Piketty's Capital in the 21 st Century and modern finance: The other [r − g] relationship

In this study we look at one wheel in the machinery of modern finance that may help evaluate Piketty's contributions in his best-seller Capital in the 21st Century (C21C): the constant-growth equity model, also known as Gordon's model. We first briefly review Piketty's text, and highlight two theories advanced by Piketty: one about the relationship between return on capital and economic growth (r − g) associated with the ratio between two variables (k/y), and another theory in which the same (k/y) relationship is associated with a ratio between the growth rate of savings-to-economic growth (i.e., k/y = s/g). Piketty uses these two devices, s/g and r > g to warn readers about a possible future of secular stagnation (a continued age of very low or even negative g's), in which the inequality r > g may create inequality levels not seen since the XIX century, or worse. The constant growth model, however, provides what Piketty's analysis does not include: transitional dynamics, the adjustments agents would make in such dire low growth scenario and system responses. Furthermore, the constant growth model shows why r > g, r − g > 0 is both a logical and a computational condition valid for all times. In sum, we show that Piketty's theoretical devices cannot support his contentions.