The Vaccine

The smoke carries a cost beyond the person who makes it. The orchard carries a benefit. A tree planted for its fruit may feed a neighbor's bees; a discovery made for one purpose may become another person's instrument. The good passes across the boundary as surely as the harm, but no corresponding payment need travel back. This is the positive externality: a benefit received by someone whose gain is absent from the decision that produces it. The distinction concerns what the decision counts, rather than the generosity of the person making it. A thoroughly public-spirited act may already reckon with its effect on others; a profitable act may leave a considerable benefit unpaid. Where the extra benefit remains outside the calculation, an activity can be worth more to everyone affected than it is to the person asked to undertake it. The market then has a reason to stop while something worth doing remains undone.

A vaccine gives this boundary a human form. Where vaccination reduces a person's likelihood of infection or onward transmission, it can also reduce other people's exposure. Someone unable to receive a particular vaccine, or insufficiently protected by it, may benefit from protection among those nearby. That indirect protection is part of what is meant by herd immunity. It is a benefit of the pattern of protection in a community, and it does not make any individual invulnerable. The argument therefore begins with a particular vaccine, a particular pathogen, and the transmission it can interrupt; it cannot infer the same external benefit from every intervention called a vaccine. The private gain remains substantial in its own right. The additional economic question is what happens when the person's willingness or ability to pay reflects that private gain while some of the protection reaches people who have contributed nothing to its purchase.¹

The missing benefit can be made visible without pretending to put a price on a dose. Consider an illustrative activity whose marginal private benefit, in money units, is twelve minus the quantity undertaken. Each unit costs four to provide and gives outsiders an additional benefit of four. Private purchase stops at eight units, where twelve minus eight equals the cost of four. Counting the outsiders raises marginal benefit to sixteen minus quantity, so the total gain continues until twelve units have been provided. The four omitted units would produce a net benefit of eight: a triangle four units wide and four high. A subsidy of four per unit would align the purchaser's marginal calculation with the full benefit in this example. The arithmetic establishes a possible shortfall in provision, not a measurement of actual vaccination. Its simplifying assumption of a constant external benefit is especially visible in a setting where each person's protection changes the risk faced by the next.²

The community's protection can also change the private incentive to help sustain it. Bauch and Earn examined this feedback in a game of voluntary vaccination: greater coverage lowers infection risk, which reduces the perceived private gain from vaccination. Under their model's assumptions, any positive perceived relative risk from vaccination leaves equilibrium uptake below the level needed to eliminate the disease. The result identifies a tension within a specified system; it does not explain every person's decision. People can care about others, receive different information, face different risks, or be unable to obtain what they want. Those features matter when moving from the model to a community. The useful insight is narrower and durable: a benefit supplied by others may make one's own contribution seem less necessary. Success can weaken the private motive that helped produce it.³

A subsidy answers a missing incentive only to the extent that an available act can respond to the price. A clinic may be distant, an appointment unavailable, or a working day too costly to lose. Making the charge at the counter zero leaves those costs in place. Conversely, a well-supplied service may still leave an unpaid benefit that a contribution toward its price could recognize. The institution must fit the obstacle. Public provision, a payment to a provider, and a payment to a purchaser can each move resources toward an activity, but they place different demands on administration and information. In the numerical example, a subsidy of four paid on all twelve units costs the treasury forty-eight. That expenditure is not the eight of newly created surplus. It is a transfer between people whose taxes and receipts must be accounted for, alongside any real costs of collection and administration. A good unpaid for is a reason to examine a remedy, not a reason to treat its financing as costless.⁴

Knowledge carries a related benefit through a different channel. A useful method can improve another person's work without being consumed in the transfer. Yet producing, explaining, and learning it can each require effort. Arrow's analysis of invention distinguished the gain from making existing information widely available from the incentive to bear the uncertain cost of discovering it. A discoverer may receive only part of the value that subsequent users obtain. Paying for inquiry and permitting its use are therefore separate decisions, even when a single institution tries to settle both. The subsidy, the research grant, the shared laboratory, and the patent address different parts of that problem. The Patent will examine the boundary drawn around an idea. Here the connection is the benefit that escapes the private account: protection reaching a stranger, or a method entering work its inventor will never see.⁵

The orchard thus corrects an easy misunderstanding of the externality. A market can miss what should be encouraged as well as what should be restrained. Its error depends upon the distance between the consequence a decision-maker counts and the consequence the decision produces. That distance can shrink through a bargain, a rule, a payment, or a person's own concern for others; its existence alone does not choose among them. The question asked by the vaccine remains pointed: if my protection reaches you, why does the account stop with me? An answer must identify the extra benefit, the act that produces it, and a practicable way of sharing its cost. The next plate turns the sign around. The Levy asks how a charge might bring an uncounted harm into the same private calculation.