Efficient Production Levels of Public Goods
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A public good is provided efficiently at the level where the combined marginal rate of substitution of all individuals is equal to the marginal rate of transformation. (The marginal rate of substitution is the rate at which an individual is willing to exchange a private good for a public good, the marginal rate of transformation is the quantity of a private good which the society has to give up in order to produce one unit of a public good).
When should a public good be provided? To illustrate the basic principle, consider a community composed of just two consumers. The government is considering whether or not to provide a park. Arthur is prepared to pay up to $200 for use of the park, while Julia is willing to pay up to $100. The total value to the two individuals of having the park is $300. If it can be produced for $225, there is a $75 gain on its production since it provides services that the community values at $300 at a cost of only $225.
Regardless of the method of providing public goods, the efficient level of such provision is still being subjected to economic analysis. For instance, the Samuelson condition calculates the efficient level of public goods production to be where the ratio of the marginal social cost of public and private goods production equals the ratio of the marginal social benefit of public and private goods production.
"If the amount of a public good can be varied continuously, the optimal quantity to produce is that quantity for which the marginal cost of the last unit is just equal to the sum of the prices that all consumers would be willing to pay for that unit." This equilibrium guarantees that the last unit of the public good costs as much to produce as the value that it gives to all of its consumers.
Read more about this topic: Public Good
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—Ralph Waldo Emerson (1803–1882)