of homogenous products á la Cournot competition. Section 2.2 and Section2.3 show and analyze the equilibrium outcomes among different regimes and in Section 2.4, we compare the different regimes of market configuration such as aggregate R&D, industrial profitability and overall social welfare. Finally is concluding remarks in Section 2.5.. 2.1 The Basic Model We consider a single market comprises one welfare-maximizing public firm (denote 0) and n profit-maximizing private firms (denote i, i = 1......., n. ) producing a homogeneous product. The market inverse demand function is given by. p = a − Q , where. n. Q = q0 + ∑ qi is total output. We postulate that each firm engages in cost-reducing R&D i =1. activity to reduce its production cost and there is no spillover. The production cost is quadratic and given by C j = (c − x j )q j + q 2j , j = 0,1......., n. which is follows Gil-Moltó et.. al. (2006)4 assumption that exists a diminishing return to scale to avoid the case of natural monopolies. However, engaging in cost-reducing activity is costly and R&D cost function is defined as D( x j ) = x2j , j = 0,1......., n.. 4. Gil-Moltó e.t al. (2006) investigated the use of subsidies to R&D in a mixed and a private oligopoly markets.. 8.

(17) Hence, public and private firm’s profit function are given by. (2.1.1). n. π 0 =(a − (q0 + ∑ qi ))q0 − C0 − xo2 . i =1. n. π i =(a − (q0 + ∑ qi ))qi − Ci − xi2 , i = 1, 2,....n.. (2.1.2). i =1. And the social welfare which is define as the sum of consumer and producer surplus is n n 1 W= (q0 + ∑ qi ) 2 +π 0 +∑ π i 2 i =1 i =1. (2.2). There is a three-stage game including preplay stage and basic stage: In Preplay Stage, public firm decides whether to privatize or not. In the Basic Stage, we divide into 2 stages. In Stage 1, R&D strategic stage, each firm chooses the R&D investment respectively or cooperatively and in Stage 2, market stage, knowing the levels of R&D investment, each firm simultaneously determines its output by maximizing its objective function. We use the backward induction method to get the subgame-perfect Nash equilibriums (SPNE). The time structure is provided in Figure 2.1.. Basic Stage Preplay Stage Stage 1. Stage 2 Time. Public firm decides whether to privatize or not.. Each firm decides the R&D investment, x j j = 0,1,....n.. Each firm makes the production decision q j , j = 0,1,....n.. Figure 2.1 Game Structure of R&D Activity and Privatization. 9.

(18) In the presence of R&D activity, we divide into two sections, non-cooperative R&D and cooperative R&D, to examine the R&D strategic behaviors, and in each section, public firm decides if privatize or not. Hence, we consider four regimes in this paper: (i) each firm chooses its output by maximizing its objective function and compete in R&D and output stage. This is a mixed oligopoly market with non-cooperative R&D and we use the superscript MN to denote the Cournot-Nash equilibriums; (ii) all (n+1) firms are profit-maximizers and compete in R&D and output stage. This is a standard privatized oligopoly market with non-cooperative R&D that we label PN to respresent equilibrium outcomes of this regime; in regime (iii) each firm chooses its output by maximizing its objective function and cooperate on R&D stage, whereas they compete in output stage. This is a mixed oligopoly market with cooperative R&D that we denote the equilibrium outcomes by using the superscript MC , and (iv) all (n+1) firms are profit-maximizing firms and cooperate in R&D stage to maximize their joint R&D investment, but compete in output stage. This is a privatized oligopoly market with cooperative R&D and use the superscript PC to denote the Nash equilibriums of this scheme.. 2.2 Oligopoly Market with Non-cooperative R&D Activity 2.2.1 Mixed oligopoly with non-cooperative R&D. Under the competitive R&D activity, we get the Cournot-Nash outcomes by backward induction. In output stage, we maximize (2.2) and (2.1.2) to obtain firms’ output respectively: n. q0 =. 3(a − c) + (3 + n) x0 − ∑ xi i =1. 9 + 2n. n. ; qi =. 6(a − c) − 3x0 + (9 + 2n) xi − 2∑ xi i =1. 3(9 + 2n). , i = 1, 2...n.. (2.3). In the R&D stage, we substitute (2.3) into (2.2) and (2.1.2) and differential its 10.

