Question

What is a Bergson-Samuelson social welfare function? Describe some of the different ways an individual’s “utility function” can be interpreted under this approach to social welfare. Explain the relationship between the form the Bergson-Samuelson social welfare function takes and the assumptions we make about interpersonal comparisons of utility.What is a Bergson-Samuelson social welfare function? Describe some of the different ways an individual’s “utility function” can be interpreted under this approach to social welfare. Explain the relationship between the form the Bergson-Samuelson social welfare function takes and the assumptions we make about interpersonal comparisons of utility.

Answer 1

Welfare economics has always grappled with the idea of measuring and rating the welfare of society. Economists have taken different approaches to welfare estimation, however, all of them come with drawbacks. One major drawback amongst all is the "economists make interpersonal value judgements while measuring social outcome". To understand this, let us take the Classical Bentham's Utilitarian Criteria.

Bentham says that social welfare function is additive i.e. U = (u1+u2+u3+...+un). This means that if person 1 gains utility by 10 points, by depriving person 2 of its utility by 5 points, then social welfare has increased. This is a very crude judgement because here Bentham believes, that person 1's 10 utils is more important over person 2's 5 utils. This is the problem of value judgement that subsequent economists tried to escape in their new models, but without success.

Then came Bergson - Samuelson's Social Welfare Function. It believed, that interpersonal judgements are a must to derive social welfare and cannot be escaped, then why not make it explicit in our model and make it more transparent. Welfare economics cannot be separated from value judgements. They gave the society's utility function as ordinal index of society's welfare.

Thus, now that the model has given the freedom to make value judgements, it needs to be seen that who is empowered to make them on society's behalf. It can either be an elected government or imposed by a dictator. Bergson and Samuelson expressed the view that all value judgements used to construct the social welfare function must be consistent which implies that if in a given situation A is preferred to B and B is preferred to C then A must be preferred to C.

If we consider a 2 people society, then:

Here a movement towards higher IC will be an improvement in social welfare. A movement from Q to T will raise utility for both A and B. Thus, it is unquestionably an improvement. But, a movement from Q to S, although takes us to a higher IC, but it reduces the individual welfare of B. Now this is the value judgement that the government is empowered to make and is necessary. Thus, social welfare now includes value judgements implicitly.

This IC map, when superimposed over the Grand Utility Possibility Frontier, a single optimum outcome can be achieved.

The drawback of this model came from K.J. Arrow. He refuted Bergson Samuelson's claim that democratic process can yield transitive i.e. consistent outcomes. Amartya Sen also went ahead to say that concept of utility in ordinal or cardinal terms is very inhuman and mechanical approach to measure an organic parameter like welfare. He believed in expanding opportunities for individuals and making them capable to develop, thus giving rise to the "Capabilitarian" approach over "Utilitarian" approach.

Thanks!