Introducing heterogeneous households to a New Keynesian small open economy model amplifies the real income channel of exchange rates: the rise in import prices from a depreciation lowers households’ real incomes, and leads them to cut back on spending. When the sum of import and export elasticities is one, this channel is offset by a larger Keynesian multiplier, heterogeneity is irrelevant, and expenditure switching drives the output response. With plausibly lower short-term elasticities, however, the real income channel dominates, and depreciation can be contractionary for output. This weakens monetary transmission and creates a dilemma for policymakers facing capital outflows. Delayed import price pass-through weakens the real income channel, while heterogeneous consumption baskets can strengthen it.