Samuelson condition

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The Samuelson condition, authored by Paul Samuelson ^[1], in the theory of public goods in economics, is a condition for the efficient provision of public goods. When satisfied, the Samuelson condition implies that further substituting private goods provision for public goods provision (or vice versa) would result in a decrease of social utility.

For an economy with n consumers the conditions reads as follows:

$\sum_{i=1}^n MRS_i = MRT$

$M R S i$ is individual i's marginal rate of substitution and MRT is the economy's marginal rate of transformation between the public good and an arbitrarily chosen private good.