The welfare impacts of a positive (consumption) externality

Back in 2023, I wrote a post about the welfare impacts of a negative consumption externality. I think I always meant to follow up that post with a companion post about the welfare impacts of a positive consumption externality, but I never did. So here goes!

To recap, 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.

There are fewer examples of positive externalities that come readily to mind than negative externalities, but let me use the example from my ECONS102 class: vaccinations. A person who gets vaccinated receives some benefit themselves, because they are less likely to get infected by whatever they have been vaccinated against. However, they also provide a benefit for other people (including those who are unvaccinated), because other people are less likely to catch the infection as well (because they are less likely to catch it from the vaccinated person).

Consider the market for vaccinations 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 vaccinations will be PM.

However, the vaccine recipients create a positive externality for other people. Since this externality arises from the buyers of vaccinations, we show this externality on the demand side of the market - we refer to it as a positive consumption externality.[*] This means that the benefits that vaccine recipients receive themselves from getting vaccinated are lower than the benefits that society receives from those vaccinations - the difference is the benefit that is received by other people. 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 vaccine recipients receive for themselves. The MSB is the marginal private benefit, plus the benefit of the externality - the marginal external benefit (MEB).

Now, society prefers the quantity of vaccinations 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 vaccinations decreased to PC (because then, more people would be willing to get vaccinated). Notice that in the diagram, relative to the quantity that society prefers (QS), the market produces too little (QM). There are too few vaccinations (or too few people getting vaccinated).

Why does society 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 FEPM. 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 PMEH. Third, the third parties are positively affected by the market. The welfare benefit of the positive externality is the area in-between marginal social benefit and marginal private benefit, up to the quantity of vaccinations received (in this case, QM). That is the area AGEF, and it is added to total welfare. Total welfare is the sum of consumer surplus and producer surplus (which is the area FEH), plus the area of the positive externality (AGEF), and is equal to the area (AGEH).

Now consider the market operating at the quantity QS (with the price PC). The consumer surplus is the area FJPC. The producer surplus is tricky, because to get the market to produce QS, that would require the seller to accept a price that is below their costs (notice that the price PC is below the firms' costs shown by the supply curve). In reality, the government would probably subsidise this good to achieve the optimal outcome, but we will instead assume that the government mandates that the seller provide vaccinations at below cost, to anyone who is willing to pay the price PC (this might make some sense in a public health care system like New Zealand, but is still just a simplifying assumption rather than a description of how this would work in practice). The producer surplus is therefore the area -PCHBJ (it is all negative, because every vaccination is provided for a price that is below the sellers' costs). The area of the positive externality is the area ABJF. Total welfare at QS is equal to ABH.[**] 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 few vaccinations (or too few people getting vaccinated), and this decreases total welfare by the area GBE. That area GBE is the deadweight loss of the externality.

Since the market produces too little, a relevant question is how could we get the market to produce more? A Pigovian subsidy (named after 20th Century economist Arthur Pigou) is one option, since subsidies increase the quantity of a good that is traded (for more on that, see this post). Of course, determining the exact 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 a positive externality as a consequence of manufacturing other goods (for example), that is a positive production externality, which we would show on the supply side of the market. An example of a positive production externality is the smell of freshly baked bread emanating from a bakery (at least, it's a positive externality for those who like the smell of bread).

[**] Calculating total welfare involves adding the consumer surplus and externality (adding FJPC and ABJF gives the area ABJPC) and then subtracting the negative producer surplus of PCHBJ, which leaves the area ABH.