Economics of carbon-dioxide abatement under an exogenous constraint on cumulative emissions

The fossil-fuel induced contribution to further warming over the 21st century will be determined largely by integrated CO2 emissions over time rather than the precise timing of the emissions, with a relation of near-proportionality between global warming and cumulative CO2 emissions. This paper examines optimal abatement pathways under an exogenous constraint on cumulative emissions. Least cost abatement pathways have carbon tax rising at the risk-free interest rate, but if endogenous learning or climate damage costs are included in the analysis, the carbon tax grows more slowly. The inclusion of damage costs in the optimization leads to a higher initial carbon tax, whereas the effect of learning depends on whether it appears as an additive or multiplicative contribution to the marginal cost curve. Multiplicative models are common in the literature and lead to delayed abatement and a smaller initial tax. The required initial carbon tax increases with the cumulative abatement goal and is higher for lower interest rates. Delaying the start of abatement is costly owing to the increasing marginal abatement cost. Lower interest rates lead to higher relative costs of delaying abatement because these induce higher abatement rates early on. The fraction of business-as-usual emissions (BAU) avoided in optimal pathways increases for low interest rates and rapid growth of the abatement cost curve, which allows a lower threshold global warming goal to become attainable without overshoot in temperature. Each year of delay in starting abatement raises this threshold by an increasing amount, because the abatement rate increases exponentially with time.