It is rare that anyone wishes to broach this general topic, on either side of the debate. This is from a new working paper by Geoffrey Heal and Wolfam Schlenker:
We highlight important dynamic aspects of a global carbon tax, which will reallocate consumption through time: some of the initial reduction in consumption will be offset through higher consumption later on. Only reserves with high enough extraction cost will be priced out of the market. Using data from a large proprietary database of field-level oil data, we show that carbon prices even as high as 200 dollars per ton of CO2 will only reduce cumulative emissions from oil by 4% as the supply curve is very steep for high oil prices and few reserves drop out. The supply curve flattens out for lower price, and the effect of an increased carbon tax becomes larger. For example, a carbon price of 600 dollars would reduce cumulative emissions by 60%. On the flip side, a global cap and trade system that limits global extraction by a modest amount like 4% expropriates a large fraction of scarcity rents and would imply a high permit price of $200. The tax incidence varies over time: initially, about 75% of the carbon price will be passed on to consumers, but this share declines through time and even becomes negative as oil prices will drop in future years relative to a case of no carbon tax. The net present value of producer and consumer surplus decrease by roughly equal amounts, which are almost entirely offset by increased tax revenues.
Here is an earlier MR post on the same topic, and it gives more of the theoretical intuition.