Carbon taxes vs cap-and-trade

Stephen Gordon at the Worthwhile Canadian Initiative blog has a nice discussion of the differences between carbon taxes and cap-and-trade. He writes

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.

Note that that in almost every way that matters, the two approaches are equivalent. The one remaining question is what happens to π, which is the difference between the price the consumers pay at B and what it costs suppliers to produce at Q1. It goes to the government when a carbon tax is applied. But if a cap (at Q1) is applied the difference turns into pure profit. As Gordon explains

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.

Thus who gets the money depends on who the permits are allocated to in the first place. Gordon notes

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.

Thus if we auction off the permits the money goes to the government in which case the cap-and-trade and a carbon tax are equivalent. That is, we get the same quantities, the same prices, and the government gets revenues equal to the area in the green rectangle in the graphs.

For those who want more, there a more sophisticated - yet accessible - analysis available at the Environmental Economics blog.