The welfare impacts of a negative (consumption) externality

As I noted earlier this week, an externality is the uncompensated impact of the actions of one person on the wellbeing of a third party. A positive externality makes the third party better off, while a negative externality makes the third party worse off. They are called externalities because they lie outside the original decision, i.e. some of the costs or benefits are external to the person whose action creates them.

The most common example that economists use to explain negative externalities is pollution. For example, from this New Zealand Herald article from earlier this year:

Two air pollutants are quietly contributing to thousands of premature deaths in New Zealand every year, shows a new analysis that’s prompted fresh calls for tougher regulations.

While New Zealand’s air quality is generally considered good by international standards, Stats NZ’s newly updated indicator has linked pollution from vehicles and fireplaces to around nine times more early deaths than last year’s road toll.

People running vehicles or fireplaces are creating a negative externality for other people - an increased risk of death from poor air quality. Let's focus on fireplaces and show that, left alone, the market will lead to too much use of fireplaces. Consider the market for fireplaces (or fireplace use) as shown in the diagram below. The market will operate at the quantity 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.

However, the fireplace users create a negative externality for other people. Since this externality arises from the buyers of fireplaces (or fireplace users), we show this externality on the demand side of the market - we refer to it as a negative consumption externality. [*] This means that the benefits that fireplace users receive themselves from operating their fireplaces are higher than the benefits that society receives from those fireplaces - the difference is the negative benefit that is imposed on other people through air pollution. We show this on the diagram by differentiating between the marginal social benefit (MSB) and the marginal private benefit (MPB). The MPB is the benefit that fireplace users receive for themselves. The MSB is the marginal private benefit, minus the cost of the externality - the marginal external cost (MEC).

Now, society prefers the quantity of fireplaces (or fireplace use) to be the quantity where marginal social benefit (MSB) is equal to marginal social cost (MSC) - I'll explain why a little later in this post. That is the quantity QS, and one way to get to the quantity QS is if the price of fireplaces (or fireplace use) decreased to PS (because then, sellers would not be willing to sell so many fireplaces). Notice that in the diagram, relative to the quantity that society prefers (QS), the market produces too much (QM). There are too many fireplaces (or too much fireplace use).

Why does the market prefer QS (the quantity where MSB = MSC)? It's because that's the quantity that maximises economic welfare. Economic welfare is the sum of all of the net benefits arising from the market. First, the consumers receive some net benefit from participating in the market. Consumer surplus is the difference between the amount that consumers are willing to pay (shown by the demand curve), and the amount they actually pay (the price). In the diagram, at the equilibrium price and quantity, consumer surplus is the area ACPM. Second, producers receive some net benefit from participating in the market. Producer surplus is the difference between the amount the sellers receive (the price), and their costs (shown by the supply curve). In the diagram, at the equilibrium price and quantity, producer surplus is the area PMCF. Third, the third parties are negatively affected by the market. The welfare cost of the negative externality is the area in-between marginal social cost and marginal private cost, up to the quantity of fireplaces (or fireplace use) traded (in this case, QM). That is the area ACHG, and it is subtracted from total welfare. Total welfare is the sum of consumer surplus and producer surplus (which is the area ACF), minus the area of the negative externality (ACHG), and is equal to the area (GEF-ECH). [**]

Now consider the market operating at the quantity QS (with the price PS). The consumer surplus is the area ABEPS, the producer surplus is the area PSEF, and the area of the negative externality is the area ABEG. Total welfare at QS is equal to GEF. [***] Notice that this total welfare is larger when the quantity is QS than when the quantity is QM. If the market is left alone, there are too many fireplaces (or too much fireplace use), and this decreases total welfare by the area ECH. That area ECH is the deadweight loss of the externality.

Since the market produces too much, a relevant question is how could we get the market to produce less? A Pigovian tax (named after 20th Century economist Arthur Pigou) is one option, since taxes reduce the quantity of a good that is traded (for more on that, see this post). Requiring permits for fireplaces would be another way to limit the number of fireplaces to QS. Of course, determining the optimal quantity QS is difficult in practice. However, we can be sure that it isn't the quantity that is provided by the market.

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[*] In contrast, when producers produce pollution as a consequence of manufacturing other goods (for example), that is a negative production externality, which we would show on the supply side of the market.

[**] Notice that the area of the negative externality ACHG first cancels out all of the total welfare that was in the area ACEG, leaving the area ECH left over. That's why only GEF is left, while ECH is left subtracting from total welfare.

[***] Notice that the area of the negative externality ABEG cancels out some of the total welfare that was in the combined consumer and producer surpluses (ABEF), leaving the area GEF.