The socially optimal quantity of a public good is provided when

• A. Marginal benefit equals total cost
• B. Marginal social cost equals marginal social benefit
• C. Price equals marginal cost
• D. Marginal private benefit equals marginal social cost

Answer: (B)

The main idea is that the efficient provision of a public good is determined by the Samuelson condition: the sum of everyone's marginal benefits from one more unit (the marginal social benefit) equals the marginal cost of producing that unit (the marginal social cost).

Because public goods are nonrival and nonexcludable, we must aggregation across all individuals to capture the total value to society. If the total marginal benefit to society from one additional unit exceeds its marginal cost, allocating one more unit raises total welfare; if it's less, we should reduce provision. The equilibrium is reached where MSB equals MSC.

This differs from price-based rules like price equals marginal cost, which apply to private goods with market-determined prices. It also isn’t about individual (private) benefit alone or about equating a single person’s benefit to cost; it requires summing benefits across all people to reflect the public nature of the good.