Oil companies raise their prices all the time. If enough companies do so, the price stays up. If enough don’t, either the price falls or the company that raised its prices loses market share and profits. Supply and demand is a major factor, but far from the only one.
That is why a simplistic claim that a carbon tax of X amount will reduce consumption by Y amount is so naive. Marginal increases in the price of fuel have short term effects on demand. Large increases in price have a longer term effect, but in a wealthy economy, there are other adjustments that eventually result in demand resuming its inevitable increase.
For example, Europe has long had taxes on gasoline triple or more of US taxes. The average retail price of a gallon of gas in the US right now is around $3.50. The average retail price in Europe is about $7,55 per gallon. And their progressives are still arguing for additional carbon taxes and actually implemented a form of cap and trade.
So pie in the sky, revenue neutral carbon taxes calculated to harmlessly decrease oil, coal and gas consumption and save the poor polar bears are misinformation.
Oh, and OPEC does not raise its prices in part to maintain demand. But just as important is the need for certain members of the cartel to be able to continue to count on the US 1) keeping some of them in power, and 2) ensuring the free flow of oil in world commerce.