Definition
A public good is one that is simultaneously non-excludable (you cannot prevent people from consuming it once it's provided) and non-rival (one person's consumption doesn't diminish the amount available to others). National defense is the canonical example: once the military protects the country, it protects everyone in it — you cannot exclude a citizen from defense, and one citizen's protection doesn't reduce another's.
These two properties destroy the private market's ability to provide the good efficiently. Non-excludability creates the free-rider problem: rational individuals will refuse to pay for a good they can consume regardless. Non-rivalry means there is no social cost to providing the good to one more person at zero marginal cost, so charging any positive price excludes people who would benefit — a deadweight loss. The result: private firms undersupply or don't supply public goods at all, requiring government provision funded by mandatory taxation.
Why it matters
The four categories of goods
The free-rider problem in depth
Why voluntary provision fails
Imagine funding a lighthouse by voluntary subscription. Each ship owner benefits from the lighthouse whether they pay or not — it's non-excludable. Knowing this, each owner rationally waits for others to fund it. If enough owners reason this way, the lighthouse goes underfunded. This is the free-rider problem — a rational individual strategy that produces a collectively irrational outcome.
Solving free-riding through taxation
The government solves the free-rider problem by compelling payment. All beneficiaries (taxpayers) contribute through taxation, regardless of their individual willingness to pay. This is not a subsidy in the usual sense — it is the organizational form required to produce goods that markets structurally cannot provide.
Quasi-public goods and the spectrum
Real goods rarely fit the pure categories neatly. A national park is non-excludable and non-rival when uncrowded — but becomes rival when congested. Basic research is a nearly pure public good (knowledge is non-rival and hard to exclude from spillovers); applied research closer to a private good. Roads are club goods when tolled; common resources when congested. The appropriate policy depends on where a good sits on the spectrum and how conditions change with use level.