Pareto-relevant and -irrelevant externalities.
More formally, an externality is said to exist whenever the benefit or profit of one person or firm (known as a bystander) is directly affected by the actions of another person or firm, and the bystander is neither compensated nor pays compensation. Externalities can be both positive and negative - but this is not the most important distinction. For the purposes of examining the consequences of the existence of externalities for the invisible hand theorem and for the role of the legal system, we will distinguish between two classes of externalities:3 
Figure 1.3.6 A negative externality
To understand this distinction, suppose that there are two individuals, 1 and 2. Suppose that person 1 undertakes an activity (the level of
which, Q, is chosen by him), which yields him benefits of B(Q) = Q - .
Suppose, however, that this activity leads to an uncompensated cost of Q2
C(Q) = being imposed on individual 2. The efficient outcome here
equates marginal benefits, which are equal to B'(Q) = 1 - Q with marginal costs, which are C'(Q) = Q. Therefore, Q  = 1 is the efficient level
of Q. The situation is illustrated in Figure 1.3.6.
This example implies two further conclusions: •
By definition, the welfare economist need only be concerned with Pareto-relevant externalities - that is, the first kind examined in this example, rather than the second.
The presence of Pareto-relevant externalities can cause the invisible hand theorem to fail. To see this, apply the previous example to a market setting. That is, suppose that there is a competitive market in which each firm has a zero marginal cost of production, and that type 1 individuals consume the good, with a demand curve of B'(Q) = 1 - Q.
Suppose that production of Q imposes a cost of C(Q) = on type 2
individuals, who do not consume the good. The competitive equilibrium here is where price equals marginal cost, which is where Q = 1. But
the efficient outcome is Q * = . Thus, the competitive market outcome
is inefficient. 2 188.8.131.52.2 Pecuniary externalities. Non-economists often make the mistake of thinking that every activity that generates an uncompensated reduction of an individual's utility level (that is, every externality) is a candidate for government intervention and regulation. But a moment's thought reveals that this view cannot be sustained.
First, some actions cause harm that is so trivial (relative to the costs of regulation) that it is appropriate, from an efficiency point of view, for the law to ignore them. Second, and more importantly, not all acts which harm others are Pareto relevant. Consider, for example, changes in prices. Increases in prices certainly tend to hurt consumers and tend to benefit producers. The opposite is true for price reductions. But do we really want to treat such price changes as externalities that are worthy candidates for regulation and intervention?
The answer, of course, is no. To see why, consider a perfectly competitive industry, and suppose that all producers experience a rise in marginal costs due to an increase in the price of an input. In the long run, this cost increase will be completely passed on to consumers in the form of an equal rise in prices. The costs of production have risen, so this will certainly reduce society's well-being - that outcome is unavoidable. The question is who should bear these costs so that the overall negative effect of higher costs is minimised. If prices rise, consumers are certainly worse off: they consume fewer units of the good, and for the units that they continue to consume, they pay a higher price. But the law does not force producers to compensate consumers for this price rise. Why not?
The reason is that the price rise is efficient: relative to a situation where prices do not rise, the price rise confers a benefit on producers that exceeds
the cost to consumers. Moreover, the size of the price rise that occurs in a competitive market minimises the overall loss to society. To see this, consider Figure 1.3.7 below. Initially, firms face a marginal and average production cost of c0, which is also equal to the market price. At this price, consumers purchase Q 0 units of the good. Then, suppose that marginal costs rise to c1 > c0. Suppose first that producers were enjoined (prevented) from passing on the price increase. Then consumers would continue to consume Q 0 units, but producers would experience a loss of A + B + C, which is greater than the loss to consumers if producers did increase prices (i.e. the change in consumer surplus of A + B). Thus, a law preventing producers from passing on price increases would reduce society's overall well-being by the additional amount C.
Now consider an alternative rule which allowed prices to rise but which forced producers to compensate consumers for the reduction in consumer surplus. Relative to the situation where the price rise is not passed on, producers gain A + B + C from increasing prices, since they avoid this loss. Thus, they would be willing to compensate consumers by the amount A + B, instead of not reducing prices and facing the loss of A + B + C. But all that the law has achieved here is to alter the distribution of costs and benefits: producers, rather than consumers, have been forced to bear the cost of the rise in input prices. There has been no overall welfare gain at all, because the price rise was actually an efficient response by producers to changing cost conditions.
Moreover, the price signal provided important information to consumers: it 'told' them to consume less of a good whose costs have gone
Figure 1.3.7 A pecuniary externality up, and to consume other goods instead. When some goods become more costly (or more scarce), that is exactly the signal that we want consumers to heed. In other words, price changes provide an incentive for economic actors to shift resources from low-valued to high-valued uses, which is exactly what is required for efficiency. Market prices tend to convey this information far more effectively than courts or regulators - that, after all, is the point of having markets.
Finally, it is very doubtful that such a law would be able achieve its aims. Production conditions and costs are changing all the time. Under the legal principle discussed above, what is meant to happen if producer costs fall? In a competitive market, the market price would fall and consumers would gain. Using the same legal principle, is the law then supposed force consumers to compensate producers for the fall in prices? Again, there would be no benefit to the community from such a rule, and very likely great costs. From an efficiency point of view, there is no role for the legal or regulatory system in dealing with the effects of pecuniary externalities.
-  A Pareto-relevant externality: This kind of externality existswhen the extent of the activity may be modified in such a way as tomake the damaged party better off without making the acting partyworse off. That is, the activity can be modified in such a way that aPareto improvement is possible. • A Pareto-irrelevant externality: This kind of externality existswhen the extent of the activity cannot be modified in such a wayas to make the damaged party better off without making the actingparty worse off. One party's benefit or profit may still be affected bythe other's actions in the aggregate, but there is no change that couldbe undertaken so as to make a Pareto improvement.
-  At any other point (say, for example, Q = 0 or Q = 1), there is a wayto make at least one of these individuals better off, without makingthe other worse off. In other words, at any point other than Q = 1/2,the externality is Pareto relevant; and • At the point Q1 = , individual 2 is still negatively affected by Q (his cost would be lower if Q were lower), but this negative externality isnow Pareto irrelevant: the extent of the activity cannot be modifiedin such a way as to make the damaged party (individual 2) better offwithout making the acting party (individual 1) worse off.