Economists call the social cost of climate (SCC) an externality. Before establishing any corrective mechanisms, it is vital to quantify SCC. The 2016 paper by Carleton and Hsiang in Science is a good resource for understanding the topic. The article summarises multiple counts of parameters such as changes in GDP, mortality, and social conflicts as a function of average temperature.
In simple terms, one needs to solve three relationships simultaneously to reach a future cost of climate. They are
Finally, you use a discount rate to bring the cost to today.
Establishing the first one, between greenhouse gas (GHG) emissions and temperature, is climate scientists’ job. The second and third are economists’ forte. Uncertainties over the parameters require equations to be solved over a range of inputs, and the simulations (Monte Carlo of hundreds of thousands of realisations) result in distributions. If you are curious about how they look, check out the Interagency Working Group (IWG) on the Social Cost of Greenhouse Gases by the United States Government.
Reference
Carleton and Hsiang, Social and economic impacts of climate: Science
Technical Support Document: Social Cost of Carbon, Methane, and Nitrous Oxide Interim Estimates under Executive Order 13990: Interagency Working Group
