This study shows how the two alternative saving motives, life-cycle consumption smoothing and parental bequests, determine the relation between population growth and R&D-based economic growth, i.e. the sign of the "weak scale-effect". We take a textbook R&D-based growth model of infinitely living agents with no weak-scale effect, and analyze it in an Overlapping Generations framework - with and without bequest saving-motive. We show how the different saving motives determine the relation between population growth and per-capita income growth, which proves to be ambiguous in general, and may also be non-monotonic. Hence, we conclude that the counterfactual weak-scale effect that is present in the second and third generations of R&D-based growth models of infinitely-living agents depends on their specific demographic structure, and thus is not inherent to R&D-based growth theory itself.