The optimal provision of a public good occurs when the sum of the marg

The optimal provision of a public good occurs when the sum of the marginal rate of substitution for all members of society equals 1, the marginal rate of transformation.

What is the relationship between the marginal rates of substitution in the competitive market? Use this relationship to explain why too few public goods are provided in the competitive market.

ANSWER

The competitive market allocation occurs where the MRS for all members of society are equal to 1. This implies that the MRS for each individual is too large relative to the optimum. In order to reduce the MRS such that the sums add up to one, we need to increase the consumption of the public good and decrease the consumption of the private good. This will reduce the MRS for each individual.