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Social Cost of Carbon

Why Measure the Social Cost of Carbon?

As the world wakes up to the increasing impacts of a changing climate - we are faced with a staggering price-tag. The cost of climate change to society comes from hurricane damage, interrupted supply chains, devastating loss from wildfire, power outages due to extreme heat, and capital required for transitioning to renewables, among other items yet to be accounted for. 

The Industrial District of Houston, Texas, USA (Jennifer Hudler's hometown)
The Industrial District of Houston, Texas, USA (Jennifer Hudler's hometown)

Human economic activity, the primary source of greenhouse gas emissions, has yet to fully account for the cost of emitting carbon to society. How we measure future costs of carbon to society is a tricky art that has governments around the world debating the best practices and policies to do this. 

But first, we must ask: What is the social cost of carbon? A number of economists are developing various models and methods for answering this question. WSC’s newest team member, Jenn Hudler, shares her thoughts on the social cost of carbon. She utilizes calculations from the DICE model, developed by William Nordhaus, to propose how we might answer this important question. We hope you find her essay on this topic as interesting as we do.

- Amber Bieg & The WSC Team

Social Cost of Carbon

By Jennifer Hudler, Originally Written May 2018

As it’s defined, the social cost of carbon, SCC, is the sum of all discounted future damages from a single ton increase of carbon dioxide today (Burkhardt). The SCC represents the economic cost to society for each marginal unit (ton) of carbon dioxide emissions (Nordhaus).  Essentially, this is the user cost presented by carbon dioxide emissions from production on future and current generations. Another take on the SCC is that it is the amount of avoided damages experienced if carbon emissions are reduced. The SCC also allows firms to incorporate the social benefits of reducing carbon emissions into their cost-benefit analyses (Burkhardt).  It is a means of putting a price on being able to reduce emissions by attempting to find the optimal dollar amount that will allow for avoided damages in the future.

For a baseline estimate of the SCC, which is found by shocking the DICE model with an additional ton of carbon and then reoptimizing the model to show the result, I found that it would be $19.26. This implies that the cost of an additional ton of carbon dioxide emissions to society is $19.26, which is the discounted sum of all future damages. It also tells firms that $19.26 in damages per ton of carbon dioxide emitted could be avoided if they reduced emissions.

Jennifer Hudler, Sustainability Analyst, Warm Springs Consulting
Jennifer Hudler, Sustainability Analyst, Warm Springs Consulting

Now in the downloaded DICE model, the discount rate is set at 3%, as shown by the bold values in the table below (Nordhaus). This implies that the value of future generations is discounted 3% to allow for a comparison of future consumption relative to current consumption in present value terms. Some economists argue for a higher discount rate because they expect future generations will be richer and would therefore be less affected by overall damages (Foster). The table below shows an array of discount rates I chose to evaluate in the DICE model to estimate the SCC. 

Discount Rate -1% 0% 1% 3% 5% 10%
SCC 112.83 70.82 45.15 19.26 8.77 1.63


“The choice of discount rate is critical to climate change policy assessments. Most of the climate-related benefits from current policy efforts would take the form of avoided damages many years from now, while many of the costs would be borne in the nearer term. A high consumption discount rate thus tends to shrink the present value of benefits relative to the present value of costs and weakens the case for aggressive current action. Relatively small differences in the choice of this rate can make a very large difference in the policy assessment. The discount rate issue has become a source of significant disagreement” (Goulder, Williams). As it is right now, the discount rate incorporates the social-welfare-equivalent discount rate and the financial-equivalent rate into one singular rate. The first of these deals more with the ethical sense of how to value future generations while the second of these is related more towards the market rates and empirical valuation (Goulder, Williams). The financial-equivalent rate “is the idea of a discount rate on goods, which is a positive concept that measures a relative price of goods at different points of time. This is also called the real return on capital, the real interest rate, the opportunity cost of capital, and the real return. The real return measures the yield on investments corrected by the change in the overall price level” (Nordhaus).

The social-welfare-equivalent rate “involves the relative weight of the economic welfare of different households or generations over time and is sometimes called the pure rate of social time preference. It is calculated in percent per unit time, like an interest rate, but refers to the discount in future welfare, not future goods or dollars” (Nordhaus). The combining of the two rates is part of the controversy over choosing a “correct” discount rate. A higher discount rate leads to a less aggressive stance on current policy because it values the present value of future costs and benefits less than a lower discount rate. A discount rate of 0% would insinuate that current and future costs and benefits are valued the same across all generations. A negative discount rate would imply a much greater value placed on the far future than on the near future or the present. Majority of literature stays within the positive range of a discount rate. Although it can be noted that a positive discount rate, particularly a large positive discount rate, will cause policy and society to ignore large costs imposed on a far distant future (Nordhaus). Even though in the 2013 DICE model the discount rate is 3%, Nordhaus himself points to a discount rate of about 4.3% as it would accurately portray what the market interest rates would be. A higher discount rate does lower the SCC and may seem more appealing to an administration that is doubtful of the true impacts of carbon dioxide emissions. A discount rate of 0% does not seem to accurately equivalent future generations value or incorporate the assumption that future consumption should increase as it’s expected future generations will be richer. Other literature that points to a lower discount rate would be weighing their recommendation more heavily on the ethical question of the social welfare of future generations in mind. “Laurie Johnson, chief economist in the climate and clean air program at the Natural Resources Defense Council and Chris Hope of the University of Cambridge’s Judge Business School,” argues for a lower discount rate as “Dr. Johnson contends that the discount rate needs to be lower because climate change has the potential to severely disrupt projected economic growth. Even if income does rise over all, the people most harmed by climate change may not be experiencing the same rate of economic growth — a factor that she says bears significant consideration” (Foster). Therefore, the optimal discount rate to set in the DICE model to estimate the SCC would depend on how the social welfare of future generations is valued and how future market interest rates are expected to behave.

