Towards an Aggregate Social Welfare Function with Application to Developing Countries

An aggregate social welfare function is theoretically proposed and empirically applied. The proposed social welfare function obeys monotonicity, symmetry, continuity, independence, common scale, and the Piguo-Dalton equity principle. It is built on a cardinal multi-dimensional framework. Critical socio-economic factors in the social welfare formulation involve Atkinson-adjusted per capita income, poverty eradication, social entitlements for clean water access and health care, education attainment, income inequality, gender equity, and life expectancy. Applying the social welfare formulation to 79 developing countries, data sensitivity charts reveal important welfare effects: (i) marginal utility of income is 0.532, (ii) an increasing welfare trigger effect is induced when income inequality (Gini index) falls below the threshold level of 0.24, (iii) social welfare becomes invariant to inequality when Gini surpasses the threshold level of 0.39, (iv) welfare variance rises linearly with clean water access, yet increases rapidly beyond 57% population access, (v) gender is highly elastic to welfare at an elasticity of 4.34, (vi) welfare is sensitive to education more than gender and health care, but less than water access and life expectancy, (vii) welfare is most sensitive to life expectancy when compared to any other factor, (viii) welfare falls when more expenditures are needed to eradicate poverty, and each $1m increase in required expenditures to eradicate poverty leads to a welfare reduction of 0.8% (PPP adjusted), and finally, (ix) welfare variance decreases with more intensive poverty. Levels of country development are then clustered around three-level categories of social welfare.