Pareto efficiency, or Pareto optimality, is an important notion in neoclassical economics with broad applications in game theory, engineering and the social sciences. Given a set of alternative allocations and a set of individuals, a movement from one allocation to another that can make at least one individual better off, without making any other individual worse off, is called a Pareto improvement or Pareto optimization. An allocation of resources is Pareto efficient or Pareto optimal when no further Pareto improvements can be made. Neoclassical economics refers to a general approach (a metatheory) to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ... Engineering is the design, analysis, and/or construction of works for practical purposes. ... This article or section does not adequately cite its references or sources. ... Factors of production are resources used in the production of goods and services in economics. ...

A strongly Pareto optimal (SPO) allocation (X) is one for which there cannot be any other feasible allocation (say X') such that the allocation (X') is strictly preferred by at least one person, and weakly preferred (not opposed) by everyone else. A (weakly) Pareto optimal (WPO) allocation is one where there is no feasible reallocation that would be strictly preferred by all agents.

The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution. Please wikify (format) this article as suggested in the Guide to layout and the Manual of Style. ... Economic efficiency is a general term for the value assigned to a situation by some measure designed to capture the amount of waste or friction or other undesirable economic features present. ... This graphic shows the distribution of gross annual household income. ...

Pareto Frontier

For a given system, the Pareto Frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto Frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters.

The Pareto Frontier, P(Y), may be more formally described as follows. Consider a system with function , where X is a compact set of feasible decisions in the metric space , and Y is the feasible set of criterion vectors in , such that . In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ...

We assume that the preferred directions of criteria values are known. A point is preferred to (strictly dominating) another point , written as . The Pareto Frontier is thus written as:

.

Pareto efficiency in economics

If an economic system is Pareto efficient, then it is the case that no individual can be made better off without another being made worse off. It is commonly accepted that outcomes that are not Pareto efficient are to be avoided, and therefore Pareto efficiency is an important criterion for evaluating economic systems and political policies. This box:  • • An economic system sucks(social institution) which deals with the production, distribution and consumption of goods and services in a particular society. ...

If economic allocation in any system (in the real world or in a model) is not Pareto efficient, there is theoretical potential for a Pareto improvement - an increase in Pareto efficiency: through reallocation, improvements to at least one participant's well-being can be made without reducing any other participant's well-being.

In the real world ensuring that nobody is disadvantaged by a change aimed at improving economic efficiency may require compensation of one or more parties. For instance, if a change in economic policy dictates that a legally protected monopoly ceases to exist and that market subsequently becomes competitive and more efficient, the monopolist will be made worse off. However, the loss to the monopolist will be more than offset by the gain in efficiency. This means the monopolist can be compensated for its loss whilst still leaving an efficiency gain to be realised by others in the economy. Thus, the requirement of nobody being made worse off for a gain to others is met.

In real-world practice, the compensation of the monopolist (or other loser) is hardly ever made. It is left hypothetical. The change is thus not Pareto efficient. The theory of hypothetical compensation is part of the Kaldor-Hicks concept of efficiency. Kaldor-Hicks efficiency is a type of economic efficiency that occurs only if the economic value of social resources is maximized. ...

Under certain idealised conditions, it can be shown that a system of free markets will lead to a Pareto efficient outcome. This was first demonstrated mathematically by economists Kenneth Arrow and Gerard Debreu. This is called the first welfare theorem. However, the result likely does not reflect the workings of real economies because of the restrictive assumptions necessary for the proof (markets exist for all possible goods, markets are perfectly competitive, and transaction costs are negligible). Among other things, there must be no externalities. A free market is an idealized market, where all economic decisions and actions by individuals regarding transfer of money, goods, and services are voluntary, and are therefore devoid of coercion and theft (some definitions of coercion are inclusive of theft). Colloquially and loosely, a free market economy is an economy... Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ... Gerard Debreu was a naturalized US citizen from France Gerard Debreu (July 4, 1921 – December 31, 2004) was a French economist and mathematician (In July 1975, he became a naturalized citizen of the United States). ... In welfare economics, the First Welfare Theorem is that a system of free markets will lead to a Pareto efficient equilibrium. ... In economics, an externality is a cost or benefit from an economic transaction that parties external to the transaction bear. ...

