Conventional wisdom holds that Fully Funded (FF) pension schemes would better prepare the community for ongoing demographic change. Many critics of FF schemes argue that these plans would encounter problems similar to those that create financial difficulties to Pay-As-You-Go (PAYG) schemes. More specifically, they maintain that, whereas in a PAYG scheme a decrease in the working population with respect to an increasing elderly population undermines the financial source of pension transfers, by the same token in an FF scheme a diminished number of young savers would make the absorption of the capital assets accumulated by the pension funds difficult. This paper assesses the mainstream claim and its criticism in the light of the neoclassical foundations of the dominant view. It will emerge that the criticism is partially correct, but we arrive at this conclusion through reasoning that does not bypass the theoretical foundations of the mainstream claim. The capital theory critique is shown to be relevant in this respect.