(19) objective functions with respect to its R&D level and have the optimal R&D:. x0 MN =. (a − c)(4n + 21) 18(a − c) ; xi MN = 2 , i = 1, 2...n. 2 6n + 56n + 105 6n + 56n + 105. (2.4). If firms compete in R&D stage, public firm will do more R&D investment than private ones ( x0 MN − xi MN =. (a − c)(3 + 4n) > 0 ). Substituting (2.3) and (2.4) into (2.1.1), (2.1.2) 6n 2 + 56n + 105. and (2.2), we get the Cournot-Nash equilibrium outcomes as follows: q0 MN =. π0. MN. (a − c)(11n + 42) 3(a − c)(9 + 2n) ; qi MN = 2 , i = 1, 2...n. 2 6n + 56n + 105 6n + 56n + 105. 21(a − c) 2 (3 + n)(21 + 5n) 18( a − c) 2 (63 + 4n(9 + 2n)) MN = ; πi = ; (6n 2 + 56n + 105) 2 (6n 2 + 56n + 105) 2. W MN =. (a − c) 2 (2205 + n(3486 + n(1727 + 6n(50 + 3n)))) . (6n 2 + 56n + 105) 2. Provided that public and private firms all compete in R&D as well as output stage, public firm’s output and profitability are large than private ones no matter the number of competitors in the industry5.. Lemma 2.1: In the presence of non-cooperative R&D activity, public firm’s R&D, output. as well as profit outweigh private ones before privatization.. 2.2.2 Privatized oligopoly with non-cooperative R&D. The industry now consists of (n+1) profit-maximizing private firms. We solve equilibriums by backward induction. In output stage, each firm maximizes its profit and obtains its respectively quantities: 5. q0 MN - qi MN =. 5( a − c )(3 + n ) 3( a − c ) 2 (6 3 + n (3 6 + 1 1 n )) >0 ; π 0MN - π iMN = > 0. 2 6n + 56n + 105 6n 2 + 56n + 105. 11.

(20) n. q0 =. 3(a − c) + (3 + n) x0 − ∑ xi i =1. 12 + 3n. n. ; qi =. 3(a − c) − x0 + (4 + n) xi − ∑ xi i =1. 12 + 3n. , i = 1, 2...n.. (2.5). At the preceding R&D stage, each firm simultaneously chooses the level of R&D by maximizing (2.1.1) and (2.1.2). After privatization, there are (n+1) profit-maximizing firms and compete in R&D, we have the following identical subgame perfect Nash equilibriums:. x0PN = xi PN =. π. PN 0. =πi. MN. 2(a − c)(3 + n) ; 42 + n(22 + 3n). 2(a −c)2[126+n(60+7n)] ; = (42+n(22+3n))2. q0 PN = qi PN =. W PN =. 3(a − c)(4 + n) ; 42 + n(22 + 3n). (a − c)2 (1+ n)[648 + n(456 + n(109 + 9n))] . (42 + n(22 + 3n))2. 2.3 Oligopoly Market with Cooperative R&D Activity 2.3.1 Mixed oligopoly with cooperative R&D. In the presence of cooperative R&D, public firm and all private firms commit to cooperate on R&D to maximize their joint R&D investment. By backward induction, in the last stage, each firm competes in output, they simultaneously choose the output by maximizing (2.1.2) and (2.2) respectively and obtain the subgame output which is present as similar as (2.3). At the preceding cooperative R&D stage, they commit to maximize the bargaining function to obtain the joint R&D investments. With allowing the symmetric solution, we assume that x0 = xi = x∗ . The bargaining function6 is the function of x∗ which is given by. 6. Bargaining between different parts of interest groups has applied to many fields, such as López and Naylor (2004), Poolsombat and Vernasca (2005) bargaining the wage between union and firm, moreover, van Witteloostuiln et. al. (2007) ,Kamaga and Nakamura (2008) bargaining over managerial contracts between owner and manager in delegation game. 12.

(21) n. β 1− β Max {Γ = W (Π) }, where Π = ∑ π i , i = 1, 2....n. x∗. (2.6). i =1. where β is the public firm’s bargaining power over R&D investment (vis á vis (1 − β ) is private’s bargaining power over R&D), β ∈ [0,1] . Public firm and private firms bargaining the weight, where public firm maximizes W , whereas private firms maximize n. aggregate profit. ∑π i =1. i. . If β =1 , all private firms do not involved in determining the level of. R&D, that is, the cooperative R&D level is fully determined by public firm. If β =0 , the joint R&D investment is completely decided by all private firms without the decision of public firm. To simplify our model, we take equation (2.6) a logarithmic type as. Max {ln Γ = β ln W + (1 − β ) ln(Π)}. 7. by monotone transformation and obtain the. ∗. x. Cournot-Nash equilibrium outcomes as follows. ∗. x MC =. (a − c)[(1539 − 891β − 8n[−321− 2n(84 + n(16 + n)) + β (171+ 2n(50 + n(12 + n)))] + Ψ] ; 2ϕ. q0MC =. 3(a − c)[8505 − 891β − 8n(−1599 − 2n(344 + n(56 + 3n)) + β (171+ 2n(50 + n(12 + n)))) − Ψ] ; 2(9 + 2n)ϕ. qiMC =. 3(a − c)[8505 − 891β − 8n(−1599 − 2n(344 + n(56 + 3n)) + β (171+ 2n(50 + n(12 + n)))) −Ψ] ; (9 + 2n)ϕ. −(a−c)2[(2673β +6(972+Ψ) +n(6093+4995β +8n(−45−2n(72+n(16+n)) +β(471+2n(86+n(15+n)))) +Ψ)) ×(3(−6561+1782β +Ψ) +n(−32283+9099β +8n(−2109−2n(240+n(25+n)) +β(771+2n(122+n(18+n))) +Ψ))] π0MC = ; [(9+2n)ϕ] 2 −(a−c)2[(1024n10(β−1)2 +1024n9(β−1)(−41+33β)+6561(−58959+11β(−1398+803β))+256n8(2857+β(−4738+1913β)). πiMC =. 7. +1024n7(6801+β(−10742+4005β))+162Ψ− ( 2379+979β)+73Ψ2 +4n2(−223697367+27β(−7616086+3070539β)−125750Ψ+ϖ] 4[ (9+2n)ϕ ] 2. Santoni (2004) presented a logarithmic type of wage bargaining function as Wi = arg max NAi ≡ (1 − z)[log(qi∗ )2 ] + z[log(Wi − m)θ qi ] , which is a weigh average of the firm’s indirect profits and union’s utility. 13.