A key drawback of Pareto optimality is its localisation and partial ordering. In an economic system with millions of variables there can be very many local optimum points. The Pareto improvement criterion does not define any global optimum. Given a reasonable criterion which compares all points, many Pareto-optimal solutions may be far inferior to the global best solution. In mathematics, a partially ordered set (or poset for short) is a set equipped with a special binary relation which formalizes the intuitive concept of an ordering. ... Polynomial of degree 4, on the right one finds a local optimum, on the left is the global optimum. ...

Criticisms

Pareto efficiency does not require a "just" or equitable distribution of wealth. An economy in which the wealthy hold the vast majority of resources can be Pareto efficient. This should, of course, not be understood as criticism of Pareto efficiency itself, but rather of the idea that Pareto efficiency is desirable or even only Pareto efficiency is desirable. Wealthy individuals tend to be the best at generating more wealth, and this shouldn't require that they hold wealth exclusively.

Amartya Sen has elaborated the mathematical reasons for this criticism, pointing out that under relatively plausible starting conditions, systems of social choice will converge on Pareto efficient, but inequitable, distributions. A simple example is dividing a pie into pieces to distribute among three people. The most equitable distribution is each person getting one third. However the solution of two people getting half a pie and the third person getting none is also Pareto optimal despite not being equitable, because the only way for the person with no piece to get a piece is for one or both of the other two to get less, which is not a Pareto improvement. A Pareto inefficient distribution of the pie might be each person getting one-quarter of the pie with the remainder discarded. Of course, this example completely ignores the origin of the pie, so it breaks down to the criticism that Pareto efficiency does not really help in determining the optimal allocation of windfalls that nobody involved actually produced, such as land, inherited wealth, broadcast spectrum, the environment, or a pie miraculously falling from the sky. Amartya Sen Amartya Kumar Sen CH (Hon) (Bengali: Ômorto Kumar Shen) (born 3 November 1933 in Santiniketan, India), is an Indian philosopher, economist and a winner of the Bank of Sweden Prize in Economic Sciences (Nobel Prize for Economics) in 1998, for his work on famine, human development theory, welfare... Social choice theory studies how individual preferences are aggregated to form a collective preference. ...

A more generalized form of this criticism lies in the definition of Pareto efficiency itself. By requiring that no participants be worse off, Pareto efficiency protects the status quo and therefore any inequity or other problems currently existing. Status Quo are an English rock band whose music is characterised by a strong boogie line. ...

See also

• Potential pareto improvement
• Deadweight loss
• First welfare theorem
• Efficiency (economics)
• Kaldor-Hicks efficiency
• Multidisciplinary design optimization
• Social Choice and Individual Values for the '(weak) Pareto principle'
• Welfare economics
• Liberal paradox
• Abram Bergson

There are very few or no other articles that link to this one. ... In economics, a deadweight loss (also known as excess burden) is a permanent loss of well being to society that can occur when equilibrium for a good or service is not Pareto optimal, (that at least one individual could be made better off without others being made worse off). ... There exists two fundamental theorems of welfare economics. ... Economic efficiency is a general term for the value assigned to a situation by some measure designed to capture the amount of waste or friction or other undesirable economic features present. ... Kaldor-Hicks efficiency is a type of economic efficiency that occurs only if the economic value of social resources is maximized. ... Multidisciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. ... Kenneth Arrows monograph Social Choice and Individual Values (1951, 2nd ed. ... Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution associated with it. ... The liberal paradox is a logical paradox advanced by Amartya Sen, building on the work of Kenneth Arrow and his general possibility theorem, which showed that within a system of menu-independent social choice, it is impossible to have both a commitment to Minimal Liberty, which was defined as the... Abram Bergson, born Abram Burk (April 21, 1914, New York City - April 23, 2003), was an American economist. ...

References

• Fudenberg, D. and Tirole, J. (1983). Game Theory. MIT Press, Chapter 1, Section 2.4. 
• Osborne, M.J. and Rubenstein, A. (1994). A Course in Game Theory. MIT Press, p. 7. ISBN 0-262-65040-1. 

Jean Tirole (born 9 August 1953) is a notable contemporary french economist, author of many works in economics, scientific director of the Industrial Economics Institute in Toulouse. ... Ariel Rubenstein (born April 13, 1951) is an economist who works in game theory. ...