More to the point: a carbon tax introduces price certainty, which (naively) allows efficient long-term planning. (Carbon caps set volume by fiat; carbon taxes set price by fiat. The other variable floats with the market).
You can look at the EU carbon market's total failure as an example. It's a cap system, where the price collapsed almost immediately, and so to date it has had zero effect of any sort [0]. The cap right now is way above what the market actually wants. It's useless.
The opposite -- price overshoots because of a too tight cap + demand inelasticity -- could also be a really bad thing. Both directly from the pain it causes, and indirectly from the predictable political backlash, which would screw up something else in a new & more creative way.
Your analysis of EU Cap is off base. The price collapsed in the first phase for two reasons:
1. They set the cap far too high; and
2. They did not allow banking between phases.
They correct the first error in the second phase of the system. For the second, they still allocated too many permits but the economic collapse in Europe led to far lower output than had been expected, and for a time declining confidence in the future existence of the EU led to a collapse in confidence in the long-term existence of the policy, making "banking" the credits for future abatement less attractive.
Finally, the cap is a "backstop" mechanism, which exists to ensure that the marginal abatement takes place, with inframarginal abatement taking place through, e.g., the Renewables Directive and the Large Combustion Directive as well as very high fuel taxes among many other mechanisms the EU uses to drive renewable energy and consumption efficiency.
The cap worked perfectly from a qualitative perspective - there is a highly visible price on carbon with complete capital market instruments available (forwards, futures, options, etc.) to give long-term investors what they need to make investment decisions. It has been the quantitative parameters that have not been ratcheted high enough. You'd have the same issues with a tax.
Both forms of pricing carbon can work, but both need good design.
I'm not sure - how arbitrarily setting prices introduces certainty? Today the Congress or EPA decides the price is X, tomorrow Republicans take the Congress and the presidency and appoint the head of EPA which drops the price to Y, then next cycle Democrats take the power and rise the price to Z, etc. etc. - where's certainty in that? I don't see any objective way of setting such taxes, and as such - any reason why they would be stable is the price is purely arbitrary and thus subject to political games.
Well it doesn't, no. IF you have stable government policies, than a carbon tax would be a predictable cost, where a cap would be highly volatile. Obviously if the policies are changing too, then you can't predict much of anything.
"I don't see any objective way of setting such taxes,"
How about: estimate the economic damage of a marginal kg of CO2 (external cost), and set the tax equal to that? [0]
As an order-of-magnitude guess: [total climate change damage] / [total CO2 emitted], both discounted to present dollars.
You can look at the EU carbon market's total failure as an example. It's a cap system, where the price collapsed almost immediately, and so to date it has had zero effect of any sort [0]. The cap right now is way above what the market actually wants. It's useless.
The opposite -- price overshoots because of a too tight cap + demand inelasticity -- could also be a really bad thing. Both directly from the pain it causes, and indirectly from the predictable political backlash, which would screw up something else in a new & more creative way.
[0] http://www.economist.com/node/21548962