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

Abstract

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 ( γ ) 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 γ in the last cycle is determined by the equation 1+ γ=(1+v)(1+k) where v is the growth rate of the profit share ( α ) in the last cycle while κ 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 α are known. Indeed, in this case it is possible to calculate the average values of γ and v from the empirical data, which then can be used in the equation to determine the average value of κ . Once the three variables are known, it is possible to calculate the parts attributable respectively to the average values of v and κ in the determination of the average value of γ . 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 κ . The paper also identifies those configurations of the relevant variables where γ > 0 out of which, when the succession of production cycles is long enough, results the inequality r > g .