Questions: Efficient Provision of Public Goods (Samuelson Condition and Lindahl Equilibrium)

Question 1

Three identical residents each have marginal benefit MB = 10 − G from G units of a public good. The marginal cost of the good is constant at 6. What is the efficient quantity?

• A. 4
• B. 6
• C. 8
• D. 10

Answer: (C)

The sum of marginal benefits is 3(10 − G) = 30 − 3G. Setting 30 − 3G = 6 gives G = 8.

Question 2

In the same town, if residents contribute voluntarily and each takes others' contributions as given, how much is provided in total?

• A. 0
• B. 4
• C. 8
• D. 12

Answer: (B)

In a Nash equilibrium, a resident adds to the total only while their own MB exceeds 6. Own MB equals 6 at G = 4, so no one adds beyond 4 in total. The town gets 4 units instead of the efficient 8.

Question 3

In a Lindahl equilibrium, every person faces the same price per unit of the public good.

• T. True
• F. False

Answer: False

Each person pays a personalized price equal to their own marginal benefit at the efficient quantity, and these prices sum to marginal cost. In the identical-resident example each pays 2 per unit, but with different preferences the prices differ.

Question 4

Explain why the efficiency condition for a public good involves the sum of marginal rates of substitution, while for a private good it involves each person's MRS separately.

Model answer: A unit of a private good can be consumed by only one person, so efficiency requires that each person's willingness to give up other goods for one more unit equal its production cost. A unit of a public good is consumed by everyone simultaneously, so its total value to society is the sum of everyone's willingness to pay. Efficiency then requires that sum to equal the marginal rate of transformation.

This is the Samuelson condition. It explains why demand for public goods is summed vertically.