The rate of change of the social cost of carbon and the social planner's hotelling rule

This paper derives the social cost of carbon (SCC) and its rate of change. It does so in a deterministic Ramsey model of optimal economic growth with carbon emissions from burning fossil fuels. It is shown that the determinants of the rate of change of the SCC are substantially almost identical to the determinants in the social planner's Hotelling rule if a unit of fossil fuel use leads to exactly one unit of carbon emission, while otherwise these formulas differ substantially. As is also shown in this paper, in the special case in which the two formulas are substantially almost identical, a Pigovian tax on fossil fuel use and a Pigovian tax on carbon emissions are both equal to the SCC, while otherwise only a Pigovian tax on carbon emissions equals the SCC.