An Irreversible Investment Problem with a Learning-by-Doing Feature

We study a model of irreversible investment for a decision maker who has the possibility to gradually invest in a project of unknown value. In this setting, we introduce and explore a feature of “learning-by-doing,” where the learning rate of the unknown project value is increasing in the decision maker’s level of investment in the project. We show that, under some conditions on the functional dependence of the learning rate on the level of investment (the “signal-to-noise ratio”), the optimal strategy is to invest gradually in the project so that a two-dimensional sufficient statistic reflects below a monotone boundary. Moreover, this boundary is characterized as the solution of a differential problem. Finally, we also formulate and solve a discrete version of the problem, which mirrors and complements the continuous version.

Funding: This work was supported by the Swedish Research Council (Vetenskapsrådet) [Grant 2023-04692].