Rawls' welfare function

In microeconomics, Rawls' social welfare function, also called Maximin SWF , is a special form of describing the overall benefit of the population in an economy. The function is named after the American philosopher John Rawls . The welfare function is borrowed from the philosophical work of Rawls, in particular from his major work A Theory of Justice (1971).

Mathematical description

A welfare function aggregates the private preferences of households or individuals. It is believed that a measure leads to welfare value. ${\displaystyle W=W(u_{1},u_{2},\dotsc ,u_{n})}$ ${\displaystyle d\in D}$ ${\displaystyle W(u_{1}(d),\dotsc ,u_{n}(d))}$

If the assumption of monotony and convexity is fulfilled, the optimal state measure can be determined from the following maximization problem: ${\displaystyle d^{*}}$

Maximization problem:

Choose to maximize. ${\displaystyle d\in D}$ ${\displaystyle W(u_{1}(d),\dotsc ,u_{n}(d))}$

In Rawls' social welfare function , the general form of a welfare function is specified as follows: ${\displaystyle W=W(u_{1}(d),\dotsc ,u_{n}(d))}$

${\displaystyle W=W(u_{1}(d),\dotsc ,u_{n}(d))=\operatorname {min} \left\{u_{1}(d),\dotsc ,u_{n}(d)\right\}}$

The incomes of the individuals are expressed here by the respective benefits of the individuals and replaced by utility functions . The function describes that the social welfare of society should be measured on the basis of the worst-off individual in society: minimax criterion . The function further emphasizes that social justice plays an important role in terms of the overall good of a society, since social justice benefits all individuals in society by maximizing the benefit of the worst-off individual (overall welfare is maximized) and thus everyone is better off . ${\displaystyle y_{i}}$

Analogy to limitational indifference curves

Social limitationale indifference curves

Since, due to the shape of the indifference curves, there can be no substitutability of the benefits of different individuals and the shape of the indifference curves is analogous to limitational indifference curves, the indifference curves of the welfare function are also referred to as social limitation indifference curves.

The shape of the indifference curves implies that a one-sided increase in the benefit of an individual does not lead to increased welfare. Only if all individuals are better off to the same degree will this lead to increased overall economic welfare. A trivial comparable example of this are left and right shoes. If you buy five left and five right shoes, buying five more left shoes is of no use.

→ Main article : Indifference curve

See also

• Minimax rule

Individual evidence

1. ^ Jürgen Eichberger: Fundamentals of microeconomics. 2004, p. 183.