Aggregate Efficiency with Heterogeneous Agents

We study aggregate efficiency when households have heterogeneous preferences and outcomes. We generalize the consumption-equivalent variation of Lucas (1987) to a multi-agent setting, asking: how much can the consumption-possibility set shrink while keeping every agent at least as well off as in their status-quo allocation? The resulting scalar — resources left over after compensating everyone — is our measure of aggregate efficiency. Efficiency rises whenever the same status-quo welfare can be achieved with fewer resources. We show how to convert this problem into an equivalent utility-maximization problem, enabling the use of tools and results normally applicable only in representative agent settings. We characterize changes in aggregate efficiency in terms of observables, like expenditures and price elasticities, and apply our results to study, among other things, the effects of productivity shocks, the costs of misallocation, and the gains from trade, both with and without costly redistribution.