social cost of carbon
The social cost of carbon (SCC) is the marginal cost of the impacts caused by emitting carbon emissions at any point in time. The purpose of putting a price on a tonne of emitted carbon or CO2 is to aid people in evaluating whether adjustments to curb climate change are justified. The social cost of carbon is a calculation focused on taking corrective measures to a "State of Nature", where there is evidence of market failure. The Intergovernmental Panel on Climate Change suggested that a carbon price of $100/tCO2e could reduce global GHG emissions by at least half the 2019 level by 2030.Prominent 2021 models of saving for the social cost of carbon calculated a damage of more than $3000/tCO2e as a result of economy feedbacks and falling global GDP growth rates, while policy recommendations for a carbon price ranged from about $50t/CO2e to $200/tCO2e.: 22 The UN accounts for many greenhouse gas emissions that contribute to climate change and report global emissions on both a tCO2e and tC basis. A tentative sense check in 2021 by A. T. Parkinson using the simple Hobbesian ratio of historic data suggested a reasonable figure in 2016 could have been somewhere between $300tC and $400tC, when considering UN and OECD accounts. It was expected that the system under evaluation is fundamentally slow response with long-run dynamics relative to the other systems that humans typically interact, hence need not be estimated with any precision frequently. However, the ability of the general public to readily audit calculation of the indicator appears vital. From the liberal perspective, the social cost of carbon (a Commonwealth Cost of Carbon, in this instance) appears a candidate key performance indicator for the overall performance of world leaders.

Calculating
Calculating the SCC requires estimating the societal damages caused by anthropogenic greenhouse gas emissions. This includes manifestations of environmental degradation as public disorder, conflict and reduced activity. Utilitarian valuations for a people can be difficult because the impacts on ecosystems do not have a market price and any ideal observer lacks legitimacy over many nation states. However, Hobbesian valuations for the global commons can be relatively simple and yield quite different outcomes.

Calculating Stability for the Global Commons
Greenhouse gas emissions are an essential good that life cannot do without. The carbon cycle is more fundamental to existence than the sovereignty of nation states. Carbon management has relevance to all decisions, activities and governance frameworks. Climate change may be considered a relatively recent symptom of a rather ancient challenge for carbon-based humanity seeking contracts in good faith within a "State of Nature". Hence, in the liberal tradition, one would be concerned with higher priority considerations than rates of saving.A theory of the social contract put forward by Hobbes in Leviathan has universal relevance to the required evaluations of this "State of Nature". Following such theory, one simply divides historic enforcement costs by anthropogenic greenhouse gas emissions to arrive at past "Commonwealth Costs of Carbon". Historic enforcement costs may be the sum total of global military, public order and safety expenditure. These costs arise through imperfections in judgements, though are a necessity to assure the peoples covenant with the global commons. Everything else that the global commons provides is of benefit. This simple approach does not require an ideal observer. All peoples are treated equally and allocations of property rights have no influence on the peoples ability to estimate, as long as the necessary accounts are public.Such an approach could be adopted by a "Society of Peoples", living free of conflict within stable, lawful and democratic communities. With such a following, Commonwealth Costs of Carbon may be regarded the principle key performance indicators of statesmanship for a Commonwealth of Peoples,  reflecting global ecosystem stability. It's important to note that the public policies of intergovernmental organisations, such as the Commonwealth of Nations or Commonwealth of Independent States, may not necessarily recognise a Commonwealth of Peoples approach.

