  We propose a model based on a large number of small competitive producers of
renewable energies, to study the effect of subsidies on the aggregate level of
capacity, taking into account a cannibalization effect. We first derive a model
to explain how long-time equilibrium can be reached on the market of production
of renewable electricity and compare this equilibrium to the case of monopoly.
Then we consider the case in which other capacities of production adjust to the
production of renewable energies. The analysis is based on a master equation
and we get explicit formulae for the long-time equilibria. We also provide new
numerical methods to simulate the master equation and the evolution of the
capacities. Thus we find the optimal subsidies to be given by a central planner
to the installation and the production in order to reach a desired equilibrium
capacity.
