Optimal diffusion of a new technology when both demand and supply are nonstatic

The investment problem of a monopolized sector selling an innovated product is explored. Learning by doing is supposed to occur on the supply side, while learning by using is introduced to explain demand growth. Pontryagin's maximum principle is applied to the resulting optimal control problem, which includes supply capacity and cumulative output as state variables. The optimal investment policy turns out to be of a very simple form: all profit is retained and invested until capacity achieves its optimal size. In spite of this, the new technology price displays a variety of time patterns that heavily depend on the actual demand and cost conditions, as one would expect in the real world.The authors express their gratitude to Professor Sergio Rinaldi for helpful comments. This work was partially supported by Centro Teoria dei Sistemi, CNR, Milano, Italy.