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.
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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.
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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
2 2
0 1 0 1 0 0 1 1
( , ) ( ) 1( 2 )
U q q =a q +q −2 q + bq q +q 11 is assumed to be quadratic, strictly and symmetric in q and 0 q , where the parameter 1 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 bqj, ,i j=0,1 , i≠ . j
Assume that two firms have identical technologies and the production cost is represented by C q( )i =qi2,i=0,1. and carry out R&D activity could reduce the production cost x per unit, ( )i C qi −x qi i, where x denotes the volumes of R&D investment. The i 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 x( )i =xi2, 0,1.i= 12, which follows Gil-Molto et. al.
11 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.
12 Gil-Molto et. al. (2006) investigated the use of subsidies to R&D in a mixed and a private oligopoly markets.
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The consumer surplus for differentiated good is 1 02 12 0 1
( )
CS =2 q +q +bq q . The social welfare is given by
0 1
W =CS+π + π (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− percentage of shares of the multi-product firm. Following Matsumuras) 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 q 0 and q to maximize the objective function given by (3.3) 1
0 1
(1 )( )
V = sW + − s π +π (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.
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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.