Income growth with high inequality implies loss of well-being: A mathematical model

Abstract

A mathematical model of measurement of the perception of well-being for groups with increasing incomes, but proportionally unequal is proposed. Assuming that welfare grows with own income and decreases with relative inequality (income of the other concerning one's own), possible scenarios for long-term behavior in welfare functions are concluded. Also, it is proved that a high relative inequality (parametric definition) always implies the loss of the self-perception of the well-being of the most disadvantaged group.