以纵向产品差异化模型为基础,研究了双寡头企业Cournot竞争中工艺创新与产品创新的关系.企业进行工艺创新降低了边际生产成本,为提升产品质量提供了资本和空间,激励企业进行产品创新.工艺创新实际上有两种不同效应:一、为更高质量产品的生产创造条件;二、边际成本降低引发激烈竞争促使企业采用差异化策略.前者促使双寡头企业都提高质量,而后者则鼓励差异化,导致低质量企业降低质量.研究表明:Cournot竞争下,高质量企业由于工艺创新的激励往往趋于提高产品质量,而低质量企业的决策则取决于与质量相关的成本函数.%We study the relationship between process and product innovation in this paper, which represents technological innovation in a different way. The theoretical literature represents process innovation by marginal cost reduction and product innovation by. Many contributions deal with the relationship between two innovations in the framework of horizontal product differentiation, as well as the vertical product differentiation of Bertrand competition. However, only few scholars study the relationship with Cournot competition. In this paper, we consider a vertical differentiation model with Cournot competition, which is considered to be more suitable to represent vertical product innovation (i.e. quality improvements) than horizontal ones. Furthermore, we assume a duopoly model even before the process innovation is adopted. The timing of the game is as follow. In the first stage, both firms simultaneously decide whether to adopt a freely available process innovation. In the second stage, firms simultaneously set the quality. In the final stage of the game, firms simultaneously set the outputs. Comparing with the standard vertical differentiation model, we add a stage at the beginning of the game. Namely, in the first stage firms decide whether to adopt a marginal cost reducing innovation. In this paper, two main choices concern market coverage and cost functions about quality. As for the former, we assumed a partially covered market, in which Cournot competition only occurs. This assumption is consistent with most of the literature on this subject. More crucial is the assumption on the latter choice concerning costs of quality. The literature of vertical product differentiation can be divided into two classes of models. The first one assumes that the choice of a better quality induces a higher marginal production cost. The second one assumes that a higher quality level implies a higher fixed cost which is considered suitable to describe the R&D investment. In the following sections of the paper, we will introduce the model and our analysis results. Section 1 introduces the formal model of vertical differentiation with Cournot competition and assumptions. In Section 2, we fully develop the model with variable cost of quality. First, we analyze comparative statics, uniqueness and existence of the equilibrium in the model without innovation. Then we introduce the game with innovation, both in symmetric and asymmetric cases. Analogously, Section 3 solves the model with fixed quality cost. In Section 4, some remarks are used to conclude the paper. The subgame perfect equilibrium is found using backwards induction. The assumption on quality cost affects results. In a duopoly with variable costs of quality, the quality of firm H and production differentiation increase, if a process innovation is available. Product quality of firm L increases in the case of equiproportional process innovation but decreases in the case of disproportional one. Differently, in a duopoly with fixed costs of quality, the results depend on the initial marginal production costs. A process innovation makes the leader firm increase its quality level and the follower one decrease it if the marginal production cost is also low before adoption. Conversely, if the marginal production cost is high before adoption, both firms will improve their quality level, but in the case of reducing vertical differentiation. The economic reason for our results is that a process innovation has two different effects. It induces reduction in marginal production costs boosting production, which makes it more convenient to increase quality and profit. It also makes competition tougher and therefore spurs vertical differentiation. The two effects work in the same direction for the high quality firm and in the opposite one for the low quality firm. Hence, the high quality firm will always improve its quality, while the low quality firm will improve it only if the former effect is stronger than the latter.
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