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The Samuelson condition, authored by Paul Samuelson, 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 for public goods (or vice versa) would result in a decrease of social utility.
For an economy with n consumers the conditions reads as follows:
MRSi 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.
If the private good is a numeraire good then the Samuelson condition can be re-written as:
where
When written this way, the Samuelson condition has a simple graphic interpretation. Each individual consumer's marginal benefit,
Hence the Samuelson condition can be thought of as a generalization of supply and demand concepts from private to public goods.