8.1 Externalities and Efficiency

In many markets, the decisions of some agents directly affect the well-being of others, even though the latter are not directly involved in the transaction. These externalities can be negative, when they generate a cost, or positive, when they generate a benefit.

A classic example of a negative externality is pollution: a firm that emits harmful substances during production imposes a cost on the community — for example, less clean air — without bearing that cost itself. A classic example of a positive externality is education: a person who studies not only increases their own human capital, but also contributes to a more productive and responsible society, generating benefits that go far beyond the individual.

Externalities create a gap between the private benefit or cost (received or borne by the individual) and the social benefit or cost (received or borne by the community). As we will see, in the presence of a negative externality, the market mechanism leads to an excessively high traded quantity compared to the socially efficient level. In the case of a positive externality, the opposite occurs: the quantity is too low.

Two Simple Examples

Before proceeding with the general analysis, we present two very simple examples that will help us intuitively understand how externalities alter the efficiency of exchange.

Negative Externality: Plastic Bottles

Alice goes to the supermarket to buy mineral water. She has two options: a crate of glass bottles priced at $5$ euros (which is also the marginal cost of the crate for the supermarket), and a pack of plastic bottles priced at $4.50$ euros (which is also the marginal cost of the pack for the supermarket). Alice considers the two goods as perfect substitutes, so she chooses to buy only the cheaper one. Her willingness to pay for either alternative is $5.10$ euros.

The choice Note that if Alice had to pay a tax of $0.50$ euros or more to buy the plastic bottles, she would choose the glass ones instead. We will discuss taxes as a remedy for negative externalities in the next section. made by Alice gives her a private surplus of $5.10 − 4.50 = 0.60$ euros. However, this choice has effects on other parties that Alice does not take into account. In fact, Alice lives in a municipality where plastic is not properly disposed of, contributing to marine pollution. This collective damage has been estimated at $0.90$ euros for each pack. The social cost of the pack purchased by Alice is therefore

$4.50$ (private cost) $+$ $0.90$ (environmental damage) $=$ $5.40$

Since Alice values the pack at $5.10$ euros, while the social cost is $5.40$ euros, the exchange results in a deadweight loss for society. The social surplus generated by Alice’s choice is $5.10-4.50-0.90=-0.30$. The market outcome is socially inefficient.

At the core of a negative externality lies the fact that the harmed parties are external to the bargaining process. Of course, in the calculation we should also include the surplus of the seller (the supermarket). But it is zero in both cases, since the supermarket sells at cost. If they could take part, they might, for example, offer Alice $0.70$ euros in exchange for giving up plastic in favor of glass. Alice would earn more than her $0.60$ euros of private surplus: she would buy a crate of glass bottles for $5.00-0.70=4.30$ euros, obtaining a surplus of $5.10-4.30=0.80>0.60$. The harmed parties, for their part, would also be better off: they would spend $0.70$ to avoid suffering a damage of $0.90$. The total surplus would increase, and everyone would benefit.

Positive Externality: the Beekeeper

Bruno, a beekeeper, is considering increasing his honey production by installing a new hive. Bruno works near cultivated fields. The new hive costs $100$ euros, and based on expected honey production, Bruno estimates it is worth $90$ euros to him. Under these conditions, Bruno chooses not to install it.

However, If Bruno received a subsidy of 10 euros or more, he would install the new beehive. We will discuss subsidies as a remedy for positive externalities in the next section. the bees would perform pollination that would improve the productivity of the nearby cultivated fields. Farmers estimate this additional benefit (higher revenue or lower costs) to be worth at least $20$ euros. The social benefit of the hive would therefore be:

$90$ (for Bruno) $+$ $20$ (for the neighbors) $=$ $110$

with a cost of $100$ euros. The potential social surplus is therefore $110 - 100 = 10$ euros. But since Bruno receives no compensation for the benefit he generates for others, he chooses not to install the hive. Once again, the market does not function as it should. And again, the core of the issue is a bargaining failure: if the farmers could participate in the transaction — for example by offering a contribution of $15$ euros — Bruno would change his decision (since $90 + 15 > 100$), and everyone would benefit.

Externalities: General Analysis

The examples of Alice and Bruno show that the market, left to itself, does not take into account the effects that consumption and production decisions have on third parties. To better understand why this happens, let us start from how an exchange normally works. The demand curve represents the marginal private benefit ($MPB$), that is, how much consumers are willing to pay for one more unit of the good; the supply curve measures the marginal private cost ($MPC$), that is, In other words, $MPC$ is what we have denoted as $MC$ in the previous chapters. how much it costs producers to supply one additional unit. The market equilibrium is found at the point where $MPB=MPC$, and this equality, when no externalities are present, ensures efficiency.

Things change For example, if $Q$ measures the tons of plastic produced, we can think of $EC(Q)$ as the cost that an environmental remediation firm would have to bear to repair the damage caused by that production, and of $MEC(Q)$ as its marginal cost. when market decisions have consequences that go beyond buyers and sellers. In the case of a negative externality, the exchange generates harm to external parties. The size of this damage, expressed in monetary terms, is the external cost, which we denote by $EC(Q)$ when the traded quantity is $Q$. The additional harm due to one more unit is the marginal external cost ($MEC$), the derivative of $EC(Q)$. In the case of a positive externality, instead, the exchange brings benefits to third parties, and we can speak of external benefit $EB(Q)$ and the corresponding marginal external benefit ($MEB$).

Based on these definitions we can distinguish between private values, which determine the decisions of consumers and producers, and social values, which also include external effects. In particular, the marginal social benefit ($MSB$), which measures how much society benefits from the exchange of one more unit of the good, is \(MSB = MPB + MEB\) while the marginal social cost ($MSC$), that is, how much the exchange of one more unit of the good costs society, is \(MSC = MPC + MEC\) The socially efficient quantity is the one such that

\(\begin{gathered} MSB=MSC \end{gathered}\)

In other words, it is socially desirable to produce and consume the good up to the point where the social benefit generated by one additional unit of the good equals the collective cost it entails.

However, in the market buyers and sellers choose on the basis of their own benefits and costs, that is, the private ones. The good is produced and consumed up to the quantity that equates demand and supply, that is, up to the point where $MPB=MPC$, and this behavior does not coincide with the social optimum ($MSB = MSC$) because it completely ignores the effects on third parties. As illustrated in the following figure, the consequence is that in the presence of a negative externality the market results in too many trades compared to the social optimum.

In the presence of a positive externality, by contrast, the quantity is lower than the socially efficient one. We illustrate this fact in the following graph, assuming for simplicity a constant marginal external benefit.