The socially optimal quantity of a public good is provided when:

• A. the average benefit to all individuals equals the marginal cost of providing the good
• B. the sum of the marginal benefits to all individuals equals the marginal cost of providing the good
• C. the marginal benefit to the individual equals the marginal cost of providing the good
• D. the total cost of providing the good equals the total benefit to society

Answer: (B)

Verified step by step guidance

1. Understand that a public good is non-rivalrous and non-excludable, meaning one person's consumption does not reduce availability to others, and people cannot be excluded from its benefits.
2. Recognize that the marginal benefit (MB) of a public good is the additional benefit received from one more unit of the good.
3. Since the public good benefits multiple individuals, the socially optimal quantity is found where the sum of the marginal benefits across all individuals equals the marginal cost (MC) of providing the good.
4. Express this condition mathematically as: \(\sum_{i=1}^n MB_i = MC\), where \(MB_i\) is the marginal benefit to individual \(i\) and \(n\) is the number of individuals.
5. Compare this to private goods, where the optimal quantity is where an individual's marginal benefit equals marginal cost, highlighting why summing benefits is necessary for public goods.