درباره نقش سرریز ورودی و خروجی، زمانی که پروژه های "تحقیق و توسعه" دارای ریسک است

This paper analyzes the impact of input and output spillovers on the expected effective cost reductions in a two-stage model of R&D where all R&D projects are risky. It is shown that, relative to the deterministic case, output spillovers tend to reduce expected cost reductions whereas input spillovers tend to increase investment in R&D and hence expected cost reductions. In particular, the relations between cost reductions in the presence of input and output spillovers known from deterministic models may be reversed under certain parameter constellations.

During the last decade, research and development (henceforth R&D) has been one of the major fields of interest in both theoretical and applied industrial economics. Although there had been some previous studies on this subject, e.g. by Ruff (1969) and Spence (1984), most of the recent (theoretical) research was inspired by the seminal work of d’Aspremont and Jacquemin (1988) who analyzed the R&D activities of oligopolistic firms within the framework of a two-stage game.1 One of the main features of their model (henceforth referred to as the AJ model) is the presence of output spillovers which means that part of the information about a firm’s completed R&D project leaks out costlessly to its competitors who are thus able to benefit from cost reductions resulting from the successful R&D as well. A related line of research is essentially based on work by Kamien et al. (1992) whose model (henceforth the KMZ model) is formally rather similar to the AJ model but which assumes input instead of output spillovers. Here, leakages of information occur at the research stage and prior to the discovery of a new technology which does not become available to the rival firms. Despite this formal similarity, the models yield rather different results with respect to R&D performance as the AJ model implies systematically higher cost reductions through R&D than the KMZ model unless there are no spillovers.2 This surprising and important distinction between the two popular models has only recently been pointed out by Amir (2000).

In this paper we have extended the well-known models of d’Aspremont and Jacquemin (1988) and Kamien et al. (1992) to the case of a risky R&D technology. The R&D projects of both firms may fail (independent of each other) with some positive probability. When deciding upon its R&D investment or rather the intended cost reductions, each firm has to take into account the possibility that none, both, or exactly one of the firms may innovate. In this environment we have identified two very different effects of input and output spillovers. The latter act as a kind of risk sharing device because a firm whose project has failed may still benefit from cost reductions caused by its successful competitor even though its own R&D investment is lost. If a firm is the only one to be successful, on the other hand, output spillovers reduce its profits and support the rival firm. These effects tend to reduce R&D investment and hence expected effective cost reductions of both firms