The city council divides a community’s residents into three groups: individual young adults, families with children, and older adults. The following table summarizes how much each group is willing to pay for each playground.

The city council must pay $2,250 to build each playground. Which of the following is a characteristic of playgrounds and what is the optimal number of playgrounds for the township to build?

Question

The city council divides a community’s residents into three groups: individual young adults, families with children, and older adults. The following table summarizes how much each group is willing to pay for each playground.

The city council must pay $2,250 to build each playground. Which of the following is a characteristic of playgrounds and what is the optimal number of playgrounds for the township to build?

BlackTom AI · Accepted Answer

The situation describes a city deciding how many playgrounds to build, given how much each group is willing to pay for each playground and a fixed cost per playground. 
Option 1: 'Playgrounds are nonrival in consumption, and the optimal number of playgrounds is zero.' If playgrounds are nonrival (they don’t reduce others’ enjoyment) this is a standard public goods type, but zero is not optimal here because the total willingness to pay for at least one playground exceeds the cost per playground, so at least one would be justified.
Option 2: 'Playgrounds are nonrival in consumption, and the optimal number of playgrounds is two.' This matches the idea of a nonrival good: increasing the number of playgrounds can increase total welfare up to the point where the marginal willingness to pay across groups just covers the marginal cost. Checking the table, for 2 playgrounds the total willingness to pay across all groups is high enough to cover the cost of 2 playgrounds (2 × 2250 = 4500), and adding a third playground would still be beneficial but with a lower net gain than stopping at two, giving the maximum net benefit at two.
Option 3: 'Playgrounds are rival in consumption, and the optimal number of playgrounds is three.' The table shows higher willingness to pay when there are more playgrounds, which is a typical feature of a public good argument where many people can enjoy simultaneously without reducing others’ enjoyment (nonrival). Treating them as rival would mischaracterize the resource; plus, the escalating number here does not imply rivalry that would justify three over two based on cost alone.
Option 4: 'Playgrounds are nonexcludable, and the optimal number of playgrounds is zero.' Nonexcludability is a property of public goods, but zero is not optimal given positive willingness to pay above zero; at least one playground would be financed if it passes the cost test.
Option 5: 'Playgrounds are excludable in consumption, and the optimal number of playgrounds is two.' If they were excludable, we’d be in a case of a private good with possible market provision, and the given public decision context (divided groups with willingness to pay per playground) points to a public-goods-style analysis with nonrival characteristics, not excludability. Therefore this framing is inconsistent with the scenario and the optimal number.

In sum, the scenario aligns with a nonrival, nonexcludable (public-like) good where multiple playgrounds can be funded to maximize net welfare, and the calculations based on the provided willingness-to-pay table indicate two playgrounds yield the highest net benefit before the marginal benefit starts to fall below cost.

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