Economic Growth and the Transition from Non-Renewable to Renewable Energy

The paper considers the transition of an economy from non-renewable to renewable energy. The Hotelling theorem suggests to extract a non-renewable resource in an optimal way such that the resource tends to be depleted when optimally extracted. Yet, it might not be reasonable to deplete non-renewable energy sources that create externalities such as CO2 emission and global warming. The resource theorem of Hotelling would imply too high a CO2 emission. The paper sets up a canonical growth model with damages in the household's welfare function and two energy sources -- non-renewable and renewable energy. We study when a transition to renewable energy can take place, and if it takes place before non-renewable energy is exhausted. A socially optimal solution is considered that takes into account the negative externality from the non-renewable energy. We also study of how the optimal solution can be mimicked in a market economy by policies using tax rates and subsidies. To solve the model version where preferences show a multiplicative effect of consumption and damages from CO2 emission, we use dynamic programming. For a simplified version, with additive arguments in preferences, we use Nonlinear Model Predictive Control to solve the model and study the transition to renewable energy.