Sen index

The Sen index is a measure of inequality (measurement of relative concentration) which bears the surname of the Indian economist and economic philosopher Amartya Kumar Sen CH.

definition

There are people who feel quite strong financially, so that the income of the neighbors is also decisive for the social evaluation of the welfare of each individual . Then why should society simply add up individual welfare benefits? But one can also ask about a welfare function for all individuals. In doing so, one should define a comprehensive welfare function as follows:

${\displaystyle W=W\left(x_{i},x_{2},\ldots ,x_{N}\right)\,,}$

which is only symmetrical, quasi-concave and monotonically increasing at individual income levels. Then you can define a more general normative inequality measure by the concept of "generalized / generalized equally distributed equivalent income " (generalized Equally distributed equivalent income) formulated. This is obviously the per capita income which, if shared by everyone, would produce the same level of as the current real distribution. It follows: ${\displaystyle x^{*}}$ ${\displaystyle W}$

${\displaystyle x^{*}=x\vert W\left(x^{*},x^{*},\ldots ,x^{*}\right)=W\left(x_{1},x_{2},\ldots ,x_{N}\right)\,.}$

Under the premise that (first equation) is quasi-concave and applies to every income distribution . The index is then: ${\displaystyle W}$ ${\displaystyle x^{*}\leq \mu }$ ${\displaystyle S}$

${\displaystyle S=1-{\frac {x^{*}}{\mu }}\,,}$

which is just a generalized version of . If the utilitarian (reference) system is used, then ask and found to be indistinguishable. ${\displaystyle A}$ ${\displaystyle S}$ ${\displaystyle A}$

It should be noted that these measures obviously indicate that there is an (income) redistribution according to growth , provided the company achieves economic welfare .

Web links

• Pramod Kumar Chaubey (eGyanKosh, IGNOU / Indira Gandhi National Open University ): Unit 11: Measures of Inequality - PD / public domain (PDF file; 3.34 MB).