An alternative measure of economic inequality under the Lorenz curve framework in analogue to the index of refraction of geometrical optics

Index of refraction is found to be a good measure of economic inequality within the Lorenz curve framework. It has origin in geometrical optics, where it measures bending of a ray of light passing from one transparent medium into another. As light refracts according to characteristics of different media, so also Lorenz curve does according to concentration of wealth or income in different strata. In line with this analogy, first I compute refractive index for each stratum under the Lorenz curve framework to evaluate condition in each and then simply add all to propose an overall measure for the whole framework. The latter appears to be pro transfer-sensitive and equivalent to the measures based on length of the Lorenz curve. Also, it is related to transfer-neutral Gini coefficient by quadratic equation. The applicability of the approach is tested utilising data on distribution of income or consumption from the WDI 2014. Results are lively and remarkable. While an index value of less than 1.00 represents an ‘anomalous refraction' in optics, such a condition of inequality appears to be too common for many of us in reality. In contrast to that, in some countries, the refractive index of the richest group exceeds that of Diamond (2.42), where an index value of 1.00 depicts an ideal condition that is enviable. Although the preliminary exercise is done with grouped data, it can be extended vividly to the case when the Lorenz curve is continuous.