Innovation and site quality: Implications for the timing of investments in renewable energy

We study the optimal sequence of investment in renewable energy when technology improves over time and the productivity of deployed capital differs with site quality. Our perspective is that of a price- and technology-taking individual or firm. We begin with a model where the price of output produced with the technology is a known constant and technology improves according to a known differential equation. We specify an optimization problem that allows for the solution of the optimal date of initial investment and the dates for optimal replacement. We then develop models where output price evolves according to geometric Brownian motion and technology evolves deterministically or stochastically, with up-jumps (breakthroughs). The possibility of breakthroughs will further delay initial investment compared to the model where technology evolves deterministically. Our analysis is relevant for the initial investment in renewable energy (wind or solar) and determining when and where to replace capital that is inefficient relative to current technology.