Carbon Taxes vs Cap-and-Trade

A review of the equivalence of carbon taxes and cap-and-trade:

Carbon taxes vs cap-and-trade, by Stephen Gordon: There are now several plans for reducing greenhouse gas emissions bouncing around the political landscape. ...

It's important to remember that in almost every way that matters, the [carbon tax and cap-and-trade] approaches are equivalent. But..., 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.

For more, see ECON 101: Carbon Tax vs. Cap-and-Trade by John Whitehead at Environmental Economics.

Update: More on this topic here. Tyler Cowen comments. My reply.

Update: See also How Low Income Consumers Fare in the Senate Climate Change Bill, CBPP.

Update: Ryan Avent responds to (and disagrees with) Pete Davis (see next update) in One Last Thing on Cap and Trade.

Update: Pete Davis at Capital Gains and Games explains why politicians favor cap-and-trade over carbon taxes:

Carbon Tax: How Much, How Soon?, by Pete Davis: The climate change debate began in earnest in the Senate yesterday afternoon. Few are questioning the science anymore... The question is how best to control carbon emissions...?

We economists usually recommend a carbon tax... We like that fact that the tax is explicit, not hidden, that it is efficient, minimizing collateral damage to the economy, and that it is effective, raising the price of greenhouse gas emissions and encouraging alternatives.

I kid my friends that "I formulated three carbon taxes for Bob Dole back in the early 1980's that are still in his filing cabinet." I'd be very surprised if the former Senate Finance Chair really kept them, but the fact that they were formulated at all shows that Senate leaders, then as now, were fully aware of of the advantages of a carbon tax. That none of those proposals saw the light of day is conclusive evidence that:

Political leaders don't want:

1. an explicit tax with their name on it;
2. an efficient tax that hurts their supporters; and
3. an effective tax may not encourage the alternatives they support. They prefer a hidden tax, which is why they are considering a cap-and-trade system of carbon allowances instead of a direct carbon tax.

They prefer a less efficient tax, which reduces the impact on the worst greenhouse gas emitters and spreads it around on others.

They prefer a less effective tax, which allows them to pick which alternatives to support and to pick which impacted Americans to compensate.

President Bush listed the objections quite well yesterday in his veto threat against the Lieberman-Warner cap-and-trade bill, S.3036, that the Senate is now debating. It would hurt consumers, shrink the economy, impose regulatory costs, implement a tax and spend system, expand entitlement spending, create new bureaucracies, create trade conflicts, and fail to achieve the bill's stated greenhouse gas emission goals. ...

There is only one thing that most senators agree upon in this debate: S.3036 will not pass this year. The bill will be debated for however long..., and then it will be shelved until next year. That's when we may enact a bill because all three presidential candidates have endorsed one version or another of carbon cap-and-trade.

Our political leaders will be watching the public and private reaction to this debate very carefully for signs of what changes they will need to make next year.

The primary change will be to water the bill down. No one wants to take credit for raising gas prices by 53 cents and electricity prices by 44% by 2030 or to cut GDP by $2.8 trillion by 2050. The path to reduced greenhouse gas emissions in next year's bill will be slower than that which is proposed now. ...