Which of the following statements is true regarding the demand curve and optimal quantity of public goods?

• A. For public goods, the demand curve is determined by horizontally summing individual demand curves.
• B. The optimal quantity of a public good is where the sum of individual marginal costs equals the marginal benefit.
• C. The demand curve for a public good is found by vertically summing individual willingness to pay at each quantity.
• D. The optimal provision of a public good occurs where total cost equals total benefit.

Answer: (C)

Verified step by step guidance

1. Understand the nature of public goods: Public goods are non-rivalrous and non-excludable, meaning one person's consumption does not reduce availability to others, and people cannot be excluded from using them.
2. Recall how demand curves for public goods are aggregated: Unlike private goods, where individual demand curves are summed horizontally (quantities added at each price), for public goods, the demand curve is found by vertically summing individual willingness to pay (prices added) at each quantity.
3. Define the optimal quantity of a public good: The optimal provision occurs where the sum of individual marginal benefits (willingness to pay) equals the marginal cost of providing the good.
4. Express the vertical summation mathematically: If individual marginal benefits are \( MB_1(q), MB_2(q), ..., MB_n(q) \), then the total marginal benefit \( MB_{total}(q) = \sum_{i=1}^n MB_i(q) \). The optimal quantity \( q^* \) satisfies \( MB_{total}(q^*) = MC(q^*) \), where \( MC(q) \) is the marginal cost.
5. Clarify why total cost equals total benefit is not the correct condition: Optimal provision is based on marginal analysis (marginal benefit equals marginal cost), not total cost equaling total benefit.