(22) −(a−c)2(2048n11(β−1)2 +1024n10(75+β(−146+67β))+512n9(2295+β(−4630+1991β))+256n8(35191+β(−83810+34591β))+256n7 ×(116223−Ψ+β(−478478+195007β+Ψ))+128n6(−5(77559+11Ψ+ ) β(−3595918+1497749β+45Ψ))+64n5(−13575847−1247Ψ+Φ))) WMC = 8[(9+2n)ϕ ]2 where Ψ=(6707529+19039536n+21213888n2 +12239360n3 +4152416n4 +872704n5 +112640n6+8192n7+256n8 −2(9+2n)2(11+4n(3+n)) ×(27+4βn(7+n))(73+4n(9+n)) +β2(9+4n)4(11+4n(3+n))2)1/2 ; ϕ =β(9+2n)2(11+4n(3+n)) −2(2511+16n(240+n(107+n(18+n))));. ϖ =62006βΨ+Ψ2)+128n6(301211−Ψ+β(−486422+171643β +Ψ))+128n5(926269−25Ψ+β(−1787050+615021β +21Ψ))+64n3(−3242841 −2705Ψ+15β(−890966+326253β +107Ψ))+32n4(4510163−1017Ψ+β(−17199862+5982851β +721Ψ))+12n(−84601665−60958Ψ +3(1269β(−9674+4521β)+8546βΨ+Ψ2))) ; Φ=β(−18022234+8000585β +835Ψ))+32n4(−113203167−14935Ψ)+8n3(−984842271+27β(−9380614+5613363β)−200798Ψ+91982βΨ+Ψ2) +4n2(−2387575845+251903763β2+Ψ− ( 741282+19Ψ)+90β(−3536109+3247Ψ)))+27(6561(−8859+11β(−18+55β))+162Ψ− ( 219+77β)) +2n(6561(−462249+β(−30262+37543β))+162Ψ− ( 8393+3037β)+103Ψ2)+3β(−19909546+9923091β +2739Ψ))). At the situation of cooperative R&D, public firm’s output as well as profit are larger than private’s no matter the parameter β is8. Increasing the bargaining power of public firm (vis-à-vis decreasing the private firms’ bargaining power), firms’ R&D investments and outputs increase no matter the number of competitors ( n ) and bargaining power ( β ) are, but industrial profitability decrease subject to the bargaining power of public firm is high enough ( β > 0.3 ), since the increase of aggregate output outweigh the decrease of total profit makes the social welfare increase with the parameter β 9. The comparative static results of bargaining power are presented in Appendix A.1.. Lemma 2.2: In the presence of cooperative R&D activity where two parts of firm. bargaining over the weight of their joint R&D, if public firm has higher bargaining power, he will put more weight on welfare makes the overall welfare enhance.. 8. q 0M C − q iM C =. ( a − c )[ − 8 5 0 5 + 8 9 1 β + 8 n ( − 1 5 9 9 − 2 n (3 4 4 + n (5 6 + 3 n )) + β (1 7 1 + 2 n (5 0 + n (1 2 + n )))) − Ψ ] > 0; 2 (9 + 2 n )ϕ. π 0M C − π iM C =. ( a − c ) 2 [8 5 0 5 − 8 9 1 β + 8 n (1 5 9 9 − 1 7 1 β + 2 n (3 4 4 − 5 0 β + n (5 6 + 3 n − β (1 2 + n ))) + Ψ ] 2 > 0. 4[(9 + 2 n )ϕ ] 2. 9. ∂ (q0 +. n. ∑. ∂β. i =1. qi ). ∂ (π >. 0. +. n. ∑. ∂β. i =1. π i). 14.

(23) 2.3.2 Privatized oligopoly with cooperative R&D. We use backward induction to obtain the SPNE. In the last output stage, all (n+1) firms maximize its profit by maximizing (2.1.1) and (2.1.2) and get the subgame equilibrium outputs as (2.5). In R&D cooperation stage, firms maximize their joint profits, Π , which is the function of x0 and xi , considering the symmetric solution x0 = xi = xˆ .. Max xˆ. n. Π =π 0 + ∑ π i. (2.7). i =1. We obtain the unique Cournot-Nash equilibriums with strategic cooperative R&D.. xˆ PC =. 2(a − c) (a − c)(4 + n) 2(a − c)2 PC PC ; qj = ; πj = , j = 0,1,2.....n. 14 + n(8 + n) 14 + n(8 + n) 14 + n(8 + n) W PC =. ( a − c ) 2 (1 + n)(72 + n (56 + n (13 + n ))) . 2(14 + n (8 + n )) 2. We then compare the equilibrium solutions of cooperation regimes between mixed oligopoly and privatized pure oligopoly10, the aggregate R&D investment and total output are larger under mixed oligopoly market than pure oligopoly market make the former have more benefit of cost-reducing and consumer surplus, hence, have higher social welfare than privatized one. However, privatized oligopoly’s total profits are larger than mixed oligopoly’s because all (n+1) firms are profit-maximizers make them have higher profit than mixed oligopoly. We have proposition 2.1.. Proposition 2.1: If public firm decide not to privatize but cooperate on R&D strategic. stage, the aggregate R&D, outputs as well as social welfare exceed the circumstance that public firm privatize with cooperative R&D. But the total profits are smaller than all (n+1) firms engage in cooperative innovation activity. 10. See Appendix A.2. 15.

