According to basic principles of economics if something is both valuable and scarce, it makes sense to put a price on it. The capacity of the atmosphere to absorb carbon dioxide without being compromised is clearly limited and we are coming up against those constraints. So a carbon tax would make sense.
You might say, what about our export and import-competing industries, how will they cope? In Australia we had a modest carbon tax (introduced in a Labor government) which had some exemptions for exporting and import-competing industries. There were cuts to income tax and increases to welfare payments to ensure that people with typical consumption patterns weren't worse off. The economics mayhem which some had anticipated did not eventuate. People and businesses mostly coped just fine.
In 2013, we had a change of government and the incoming Coalition government abolished the carbon tax. The tax cuts and welfare increases which were introduced as compensation for the carbon tax remained in place. You might think at least people who don't care about or don't believe in climate change had reason to be happy because they got to keep the tax cuts and electricity prices would surely go down. As it turned out, electricity prices went up and are higher now, even after allowing for inflation, then during the carbon tax.
How do we make sense of this paradox? In the "The Economic Case for Climate Action" section, I explain this in more detail, but in essence there was a general sense of disparagement towards renewable energy and so renewable energy investment dropped off.
There is one interesting question: Removal of the carbon tax failed to reduce electricity prices. So where did the approximately $A 7 Billion dollars per year that would have been raised by the tax go? The answer is on escalating maintenance costs on coal fired power stations that should have been retired years ago as well as profits for owners of existing generating capacity who faced less competition from new generating capacity.
An alternative to a carbon tax is a trading system where permits to emit carbon dioxide are internationally traded. There are question marks about the integrity of such schemes. But the bigger problem is this: If Australian carbon emitters were to buy permits rather than reduce emissions, we would be paying other countries to modernise their economy as opposed to modernising our own.