carbon price = carbon tax. And I never had sex with that woman - Monica Lewinsky.
If the market determines the carbon price then it is in fact a "price". But as it is determined by the government, and as it is not in fact a "price" (which implies something of value that people want to buy) but it is in fact a punative levy, more like tobacco tax, then it can only be called a tax. Governments levy taxes to destimulate an activity, not to encourage it. Does the tobacco tax increase jobs? I dont think so.
