From Roger Pielke:
a “carbon cap” necessarily means that a government is committing to either a cessation of economic growth or to the systematic advancement of technological innovation in energy systems on a predictable schedule, such that economic growth is not constrained. Because halting economic growth is not an option, in China or anywhere else, and because technological innovation does not occur via fiat, there is in practice no such thing as a carbon cap.
Pointer from Mark Thoma.
If you assume a Leontief production function, then this is correct. You either come up with a way to reduce the fixed coefficient of carbon/output or you reduce output.
Instead of a fixed-factor production function, assume some substitutability, in which you can produce the same output with less carbon emissions and more of some of other factor of production–labor, capital, or other forms of energy. That would mean that you can vary the carbon/output ratio with existing knowledge, so that Pielke is not correct. He might argue that the elasticity of substitution is quite small, which may plausibly be the case.
I am skeptical that a carbon cap would be implemented effectively. The more narrowly it is implemented, the more the substitution will be between two different sources of carbon emissions rather than away from overall carbon emissions. Thus, the recent announcement by the EPA that it will target the electric power industry for a 30 percent reduction in emissions over a period of decades strikes me as unwise from even the most staunch environmentalist perspective. Assuming that the policy were to stick and the reduction were to be achieved within that industry, it would most likely be the result of a shift of carbon-intensive energy sources to uses in other sectors. It is not hard to picture a scenario in which total carbon emissions actually increase as a result, because you are directing carbon-based energy sources into less efficient uses.
Regardless, the EPA announcement works well as a gesture. And politics seems to be mostly about gestures. In Hansonian terms, politics is not about policy.