Samuelson condition
Encyclopedia
The Samuelson condition, authored by Paul Samuelson
, in the theory of public good
s in economics
, is a condition for the efficient provision of public good
s. 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 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
is the marginal benefit to each person of consuming one more unit of the public good, and MC is the marginal cost of providing that good. In other words, the 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. (Remember that public good
s are non-rival, so can be enjoyed by many consumers simultaneously).
When written this way, the Samuelson condition has a simple graphic interpretation. 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 represent the aggregate willingness to pay or aggregate demand. The marginal cost is, under competitive market conditions, the supply for public goods.
Hence the Samuelson condition can be thought of as a generalization of supply and demand concepts from private to public goods.
Paul Samuelson
Paul Anthony Samuelson was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in...
, in the theory of public good
Public good
In economics, a public good is a good that is non-rival and non-excludable. Non-rivalry means that consumption of the good by one individual does not reduce availability of the good for consumption by others; and non-excludability means that no one can be effectively excluded from using the good...
s in economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, is a condition for the efficient provision of public good
Public good
In economics, a public good is a good that is non-rival and non-excludable. Non-rivalry means that consumption of the good by one individual does not reduce availability of the good for consumption by others; and non-excludability means that no one can be effectively excluded from using the good...
s. When satisfied, the Samuelson condition implies that further substituting private for public goods (or vice versa) would result in a decrease of social utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
.
For an economy with n consumers the conditions reads as follows:
MRSi is individual i marginal rate of substitution
Marginal rate of substitution
In economics, the marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility.-Marginal rate of substitution as the slope of indifference curve:...
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
is the marginal benefit to each person of consuming one more unit of the public good, and MC is the marginal cost of providing that good. In other words, the 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. (Remember that public goodPublic good
In economics, a public good is a good that is non-rival and non-excludable. Non-rivalry means that consumption of the good by one individual does not reduce availability of the good for consumption by others; and non-excludability means that no one can be effectively excluded from using the good...
s are non-rival, so can be enjoyed by many consumers simultaneously).
When written this way, the Samuelson condition has a simple graphic interpretation. 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 represent the aggregate willingness to pay or aggregate demand. The marginal cost is, under competitive market conditions, the supply for public goods.Hence the Samuelson condition can be thought of as a generalization of supply and demand concepts from private to public goods.