TITLE:
The Origin of Piketty’s Inequality r > g Considered in a General Framework
AUTHORS:
Alberto Benítez Sánchez
KEYWORDS:
Growth Rate, Income/Capital Ratio, Piketty, Profit Rate
JOURNAL NAME:
Theoretical Economics Letters,
Vol.8 No.10,
June
20,
2018
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.