The stochastic learning curve: Optimal production in the presence of learning-curve uncertainty

Theoretical analyses incorporating production learning as typically deterministic costs are posited to decrease in a known, deterministic fashion as cumulative production increases. This paper introduces a stochastic learning-curve model that incorporates tandem variation in the decreasing cost function. We first consider a discrete-time, infinite-horizon, dynamic programming formulation of monopolistic production planning when costs follow a learning curve. This basic formulation is then extended to allow for random variation in the learning process. We also explore properties of the resulting optimal policies. For example, in some of the stochastic models we analyze optimal production is shown to exceed myopic production, echoing a key result from the deterministic learning-curve literature; in other of the stochastic models, however, this result does not hold, underscoring the need for extended analysis in the stochastic setting. We also provide new insights in the deterministic setting: for example, while an increase in the learning rate leads to an increase in the firm's expected profits in the deterministic case, there is not necessarily an increase in the optimal policy – faster learners do not necessarily produce more.