Learning by doing in a T-period production planning: Analytical solution

The firms in many industries shift down the production cost function as they accumulate experience (learning by doing). The intertemporal production decision of the firm under learning by doing can be formulated as a Dynamic Optimization problem. Though properties of the solution to that problem are known, in general this analytical solution has not been presented in the literature. In this paper we present the analytical solution for a class of discrete time T-period learning by doing problems. This allows us to gain insight into practical aspects such as determining when current losses are expected to occur or when the firm will become fully efficient. Examples are provided.