This paper combines technology adoption with capital accumulation taking into account technological progress. We model this as a multi-stage optimal control problem and solve it using the corresponding maximum principle. The model with linear revenue can be solved analytically, while the model with market power is solved numerically. We obtain that investment jumps upwards right at the moment that a new technology is adopted. We find that, if the firm has market power, the firm cuts down on investment before a new technology is adopted. Furthermore, we find that larger firms adopt a new technology later.
- optimal control
- multi-stage maximum principle
- capital accumulation
- technology adoption