9 - On the optimal schedule for introducing a new technology, when there is learning by doing

Summary

Abstract

A known, time-dependent output stream can be produced by either of two technologies. We ask: What mixture of these technologies should be used to minimize the discounted present value of the cost of production? Each technology is characterized by a unit cost function that declines with experience. Typically one of these functions (the “new technology”) starts out higher, but has a lower final asymptote than the other (the “old technology”).

We show that there exists an optimal policy that never uses both technologies at once. We also show that if the two cost functions cross at most once, then there exists an optimal policy that switches at most once.

We also explore two examples. In the first example, output is constant, but the cost of the “new” technology declines exogenously while we are waiting to use it. In the second example, demand jumps abruptly from a lower to a higher constant value. A variety of optimal policies, depending on parameter values, is displayed.

Finally, we discuss what changes in assumptions might lead to optimal policies that are mixed, rather than extreme.