Optimal Dynamic Management of a Renewable Energy Source under Uncertainty

I consider a risk averse and prudent social planner who has access to different energy sources to produce electricity: hydroelectricity produced with a dam and thermal electricity with unlimited supply at some exogenous cost. The dam is supplied with a random water flow. The presence of constraints on a minimal and on a maximal storage capacity makes electricity consumption smoothing possible only when the quantity of water available to the agent lies in a certain range that I determine. Consumption smoothing is possible even when the dam is almost empty thanks to the alternative costly energy source. Moreover a comparative static analysis reveals that the marginal propensity to produce hydroelectricity is an increasing function of the cost of the second technology. Therefore, the availability at a low cost of the fossil source improves time diversification. Finally, the optimal electric park is composed of a number of dams that is increasing with the cost of the second technology