An approach to adaptive carbon taxes in the presence of global warming

The optimal extraction path of fossil fuels and the corresponding corrective tax on extraction are derived when two types of externalities associated with emission of carbondioxide (CO2) are taken into account. The optimal path is derived as a feedback control, that is, as a function of time and pollution. The tax-path is thereby adaptive to the aggregated level of carbondioxide. The two types of externalities are flow externalities associated with the extraction, defined as the difference between private and social marginal costs, and stock externalities associated with the aggregated level of CO2. The total time horizon is divided into two periods: an initial phase with extraction and a terminal phase without extraction. The lengths of these periods are endogenously determined, as is the scarcity rent of fossil fuels and the shadow cost of CO2. The mathematical model is completely general in the state variable, CO2, the decay function included. Furthermore, there are no assumptions about separability in the objective function, which is to maximize social benefit