Racing in two dimensions

In this paper we study an industry in which there is an ongoing sequence of R&D races between two firms. Firms are engaged in product innovation. Products are horizontally and vertically differentiated. There are two key characteristics/dimensions to products, and the level at which these are embodied in products can be increased by R&D. At each time firms can spend R&D on improving their product in one or both dimensions. We allow the possibility of economies scope — so R&D undertaken in one dimension can spillover to the other. The question we are interested in is whether a firm that is ahead in a single dimension but behind in another will focus all its R&D effort in the area in which it is ahead (product specialisation), or whether it will try to do R&D in both dimensions in the hope that it might get ahead in both and end up with a superproduct that dominates in both characteristics. The outcome of this R&D competition determines a Markov transition probability matrix determining the evolution of the industry. We show that when the R&D technology is characterized by constant returns then the only steady-state outcome is one in which the economy stays forever in a position in which one firm produces a super-product and the other gives up doing R&D altogether. This outcome is unaffected by the degree of economies of scope. When the R&D technology is characterised by decreasing returns, then the industry will visit all states and so will exhibit both product specialisation and superproduct dominance at various times. Now the extent of economies of scope matters and we show that the greater the extent of economies of scope, the less likely is the industry to exhibit product dominance, and the more likely it is to exhibit product specialisation.