A solution Method for a Class of Learning by Doing Models

A phenomenon widely observed in industries which are in an early stage is that they reduce their costs as a result of accumulating experience, that is, they reduce their costs with their output. This is known in the economic literature as the learning by doing effect, and it was studied for the first time by Arrow in 1962. There are a lot of references about the relationship between the structure of the industry and the learning by doing effect. In general, the results available in the literature give properties of the optimal policy, but they do not find the optimal policy in a closed-form. In this paper we present a solution method that obtains the closed-form optimal policy for a class of learning by doing models. We study a model with a single agent, monopolist, without possible competition. The demand function is linear. The problem is deterministic, dynamic, with a finite time horizon and it is formulated in discrete time.