Turn the wedge the other way and a second failure appears. The orchard can feed bees beyond its owner's fence; a useful discovery can enter the work of people who paid nothing toward it. Some activities confer benefits that spill beyond the one who undertakes them. The sign has changed, but the accounting problem is familiar: the consequence reaches farther than the decision that produces it. A private calculation can stop while something worth doing remains undone. The trees left unplanted are harder to see than the smoke already in the air. They nevertheless belong in the account of what a market leaves outside its price.
The benefit matters at the point where another act is being considered. A grower may earn enough from the fruit to plant one more tree, or may decide that its yield will not cover the ground, care and water it requires. If that tree also supplies an unpaid service to someone nearby, its full contribution exceeds the return the grower receives. There can then be a range in which the tree costs more than its private return but less than the combined benefit. The shortfall arises only insofar as the extra benefit remains outside the decision. A grower who values the neighbor's gain, receives a payment for it or owns both enterprises may already have a reason to count it. The fact that a consequence crosses a fence does not tell us whether it crosses the boundary of the owner's reckoning.
The orchard itself teaches why that boundary must be investigated. Steven Cheung's 1973 study of beekeeping in Washington found contracts and payments where the familiar example had invited readers to imagine an unpaid service. Pollination and honey could be joint products of the same hive, and the payment could depend on the value of each. A grower might pay for pollination; a beekeeper might pay for access to a valuable nectar source. Cheung also reported that the apple blossoms in his setting yielded little or no honey, a useful rebuke to the ease with which a charming picture can become an assumed fact. His investigation did not abolish the positive externality. It showed why the analyst must look for the bargain before declaring the benefit unpriced.
A small numerical orchard can isolate what the missing payment would change. Suppose the marginal private benefit of an activity is eighteen minus twice its quantity, each unit costs six, and each gives outsiders an additional benefit of six. These are illustrative money-valued schedules, with divisible units, fixed valuations and no other effects. Private provision stops at six units, where the private marginal benefit has fallen to six. Counting the outsiders raises marginal benefit by six and carries the efficient quantity to nine. Between six and nine lie three units whose total benefit exceeds their cost. The gain forgone is nine: a triangle three units wide and six high. Nothing in that calculation tells us how many actual trees, lessons or laboratory hours are missing. It identifies the evidence that an estimate would need: the extra benefit, the response of provision and the resources that provision consumes.
A subsidy can carry the omitted benefit back into that private choice. In the example, paying six for each unit makes the provider count a reward equal to the external benefit and choose nine. The treasury pays fifty-four. The added gain remains nine. The distinction matters because the payment covers units that would have been provided anyway as well as the three newly induced units. A transfer can be needed to change the decision without itself constituting new value. Its financing, administration and the opportunities forgone elsewhere also require an account. If those additional real costs were twelve, the specified remedy would consume more than the nine it created. The original shortfall would still exist; this particular means of closing it would fail the comparison.
The useful subsidy follows the additional benefit that is still omitted. If the grower already receives the full six through a pollination contract, paying another six on top would count the same service twice. If the benefit is zero, the justification supplied by this example disappears. If the payment induces an activity whose external benefit is smaller than was assumed, the chosen quantity can pass the point at which further provision is worth its cost. These are questions about the effect of the payment, not the reputation of the recipient. Calling an industry helpful does not identify which act should be encouraged, how much it helps others, or whether the proposed support changes that act at all.
Knowledge makes the uncollected benefit both more extensive and harder to delimit. A method can improve another person's production without being used up in the transfer. Producing the method, explaining it and learning to use it may each be costly, however, and the people who benefit can be far removed from the inquiry that made it possible. Arrow separated the efficient use of information already obtained from the incentive to undertake its uncertain production. Free access can serve the first purpose while leaving the second unfunded. A charge can help reward discovery while excluding users whose gain exceeds the small additional cost of communicating what is known. The institution must decide how to support the making without needlessly obstructing the use.
The research grant and the right to exclude therefore work on different parts of the problem. A grant can pay toward the inquiry before its result is known, while leaving the resulting method available. An exclusive right can make successful use a source of private revenue, while changing the terms on which others may build upon it. Neither description establishes the best arrangement in every field. Someone must select the inquiry, assess performance, define the right and bear the risk of failure. The old orchard question survives inside each device: how much of the benefit reaches the person making the costly decision, and what else must be given up to bring it there? The answer is an institutional account, not merely a higher number written above the private-benefit curve.
A common benefit also gives its recipients a reason to wait for someone else to pay. Cleaner shared air or a freely available result can reach a person after that person declines to contribute. The value received and the contribution offered can consequently diverge. Samuelson's analysis of collective consumption made the information problem explicit: when payment depends on declared benefit, a person can have a private incentive to understate what the common service is worth. The difficulty is not resolved by adding everyone's statements as though they were observed market purchases. Nor does the existence of that incentive prove that cooperation is impossible. It explains why arrangements for contribution, assurance and representation form part of the provision of the good itself.
The benefit may also depend on how many others have already acted. One person's contribution can be most valuable when it fills a particular gap, or when it completes an arrangement that would otherwise fail. In such cases a constant payment per unit is a simplification. The desired rule must follow the relevant margin, including location, timing and the response of other people. The same need for specificity applies to education and public knowledge. A higher private wage is a return to the person educated; a demonstrable improvement in someone else's work is a different effect. Both can matter, but adding them requires care about what has already been counted. The phrase social benefit cannot do the work of identifying its recipient and mechanism.
A claim to spillovers must therefore survive a comparison with what would happen without the proposed support. Would the research proceed anyway? Would a contract pay for the service? Would the recipient expand the activity, or simply receive more for an unchanged output? Would the same resources produce a larger benefit elsewhere? Cheung's warning reaches beyond the bees: an imagined failure and an imagined costless remedy can be made to fit one another perfectly. An actual proposal must meet the institutions, information and incentives that exist. The test preserves the reason to support valuable unpaid benefits while denying the label to claims that have never shown where the unpaid benefit lies.
The good that reaches a stranger can still be missing from the reason to make it.
The gift ends where the account becomes adequate to the decision. Sometimes a payment can bring the escaped benefit home; sometimes a shared institution must undertake work that no isolated receipt will finance; sometimes the supposed omission has already been answered by a bargain. The inquiry is exacting because the unmade good leaves no invoice to inspect. It asks us to identify an opportunity rather than merely admire an intention, and to compare the cost of securing it with the benefit it would add. Across the next road, the sign turns again: the crowd makes a cost that each arrival partly leaves to others. The argument remains open.