Using a Pigovian tax to correct for a negative (consumption) externality

In my previous post, I demonstrated that, if left alone, a market with a negative externality produces too much of a good, and creates a deadweight loss. At the end of that post, I noted that, if we wanted to reduce the quantity that is traded in the market, we could use a tax. Such a tax is called a Pigovian tax (named after 20th Century economist Arthur Pigou), and is the focus of this post.

Consider the same market as that previous post (the market for fireplaces, or fireplace use), as shown in the diagram below. The market operates at the point where supply (S) meets demand (D) - that is, the quantity traded will be QM (and the price of fireplaces, or fireplace use) will be PM. Consumer surplus is the area ACPM, producer surplus is the area PMCF, the welfare cost of the negative externality is the area ACHG, and total welfare (which is the sum of consumer surplus and producer surplus, minus the area of the negative externality) is equal to the area (GEF-ECH).[*]

Now consider what happens when the government imposes an excise tax on fireplaces (or fireplace use). We will assume that the per-unit cost of the tax is exactly equal to the marginal external cost (MEC), and that the tax would be paid to the government by the sellers of fireplaces (or fireplace users). We represent the tax with a new curve, S+tax, which is exactly the same distance above the supply curve as the MSB curve is below the demand curve (that's because the tax is exactly equal to MEC). The price that consumers pay increases to PC. The effective price that producers receive (after paying the tax to the government) decreases to PS. The quantity of fireplaces (or fireplace use) decreases to QS.

What happens to economic welfare? The consumer surplus is the area ABPC, and the producer surplus is the area PSEF. The government receives tax revenue equal to the area PCBEPS (this is part of total welfare, because the government can use that revenue to provide services like schools or hospitals). The area of the negative externality is the area ABEG. Total welfare with the tax is equal to GEF. [**]

In other words, the Pigovian tax not only reduces the quantity of fireplaces (or fireplace use), but leads to an increase in total welfare (in fact, it leads to total welfare being maximised and the deadweight loss being eliminated). Economists aren't often in favour of excise taxes, but this is one case where an excise tax can make society better off.

Read more:

• The welfare impacts of a negative (consumption) externality

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[*] For the explanation of these welfare areas, see my previous post.

[**] Note that this is the same total welfare as occurred at the quantity QS in my previous post. To recap, that's because the area of the negative externality ABEG cancels out some of the total welfare that was in the combined consumer and producer surpluses and government revenue (ABEF), leaving the area GEF.