Calculating Rates of Saving for a People
Alternatively, it has been popular to compare rates of saving over time involving a discount rate or time preference. These rates determine the weight placed on impacts occurring at different times, applying a theoretical model of inter-generational welfare developed by Ramsey.Such utilitarian estimates of the SCC come from integrated assessment models (IAM) which predict the effects of climate change under various scenarios and allow for calculation of monetized damages. One of the most widely used IAMs is the Dynamic Integrated model of Climate and the Economy (DICE).The DICE model, developed by William Nordhaus, makes provisions for the calculation of a social cost of carbon. The DICE model defines the SCC to be "equal to the economic impact of a unit of emissions in terms of t-period consumption as a numéraire".Other popular IAMs used to calculate the social cost of carbon include the Policy Analysis for Greenhouse Effect Model (PAGE) and the Climate Framework for Uncertainty, Negotiation, and Distribution (FUND).In the United States, the Trump Administration was criticised for using existing IAMs to calculate the SCC that lacked appropriate calculations for interactions between regions. For instance, climate catastrophes caused by climate change in one region may have a domino impact on the economy of neighboring regions or trading partners.The wide range of estimates is explained mostly by underlying uncertainties in the science of climate change including the climate sensitivity, which is a measure of the amount of global warming expected for a doubling in the atmospheric concentration of CO2, different choices of discount rate, treatment of equity, and how potential catastrophic impacts are estimated.
The Interagency Working Group in the United States usually uses four values when calculating the cost. The values come from using a discount rate of 2.5%, 3%, and 5% from the integrated assessment models. The SCC that is being found must include the different probabilities based on what mitigation is being used for climate change that betters or worsens the environment. This is where the fourth value comes into play, because there can be lower-probability, but higher-impact outcomes from climate change. The fourth value zones in on the 3% discounts rate and is set to the 95th percentile when distributing the frequency estimates.
In "The U.S. Government's Social Cost of Carbon Estimates after Their First Two Years: Pathways for Improvement", Kopp and Mignone suggest that these calculation rates do not reflect the multiple ways that humans can respond to climate change. They propose an alternative approach that should be considered by calculating through a cost-benefit optimization analysis based on if the public "panics" about climate change and implement mitigation policies accordingly.

Discount rate
What discount rate to use is "consequential and contentious" because it defines the relative value of present costs and future damages, an inherently ethical and political judgment. A 2015 survey of 200 general economists found that most preferred a rate between 1% and 3%. Some, like Nordhaus, advocate for a time discount rate that is pegged to the current average rate of time discount as estimated from market interest rates–this is spurious reasoning because intragenerational interest rates have nothing to do with the intergenerational ones in question. Others, like Stern, propose a much smaller discount rate because "normal" discount rates are skewed when applied over the time scales over which climate change acts. A 2015 survey of 1,100 economists who had published on climate change found that those who estimated discount rates preferred that they decline over time and that explicit ethical considerations be factored in.

Carbon pricing recommendations
According to economic theory, a carbon price should be set equal to the SCC. In reality, carbon tax and carbon emission trading only cover a limited number of countries and sectors, which is vastly below the optimal SCC. The social cost of carbon ranges from −$13.36 to $2386.91/tCO2, while the carbon pricing at present only ranges from $0.50 to $137.30/tCO2 in 2022. From a technological cost perspective, the 2018 IPCC report suggested that limiting global warming below 1.5 °C requires technology costs around $135 to $5500 in 2030 and $245 to $13000/tCO2 in 2050. This is more than three times higher than for a 2 °C limit. 
In 2021, the study "The social cost of carbon dioxide under climate-economy feedbacks and temperature variability" estimated even costs of more than $3000/tCO2e. A study published in September 2022 in Nature estimated the social cost of carbon (SCC) to be $185 per tonne of CO2—3.6 times higher than the U.S. government's then-current value of $51 per tonne.Large studies in the late 2010s estimated the social cost of carbon as high as $417/tCO2e, or as low as $54/tCO2e. Both those studies subsume wide ranges; the latter is a meta-study whose source estimates range from -$13.36/tCO2e to $2,386.91/tCO2e. Note that the costs derive not from the element carbon, but the molecule carbon dioxide. Each tonne of carbon dioxide consists of about 0.27 tonnes of carbon and 0.73 tonnes of oxygen.
According to David Anthoff and Johannes Emmerling, the social cost of carbon can be expressed by the following equation: 
  
    
      