(24) 2.4 Comparisons of Market Configuration Comparing all subgame perfect Nash equilibriums between strategic cooperative R&D and R&D competition that each strategic behavior includes the mixed oligopoly and privatized pure oligopoly cases respectively. 2.4.1 R&D Investment. We first compare the condition between cooperation and non-cooperation mixed oligopoly regimes. For the view of aggregate R&D, provided that the number of private firm is sufficiently large and the bargaining power of public firm is large, the joint aggregate R&D of cooperative regime is larger than non-cooperative one in mixed market (i.e.. X MC > X MN ). Otherwise, the ranking of total R&D investment will reverse, that is, the aggregate R&D of non-cooperative condition is larger than cooperative one. See Figure 2.2.. 1. X MC > X MN. 0.45. 0.1. β. 10. XMN−XMC 0 -0.1 -0.2 0. 8. X MN > X MC. 6 n. 0.2. 4. 0.4 β 0.6. 0. 2. 0.8. n. 1. ∞. Figure 2.2 R&D Comparisons between Cooperative and Non-cooperative Regime in a Mixed Oligopoly Market. We compare four regimes between privatization policies (mixed or privatized market) and R&D strategies (cooperative or competitive R&D) of aggregate R&D investment, we have following proposition. 16.

(25) Proposition 2.2: The ranking of the total R&D among different regimes under the privatized ⎧ X PN >X MC > X MN > X PC , if n is large enough and β > 0.45. and R&D strategic policies are ⎪⎨ PN MN MC PC ⎪⎩ X >X > X > X , otherwise.. Provided that the number of private firm is sufficiently large and the bargaining power of public firm is large enough, public firm privatizes and competes in R&D stage has the highest R&D investment, the second order is the regime of mixed oligopoly with cooperative R&D and the mixed oligopoly with non-cooperative R&D scheme is lie in the third ranking, while the lowest aggregate R&D is all (n+1) firms cooperate on R&D. However, if the bargaining power of public firm is relatively small, the middle two ranking of total R&D will reverse, non-cooperative regime has higher aggregate R&D than cooperative one in a mixed market. 2.4.2 Industrial aggregate output. At first, we compare the order of cooperative and competitive R&D in a mixed oligopoly market, at the circumstance that the numbers of rivals in the market is larger enough and the bargaining power of public’s is sufficiently large, strategic cooperative R&D behavior has higher production than non-cooperative regime. See Figure 2.3.. 1 Q MC > Q MN 0.03 0.02 QMN−QMC 0.01 0 -0.01 0. 0.45. 10. β. 8 6 n. 0.2 0.4 β 0.6. QMN > QMC. 4 2. 0.8. 0. 1. n. ∞. Figure 2.3 Output Comparisons between Cooperative and Non-cooperative R&D in a Mixed Oligopoly Market 17.

(26) Second, comparing the output ranking of privatized non-cooperative regime with mixed cooperative scheme, the latter total quantity is larger than the former one subject to the private competitors is less than four or lies between four and nine attached with high bargaining power of public’s, however, the order will reverse when the number of private firm is larger than four with relatively low bargaining power or the market is relatively competitive (i.e. n ≥ 9 ). 0.02. 0.2 0 0.4 0.6 0.8 1 β. 0 QPN−QMC -0.02 -0.04 -0.06. 2. 4. 6. 8. 10. n. 1. Q MC > Q PN. β. 0. Q PN > Q MC. 4. n. 10. Figure 2.4 Output Comparisons between Privatized Competitive R&D and Mixed Non-cooperative Regime. Combining above ranking and comparing four regimes between privatization policy and R&D strategic behaviors, we obtain:. 18.

(27) Proposition 2.3: The orders of aggregate quantities among different regimes are. ⎧⎪QMC >QMN > QPN > QPC , if n ≤ 4, 0 < β < 1 or 4 > n > 9, β > 0.45. ⎨ PN MN MC PC ⎪⎩Q >Q > Q > Q , otherwise. If the market is not very competitive but the bargaining power of public firm is corresponsively large (i.e. n ≤ 4, 0 < β < 1 or 4 > n > 9, β > 0.45 ), the aggregate output of mixed market is larger than privatized oligopoly no matter they cooperate or compete on R&D. Thus, public firm not to privatize and cooperate on R&D investment has highest quantity, the second order is the regime of non-cooperative R&D under mixed oligopoly and all (n+1) firms are profit maximizing firms compete on R&D is lie in the third ranking. However, all (n+1) firms maximize their joint R&D scheme has lowest total production. If the numbers of firms are larger than nine, competing on R&D has higher output than cooperative regime irrespective of privatization or non-privatization policy.. 2.4.3 Industrial Profitability of cooperation. At first, ranking the individual profitability among privatization policies as well as strategic R&D behaviors, we have proposition 2.4: Proposition 2.4: The profit ranking of private firm among distinct regimes is. π iPC > π iPN > π iMC > π iMN . This proposition is say that the profitability of privatized oligopoly market is larger than mixed oligopoly scheme no matter they cooperate or compete on R&D, and R&D cooperation scenario is more profitable than R&D competition one. In sum, privatized scheme accompany with strategic cooperative R&D has the highest profitability among four regimes.. 19.

