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Piketty’s Laws: Piketty’s Laws in economics include First Fundamental Law α = r × β → The share of capital in national income (α) depends on the return on capital (r) and the capital-to-income ratio (β). Second Fundamental Law β = s/g → The capital-to-income ratio (β) grows when the savings rate (s) exceeds economic growth (g), leading to wealth accumulation. See also Thomas Piketty, Piketty-Model, Piketty hypothesis.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
Author Concept Summary/Quotes Sources

Thomas Piketty on Piketty’s Laws - Dictionary of Arguments

Bofinger I 77
Piketty's laws/capitalism/savings/Piketty/van Treek: Piketty speaks of “fundamental laws of capitalism”, in fact the model only consists of an identity equation (equation 1) and a simple arithmetic principle (equation 2). This is precisely why the model is valid beyond basic theoretical conflicts (e.g. Keynesian versus neoclassical macroeconomics), provided that a long-term equilibrium concept (steady state) is applied.
>Keynesianism
, >Neoclassical Economics.
I.
In the “first fundamental law”, the share of capital income (P) in national income (Y) is denoted by ∝ and defined as the product of the return on capital (r) and the ratio of total economic net assets (W) to national income (Y), which is denoted by β:

(1) ∝ = P/Y = r * β = rW/Y

II.
In the long-run equilibrium, β converges according to the “second fundamental law” against the relation from
Bofinger I 78
macroeconomic savings rate (s) and the nominal growth rate of national income (g):

(2) β = s/g

These correlations become more important for the development of income and wealth distribution due to two empirical observations:
1) First, high-income individuals save a larger share of their income and inherit more relative to their income than low-income individuals. This contributes decisively to the fact that wealth is distributed more unequally than income and that inheritances gain in importance over time compared to earned income.
2) Secondly, according to Piketty, the return on capital (r) has historically often been higher than the growth rate of national income (g).
Cf. >Method/Piketty.
Van Treek: This means that if wealth owners save a sufficiently large proportion of their income, wealth tends to rise faster than labor income. If savings from capital income exceed the growth rate of national income, the wealth-to-income ratio (β) rises continuously. This leads to an ever greater share of capital income in national income (∝), which ultimately implies ever greater income inequality.(1)
Distribution/van Treek: The distributional significance of a large r-g ratio only arises from the different savings rates of different income groups.
Savings rates: If savings rates were independent of income, then the ratio of wealth to income for individual households would also be independent of their income.
Bofinger I 79
With uniform savings rates, the distribution of wealth and income would also be identical to the distribution of wages in the long term, and the ratio of r and g would be irrelevant for the development of distribution.

Some basics for Piketty:
>Cambridge Capital Controversy,
>Geoffrey C. Harcourt,
>Capital reversing,
>Capital/Joan Robinson,
>Exploitation/Robinson,
>Reswitching/Robinson,
>Reswitching/Sraffa,
>Reswitching/Economic Theories,
>Neo-Keynesianism,
>Neo-Neoclassical Theories.

1. Formally, β increases infinitely if and only if sPr > g, where sP is the savings rate from capital income.

Till van Treeck. 2015. „Zur Bedeutung von r > g in Pikettys „Kapital im 21.Jahrhundert“.“ In: Thomas Piketty und die Verteilungsfrage. Ed. Peter Bofinger, Gustav A. Horn,
Kai D. Schmid und Till van Treeck. 2015.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.



Piketty I
Thomas Piketty
Capital in the Twenty First Century Cambridge, MA 2014

Piketty II
Thomas Piketty
Capital and Ideology Cambridge, MA 2020

Piketty III
Thomas Piketty
The Economics of Inequality Cambridge, MA 2015

Bofinger II
Peter Bofinger
Monetary Policy: Goals, Institutions, Strategies, and Instruments Oxford 2001

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