Estimate of the optimal tax rate on CO2 (pdf), by Lennart Stern

Summary
The optimal tax rate for a person P is defined to be the tax rate that maximises the sum of quality of life over all people.
We consider the following consequences of climate change predicted by the Stern Review:

- 400 million people more in hunger, often associated with violent conflict as it is the case in Africa, 70 million people more with malaria
– Let us ascribe the quality of life change for each of these people, where is the change in quality of life for the person P arising from a 5% change in income.

- Some estimates suggest that 200 million people may become permanently displaced by the middle of the century due to rising sea levels, more frequent floods, and more intense droughts. – Let us ascribe the quality of life changefor each of these people.

- the number of children in primary education will decrease (in the Stern Review it is said that the numbers have not been estimated): Assuming that the decrease in education levels will be proportional to the decrease in income of 5% on average for the 2 billion people living below 2 dollars per day: 100 million people less in primary education: - Let us ascribe the quality of life changefor each of these people.

-For the remaining 5830 people of the population we will take the same value of change in quality of life as the person P. (According to the Stern Review, they are on average affected by a 5% decrease in income. So this is a very conservative estimate, as the poorer people are, the more a percentage decrease in income affects their quality of life.)
From the fact that the carbon tax on the redistribution of income achieved by the tax system can be treated independently and from the assumption that possible improvements on the overall quality of life without taking into account the cost arising from climate change can be treated independently, one can show through a calculation that the optimal tax rate on CO2 is 22 as high as the on proposed in the Stern Review. This will mean that the tax on energy generated by fossil fuels, i.e. heating, transport, electricity should be about 11 times the free market price, rather than 1.5 times the free market price as it is now.

See also

Hoel M, Sterner T (2007) Discounting and relative prices. Clim Change 84:265–280