This paper studies welfare assessments in economies with rich demographics. We introduce the notion of demographically disconnected economies, those with no date at which all individuals are concurrently alive. We identify the unique class of units that enables meaningful welfare comparisons in such economies: those based on perpetual consumption, that is, consumption at all dates. Using this metric, we uncover a novel possibility: feasible perturbations of Pareto efficient allocations can yield Kaldor-Hicks efficiency gains. We also introduce a decomposition that attributes intertemporal-sharing efficiency gains to financial frictions or demographic differences. These results allow us to derive new insights in three workhorse intergenerational models: (i) Samuelson(1958) two-date-life model, offering a novel rationale for social security; (ii) Diamond(1965) growth model, providing a new theory for capital taxation and capital over-/under-accumulation; and (iii) Samuelson (1958) three-date-life model, decomposing the efficiency gains from intergenerational transfers into frictional and demographic sources.