Missing equation in Piketty’s r-g theory

Yasunori Fujita


Although Thomas Piketty has revolutionized our understanding of inequality, logic behind his r-g theory is not developed formally in his researches. The present paper, by finding out the missing part of Piketty’s r-g theory, present a complete version of Piketty’s framework. It is revealed that necessary and sufficient condition for the r-g theory is SY(t)+AY(t)=CF(t). That is, savings in a broad sense (left hand side) is equal to the consumption using financial capital (right hand side). We also reveal that the problem is not in the Second Fundamental Law of Capitalism, but in the formulation of capital accumulation dynamics. Furthermore, it is demonstrated that the two Fundamental Laws of Capitalism are not necessary for deriving the r-g theory.

Full Text:



Alvaredo, Facundo, Anthony B. Atkinson, Thomas Piketty, and Emmanuel Saez. (2013) The Top 1 Percent in International and Historical Perspective, Journal of Economic Perspectives, 27(3), 3–20.

Atkinson, Anthony B. and Allan J. Harrison. (1978) Distribution of Personal Wealth in Britain, 1923-1972 (Cambridge University Press, Cambridge).

Jones, Charles I. (2015) Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality, Journal of Economic Perspectives, 29(1), 29–46.

Keynes, John M. (1936) The General Theory of Employment, Interest and Money, (Macmillan, London).

Krugman, Paul. (2014a) The Piketty Panic, The New York Times, April 24.

Krugman, Paul. (2014b) Why We’re in a New Gilded Age, New York Review of Books, May 8.

Krusell, Per and Tony Smith. (2014) Is Piketty's “Second Law of Capitalism” Fundamental? Mimeo.

Kuznets, Simon. (1955) Economic Growth and Income Inequality, American Economic Review, 45(1): 1– 28.

Marx, Karl. (1867) Capital, translated by A. Moore and E. Aveling (International Publisher, New York).

Milanovic, Branko. (2014) The Return of “Patrimonial Capitalism”: A Review of Thomas Piketty’s Capital in the Twenty-First Century, Journal of Economic Literature, 52(2), 519–534.

Piketty, Thomas, and Emmanuel Saez. (2003) Income Inequality in the United States, 1913–1998, Quarterly Journal of Economics, 118(1): 1–39.

Piketty, Thomas. (2011) On the Long-run Evolution of Inheritance: France 1820–2050, Quarterly Journal of Economics, 126(3): 1071–1131.

Piketty, Thomas. (2014) Capital in the Twenty-First Century, translated by Arthur Goldhammer (Belknap Press).

Piketty, Thomas. (2015) Putting Distribution Back at the Center of Economics: Reflections on Capital in the Twenty-First Century, Journal of Economic Perspectives, 29(1), 67–88.

Piketty, Thomas, and Emmanuel Saez. (2014) Inequality in the Long Run, Science, 344, 838–844.

Piketty, Thomas, and Gabriel Zucman. (2014) Capital is Back: Wealth-Income Ratios in Rich Countries 1700-2010, Quarterly Journal of Economics, 129(3), 1255-1310.

Samuelson, Paul A.(1948) Economics: An Introductory Analysis (McGraw-Hill, New York).

Stiglitz, Joseph E. (1969) Distribution of Income and Wealth among Individuals, Econometrica, 37, 382-397.

DOI: https://doi.org/10.17811/ebl.4.2.2015.57-62


  • There are currently no refbacks.

ISSN: 2254-4380