The Effects of R&D Externalities in a Spatial Model

This paper deals with the physical location of firms although other interpretations are also possible. It is a well-known fact that firms in certain industries tend to cluster. However, since you would expect competition to be more intense when goods are less diversified in a locational sense there must be some explanation to these observations which is not usually dealt with in standard economic theory. One striking example is of course the American west coast high-tech industry clustering in Silicon Valley, but others are not difficult to find. There is a broad range of possible explanations to these phenomena. The focus of this paper is to explore the possibilities to explain c1ustering in terms of external effects in the R&D process. This is done through the introduction of R&D investments into a version of the Hotelling spatial duopoly model. We consider only cost reducing innovations (i.e. process innovations). The investment decisions and the locational decisions are taken simultaneously. Then firms compete in prices, conditional on their choices in the first period. Marginal costs are reduced both through own investments and by spillovers from the competitor and these spillovers are decreasing in the distance between firms. The most surprising finding is that clustering will occur only if it is totally costless in terms of competition in the product market, that is, only when both firms act as unconstrained monopolists. Extending the model into an infinitely repeated game opens up the possibility to sustain locational equilibria characterized by clustering if the discount factor is large enough. This is so since the optimal collusive locational pattern implies at least some amount of c1ustering.