For starters, theoretically, cap-and-trade is identical to a carbon tax. That is, if you know the elasticity of demand for carbon, and the value of carbon emissions to the economy, you can get to the desired amount either by capping the amount of carbon, or changing the price of emitting it.
In practice, of course, these things are hard to know. Carbon cappers favor the cap because they know, absolutely, how much carbon we’ll end up emitting.
The carbon taxers have two objections to this, both of which are compelling. The first is that, politically, it is hard to get the carbon cap to the right level–as the EU example shows, governments often end up giving out permits. Those permits go to favored interest groups, distorting economic activity; or too many of them are issued, which doesn’t distort economic activity between sectors, but rather moots the purpose of setting up the carbon trading regime. (To be fair, Europe is trying to fix this latter problem. But they’re not there yet.)
The second objection to cap-and-trade is that emitting carbon has value–not just monetary value to evil, polluting corporations, but actual hedonic value to Americans who like to do things like flip a switch and have the lights come on.
Ideally, we should understand what the economic cost of carbon emissions is, and use a carbon tax to raise the price until it includes the cost of that negative externality. If, once we have raised the cost of carbon to the price of the utility + the negative utility, and people still continue consuming carbon-intensive goods, then that is telling us something important about the value of that added carbon-intensive economic activity.
This is, needless to say, not a popular view with environmentalists who place a value on (other peoples’) extra carbon-intensive economic activity of zero, or less than zero.
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