We establish a general relationship between the standard form of the individualistic social-welfare function and the “reduced-form” version that is expressed in terms of inequality and mean income. This shows the relationship between the property of monotonicity and the slope of the equity-efficiency trade-off. Particularly simple results are available for a large class of inequality measures that includes the Gini. These results do not require differentiability of the social welfare function.
Amiel, Y. and Cowell, F. (2003), "2. Inequality, welfare and monotonicity", Inequality, Welfare and Poverty: Theory and Measurement (Research on Economic Inequality, Vol. 9), Emerald Group Publishing Limited, Bingley, pp. 35-46. https://doi.org/10.1016/S1049-2585(03)09003-3Download as .RIS
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