THE RELATIONSHIP BETWEEN RESEARCH-AND-DEVELOPMENT EFFORT RATE AND THEPRICING OF AN EXHAUSTIBLE RESOURCE

We attempt a study of the optimal pricing strategy of a cartel selling an exhaustible resource and the optimal R&D effort rate of potential entrants trying to find a substitute for the resource. If entry occurs , the entrant can expand by investing in capacity. The model is formul ated as a differential game and closed- and open-loop Nash optimal sol utions are studied using numerical and phase portrait analysis. We sho w that the entrant's capacity expansion rate for an open loop strategy will equal or exceed the corresponding rate for the closed-loop strat egy. Using numerical analysis, we show that the closed-loop strategy i s beneficial for both sides. It is likely that this happens because of the excess capacity creation by the entrant under the open-loop strat egy. If the terminal market share of the entrant is high, the cartel w ill try to prevent entry; if the terminal market share is small, the e ntrant will give up with minimal resistance from the cartel; and if th e terminal market share is medium, the cartel might allow entry. It is most likely that the cartel's price after entry will decrease with ti me. (C) 1997 John Wiley & Sons, Ltd.