Question

Consider an economy with three people and two goods, one public (g) and one private (x). The utility functions for the three people are UA = xA +20lng, UB = xB +30lng, and UC = xC +10lng. The marginal cost of g is constant at 10. According to the Samuelson condition, what is the socially efficient amount of the public good in this economy? Explain why the Samuelson condition picks out the efficient amount of a public good.

Answer 1

According to Samuelson condition, socially efficient amount of the public good is a condition where Marginal cost(or marginal rate of Transformation ) is EQUAL to the sum of Marginal rate of substitutionMRSs (between public and private goods), rather than MC and MRSs being equal to each individual MRS. This is called the Samuelson rule (Samuelson, 1954)

Samuelson condition picks out the efficient amount of a public good because according to his condition public good should be provided as long as the overall benefits to consumers from that good are at least as great as the cost of providing it. However, it must be kept in mind that public goods are non-rival, so they can be enjoyed by many consumers simultaneously).

Above Figure shows the Supply and demand interpretation of Samuelson condition

the Samuelson condition has a simple graphic interpretation.According to Samuelson,each individual consumer's marginal benefit, represents his or her demand for the public good, or willingness to pay. The sum of the marginal benefits shows the aggregate willingness to pay or aggregate demand. The marginal cost is the supply for public goods( under competitive market conditions)

Hence the Samuelson condition can be thought of as a generalization of supply and demand concepts from private to public goods.