TITLE:
Two Simple Formulas Relating the Growth and Profit Rates
AUTHORS:
Alberto Benítez Sánchez
KEYWORDS:
Growth Rate, Income Inequality, Piketty, Profit Rate
JOURNAL NAME:
Theoretical Economics Letters,
Vol.11 No.3,
June
28,
2021
ABSTRACT: This article compares the magnitudes of the growth
and profit rates within an economic model that represents two successive
periods of production. Its main result is a pair of simple formulas determining
respectively the (growth rate)/(profit rate) ratio and the (profit rate) – (growth rate) difference. The first formula
permits to show that the ratio is a decreasing function of the capital/income
ratio. The second formula allows us to point out that the difference, as a
general rule, is an increasing function of the capital/income ratio although,
under certain conditions, it may be otherwise. Both formulas consider the
simplest case, when savings equals capital increase and, in addition, the
capital/income ratio is constant. The general case in which these conditions
are not necessarily satisfied is also considered. In the simplest case, the
ratio between the two rates is equal to that between the savings rate and the
capital share while the difference is equal to that between these same
variables divided by the capital/income ratio. In the general case, the results
just indicated are modified by a quotient having in both formulas the same
numerator: the capital increase not due to savings (as a fraction of income)
minus the increase in the capital/income ratio. In the first formula, the
quotient is preceded by a positive sign and its denominator is the capital
share while in the second one it is preceded by a negative sign and its
denominator is the capital/income ratio. As illustrated by means of an
empirical application, these results help to
explain the inequality between the growth and profit rates whose
importance for income distribution is underlined by Piketty.