The Origin of Piketty’s Inequality r > g Considered in a General Framework

This paper studies the origin of Piketty's inequality between the profit rate (r) and the growth rate of the national income (g) by focusing on the growth rate (gamma) of the r⁄g ratio in an economy that grows gradually along a succession of production cycles. It is shown that, given a succession of three production cycles, the value of gamma in the last cycle is determined by the equation 1+gamma=(1+ ni)(1+ kappa) where ni is the growth rate of the profit share (alfa) in the last cycle while kappa is a function of three variables: the income/capital ratio of the last cycle, the values of the savings rate in the first two cycles and those of the growth rate of the income/capital ratio in the last two. The equation just presented is also relevant for a succession of more than three production cycles for which the yearly values of r, g and alfa are known. Indeed, in this case it is possible to calculate the average values of gamma and ni from the empirical data, which then can be used in the equation to determine the average value of kappa. Once the three variables are known, it is possible to calculate the parts attributable respectively to the average values of ni and kappa in the determination of the average value of gamma. A similar result is obtained regarding the part attributable to the average changes in the savings rate and in the growth rate of the income/capital ratio, taken together, in the determination of the average value of kappa. The paper also identifies those configurations of the relevant variables where gamma>0, out of which, when the succession of production cycles is long enough, results the inequality r>g