Growth and inequality trade-offs to eradicate absolute poverty

The relationship between growth, inequality and poverty remains elusive, despite considerable scholarship. To what extent can governments rely on growth to eradicate poverty without reducing inequality? We derive a closed-form relationship between a minimum income threshold, changes in the Gini index of income inequality and average national income required to meet this target, independent of the form of income distribution. We develop a generalized form of redistribution and validate it against historical changes in inequality. We use this formulation to illustrate feasible growth-redistribution strategies to raise entire populations above the International Poverty Line ($1.90/day) by 2030, the Sustainable Development Goal 1, in two selective countries: India and Rwanda. We show that meeting this target would require unprecedented rates of both growth and inequality reduction in Rwanda. India could not eradicate acute poverty by 2030 with growth alone, but it could with only a modest reduction in inequality.