Carbon taxes vs cap-and-trade

There are now several plans for reducing greenhouse gas emissions bouncing around the political landscape. The BC Liberals have implemented a carbon tax and the federal Liberals are also floating the idea. For their part, the federal NDP is talking about a cap-and-trade model, as are the premiers of Ontario and Quebec. And a cap-and-trade model also happens to be the federal Conservative government's policy.

It's important to remember that in almost every way that matters, the two approaches are equivalent. But since the various political parties are all trying to squeeze out as much torque as possible from their own proposals, this point is easy to overlook. So as a public service, here is the Econ 101 explanation of how the two policies work, and why they are equivalent.



Before the policy, the intersection of the supply and demand curves for ghg-emitting products - point A on the graphs - will generate emissions equal to Q₀, and the price will be P₀. Suppose that the government wants to reduce the quantity to Q₁.

• Carbon tax: Suppose that a carbon tax π is added into the price. For a given quantity, the supplier's price will be the old price plus the amount of the tax, and the supply curve will shift up to S*. The new equilibrium is at point B, the quantity is the target Q₁, and the price will increase to P₁. Note that the price increase will be less than the tax, although if the demand curve is fairly steep (i.e., inelastic, or relatively insensitive to changes in price), the increase in the price will be pretty close to π.
• Cap-and-trade: Suppose that the government restricts emissions to a level consistent with Q₁. The new supply curve - denoted by S* - is now vertical at the target: no matter how high the price goes, supply will remain fixed at Q₁. The new equilibrium is again B: the quantity is determined by the cap at Q₁, and the price will rise to P₁.

So as far as prices and quantities go, the two policies are equivalent: as we go from A to B, quantities fall to the target Q₁, and prices rise to P₁. From the consumer's point of view, that's all that matters.

What distinguishes the two is what happens to π - the difference between the price the consumers pay at B and what it costs suppliers to produce at Q₁. In the case of the  carbon tax, the money goes to the government. But if output is capped at Q₁, that difference is pure profit: a permit to produce one unit of output allows its owner to collect a rent equal to to the difference between the selling price and the cost of production. If permits are traded, their price will be bid up so that their price will be equal to π. So where that money goes depends on how the permits are allocated in the first place. If the permits are simply given to existing emitters, then those profits are pocketed by the firms. If the permits are auctioned off, the price will be bid up to π, and the government gets the money.

So if permits are auctioned off by the government, then cap-and-trade and a carbon tax are equivalent: same quantities, same prices, and the government gets revenues equal to the area in the green rectangle in the graphs.

Update: Mark Thoma reminds us of a more sophisticated - yet still very accessible - analysis at Environmental Economics.

Comments

[Brian]

Thank you for the clear description! I've heard many people claim a carbon tax is basically the same as a cap-and-trade system with auctioned permits, but this is the first explanation I've seen for why.

However there are still ways that matter in which the approaches are not equivalent. For one, ultimately what we're trying to do is reduce GHG emissions. The environment is directly affected by the absolute amount we are polluting. A cap-and-trade approach allows us to control this absolute amount directly, instead of guessing an appropriate value for a tax. We would inevitably guess wrong and be constantly correcting in an unpredictable way.

[ramster]

Assuming that we have en emissions target Q1, how do you set the carbon tax such that you achieve it? Doesn't this imply that you know the slopes of the curves?

[Marc Bilodeau]

One significant difference is that quotas don't have to be 100% auctioned with the government collecting the proceeds, as is the case with a Pigouvian tax. When the quotas are just given away to the polluting firms, the country is essentially in a "pollutees pay" regime and citizens who are harmed by pollution could buy and retire some pollution permits (if they can overcome free-riding), with the money going to the firms as compensation for reducing their pollution. Alternatively, if the permits were given to the citizens, the country would be in a "polluters pay" regime as polluters would need to buy permits from citizens in order to release any pollution. I suppose we could call a regime where permits are auctioned directly by the government as being a form of polluters pay if we take the government to be the agent for citizens.

One possible advantage of permits over a tax is that it allows the government the possibility of giving away some permits to polluters and auctioning others (i.e., less than 100% auction), which, by giving some property rights to polluters might mollify their opposition. Whether doing so would be necessary depends on their lobbying power and ability to prevent the measure from being adopted. There are also conservatives (especially in the US) who are allergic to the word tax and would have a knee-jerk reaction against anything that is called a tax. For these people, calling the measure cap-and-trade may frame it in a more palatable way.

[JV]

Dropped by your blog after posting on economists view to see what others are doing. Just started posting my own keyhole into alternative energy and all that means. All about money in the end.

So, how much does Canada get for the tar sands that T. Bonne Pickens wants to harvest?