Public Goods: Vertical Summation vs. Private Demand

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

Read Two Free-Rider Examples

Add Private-Good Quantities at a Common Price

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.

State the Public-Good Model’s Conditions

In a pure-public-good model, beneficiaries share a service level without substantially reducing one another’s benefits, and excluding nonpayers is difficult. A warning broadcast can fit those conditions within its coverage area. An idea may be nonrival, yet a paywall, patent or other enforceable access rule can make particular uses excludable; the word “knowledge” alone does not settle both classification tests.

Sum Values for the Same Shared Unit

For a pure public good, add marginal benefits for the same shared quantity. In a two-household model, if A values a third shared siren at $400 and B at $250, its social marginal benefit is $650. Assume both households benefit from that same siren and these are all the relevant benefits. In the standard benefit–cost benchmark, add it if its benefit exceeds its marginal resource cost; equality makes that particular marginal unit break even.

Distinguish Rivalry from Exclusion

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.

Explain Why Contributions Can Hide Value

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.

Compare Each Additional Unit with Its Cost

Public-good demand uses vertical addition because the modeled households experience the same service quantity. At the second shared unit of flood protection, A is willing to pay $80, B $50 and C $30. Their summed marginal benefit is $160. If that unit’s marginal resource cost is $140 and all relevant benefits and costs are included, it adds $20 of net benefit. If the next unit’s summed benefit is $110 and its marginal cost remains $140, omit that next unit. Without its cost, a lower benefit alone would not establish the stopping point.

Keep Dollars and Quantities Separate

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.

Separate the Benefit Calculation from Financing

Tax financing can address the collection problem, but raising revenue can have costs and 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.

Classify by Consumption and Access Conditions

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.

Check Crowding and Capacity

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 helps you reject choices that confuse ownership, funding, rivalry and access.

Check the Rule and Its Assumptions

OpenStax’s public-goods explanation distinguishes the two defining properties and the free-rider problem. Free access, public funding and government ownership do not by themselves establish those properties.

Pearson’s public-goods study guide adds individual marginal benefits vertically for a shared unit. The EconGraphs lesson for Stanford Economics 50 contrasts horizontal private-good demand with the public-good efficiency condition and distinguishes calculating a desirable quantity from getting people to finance it.

These dollar-benefit exercises use a standard simplified model: all relevant beneficiaries and resource costs are included, benefits are measured consistently, and additional financing distortions are absent. In an actual policy choice, income effects, truthful preference measurement, distribution and the cost of collection can matter. The numerical condition does not supply that missing evidence.

Solve a Continuous Shared-Service Example

Consider an invented warning service with a feasible shared level G from 0 to 6. Exactly two households benefit. Their marginal benefits, in dollars per additional unit, are MB_A = 18 − 2G and MB_B = 12 − G. Marginal resource cost is a constant $18 per unit. Assume no other relevant effects, fixed costs or financing distortions. Which feasible G maximizes net benefit in this model?

Try Three Demand-Summation Questions

Connect the Rule to Related Choices

Compare common-resource overuse and shared costs, distinguish congestion from nonrival use, and continue through the CLEP Microeconomics learning hub for related models.