On the transition from nonrenewable energy to renewable energy

In this paper we use the CMM model (Chakravorty et al., 2006) in discrete time and obtain more results concerning the exhaustion time of Non-Renewable Resource (NRE), the dynamic regimes of energy prices, of the stocks of pollution. We show that NRE is exhausted in finite time and is directly influenced by the initial stock of NRE and the costs of NRE and RE. Higher is the initial stock of NRE, far is the time of exhaustion of NRE. Higher is the cost of NRE (resp. the difference of unit costs between RE and NRE), far is the time of exhaustion of NRE. Furthermore, we show that the abatement intervenes, when necessary, not more than two periods. We also show that, when the unit extraction cost of RE is not very high, the stocks of emissions will never be binding if and only if, the initial stock of NRE is less than a critical value