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### Social cost of carbon

The social cost of carbon (SCC) is a commonly cited metric which estimates the increase in harms from additional emissions. To estimate this, webDICE runs the model once (under your chosen parameters) and then again with one additional ton of CO2 and calculates the difference in the two cases. The increase in harms from the additional ton is the social cost of carbon. U.S. government agencies are required to use this metric in cost-benefit evaluation of new programs. Although the commonly used term is social cost of carbon, it is standard to report the value in dollars per ton of carbon dioxide, not carbon. webDICE follows this practice.

webDICE calculates the social cost of carbon for each period by sequentially adding the additional ton in each period. For example, the social cost of carbon in 2055 is the increase in harms one an additional ton of CO2 is added in the year 2055. more

webDICE model estimates the SCC by first determining the consumption pathway implied by the user’s choice of parameter values, $C_{b}$. Next, it adds a ton of carbon to total emissions in year $t$ and recalculates the consumption pathway after that year. $C_{b+1}$. webDICE then finds the difference in the two pathways in each year, applies the appropriate discount rate, and sums the differences. This value is multiplied by $12/44$ to covert from dollars per ton of carbon to dollars per ton of carbon dioxide: $SCC_{\tau}=\sum_{t=\tau}^{Tmax}\frac{\left(C_{b}-C_{b+1}\right)_{t}}{\left(1+r\right)^{t}}$

This process is repeated for each of the twenty time periods displayed in webDICE (although it calculates the SCC using the differences in damages over all $Tmax-\tau$ relevant time steps).

webDICE’s estimates of the SCC will not match those used by the federal government for cost-benefit analysis. Although those estimates were in done in part using DICE, the government modified DICE to have exogenous emissions, GDP and population to enable comparison across three distinct models.