Survey_Escrihuela-Villar_2004

Abstract

We consider a market whose demand is given by a linear inverse demand function, where P is the price and Q is total quantity supplied in the market. There are n firms competing in quantities and selling a homogeneous good4, with Q = Pn i=1 qi. The unit production cost depends on the R&D activity performed by the firm in such a way that the R&D outcome reduces the constant marginal cost of producing the final good. Where ci < a is the initial level of unit production cost of firm i, and xi is the level of firm i R&D investment, where i = 1, ..., n. That is, as indicated by the subscripts, we do not restrict firms to be equal. The R&D costs are given by ?x2 i with ? > 0. We assume ? to be equal across firms. This is done for convenience as my interest lies in how asymmetries in costs functions, and therefore in firms’ size in terms of market share, affect industrial policy and market structure. We assume in our model that R&D is strategic and it involves a two-step game. The corresponding nonstrategic model would be one in which R&D would be used only to minimize costs, and the equilibrium would be the standard cost-minimization Cournot equilibrium that would naturally arise if R&D and output were simultaneously determined. In our model, firms simultaneously choose R&D levels, these R&D levels are made known to each other, and then output levels are also simultaneously determined. In the first stage, firms choose R&D levels, and in the second stage, output levels. I look for the subgame perfect Nash equilibrium of this two stage game. To obtain the equilibrium in the first stage we make use of a technique developed in Saracho (2002) to deal with asymmetric situations. Although, in fact, firms choose the level of R&D (xi), for computational reasons it will be more convenient to think that they choose the level of its marginal cost in the production stage (di). (2) relates directly both variables. We assume also ? ? 1 , and therefore the convexity property required with respect to xi to ensure that second-order condition of firm i 0s maximization problem is satisfied. Firm i looks its final unit cost of production (di) that maximizes its profits.