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    {\displaystyle SCCx=(\partial w/\partial cx0)^{-}1\sum _{t=0}^{T}\sum _{r=1}^{R}\partial w/\partial c}
  .This equation represents how one additional ton of carbon dioxide impacts the environment and incorporates equity and social impact. Chen, Van der Beek, and Cloud inquire upon the benefits of incorporating a second measure of the externalities of carbon by accounting for both the social cost of carbon and risk cost of carbon. This technique involves accounting for the cost of risk on climate change goals. Matsuo and Schmidt suggest that carbon policies revolve around two renewable energy targets. They focus on bringing the cost down of renewable energy and growth of the industry. The problem with these objectives in policy is that prioritization can affect how the policy plays out. This can result in a negative impact on the social cost of carbon by affecting how renewable energy is incorporated into society. Newbery, Reiner, and Ritz discuss a carbon price floor as a means of attributing to the social cost of carbon. They discuss how incorporating a CPF in SCC can have a long-term effect of less coal usage, an increase in electricity pricing, and more innovation and investment in low-carbon alternatives. Yang et al. estimated the social cost of carbon under alternative socioeconomic pathways. According to their results, regional rivalries with increased trade friction can increase the social cost of carbon by a factor of 2 to 4.

Use in investment decisions
Organizations that take an integrated management approach are using the social cost of carbon to help evaluate investment decisions and guide long-term planning in order to consider the full extent of how their operations impact society and the environment. By placing a value on carbon emissions, decision makers can use this value to expand upon traditional financial decision-making tools and create new metrics for measuring the short and long-term outcomes of their actions. This means taking the triple bottom line a step further and promotes an integrated bottom line (IBL) approach. Prioritizing an IBL approach begins with changing the way we think about traditional financial measurements as these do not take into consideration the full extent of the short and long-term impacts of a decision or action. Instead, return on investment can be expanded to return on integration, internal rate of return can evolve into integrated rate of return and instead of focusing on net present value, companies can plan for integrated future value.

By country
The SCC is highly sensitive to socioeconomic narratives. Because carbon dioxide is a global externality, a liberal society would never want to set policy based on anything other than the global aggregate value (hence, treating all peoples as equal in their judgement). One might expect any international contracting in the interest of the global commons could be made in good faith. However, given a lack of trust between governments and popular adoption of other philosophical doctrine, the country-level or regional-level social cost of carbon is also calculated. Yang et al. calculated the regional social cost of carbon using regional cost-benefit IAM (RICE). Generally, SCCs in developing countries are much more sensitive to socioeconomic uncertainty and risk valuation - average SCCs in developing regions are 20 times higher than developed regions. Cost-benefit IAM requires more computational resources to provide SCC at the country level, so Ricke et al. calculate the social cost of carbon based on discounted future damage. Their estimation shows countries that incur large fractions of the global cost consistently include India, China, Saudi Arabia and the United States.

United Kingdom
The UK government has estimated social cost of carbon since 2002, when a Government Economic Service working paper Estimating the social cost of carbon emissions suggested £19/tCO2 within a range of £10 to £38/tCO2. This cost was set to rise at a rate of £0.27/tCO2 per year to reflect the increasing marginal cost of emissions. In 2009 the UK government conducted a review of the approach taken to developing carbon values. The conclusion of the review was to move to a "target-consistent‟ or "abatement cost" approach to carbon valuation rather than a "social cost of carbon" (SCC) approach. Following a cross-government review during 2020 and 2021, UK carbon valuation are further updated to reflect consistency to the global 1.5°C goal and its domestic targets.