(28) We then compare the industrial profitability and initial concentrate on the mixed oligopoly between cooperative and non-cooperative R&D: when the competitors of private firm are more than three and the bargaining power of private firm is sufficiently small (i.e. β >0.8 ), the total profitability of mixed oligopoly with R&D competition is larger than R&D cooperation. However, if the bargaining power of private firm is higher (i.e. β < 0.8 ) or the number of private firms is less than three no matter what the parameter β is, the total profit ranking will reverse, the profitability of cooperative R&D is larger than competitive one.. 3. 1. ΠMN > ΠMC 0.8. 0.005 0 .0025 ΠMN−ΠMC 0 -0.0025 -0.005. β. 10 8. ΠMC > ΠMN. 6. 0. n. 0.2. 4. 0.4 β 0.6. 2. 0.8. 0. 1. n. ∞. Figure 2.5 Profit Comparisons between Cooperative and Non-cooperative R&D in a Mixed Oligopoly Market. Then, comparing the profit ranking of privatized non-cooperative regime with mixed cooperative scheme in Figure 2.6, the horizontal line area is the situation that the industrial profitability with cooperative R&D in mixed market is larger all (n+1) firms are profit maximizer and compete on R&D. Exclude this area, the ranking will reverse, privatized market with R&D competition is larger than cooperative mixed oligopoly.. 20.

(29) 1. 0 0 .0 4.2 0 . 6 0 1.8 β. 0.02 ΠPN−ΠMC0.01. Π PN > Π MC. β. Π MC > Π PN. 0 2. 4. 6. 8. 10 0. n. n 5. ∞. Figure 2.6 Profit Comparisons between Cooperative Mixed Market and Non-cooperative Privatized Market. Furthermore, we compare the industrial profit among four regimes of privatization policy and R&D strategic decisions, the ranking of industrial profitability among variant ⎧ ⎧⎪Π PC > Π PN I if n ( ) 6, < ⎪ ⎨ PC PN ⎪⎩Π > Π ⎪ regimes are ⎨ ⎧⎪ Π PC > Π MC ⎪ ⎪( II ) if n ≥ 6, ⎨ Π PC > Π MN ⎪⎩ ⎩. > Π MC > Π MN , β < 0.8. > Π MN > Π MC , β > 0.8. > Π MN > Π PN , β < 0.8. > Π MC > Π PN , β > 0.8.. It tells that regardless of the parameter n and β are, all firms are profit maximizing firm and maximize their joint R&D has the highest profitability. We initial concentrate on condition ( I ) , the market is not relatively competitive ( n < 6 ): if the bargaining power of private firm is large vis á vis public firm’s bargaining power is relatively small ( β <0.8 ), public firm privatize has higher profit compared with mixed oligopoly market irrespective of cooperative R&D or competitive R&D. Moreover, cooperative regime is more profitability than non-cooperative one, Π PC > Π PN > Π MC > Π MN . However, if β >0.8 , public firm has sufficiently high bargaining power, the last two ranking will reverse makes, the total profitability of competitive R&D is larger than cooperative one, Π MN > Π MC . On. 21.

(30) the condition ( II ) of the market is more competitive (i.e. n ≥ 6 ), all (n+1) firms cooperate in R&D stage have the highest profit, mixed oligopoly market with cooperative R&D scheme and mixed market with non-cooperative one are lie in the second and third ranking respectively, while all firms are profit maximizers and compete in R&D has the lowest profitability subject to the bargaining power of public firm is small ( β <0.8 ). Then, provide that the bargaining power of public firm is large, the middle to ranking will reverse, mixed competitive R&D has higher profitability than mixed cooperative R&D regime.. 2.4.3 Welfare comparison. Before comparing the welfare among four regimes, we first analyze the cooperative and non-cooperative regimes under a mixed market, all firms maximize their joint R&D has higher overall welfare compared with non-cooperative regime subject to the market is sufficiently competitive and bargaining power of public firm is larger than 0.4. Otherwise, the non-cooperative regime is larger than cooperative one. See Figure 2.7.. 1 W MC > W MN 0.005 W −W MC. MN. 10. 0 8. -0.005 6. 0. W MN > W MC. n. 0.2. 4. 0.4 β 0.6. 0.4. β. 2. 0.8 1. 0. n. ∞. Figure 2.7 Welfare Comparisons between Cooperative and Non-cooperative R&D in a Mixed Oligopoly Market. 22.

