Public Goods and Free Riding
A small neighborhood with 10 residents is considering building a community garden. The garden is a public good. Each resident's marginal benefit from the garden is given by MB = 100 - Q, where Q is the size of the garden in square meters. The marginal cost of providing the garden is constant at $200 per square meter. The residents are considering voluntary contributions.
1. Determine the socially optimal size of the garden. Show your calculations.
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For a public good, the socially optimal quantity is where the sum of marginal benefits equals marginal cost. Since all residents have identical marginal benefit curves, the total marginal benefit (TMB) is 10*(100 - Q) = 1000 - 10Q. Set TMB = MC: 1000 - 10Q = 200 => 10Q = 800 => Q = 80. So the optimal garden size is 80 square meters.
2. If residents contribute voluntarily, what is the likely outcome? Explain using the concept of free riding.
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With voluntary contributions, each resident has an incentive to free ride because the garden is non-excludable and non-rival. Each resident will contribute only if their private marginal benefit exceeds the cost of their contribution, but they will hope others contribute. In the Nash equilibrium of voluntary contributions, the total contribution will likely be less than the optimal amount, possibly zero if each resident's individual marginal benefit at Q=0 is $100, which is less than the marginal cost of $200 per unit. Since no single resident's marginal benefit ($100) exceeds the marginal cost ($200), no one will voluntarily contribute. Thus, the garden will not be provided at all, resulting in a complete market failure.