IMPOSSIBILITIES OF PARETIAN SOCIAL WELFARE FUNCTIONS FOR INFINITE UTILITY STREAMS WITH DISTRIBUTIVE EQUITY

This paper examines the existence of social welfare functions satisfying some reasonable axioms of distributive equity and Pareto efficiency in aggregating infinite utility streams. Our main results show that there exist social welfare functions that satisfy both the Pigou-Dalton transfer principle and weak dominance.a weak version of the Pareto principle., but there exists no social welfare function that satisfies any of our distributive equity axioms and weak Pareto principle simultaneously. Thus, we prove that no Paretian ranking can satisfy numerical representability and any of distributive equity axioms in the setting of intertemporal social choice.