(31) Regarding the social welfare among privatization policy and strategic R&D behaviors, the following proposition can be stated: Proposition. 2.5:. The. ranking. of. the. overall. social. welfare. is. ⎧⎪W PN >W MC > W MN > W PC , if n is sufficiently large and β > 0.4. ⎨ PN MN MC PC ⎪⎩W >W > W > W , otherwise. The explanation of proposition 2.5 is clearly said that if public firm full privatize and all firms compete in R&D that each firm determines its R&D by maximizing its profit has the highest welfare no matter the parameters n and β are, while the welfare of the regime all (n+1) firms are profit maximizing firms and cooperate on R&D to maximize their joint R&D is inferior to other three cases. The middle two ranking under mixed oligopoly is determine by the parameter n and β . Provided that the market is sufficiently competitive and public firm’s bargaining power is relatively large, cooperative R&D strategy has higher welfare than R&D competition regime. However, if the bargaining power of public firm is small, the ranking of middle two regimes reverse, firms compete in R&D investment is beneficial to the social welfare. Knowing the ranking of firm’s profitability as well as social welfare among four regimes, we go on to examine whether the public firm and private firms have incentive to cooperate on R&D. The dynamic game of the decision of R&D cooperation is present in Figure 2.8. There is a two-stage game tree, the equilibrium specifies a combination of strategies that public firm has to decide whether to privatize and then each private firm choose if cooperate on R&D stage or not. By backward induction to find the subgame perfect equilibrium that corresponds to the assumption that the each player will act rationally and choose the action that gives it the highest payoff. We initial compare the individual profitability of private firm between cooperative and non-cooperative R&D of. 23.

(32) privatized and mixed oligopoly model, π iPC > π iPN > π iMC > π iMN . Regardless of public firm privatize or not, private firm will choose to cooperate to maximize their joint R&D investment compared with non-cooperative regime, in the proceeding stage, comparing the social welfare of privatized cooperative R&D with mixed cooperative R&D, since. W MC > W PC regardless of the number of players in the market as well as the bargaining power between two parts of firms, public firm would not like to privatize. Hence, we obtain the subgame perfect equilibrium (superscript **) is that public firm and private firms determine to cooperate on R&D to maximize their joint R&D investment and public firm will not decide to privatize at the same time.. Cooperate (C). (W PC , π iPC ). 2 Privatize (P) Non-Cooperate (N). (W PN , π iPN ). 1 Cooperate (C). (W MC , π iMC )**. Non-Privatize (M). 2 Non-Cooperate (N). (W MN , π iMN ). Figure 2.8 The Dynamic Game of R&D Strategic Decision R&D cooperation has an effect of synergy that it not only accelerates inventions and product innovation but also reduces the production investment cost as well as risk makes invest efficiently to reduce the marginal cost and then exalt the total production. It is note 24.

(33) that if firms select and adopt strategic cooperative R&D, each firm should sign a contract to ensure the behavior they act is identically and do not violate the contract.. Proposition 2.6: Cooperation has an effect of synergy that it not only accelerates product. innovation but also reduces the production cost as well as repeated investment cost. Moreover, it disperses the overall risk makes invest efficiently to reduce the marginal cost. Hence, public firm dose not privatize and they cooperate to maximize their joint R&D investment is the best policy.. 2.5 Concluding Remarks In this paper, we assumed that there is a single market make up of one welfare-maximizing public firm and n profit-maximizing private firms produce a homogeneous good and all firms engage in cost-reducing R&D activity without spillovers. We demonstrated that in the presence of cooperative R&D activity where two parts of firm bargaining over the weight of their joint R&D, if public firm has higher bargaining power, the overall welfare will enhance. Moreover, public privatized has higher R&D level compared with mixed market. Although it has lower output, it could set a higher price to have higher profitability, and then evaluate the overall social welfare. Under the situation that firms choose whether to cooperate or compete on R&D and public decided if privatize or not. Public firm dose not privatize and cooperative on R&D is the best policy. To sum up, cooperation on innovation activity has many advantages make firms have more incentives to do so, for instance, it could accelerate technological innovations, reduce production cost and reinvestment cost, in addition, it can achieve an effect of synergy. Hence, facing this rapidly progress and strongly competitive environment, firms adopt strategic cooperative R&D to maintain its position is a feasible way. 25.

(34) CHAPTER THREE: R&D, MERGER AND MULTI-PRODUCT FIRM IN A DIFFERENTIATED MIXED DUOPOLY. International businesses use strategic merger to maintain its dominance or obtain competitive advantages, such as time, technology, information and market access are great focus. There are many reasons that enterprises have incentives to merge with other enterprises. For instance, competitors merge with rivals in order to achieve economic of scale, cost-reducing as well as gain higher market share, moreover, they even want to obtain resources or advanced technology from opponents to enlarge market field. The strategic activities can also impede opponents to entry the market. There are many merger cases throughout the world. We take Taiwan Epister Corporation for example. Epister is a corporation which specializes in producing Light Emitting Diode (abbreviate as LED), the corporation using its own MOVPE technology to highly develop LED products and expanded it’s own market scope by merging some industries (e.g. Epitech and Highlink ) with lower threshold or exist insignificant economic of scale continuously. Up to now, Epister is the fourth LED firm all over the world. In real world, there are many merger cases are accompanied with R&D innovation activity. Hence, we combine the issues of merger and R&D activity and act Bárcena-Ruiz and Garzón’s (2003) model as a benchmark to takes pre-merge innovation activities without spillovers into consideration. The remainders of this chapter are organized as follows. Section 3.1 is the basic model including the definitions of profit and social welfare function. In Section 3.2, we set up a three-stage model and divide into three regimes to analyze the merger decisions of firms. Section 3.3 is compare the outcomes among these three distinct scenarios and finally is concluding remarks in Section 3.4.. 26.

