Optimal development of production technology when autonomous and induced learning are present

Abstract

In this paper, we explore the effect of learning rate difference between external and internal innovation on operations improvement. We consider a certain type of production technology that must grow, either externally or internally, to maturity to be fully effective in existing production systems. For optimal operations, manufacturing firms must determine when and how much external technology in different development stages should be brought into the internal production system. Employing an optimal control model, we derive two nontrivial implications. First, the optimal dynamics to bring external technology inside the production system is sensitive to the difference between autonomous (i.e., external) and induced (i.e., internal) learning rate: the higher the internal learning rate, the more “external technology” the firm should acquire. Second, whether the optimal amount of technology acquired increases over time and/or across technology_age depends on the boundary condition that determines if an acquired technology can fully mature in time: a significant redirection of the optimal dynamics occurs around the boundary in the “ time–technology_age” space, since the technology must mature to be fully effective within a limited time period.