Pareto Efficiency in Allocation of Goods (With Diagram)

Welfare economics is the study of efficiency and equity of resource allocation. Allocative efficiency is the point at which allocations maximize total net benefits of society. Pareto efficiency or optimality is another way to measure efficiency.

Developed by Vilfredo Pareto, (1848 – 1923) Pareto efficient allocation of goods occur when no other possible allocation makes at least one individual better off with­out making anyone else worse off.

Pareto efficiency analysis uses individuals as the basis of evaluation. The Pareto improvement im­plies to a change in economic organizations that results in everyone becoming better-off.

According to Pareto, optimality in resources allocation is reached when the allocation of resources is at an opti­mum level so that no further increases in the economic welfare of one person is possible without a decrease in that of another.

In Pareto’s words “We are led to define as a position of maximum optimality (welfare) one where it is impossible to make a small change of any sort such that optimality of all the individuals, except those that remain constant are either all increased or all diminished”. Given certain rules of distribution any economic re-organisation is said to increase social welfare, if the welfare of some person is increased without any decrease in the welfare of others.

In terms of indifference curve analysis an optimum position is one in which, it is not possible to put any person on a higher indifference curve without causing someone to drop to a lower one, A change in resources allocation is said to constitute Pareto improvement if at least one person is made better off as a result of the change and no one is worse off. A Pareto optimum is therefore a situation in which no Pareto improvement is possible.

Take the case of the society that contains fixed amounts of two goods. 10 loaves of bread and 20 gallons of water, and two individu­als, A and B. There are many possible allocation of these two com­modities for the society consisting of A and B.

All bread and water could be allocated to one individual. Otherwise each individual could receive half of the good. Some other ways of allocation can be de­vised to distribute available bread and water. In welfare economics, we examine which type of allocation satisfies Pareto efficiency. Let us explain Pareto criterion with the help of Samuelson utility possibil­ity curve.

Given the many possible allocations of bread and water, the given graph plots the appropriate utility possibility curve UU’ for indi­viduals A and B. Each point along UU’ represents the separate well beings of A and B, associated with different allocations of bread and water.

The point ‘a’ corresponds to allocations that sum less than 20 gallons of water and 10 loaves of bread.

The point ‘b’ which are on the exterior of UU’ corresponds to bread and water combinations that exceeds the fixed quantities of goods available. However all points along UU’ represent maximum attainable utilities of A and B. This reflect optimum allocation of the commodities.

It should be noted that points interior to utility possibilities curves are not Pareto efficient. A point ‘a’ for example, the allocations exist that improve the well-being of one individual without lowering the well, being of other individual.

A move from ‘a’ to ‘d’ is called a Pareto superior move since it allows person ‘B’ to experience higher utility without lowering the utility of the other person ‘A’.

A horizontal move from ‘a’ to ‘f’ is another Pareto superior move since ‘A’ experience higher utility without lowering ‘Bs’ utility. A move from ‘a’ to ‘e’ is also a Pareto superior move. In general all points within the interior of utility possibilities curves are Pareto inefficient. For UU’ all points defined by area adf’ are Pareto superior to ‘a’. Likewise all points along utility possibilities curves are Pareto efficient. At point ‘e’ a move to ‘d’ increases Bs well-being and lowers ‘As‘. A move from ‘e’ to ‘f’ results in higher well-being for ‘A’ and lower well-being for ‘B’. All points along the curve are Pareto efficient. Efficiency in allocation therefore means that ‘A’ and ‘B’ receives allocation that corresponds to points along UU’. Once a point along the utility possibilities curve is reached, any change from the point is a Pareto inefficient move for society.

Even though Pareto-optimality is a good criterion to assess re­source allocation efficiency, the problem of how to quantify and com­pare welfare is an issue to be tackled. To achieve a Pareto-optimal allocation of resources is very difficult.

In the real world a number of factors, inhibit the attainment of Pareto-optimality. Most changes in the economy cannot be judged according to the Pareto principle as stated above, since they involve some persons being made better off and others worse off. This involves interpersonal comparisons be­tween the gainers and losers. This is very difficult to materialize.

Moreover the criterion of Pareto efficiency does not allow us to judge which Pareto efficient point is most equitable.

In welfare economics both efficiency and equity must be studied. However it is not clear which attribute is more important.

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