A simple model of investment with an infinite number of technologies

This paper investigates technology adoption of a single firm in a continuous time model with an infinite planning horizon and an infinite number of investment opportunities. Technological progress is exogenous and modeled either by a poisson process or a geometric poisson process. For both processes, we characterize the optimal investment strategies. In the case of a poisson process we show that a cyclical investment pattern, that is adopting every m-th technology is optimal. If technological progress is modeled as a geometric poisson process, we argue that the number of technologies not adopted between two adoptions decreases with time, until finally each new technology will be adopted.