December 31, 2014

First Fundamental Law vs. Fundamental theorem of income distribution

Comment on RWER issue 69 on Piketty's Capital

Blog-Reference

“In the early pages of Capital in the Twenty-First Century, Thomas Piketty states a 'fundamental law of capitalism' that α = rxβ, where α is the share of profit in income, β is the capital/output ratio, and r is the rate of return on capital, or the rate of profit. Thus: r = α/β.” (Galbraith, 2014, p. 145)

The fundamental law does not hold because the fundamental theorem of income distribution states: Profit is not a factor income (2012, p. 4).

Piketty does not realize that profit and distributed profit are fundamentally different economic entities. Therefore, there is no such thing as “a share of profit in income” but there is “a share of distributed profit in income”.

The correct Profit Law reads:

(i) for the pure consumption economy
Qm = Yd-Sm (2012, p. 4, eq. (5))

(ii) for the investment economy
Qm =Yd+I-Sm: (2014, p. 8, eq. (18))

Legend: Qm: monetary profit, Yd: distributed profit, Sm: monetary saving, I: investment expenditure

The structural axiomatic Profit Law gets a bit more sophisticated when foreign trade and government is included. By summing up investment expenditures over time and taking depreciation into account (ii) ultimately yields the profit rate (2011b, Sec. 6.2).

Note that profit for the economy as a whole does not depend on productivity. What holds for a single firm does not hold for the economy as a whole. One has to be careful here not to commit a fallacy of composition.

Changes of the valuation price of assets are captured by nonmonetary profit Qn. This is a different and lengthy issue (2011a).

From the fact that Piketty's profit theory is not correct follows logically that his First fundamental law is not correct either.

Time to get the formal foundations right (see here).

Egmont Kakarot-Handtke


References
Galbraith, J. K. (2014). Unpacking the First Fundamental Law. real-world economics
review, (69): 145–148. URL
Kakarot-Handtke, E. (2011a). Primary and Secondary Markets. SSRN Working
Paper Series, 1917012: 1–26. URL
Kakarot-Handtke, E. (2011b). Squaring the Investment Cycle. SSRN Working Paper
Series, 1911796: 1–25. URL
Kakarot-Handtke, E. (2012). Income Distribution, Profit, and Real Shares. SSRN
Working Paper Series, 2012793: 1–13. URL
Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics:
Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL

The 'First fundamental law of capitalism' is the Profit Law (see here).