I am not an expert on this but I assume the total amount of carbon on the earth is essentially constant. I am guessing for the most part it exists on earth as (1) plants and other life forms (2) fossil fuels and (3) other non-living stored carbon, in things like plastics and lumber. In the air it is mainly carbon dioxide. The more we store on earth the less there will be in the air.

Maybe we need a plant and trade system rather than cap and trade. Whenever fossil fuels are sold, a corresponding amount of carbon must be stored, either through new plants of in other sequestered carbon.