Lindahl–Bowen–Samuelson conditions on:
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The Samuelson condition, authored by
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 goods 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 (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he " ...
,Samuelson, Paul A. (1954), The Theory of Public Expenditure, in: Review of Economics and Statistics 36, pp. 386–389. in the theory of public goods in economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
, is a condition for the efficient provision of public goods. When satisfied, the Samuelson condition implies that further substituting public for private goods (or vice versa) would result in a decrease of social utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...
.
For an economy with ''n'' consumers the conditions reads as follows:
:
MRS''i'' is individual ''i'' marginal rate of substitution
In economics, the marginal rate of substitution (MRS) is the rate at which a consumer can give up some amount of one good in exchange for another good while maintaining the same level of utility. At equilibrium consumption levels (assuming no exte ...
and MRT is the economy'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 goods 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.
See also
* Lindahl equilibriumReferences