In the absence of government action, the private sector will increase emissions up to the point where there is no further marginal benefit. That is, emissions will rise to whatever level is implied by profit-maximization, paying no attention to the effects on the environment.Krugman is making a case for limiting emissions, and that argument is pretty solid accordng to basic economic theory. But he goes too far when he says that because a case for reducing emissions makes sense, it necessarily means that cap-and-trade makes sense. The problem with cap and trade lies not in economic theory, but in political realities. Cap and trade cannot work in the real world -- Krugman's means cannot achieve the ends he seeks. He just assumes policy success, which is easy to do in theoretical arguments, but pretty far from the real world where we actually have to live with the policies that emerge from the messy legislative process.
If cap and trade cannot work, then it would be logical that we should be exploring other means to reducing emissions. But instead, Krugman tries to shut down any discussion of alternative approaches by saying that if you don't accept his means, then you must not accept his ends. Krugman is ironically contributing the the very policy failure he seeks to avoid. Nothing like some messy facts to trouble an elegant theory.