Towards an Aggregate Social Welfare Function with Application to Developing Countries

Towards an Aggregate Social Welfare Function with Application to Developing Countries Tarek H Selim (World Economic Forum) and Nyiwul L Mabughi (Gettysburg College) September 2024 Abstract An aggregate social welfare function is analytically proposed and empirically applied with application to developing countries. The 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 socioeconomic 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: (a) marginal utility of income is estimated at 0.532, (b) an increasing welfare trigger effect is induced when income inequality (Gini index) falls below a threshold level of 0.24, (c) social welfare becomes invariant to inequality when Gini surpasses a threshold level of 0.39, (d) welfare variance rises linearly with clean water access, yet increases rapidly beyond 57% population access, (e) gender is highly elastic to welfare at an elasticity of 4.34, (f) welfare is sensitive to education more than gender and health care, but less than water access and life expectancy, (g) welfare is most sensitive to life expectancy when compared to any other factor, (h) welfare falls when more expenditures gaps are needed to eradicate poverty, and each $1m increase in required expenditures gaps to eradicate poverty leads to a welfare reduction of 0.8% (PPP adjusted), and finally, (i) welfare variance decreases with more intensive poverty. Levels of country development are then clustered around three-level categories of social welfare: (1) high welfare countries, (2) medium welfare countries, and (3) low welfare countries, using adjusted welfare scores and their corresponding socio-economic factors. Author AffiliationsTarek H. SelimGlobal Expert Council, World Economic ForumProfessor of Economics (Emeritus), American University in CairoContact: tarekhassanselim@gmail.com Research & Publications: https://sites.google.com/view/tarekhselim/research Nyiwul L MabughiChairman and Professor of EconomicsGettysburg College, Pennsylvania, USAContact: lnyiwul@gettysburg.edu Website: https://www.gettysburg.edu/academic-programs/economics/info/ Note: This is an updated version (2024) of the paper originally released in 2022 as MPRA Paper No. 118615.