The Origin of Piketty’s Inequality r > g Considered in a General Framework - Theoretical Economics Letters

TEL > Vol.8 No.10, June 2018

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

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DOI: 10.4236/tel.2018.810115 639 Downloads 1,755 Views

Author(s)

Alberto Benítez Sánchez

Affiliation(s)

Economics Department, Universidad Autónoma Metropolitana, México D.F., México.

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.

KEYWORDS

Growth Rate, Income/Capital Ratio, Piketty, Profit Rate

Share and Cite:

Benítez Sánchez, A. (2018) The Origin of Piketty’s Inequality r > g Considered in a General Framework. Theoretical Economics Letters, 8, 1752-1771. doi: 10.4236/tel.2018.810115.

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