Pareto Efficiency

Pareto efficiency, also called Pareto optimality, is a state of allocation in which it is impossible to make anyone better off without making at least one other person worse off. If some change could help at least one person while hurting no one, that change is a "Pareto improvement", and the starting point was not efficient. Pareto efficiency is the standard definition of economic efficiency in welfare economics and the benchmark against which markets, taxes and regulations are judged.

The concept is named after the Italian economist and sociologist Vilfredo Pareto (1848–1923), who developed it in his Manual of Political Economy (Italian edition 1906). It is central to the two "fundamental theorems of welfare economics", which link competitive markets to efficient outcomes. It should not be confused with the Pareto distribution, a statistical pattern for income and wealth that Pareto also studied, or with fairness: an allocation can be Pareto efficient and still be extremely unequal.

Imagine two flatmates sharing a fridge. One has three yogurts she does not like; the other has two apples he never eats but would happily swap for yogurt. As long as they can trade and both end up happier, the fridge is not yet "efficient". Once every swap that would please someone without upsetting the other has been made, nothing more can be done without one of them losing out.

That end point is Pareto efficient. Note what it does not say: if one flatmate owns almost everything in the fridge, the arrangement can still be efficient, because taking food from her would make her worse off. Pareto efficiency is about not wasting chances for mutual gain, not about who should have what.

An allocation $x$ is Pareto efficient if there is no other feasible allocation $y$ such that, for every person $i$:

• $u_i$ is person $i$'s utility, a measure of how well off they are.
• $x$ is the current allocation of goods.
• $y$ is any alternative allocation that the available resources allow.

Worked example: Ana has 10 apples and 0 oranges; Ben has 0 apples and 10 oranges. Suppose that, at these starting points, each orange is worth 3 points to Ana and each apple she gives up costs her only 1 point, and Ben feels the same way in reverse. If Ana swaps 4 apples for 4 oranges, she loses 4 points and gains 12, a net gain of 8; Ben gains 8 in the same way. Both are better off, so the starting allocation was not Pareto efficient. Trading continues until no further swap helps one without hurting the other.

Economists including Kenneth Arrow and Gérard Debreu proved in the 1950s, under specific assumptions, two results:

1. The first welfare theorem. Under perfect competition, with complete markets, full information and no externalities, any economic equilibrium is Pareto efficient. This is often presented as a formal version of Adam Smith's invisible hand.
2. The second welfare theorem. Under additional conditions, any Pareto-efficient allocation can be reached as a competitive equilibrium after a suitable lump-sum redistribution of starting endowments. In principle, this separates the question of efficiency from the question of equity.

Arrow received the Nobel Memorial Prize in Economic Sciences in 1972 and Debreu in 1983, partly for this work.

When the welfare theorems' assumptions fail, markets may not reach a Pareto-efficient outcome. Economists call this market failure. Common causes include:

• Monopoly power. A monopoly restricts output to raise price, leaving trades unmade that would benefit both buyers and society; the loss is measured as deadweight loss.
• Externalities. Pollution imposes costs on people outside a transaction. Remedies include a Pigouvian tax, tradable permits or bargaining as described by the Coase theorem.
• Public goods. Goods that are non-rival and non-excludable, such as national defense, are under-supplied because of the free-rider problem; see public goods.
• Information problems. Asymmetric information can lead to adverse selection and moral hazard, so mutually beneficial deals do not take place.

In practice, almost every policy creates some losers, so strict Pareto improvements are rare. Policy analysis therefore often uses the Kaldor–Hicks criterion, proposed by Nicholas Kaldor and John Hicks in 1939: a change is efficient if the winners gain enough that they could, in principle, compensate the losers, even if no compensation is paid. This test underlies most cost-benefit analysis. In game theory, a Nash equilibrium need not be Pareto efficient, as the prisoner's dilemma shows; see game theory.

The main criticism is that Pareto efficiency says nothing about distribution. Amartya Sen pointed out that a society can be Pareto optimal with some people in extreme poverty and others in luxury, as long as making the poor better off would require taking something from the rich. Because there are usually many Pareto-efficient allocations, the concept cannot by itself choose among them; that requires value judgments about economic inequality and social welfare.

Others note that the welfare theorems rely on assumptions, such as complete markets and perfect information, that never hold exactly, so real economies are at best approximately efficient. Lump-sum transfers needed by the second theorem rarely exist in practice; real taxes change incentives. From a free-market perspective, some economists warn that "market failure" findings can be used to justify interventions that themselves fail, a point stressed by public choice theory. Despite these limits, Pareto efficiency remains the common language economists use to identify waste.

• Nobel Prize in Economic Sciences 1983 (Gérard Debreu)
• Nobel Prize in Economic Sciences 1972 (Hicks and Arrow)