(35) 3.1 The Basic Model We consider there are two firms in an industry: One is public firm and the other one is private firm denoted by 0 and 1 respectively. They produce a differentiated product. The utility. function. of. the. representative. consumer. is. given. by. 1 U (q0 , q1 ) = a(q0 + q1 ) − (q0 2 + 2bq0 q1 + q12 ) 11 is assumed to be quadratic, strictly and 2 symmetric in q0 and q1 , where the parameter b measures the degree of horizontal differentiation between the goods; the good are completely independent if b = 0 , while they are homogeneous provided that b = 0 . We only focus on substitutes case and assume that 0 < b < 1 . The inverse demand function is given by: pi = a − qi − bq j , i, j = 0,1 , i ≠ j .. Assume that two firms have identical technologies and the production cost is represented by C (qi ) = qi2 , i = 0,1. and carry out R&D activity could reduce the production. cost xi per unit, C (qi ) − xi qi , where xi denotes the volumes of R&D investment. The amounts of R&D and effective cost reduction move in the same direction, the more of R&D they carry on, the more of production costs they save. However, engaging in R&D activity is costly and R&D cost function is D( xi ) = xi2 , i = 0,1. 12, which follows Gil-Molto et. al. (2006) assumption. The profit function of firm i is. Max π i = pi qi − C (qi ),. i, j = 0,1, without R & D activity. qi. π i = pi qi − C (qi ) + xi qi − xi , i, j = 0,1, with R & D activity *. 11. 12. 2. (3.1). Singh and Vives (1984) analyzed the duality of prices and quantities in a differentiated duopoly, and showed that Bertrand competition results in larger output, consumer surplus and welfare, and lower prices than Cournot competition. Moreover, Zanchettin (2006) extended the Singh and Vives’ model by allowing for a wider range of cost. Gil-Molto et. al. (2006) investigated the use of subsidies to R&D in a mixed and a private oligopoly markets. 27.

(36) 1 The consumer surplus for differentiated good is CS = (q0 2 + q12 ) + bq0 q1 . The social 2 welfare is given by W = CS + π 0 + π 1. (3.2). Private firm chooses the output by maximizing the profit function which is given by (3.1), while the public firm determines the output by maximizing the social welfare given by (3.2). Two firms decide whether to merge and set up a multi-product firm. If they choose to merge, we assume that the government owns s percentage of shares vis á vis private one owns (1 − s ) percentage of shares of the multi-product firm. Following Matsumura 13 (1998), we consider a firm who is jointly owned by two sectors, the public and private sectors, and maximize the weight average of social welfare and their corresponding profit. We should note that both private and public firm are owned by domestic shareholders. Hence, for a merger case, the multi-product firm of two sectors choose their own output q0 and q1 to maximize the objective function given by (3.3). V = sW + (1 − s )( π 0 + π 1 ). (3.3). In the presence of R&D activity, we consider three regimes: (i) both public firm and private firm engage in R&D activity; (ii) only public firm engages in R&D activity and (iii) only private firm engages in R&D activity and propose a three-stage game including preplay stage and basic stage. In the preplay stage, firms decide whether to merge and set up a multi-product firm which is jointly owned by two sectors. In basic stage, we divide into 2 stages. Stage 1, each firm chooses the amount of R&D once it decides to carry out R&D 13. Matsumura (1998) argued that with the exception of the USA, he observed many firms with a mixture of private and public ownership and showed that this type of firm is a reasonable choice for the government in a mixed duopoly with single product firm. 28.

(37) activity. Stage 2, the single product firm or the multi-product firm make the production decision. We can get the subgame-perfect Nash equilibrium (SPNE) by using backward induction method. The time structure is provided in Figure 3.1.. Basic Stage Preplay Stage Stage 1. Stage 2 Time. Firms decide whether to merge and set up a multi-product firm. Each firm decides the amounts of R&D x0 and x1 , respectively.. Each firm simultaneously makes the production decision q0 and q1 .. Figure 3.1 Game Structure of Merger and R&D Activity. 3.2 The Decisions of Firms to Merge and Engage in R&D activity In each regime, there are two cases to analyze, that is the firms’ action whether to merge and set up a multi-product firm. In Case I, both firms do not merge in a mixed duopoly that we denoted this case by the superscript N ; in Case II, two firms decide to merge and build up a multi-product firm and denoted this case by the superscript M .. 3.2.1 Both firms engage in R&D activity Case I: Public and private firms do not merge. We use backward induction method to get the equilibrium solutions. In Stage 2, public and private firm simultaneously choose the output by maximizing (3.2) and (3.1). At proceeding R&D Stage, they choose the level of R&D investment by maximizing its 29.

