OPTIMAL PATTERN OF TECHNOLOGY ADOPTIONS IN A FINITE HORIZON MODEL VIA SOLVING MULTI-STAGE OPTIMAL CONTROL PROBLEMV

H. Çağrı SAĞLAM (Université Catholique de Louvain )

This paper analyzes the optimal pattern of technology adoptions under embodiment within a finite planning horizon via solving multi-stage optimal control problem. The economy is characterized by the existence of the exogenously growing technology frontier and the technology specific learning by doing. We first present the necessary conditions for $J$-stage discounted optimal control problem where J is itself a choice variable and the adjustable switching times appear as an argument of the state equation. We show that a finite planning horizon implies time varying durations for the adopted technologies to be in use. We show that optimal pattern of technology adoptions depends on the growth advantage of switching net of not only eventual learning costs but also the non-negligible obsolescence costs inherent to embodiment. We analyzed numerically the effects of changes in the planning horizon, speed of learning, rate of growth of technology and the impatience rate on the optimal number of technology upgrades and the timing of them.