United States
In February 2021 the US government set the social cost of carbon to $51 per tonne, based on a 3% discount rate, but it plans a more thorough review of the issue.  However, in February 2022 a court ruled against the government and said the figure was invalid as only damage within the US could be included. In March 2022, a three-judge panel of the 5th Circuit Court of Appeals stayed his injunction, permitting continued use of the interim figure. The social cost of carbon is used in policymaking.Executive Order 12866 requires agencies to consider the costs and benefits of any potential regulations and, bearing in mind that some factors may be difficult to assign monetary value, only propose regulations whose benefits would justify the cost. Social cost of carbon estimates allow agencies to bring considerations of the impact of increased carbon dioxide emissions into cost-benefit analyses of proposed regulations.
The United States government was not required to implement greenhouse gas emission requirements until after the 2007 court case Massachusetts v. EPA. The U.S. government struggled to implement greenhouse gas emission requirements due to the lack of an accurate social cost on carbon to guide policy making.Due to the varying estimates of the social cost of carbon, in 2009, the Office of Management and Budget (OMB) and the Council of Economic Advisers established the Interagency Working Group on the Social Cost of Greenhouse Gases (IWG) in an attempt to develop standards estimates of SCC for the use of federal agencies considering regulatory policies. This establishment was formerly named Interagency Working Group on the Social Cost of Carbon, but has now extended to include multiple greenhouse gasses. The IWG works closely with the National Academies of Sciences, Engineering, and Medicine when researching and creating an up to date report on the SCC.
When developing the 2010 and 2013 social cost of carbon estimates, the U.S. Government Accountability Office used a consensus-based approach with working groups alongside of existing academic works, studies, and models. These created estimates for the social costs and benefits that government agencies could use when creating environmental policies. Members of the public are able to comment on the developed social cost of carbon.Along with the Office of Management and Budget (OMB) and the Council of Economic Advisers, six federal agencies worked in the working group. The agencies involved included, The Environmental Protection Agency (EPA), United States Department of Agriculture, United States Department of Commerce, United States Department of Energy, United States Department of Transportation (DOT), and the United States Department of Treasury. The Interagency Working Group analyzed and advised that policy surrounding the social cost of carbon must be implemented based on global impacts instead of domestic. Support for this expansion in scope stems from theories that climate change may lead to global migration and political and environmental destabilization that affects both the national security and economy of the United States, as well as its allies and trading partners. The social cost of carbon In the United States Government should be seen as a way to continuously update estimates with an end goal of public and scientific approval in order to make efficient environmental policy.The price being set for the social cost of carbon is dependent upon the administration in charge. While Obama was in office, the administration paved the way for the first estimate of putting a price on carbon emissions. The administration estimated that the cost would be $36 per tonne in 2015, $42 in 2020, and $46 in 2025.The Trump administration estimated between $1–$7 in economic damage in 2020. Trump's Executive Order 13783 mandated that SCC estimates be calculated based on guidelines from the 2003 OMB Circular A-4, rather than guidelines based on more recent climate science.In November 2022, the EPA issued an estimate of $190 per ton for 2020.

Criticism
Longer-term planning using the SCC has been criticized as being extremely uncertain, having to change over time and according to the level of emissions, and is claimed to be useless to policymakers of nation states as the Paris Agreement has a goal of 2 °C temperature rise.Calculating the SCC using the Ramsey model brings about a degree of uncertainty particularly due to unknown future economic growth and socioeconomic development paths. Societal preferences over development, international trade, and the potential for technological innovation, as well as national preferences regarding energy development should be taken into account. The discount rate, damage and pending climate system response also contribute to uncertainty.
Furthermore, the figures produced from the SCC using the Ramsey model cause calculations to be produced on a range with the most commonly utilized number being the central case value (an average over the entire data set at a given discount rate). The SCC is no longer used for policy appraisal in the UK by the nation state or the policymakers of the EU.There are also important ethical concerns in applying Ramsey models to longer-term development plans. Nobody can legitimately command sufficient support as the "ideal observer" for the entire global ecosystem, needed to justify any modelling assumptions. There is widespread doubt as to whether utilitarianism is a philosophy fit for humanity and it is perceived as a distasteful approach to many. Issues with moderating Nozick's "utility monster", difficulty in forecasting rightful interventions to assure civil liberties, and the need for necessary allowances for a reasonable plurality in rightful beliefs amongst leaders are all severe shortcomings.
None of these criticisms are relevant to use of Commonwealth Costs of Carbon for more immediate decision-making by Peoples of the Global Commons.

History
The concept of a social cost of carbon was first mooted by the Reagan administration of the United States in 1981. Federal agencies such as the Environmental Protection Agency and Department of Transportation began to develop other forms of social cost calculations from carbon during the George H. W. Bush administration. Furthermore, economic social cost from carbon was judicially mandated in cost-benefit analysis for new policy in 2008 following a decision by a federal appellate court. The year following in 2009 there was a call for a uniform calculation of social cost from carbon to be utilized by the government.

Notes
References
IPCC
de Coninck, H.; Revi, A.; Babiker, M.; Bertoldi, P.; et al. (2018). "Chapter 4: Strengthening and Implementing the Global Response" (PDF). Global Warming of 1.5 °C. pp. 313–443.


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