Playground Contributions: Maximizing Value and Efficiency
How does voluntary contributions impact the size of a playground?
Suppose two people, person 1 and person 2, want to produce a playground to share between them. The value of the playground of size s to each person is Vs, where s is the number of pounds spent building it. Show that under voluntary contributions the size of the playground is and that the efficient size is 1.
Under voluntary contributions, the size of the playground will likely be undersupplied or zero. The efficient size of the playground is one.
Under voluntary contributions, each person independently decides how much to contribute to the playground. However, due to the free-rider problem, where individuals have the incentive to benefit without contributing, it is likely that neither person will contribute, resulting in an undersupplied or non-existent playground.
The efficient size of the playground is one because it maximizes the total value (V) derived from the playground. When the playground size is one, both individuals can fully enjoy the benefits (Vs) without any waste or duplication. By pooling their resources and building a playground of size one, they achieve the optimal outcome where the total value derived from the playground is maximized, benefiting both individuals. This efficient size ensures that they overcome the free-rider problem and create a mutually beneficial outcome.