Everything about Pareto Efficiency totally explained
Pareto efficiency, or
Pareto optimality, is an important concept in
economics with broad applications in
game theory,
engineering and the
social sciences. The term is named after
Vilfredo Pareto, an Italian economist who used the concept in his studies of
economic efficiency and
income distribution.
Given a set of alternative allocations of, say,
goods or income for 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. An allocation is
Pareto efficient or
Pareto optimal when no further Pareto improvements can be made. This is often called a
strong Pareto optimum (SPO).
A
weak Pareto optimum (WPO) satisfies a less stringent requirement, in which a new allocation is only considered to be a Pareto improvement if it's strictly preferred by
all individuals (for example,
all must gain with the new allocation). The set of SPO solutions is a subset of the set of WPO solutions, because an SPO satisfies the stronger requirement that there's no allocation that's strictly preferred by one individual and weakly preferred by the rest (for example, no individual loses out, and at least one individual gains).
A common criticism of a state of Pareto efficiency is that it doesn't necessarily result in a socially desirable distribution of resources, as it may lead to unjust and inefficient inequities.
Pareto efficiency in economics
An economic system that's Pareto inefficient implies that a certain change in allocation of income (for example) may result in some individuals being made "better off" with no individual being made worse off, and therefore can be made more Pareto efficient through a Pareto improvement. Here 'better off' is often interpreted as "put in a more preferred position." 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 public policies.
If economic allocation in any system (in the real world or in a model) isn't Pareto efficient, there's 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 while still leaving an efficiency gain to be realized 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 principle often appealed to is hypothetical. That is, for the alleged Pareto improvement (say from public regulation of the monopolist or removal of tariffs) some losers are not (fully) compensated. The change thus results in distribution effects in addition to any Pareto improvement that might have taken place. The theory of hypothetical compensation is part of
Kaldor-Hicks efficiency (Ng, 1983).
Under certain idealized conditions, it can be shown that a system of
free markets will lead to a Pareto efficient outcome. This is called the
first welfare theorem. It was first demonstrated mathematically by economists
Kenneth Arrow and
Gerard Debreu. However, the result doesn't rigorously establish welfare results for real economies because of the restrictive assumptions necessary for the proof (markets exist for all possible goods, all markets are in full equilibrium, markets are perfectly competitive, transaction costs are negligible, and there must be no
externalities).
Formal representation
Pareto frontier
Given a set of choices and a way of valuing them, the
Pareto frontier or
Pareto set is the set of choices that are Pareto efficient. The Pareto frontier is particularly useful in engineering: by restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter.
The Pareto frontier is defined formally as follows.
Suppose we've a design space with
n real parameters, and for each design-space point we've
m different criteria by which to judge that point. Let
for
i,k=1,...,m and
j,s=1,...,n.
Criticism
partial ordering. In an economic system with millions of variables there can be very many local optimum points. The Pareto improvement criterion doesn't 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.
Further Information
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