The next parameter chosen to evaluate is the coefficient on temperature squared, which shows the relationship between rising temperatures and the effect on damages to society. As it is seen in the table, a higher coefficient on temperature squared implies greater damages and therefore a larger SCC (Nordhaus). However, since the damage function attempts to incorporate all possible sectors, both market and non-market, there is a lot of uncertainty surrounding the appropriate amount of the SCC as a result. There is the chance it could be too high or too low depending on how many other possible damages are excluded or overestimates and underestimates on potential damages already included in the function (Gayer). 

Damage Coefficient on Temperature Squared 0.00213 0.0022 0.0025 0.003 0.005
SCC 19.26 19.81 22.17 25.94 38.88


The recommendation I would disclose would be a discount rate in the range of 2%-4%, but personally leaning towards a discount rate somewhere between 2-3%. This would allow for a SCC between $25-$30 and incorporate the social welfare of future generations by still floating the rate around observed market interest rates but keeping it on the lower end to ensure larger avoided future damages. With the uncertainty surrounding the damage coefficient, I would remain on the lower end of the numbers estimated and probably stay in the realm of Nordhaus’s DICE model estimate. With this being said, I would recommend a Pigouvian taxing structure for the carbon tax as the carbon dioxide emitted poses an externality on society and taxing at the rate of the SCC would internalize the difference in cost between the social marginal cost and the private marginal cost of firms. This carbon tax would be on each ton of carbon dioxide emitted and be equivalent to the decided SCC. I would only recommend a tax because if the tax is imposed at the amount of the SCC then also implementing a subsidy would cause an inefficient allocation of resources causing costs to outweigh benefits. This tax recommendation would be imposed on the oil and coal market, taxing every 2.3 barrels of oil because each 2.3 barrels of oil emits a ton of carbon dioxide and each 1,094 pounds of coal burned for the same reasoning mentioned previous (EPA). The initial suppliers of these two resources would be who is directly taxed. Taxing sooner in the production process would lead to spillover into other carbon emitting producers as the cost of this tax would be passed on to these other producers and hopefully cause a significant reduction in their overall emissions. 

The effects of a tax on the electricity sector would result in prices going up and overall quantity supplied going down because energy producers using fossil fuel sources would supply less with it becoming costlier to produce with carbon emitting generators. This would be the immediate short run effect relative to if no tax were implemented. However, in the long run assuming renewable sources are already available and producing electricity, the tax would have a similar effect as implementing a subsidy in the renewable market as prices would decrease, the overall quantity supplied would increase with more producers using renewable energy sources to compensate the initial loss the tax imposed on them and fossil fuel supplying generators would continue to decrease. The types of vehicles consumers purchase would likely change more in the long run scenario with prices decreasing and still less fossil fuel generators supplying to the market. When the prices decline, most likely it would be seen that consumers would purchase electric vehicles over gasoline run vehicles. While prices increase in the short run, consumers would likely remain driving gasoline vehicles but possibly driving less mileage as a way to conserve the gas in their tank as it would be costlier to fill up. Although if the tax on oil causes a spike in gasoline prices early on, then consumers might switch to electric vehicles sooner because it may become costlier to own a fuel-based vehicle. It all depends on how the tax imposed on the oil and coal markets is passed on to other producers in related markets and whether or not they react by substituting other power sources or passing on the tax to consumers by increasing electricity and fuel prices more than discussed. Regionally, it would be seen that specifically the Southern U.S. would be affected as they harvest majority of the coal and oil production of the United States. 

Another policy option would be to use the revenue generated from the tax imposed on the oil and coal markets to help subsidize cleaner energy sources. A similar idea would be to both subsidize cleaner energy sources and to subsidize the electric vehicle market to help reduce the initial costs of these vehicles to encourage consumers to purchase electric vehicles sooner than in solely the long-run. The timing of the tax and implementation of subsidies would be critical, as per mentioned above, if both done at the same time, the allocation of resources would prove to be inefficient. My recommendation would be to tax until the beginning of the long-run implications of producers moving to cleaner sources of generation and then implement a subsidy to further the push into these renewable energy producers. This could cause the long-run effects to begin appearing sooner in the market equilibrium and help reduce prices even more as well as further decrease carbon emissions.



Burkhardt, Jesse. “Lecture Slides”

Foster, Joanna M. The SCC: How to Do the Math? The New York Times, The New York Times, 18 Sept. 2012.

Gayer, Ted. The Social Costs of Carbon. Brookings, Brookings, 28 Feb. 2017.

Greenhouse Gas Equivalencies Calculator. EPA, Environmental Protection Agency, 13 Mar. 2018.

Nordhaus, William D. Revisiting the SCC. PNAS, National Academy of Sciences, 14 Feb. 2017.

Nordhaus, William. The Stern Review on the Economics of Climate Change. 3 May 2007.

Goulder, Lawrence H, and Roberton C Williams. THE CHOICE OF DISCOUNT RATE FOR CLIMATE CHANGE POLICY EVALUATIONClimate Change Economics, Stanford University, 31 Dec. 2012.