The relationship between R & D effort rate and the pricing of an exhaustible resource

The paper attempts a study of the optimal pricing strategy of a carted 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 formulated as a differential game and closed- and open-loop Nash optimal solutions are studied using numerical and phase portrait analysis. The paper shows that the entrant’s capacity expansion rate for an open loop strategy will equal or exceed the corresponding rate for the closed-loop strategy. Using numerical analysis, it is shown that the closed-loop strategy is beneficial for both sides. It is likely that this happens because of the excess capacity creation by the entrant under the open-loop strategy. It is likely that this happens because of the excess capacity creation by the entrant under the open-loop strategy. If the terminal market share of the entrant is high, the cartel will try to prevent entry; if the terminal market share is small, the entrant will give up with minimal resistance from the cartel; and if the terminal market share is medium, the cartel might allow entry. It is most likely that the cartel’s price after entry will decrease with time.