Optimal transition to backstop substitutes for nonrenewable resources

We analyze the optimal transition from a primary, nonrenewable resource to a backstop substitute for a class of problems characterized by the property that the backstop cost decreases continuously as learning from R&D efforts accumulates to increase the knowledge base. The transition policy consists of the R&D process and of the time profiles of the primary and backstop resource supply rates. We find that the optimal R&D process follows a most rapid approach path (MRAP): the knowledge process associated with R&D should approach some (endogenously derived) target process as rapidly as possible and proceed along it thereafter. Thus, if the initial knowledge level is sufficiently low and the cost structure justifies R&D activities, the R&D efforts should be initiated without delay at the highest affordable rate and slow down later on. This pattern contrasts previous findings that typically recommend a single-humped R&D process with a possible initial delay.