Fossil fuels are the main cause of global warming. And a high price is still the simplest way of reducing consumption of anything.
Whoever burns oil, gas or coal gets the benefits but spreads the bad consequences over the entire world population in the form of planet-warming CO2. Such drawbacks faced by people who have nothing to do with the fuel are called negative externalities. To solve the problem, one may list the negative externalities generated by the production and consumption of crude oil (starting with the impact of CO2 on the climate) and compute their cost. The polluters then pay the cost of preventing or undoing the pollution. Economists call this internalizing negative externalities or a Pigouvian tax, and the general public knows this as the polluter-pays principle.
Such taxes do work: taxes on tobacco and alcohol did help bring down consumption. Likewise, thanks to taxes on gasoline and diesel in Europe and Japan, cars there consume (and pollute) a lot less than North American ones. (An extra advantage in the case of fuels with very volatile prices is that a doubling of the price of crude oil does not lead to a doubling of the price of fuel, because taxes do not double, so the price of gasoline is more volatile in the U.S. than in Europe, which hurts the economy and the peace of mind of the population.)
It can be hard to calculate an exact cost for a Pigouvian tax (imagine that a neighbor wakes you up by driving his motorcycle very early in the morning, how would you calculate your loss?). One can simply say that the cost of pollution must be increased enough for pollution not to be taken to lightly. The question then is not how much it costs to undo the harm but rather how hefty a tax would concretely reduce the harm. The tax should start at a moderate level and be increased over time (this is what has been happening with tobacco: taxes have increased regularly and rather predictably), giving time to the population and to the alternative technology to gradually switch out of fossil fuels.
Say a factory can produce a good for 10 euros without pollution or, using a different technology, for 9 euros but generating 3 euros worth of pollution. The former is better for society (the total cost being 10 euros against 12 euros), whereas the latter is better for the company (with a production cost of 9 euros against 10 euros). A strict polluter-pays policy (internalizing the whole negative externality) would lead to a production cost of 12 euros in the latter case. But if just half of the pollution costs were paid in the form of a tax, the polluting technology would cost 10.50 euros and the clean one 10 euros. Going clean would then make economic sense — mission accomplished.
Note that with a tax of less than 1 euro the company would decide to produce dirtily for less than 10 euros (including up to 1 euro of tax), whereas at a tax level above 1 euro it would go clean and not pay the tax. When the tax is sufficiently high it no longer gets paid. Consequently the total amount collected may go down — such a success should not be mistaken as evidence of cowardice on the government's part.
Coal-firing power plants are a major source of CO2. Plants using carbon capture and storage (CCS) technology, whereby the CO2 is captured and buried in the ground, would pollute less but would be more expensive (and low cost is precisely the one advantage of coal). If CO2 emissions were taxed at a low rate, then coal would become more expensive and less competitive (especially given that the cost of renewables can be expected to keep decreasing); and at a high rate then CCS would be the economic choice: utilities would then choose to stop polluting instead of paying the tax.
The proceeds from a tax on fossil fuels can be used to fund clean energy technologies and reduce other taxes such as income tax (or to reduce mandatory withdrawals for health care or retirement), getting closer to the idea "tax bads, not goods". Less taxation of labor and more taxation of fossil fuels also means that labor-intensive activities will get cheaper and energy-intensive ones more expensive, making for instance repairing more competitive against making anew, or organic farming vs. synthetic fertilizers.
A major political difficulty is that a big shift in taxation has too legs: reducing income taxes and increasing taxes on detrimental activities and products; and voters probably trust politicians with the latter far more than with the former — voting for such policy requires a leap of faith. Another political difficulty is that many people on the left (especially in Europe where the green movement is far to the left) want to reduce unemployment (like anybody else) and mitigate climate change, but are often against reducing taxation of labor.
This extent is: when oil is cheap it can only be economically produced in certain ways and places. The recent drop by half of crude prices in the second half of 2014 (from a US$85–105/barrel range in 2012–13 to under US$50 at the time of writing) will have little impact on Saudi Arabia because they can make money producing oil at about any price. The lower crude price will instead rule out tar sands, deepwater rigs, the Arctic, etc. with average break-even costs of US$55–80 per barrel. These are the most destructive of the environment and also the most inefficient (a good deal of the oil is burnt to provide energy for the production itself). As it happens, the cheaper the oil, the less bad it is for the environment. And, for the longer run, cheap oil means little search for and investment in oil fields where production costs (and environmental damage) are high.
Of course, cheap oil, gas and coal also mean that renewable energy becomes uncompetitive overnight (even though this applies more to coal and gas, burnt in power plants, than to oil, which is used mostly in vehicles). This is why fossil fuels must be both cheap and expensive. They must be cheap to the producers to favor the less polluting and more efficient sources. And they must be expensive to the buyer to reduce consumption and thus CO2 emissions and global warming (and induce a switch to renewable energies). A carbon tax, or equivalent mechanism, makes this possible. And, as says Lawrence Summers, "the fall in oil prices and declines in other energy prices make the case for a tax overwhelming".
If the price of petrol doubles over time, consumption will be reduced (thanks to smaller, more efficient cars for instance), but probably by less than half. This will mean a net increase in cost for consumers. But it is important to understand that this small loss for consumers will be more than compensated by a large gain for the State budget (the difference between the two corresponding to a loss for oil producers, due to a drop in sale volume). A clear advantage of a tax is thus that more money will stay in the country instead of being sent to Saudi Arabia or Texas.
If all the crude oil, natural gas and coal that are in the ground were extracted and burnt, the Earth would be as hot and unlivable as hell. The alternative is for some of these resources to stay in the ground rather than warm up the planet. But this of course would reduce the assets of the companies and countries that own them.
This is important for investors as well as for the investment decisions of the producer companies and countries: if the retail price of fuel goes up due mostly to taxes, their sales will be hurt by a high (after-tax) price and the profit margin will be hurt by a low (before-tax) price. Crude oil that is harder and more expensive to produce has an external cost in terms of CO2 (because energy is needed for production itself, the CO2 emissions are greater than the direct emissions) and of pollution. Internalizing these costs will reduce the value of the companies with inefficient and polluting production more than their relatively cleaner competitors. The environmental impact per barrel produced will thus be reduced, reverting the trend of recent years. (The actual value of reserves being overestimated is a better argument than moral calls to sell the stocks of fossil fuel companies: since shares are exchanged on a secondary market, selling them has little impact on the companies and only contributes to feeling good about oneself.)