Private goods use market demand; public goods require vertical benefit addition

Free riding can hide willingness to pay for a public good.

A private good is both rival and excludable. One person’s meal cannot be eaten by someone else, and a restaurant can require payment before serving it. Because different buyers can consume different quantities, market demand is found by adding individual quantities horizontally at each price. Exclusion lets the seller connect payment with access, while rivalry assigns the unit to one user. These features make the familiar private market possible. They do not guarantee perfect competition or eliminate every other market failure.

National defense, basic flood warnings, and some knowledge are nonrival and nonexcludable. Once provided, another user does not meaningfully reduce the benefit, and excluding nonpayers is difficult. A person can therefore hope others pay, causing voluntary contributions to understate true benefit and private provision to be too low.

For a public good, everyone consumes the same quantity, so individual marginal benefits are added vertically at each quantity. If household A values the third siren at $400 and B at $250, social marginal benefit is $650. Provide the unit if that sum is at least marginal cost.

A pure public good has two properties. It is nonrival: one person’s benefit does not substantially reduce the amount available to others. It is also nonexcludable: preventing nonpayers from receiving the benefit is difficult or prohibitively costly. National defense and a community tornado siren fit the model more closely than services such as public buses, which can be crowded and can charge fares.

Nonexcludability creates the free-rider problem. A person can enjoy the siren after neighbors pay for it, so the person has an incentive to understate willingness to pay. This is individually tempting but collectively damaging: if everyone waits for someone else, a project whose total benefit exceeds cost may not be financed. The problem is an incentive to conceal value, not proof that people place zero value on the good.

Public-good demand uses vertical addition because everyone consumes the same quantity. At the second unit of flood protection, Household A is willing to pay $80, B $50, and C $30. Social marginal benefit is $160 for that shared unit. If marginal cost is $140, provide it. If the next unit’s summed benefit is only $110, stop before that unit.

Do not add quantities

At a common price of $10, two buyers might demand 3 and 4 sandwiches, so private-good market quantity is 7. For a public siren, households do not consume separate numbers of the same siren. Add their dollar values for one shared siren instead.

Government provision can solve the collection problem through taxation, but it does not make benefit information perfect. Officials may use voting, surveys, property values, or benefit-cost analysis, each with limitations. Private provision can also occur through philanthropy, bundled products, advertising, social norms, or selective incentives. The economic claim is that ordinary voluntary-market incentives tend toward underprovision, not that provision is impossible.

Do not classify a good by who supplies it. A privately operated fireworks display may generate a public-good benefit if viewers cannot be excluded. Municipal water delivered through metered pipes is publicly supplied but rival and excludable, so it behaves more like a private good. The physical and institutional properties determine the category.

Finally, a public good is not merely “good for the public.” A park at dawn may be nearly nonrival, but a crowded park becomes rival at the margin. Gates can make it excludable. State both dimensions and use the facts at the quantity being analyzed. That habit prevents nearly every classification distractor.