Question

This question refers to the Bergson-Samuelson social welfare function

(a) State and explain the conceptual basis of the Bergson-Samuelson social welfare function

(b) Draw a diagram and use it to explain why a Bergson-Samuelson social welfare optimum will be Pareto efficient 6

(c) If an economy is at a Bergson-Samuelson social welfare optimum will there be efficiency in production? Explain

(d) If economic allocations are not Pareto efficient does it make sense to use a Bergson-Samuelson social welfare function to evaluate them? Discuss

Answer 1

A Bergson–Samuelson social welfare function considers welfare for a given set of individual preferences or welfare rankings. An Arrow social welfare functionconsiders welfare across different possible sets of individual preferences or welfarerankings and seemingly reasonable axioms that constrain the function.

The concept of ‘Social Welfare Function’ was propounded by A. Bergson in his article ‘A Re­formulation of Certain Aspects of Welfare Economics’ in 1938. Prior to its various concepts of social welfare had been given by different welfare theorists but they failed to provide a satisfactory solu­tion to the problem of maximisation of social welfare and measurement. Bentham talked of welfare in terms of ‘the greatest happiness of the greatest number.’

Neo-Classical welfare theorists dis­cussed the problem of social welfare on the basis of cardinal measurability of utility and interper­sonal comparison of utility. Analysis of Pareto optimality maximises social welfare by satisfying various marginal conditions of production, distribution and allocation of resources among products. But unfortunately they are not fulfilled due to the existence of various externalities and imperfec­tions in the market. Moreover, Pareto optimality analysis fails to measure the changes in welfare resulting from any change which benefits one section of society and harms the other.

Compensation principle as given by Kaldor-Hicks-Scitovsky attempts to measure the changes in social welfare resulting from such economic changes which harm some and benefit others through hypothetical compensating payments

Compensation theorists claimed to give a value-free objective criterion based on ordinal concept of utility but, this is based upon implicit value judgements and does not evaluate changes in social welfare satisfactorily.

By providing the concept of social welfare function Bergson and Samuelson have attempted to provide a new approach to welfare economics and have succeeded in rehabilitating welfare econom­ics. They have put forward the concept of social welfare function that considers only the ordinal preferences of individuals.

They agree to Robbins’ view that interpersonal comparison of utility involves value judgements but they assert that without making some value judgements, economists cannot evaluate the impact of changes in economic policy on social welfare.

Thus, according to them, welfare economics cannot be separated from value judgements. According to them, welfare economics is essentially a normative study. But the approach to study it must be scientific despite the fact that the use of value judgements in it is unavoidable.

Bergson-Samuelson Social Welfare Function:

Social welfare function is an ordinal index of society’s welfare and is a function of the utility levies of all individuals constituting the society.

Bergson-Samuelson social welfare function can be written in the following manner:

W= W(U1, U2,U3…………. , Un)

Where W If represents the social welfare U1, U2, U3, . .. ., Un represent the ordinal utility indices of different individuals of the society. The ordinal utility index of an individual depends upon the goods and services he consumes and the magnitude and kind of the work he does. The important thing to note about social welfare function is that in its construction explicit value judgements are introduced.

Value judgements determine a form of the social welfare function; with a different set of value judgements, the form of social welfare function would be different. Value judgements are es­sentially ethical notions which are introduced from outside economics. The value judgements re­quired to construct a social welfare function may be obtained through democratic process with voting by individuals or it may have to be imposed on the society in a dictation manner.

Whatever the case may be, the form of social welfare function depends upon the value judgements of those who decide about them since it expresses their