Carbon taxation plays out as a consumption tax on goods people consume in roughly the same quantities independent of income.
Take fuel as an example. The average american adult consumes about 550 gallons of gas a year for driving. It doesn't matter substantially how wealthy you are - there are only so many hours in the day to drive.
A $20/Metric Ton CO2eq carbon tax means a fuel price increase of 0.18c/gal, or about $100 a year per person. So we'd expect to see consumers either pay this additonal 18c to keep driving on gas, or some close equivalent cost if they find a competitive renewable fuel at this new price point.
So:
- If you are at the 10th income percentile, you make $11/hr and society now expects 9 hours of labor from each adult in your household a year to pay for energy transition
- If you are at the 90th income percentile, you make $29/hr, society expects you to work 3.4hrs a year to pay for transition.
This makes carbon taxation, and related schemes like gas taxes, politically unpopular. See for instance yellow vest protests in France, where gas taxation was a key issue.
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Incomes: https://www.bls.gov/oes/oes_perc.htm
Carbon tax -> fuel cost: http://www.rff.org/blog/2017/calculating-various-fuel-prices...
Fuel consumption: https://www.fool.com/investing/2017/01/14/heres-how-much-gas...