Piketty's Prediction meets technical progress in Harrod-Domar's Dynamics and Solow Swan's Surrogate

Thomas Piketty [2014] uses mainly UN projections that the world GDP growth rate g can fall by half in 2010-2100, to predict that the capital or wealth share in world national income, αK, may double. This prediction for αK contradicts at least one of Kaldor's stylized facts and possibly the Kuznets curve. Negating somewhat this prognosis, we show here formally, that exogenous technical progress can vary the αK trajectories in either direction, even with the saving rate, s, held constant. Further, we show how s can be used not only to stabilize αK but also to allow GDP growth g to accompany its only true engine, technical progress. Like Piketty, we use the Solow-Swan model and ignore the recent literature which, since about 1985, tries to make endogenous this mother lode of growth. Finally, the paper suggests that the policy recommendation of this literature, for the great majority of the world's population, should continue to emphasize growth in per capita GDP, at least while the gap with the rich economies is so wide. The issue remains income distribution, not the ones within each economy, Piketty's contribution, but rather the one across them all.