(38) objective function, (3.2) and (3.1) respectively; we get the subgame outcome of R&D: x0N =. a (b3 − 3b 2 − 15b + 42) 6a(−2b + 5) ; x1N = 4 4 2 2b − 45b + 210 2b − 45b 2 + 210. (3.4). Substituting (3.4) into (3.1), (3.2) and subgame outcome of quantity, we have: q0N =. π0N =. a (2b3 − 8b 2 − 25b + 84) a(2b − 5)(b 2 − 12) N ; q = ; 1 2b 4 − 45b 2 + 210 2b 4 − 45b 2 + 210. a2 (b + 3)(b2 −8b +14)(3b3 −11b2 − 40b +126) 2a2 (−2b + 5)2 (b4 − 24b2 +126) N = π ; ; 1 (2b4 − 45b2 + 210)2 (2b4 − 45b2 + 210)2. WN =. a 2 (8b 7 − 22b 6 − 300b5 + 789b 4 + 3660b3 − 9543b 2 − 12960b + 33840) . 2(2b 4 − 45b 2 + 210) 2. And from x0N − x1N =. a(b3 − 3b 2 − 3b + 12) a (b + 3)(3b − 8) > 0 ; q0N − q1N = − 4 > 0 , it is 4 2 2b − 45b + 210 2b − 45b 2 + 210. easy to get that the more amounts of R&D investment would have more production costs to save makes it has higher output. From the above results, we know that the public firm has higher amounts of R&D investment than private firm. Hence, the public firm’s output is unambiguously higher than the private one regardless of the parameter values (eg. De Fraja and Delbono, 1989；White, 1996； Poyago-Theotoky, 2001…etc.). Case II : Public and private firm merge and set up a multi-product firm Solving the equilibrium results by backward induction. In last Stage, each firm simultaneously chooses the output level by maximizing (3.3) and in Stage 1, they choose the R&D investment by maximizing (3.3). We obtain the following Cournot-Nash equilibriums: x0M = x1M =. Q M = q0M + q1M =. a 2a ; q0M = q1M = ; 4b − 2s(b +1) + 7 4b − 2s(b + 1) + 7. 4a 2a 2 [4b − 4 s (b + 1) + 7] ; Π M = π 0M + π 1M = ; [2 s + 2b( s − 2) − 7]2 4b − 2s (b + 1) + 7. 30.

(39) WM =. 4a 2 (b + 1) . [2 s + 2b( s − 2) − 7]2. We then analyze whether two firms want to merge and set up a multi-product firm: From the perspective of the private firm, if two firms merge, the private firm owns (1 − s) percentage of shares of the multi-product firm. Therefore, the private firm would want to merge if the profit in the multi-product firm, (1 − s )Π M , is larger than the profit in the mixed duopoly, π 1N . Let s p* and s p** denote the parameter such that (1− s)ΠM = π1N and present in Appendix 3.1. For any values of parameter b ∈ (0,1) , s p* is violate the constraint of s ∈ [0,1] . For the given value of the degree of product differentiation ( b ), ∂(1− s)ΠM a2[(4b + 7)2 − 2s(b +1)(8b +17)] = < 0 . We see ∂s (2s + 2b(s − 2) − 7)3. (1 − s )Π M decreases with the. parameter s , and obtain the Lemma 3.1.. Lemma 3.1: (1− s)ΠM > π1N if and only if s < s**p .. This lemma shows that the private firm will want to merge with the public firm if after the merger, the shareholders of the private firm owns a high enough percentage of the shares in the multi-product firm (i.e. s < s**p ), while the percentage of private firm is lower than the threshold (i.e. s > s**p ), private firm would not merge. Figure 3.2 shows the merger decision of the private firm depends on the parameter b and s . When parameter s is sufficiently low, the shareholder of the private firm will want to merge since they have high percentage of shares in the multi-product firm. When parameter s is high enough, private firm would not merger since it has lower percentage of shares in the multi-product firm after merge. When parameter s is an intermediate value, parameter b becomes important to explain the decision of the private firm whether to merge or not. If parameter b is close to zero, the degree of product differentiation is 31.

(40) sufficiently large, private firm would not like to merge since differential goods between firms make they would compete in quantity rather than merge and set up a multi-product firm. If the product is nearly homogeneous goods, private firm would like to merge while it owns more than 75 percentage of shares of the multi-product firm.. s 1 The private firm does. S=0.5792. s p (without doing. not want to merge. R&D activity). s > s**p S=0.4901. S=0.2606. s** p. The private firm wants to merge. (with doing. R&D activity). s < s *p*. 0. 1. b. Figure 3.2 Illustration of Lemma 3.1. From the Figure 3.2, the dotted line s p is the benchmark case without carrying out R&D activity. Compare line s p with line s**p , if both firms engage in cost-reducing R&D, private firm has lower incentive to merge and set up a multi-product firm with public one, because engage in R&D activity exists a benefit to reduce the production cost that transfer firms’ cost from a high cost firm to a low cost firm makes private firm prefers mixed duopoly rather than multi-product firm. The private firm might want to merge provided that it has higher percentage of shares after merge.. 32.