The canonical infinite horizon framework with heterogeneous consumers, used in macro and financial literature, lacks a preference-based welfare index that produces consistent normative predictions for different policies. In particular, the classic preference-based indices, such as equivalent or compensating variations, do not aggregate and they are not additive on the set of policies. This paper offers a positive result. We show that for arbitrary heterogeneous von Neumann Morgenstern preferences with common discount factor, an equivalent (compensating) variation is nearly additive and admits a representative agent representation, as long as consumers are patient. Therefore, this index generates consistent quantitative comparisons of welfare effects in a wide variety of problems studied in the macro and finance literature. These problems include, among others, predictions regarding welfare impacts of fiscal or monetary policies, costs of real business cycles, or welfare costs of policies implemented in financial markets.