The beam reaches the second ship without taking anything from the first. Once the lamp is lit, another captain can read its warning without dimming the message or exhausting a stock of safety held inside the tower. The pasture and the beacon therefore present different troubles. On the pasture, one person’s taking can leave less for the rest. At the beacon, the difficulty is to obtain the work whose result can serve them together. The light is useful precisely because it travels beyond its keeper’s hands. That same reach makes it difficult to turn every use into a sale.
Shared consumption and difficult exclusion are distinct properties. A good is non-rival over the relevant range when another person’s enjoyment does not subtract from what remains for others. Exclusion concerns the possibility and cost of keeping a nonpayer away. These dimensions can change independently. A signal can serve another receiver cheaply while access to the signal is controlled; a harbor can admit only paying vessels and still become crowded. The public-good problem is sharpest when the benefit can be shared without depletion and the people who finance it cannot readily confine it to themselves. Neither description makes construction free. The beam costs little to share after the tower, lamp and maintenance have been supplied.
Samuelson’s contribution was to ask how much of such a good should be supplied when everyone consumes the same quantity. For a private good, the unit placed in one person’s hands cannot ordinarily be placed in another’s at the same time. The public unit can benefit them both. The relevant comparison therefore adds their marginal valuations of that same unit and sets the sum against the resources it costs to produce. A project can be worth undertaking even when no one person would buy it alone. The benefits have to be added across the people reached by the light, rather than assigned to an imaginary buyer who receives them all.
Consider two households and a shared service whose quantity we can vary. In this invented example, the first household values the next unit at eight minus the quantity already supplied; the second values it at six minus that quantity. Each unit costs six. At a quantity of four, their marginal valuations are four and two, which together meet the cost. Four is the efficient quantity in this deliberately simple setting. If each instead buys additions to the shared service at the full price of six, the first household stops at two and the second supplies nothing further. Both receive those two units. Voluntary provision is positive, but too small: one household’s purchasing decision leaves out the benefit its payment would confer upon the other.
The arithmetic also identifies a temptation. If the households could be charged four and two per unit respectively, both would want the quantity four, and the charges would cover its cost. But writing the right personalized prices is easier than discovering them. A household that expects its contribution to depend upon its stated benefit has a reason to understate that benefit while hoping the service will still arrive. Samuelson’s warning concerned this failure of ordinary decentralized price signals to elicit the needed information. It did not establish that every institution for funding a shared service is impossible. It established why the private-good recipe cannot simply be carried over unchanged.
The actual lighthouse had a shore as well as a beam. Coase’s historical study made the shore decisive. The inability to collect a coin from every vessel while the light was guiding it did not prevent a system of payment from being built around the voyages those vessels made. Private lighthouse promoters in his English account obtained patents authorizing construction and specified tolls. Agents collected the dues at ports, commonly through customs officials. The beam remained open to view. Payment became collectible at another point in the voyage, through rights and procedures that did not require the keeper to extinguish the lamp whenever a debtor came into sight.
That history supports a more exact conclusion than the slogan that the lighthouse was privately provided. Construction, ownership, operation, the source of revenue and the authority to collect it are separate questions. Coase found private enterprise at work within a legally supported toll system, later followed by different arrangements under Trinity House. This is evidence against the claim that a lighthouse could only be built and run by a government department. It is not evidence that the beam could finance itself through unrestricted voluntary payments, or that public authority had been absent from the arrangement. Coase himself ended by reserving judgment about the best system of lighthouse finance pending further study.
Collecting money at a port can solve one difficulty while creating another. If the charge deters a voyage whose additional use of the existing light costs almost nothing, some useful use may be lost. If the charge is removed, the expense still has to fall somewhere: on taxpayers, other port users, donors, or the return from another service. One cannot compare a real toll system with a free treasury that has neither collection costs nor competing demands. The relevant choice joins a funding rule to its consequences for use, maintenance and decisions about new construction. The place where the money is collected can influence whose judgment counts when the next light is proposed.
Even perfect knowledge of the two households’ valuations would not settle every public decision. Their willingness to pay reflects what they can pay and what alternatives their wealth allows. A benefit to a person with little money need not matter little merely because it produces a small bid. Conversely, calling an undertaking public does not make its benefits exceed its costs. A lighthouse in the wrong place can be a useless tower. A warning can be widely shared and still fail to address the danger people actually face. The calculation of efficient provision has to be placed inside a judgment about distribution, necessity and the purposes the institution is meant to serve.
The light can be shared without being free to provide. Its reach explains the problem; the means of paying for it determine the possible answers.
The same discipline is needed when moving from the beacon to common knowledge or clean air. Knowledge already disclosed can often be used by another person without being used up, but producing it, communicating it and making it usable remain costly activities. Clean air can be jointly enjoyed while the atmosphere’s capacity to receive harmful emissions becomes a scarce shared resource. The categories identify different margins within a situation; they do not turn every useful thing into a pure public good. A good diagnosis asks which additional use costs something, which beneficiaries can be reached by a charge, and which effects remain outside the proposed arrangement.
Who is to build the beacon, then? Whoever can be placed within an arrangement that secures the resources, rewards competent provision, and remains answerable for the service. That may join public finance to private construction, user charges to a common authority, or a community’s contributions to work it carries out itself. The classification does not choose among them. It explains why the choice has to be made with care. The light’s refusal to distinguish its beneficiaries leaves an institutional task on shore. The next plate considers the opposite response: drawing a boundary around the resource itself, and deciding who may stand inside it.