Sen’s Social Welfare Function | Economics Optional Notes for UPSC PDF Download

Introduction

• The concept of social welfare function was first introduced by Prof. Bergson and later on developed by Samuelson, Tintner and Arrow. They are of the view that no meaningful propositions can be made in welfare economics without introducing value judgments. The concept of social welfare is an attempt at providing a scientifically normative study of welfare economics.
• A social welfare function shows the factors 011 which the welfare of a society is supposed to depend. Bergson defines it “as a function either of the welfare of each member of the community or of the quantities of products consumed and services rendered by each member of the community.”
• In its original form the Bergson social welfare function is formulated in a completely general manner. It is a function which establishes a relation between social welfare and all possible variables which affect each individual’s welfare, such as a services and consumption of each individual. It is an ordinal index of society’s welfare and is a function of individual utilities. It is expressed as
  W = F (U₁,.U₂, Un)
  where W is the social economic welfare, F is for function, and Ur U₂……………… UN is the levels of utilities of 1, 2,…individuals. W is an increasing function of these utilities.
• The general properties of the social welfare function are similar to those of an individual utility function. In particular, the value of the welfare index increases whenever the utility level of one individual is increased without lowering that of the other individual. Thus the social welfare function is consistent with the Pareto optimality criterion, but it goes much further, since it assigns a value to every economic state, including those which according to the Pareto criterion are regarded as non-comparable. The existence of a social welfare function, therefore, implies a comparison of the welfare position of the individual members of society.

Assumptions:

The Bergson social welfare function is based on certain assumptions:

• It assumes that social welfare depends on each individual’s wealth and income and each individual’s welfare depends, in turn, on his wealth and income and on the distribution of welfare among the members of the society.
• It assumes the presence of external economies and diseconomies with their consequent effects.
• It is based on ordinal ranking of combinations of those variables which influence individual welfare.
• Interpersonal comparisons of utility involving value judgments are freely permissible.

Explanation:

• Given these assumptions, it is possible to depict the social welfare function on a diagram by drawing a series of ‘well-behaved social indifference curves’ with commodities measured along the two axes. Each indifference curve shows various distributions of utility among individuals which have the same level of social welfare. Such curves help the policy maker to find out whether a particular policy brings an improvement or not. If a change moves individuals to a higher indifference curve, social welfare is said to have increased.
• The social welfare function is explained diagrammatically in terms of Figure 4. FF₁ is the utility frontier which represents the boundary of all utility combinations possible with the given resources of the economy. It is an envelope of a number of overlapping utility possibility curves. W, W₁ and W2 form the family of curves representing the social welfare function. Each welfare curve shows a locus of welfare combinations of the utilities of two individuals A and В who are indifferent.

• Each welfare curve represents a level of social welfare. The welfare curve W₁ depicts a higher level of social welfare than curve W and W₂ higher level than W₁. The point of maximum social welfare or optimum position is one where the utility frontier curve FF, is tangent to the welfare curve. In the figure, point E clearly represents the situation of maximum social welfare or the bliss point.
• Within the constraints of given technology and fixed quantities of inputs, of all the welfare combinations open to society, E has the highest social value. Point i is on a lower welfare curve W and represents a lower level of social welfare, whereas point С on the W₂ curve is beyond the utility frontier FF, of the society. Thus point E represents maximum social welfare.

Criticism

• The assumptions of the Bergson criterion have tended to make the social welfare function ‘as broad and empty as language itself —and as necessary,’ according to Samuelson. Others have hailed it ‘as a major contribution to welfare economics’, while for Dr. Little, it completes the formal mathematical system of welfare economics. Scitovsky regards it as ‘completely general’.
• Baumol judges it as ‘right, not very helpful,’ while to Robertson it is a ‘vast partly coloured mathematical balloon’. Paul Streeten praises it as ‘a device which is supposed to purify economic investigation of all vestiges of unscientific matter’. In the intermingling of these approvals and half- approvals are to be found the following limitations of these criterions.

Not Applicable either to a Totalitarian State or a Democratic One:

• The social welfare function is analogous to the individual consumer’s utility function which provides a ranking-‘from the point of view of a benevolent despot, or a complete egoist, or all men of goodwill’— of alternative utility levels enjoyed by different individuals. But Little regards it as inapplicable in a totalitarian state and more so in a democratic one “where there would be as many (vague) welfare functions as there are individuals. It can be regarded only as ‘a formal device necessary to a perfectly general abstract system of welfare,’ which bears no relation to practical policy.”

Construction of Welfare Function Difficult:

• Another difficulty arises with regard to the construction and shape of the welfare function. The social welfare function is constructed by aggregating each individual’s preferences. But the problem is whether individual preferences should be given equal or different weights. This makes the construction of the social welfare function a difficult task.

Arbitrary and Imaginary:

• The representation of the social welfare function in terms of either equations or social an indifference curve does not help solve the problem because individual welfare functions cannot be known. Therefore, all equations and curves representing the social welfare function are arbitrary and imaginary.

The Concept of “Maximum ‘ without any Empirical Significance:

• According to Little, “The maximum is a concept without any possible empirical significance, and therefore it seems preferable not to use it. It is more meaningful to derive the ‘optimum’ conditions as sufficient conditions for an improvement with- out attempting to define a maximum position.”

Contradictory Results:

• Prof. Arrow points out that the construction of a social welfare function on the basis of ordinal preferences leads to contradictory results if individuals are required to make choices from among more than two alternatives.

Not Helpful in Solving Problems:

• According to Prof. Baumol, “The social welfare function does not come equipped with a kit and a set of instructions for collecting the welfare judgments which it requires.” Thus it is not of much help in solving the main problems of welfare economics.