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Piketty’s Theorems · Free Liberal

Free Liberal

Coordinating towards higher values

Piketty’s Theorems

by , Senior Editor , Free Liberal

This is part II of “Piketty’s Potlatch”. It began:

“Capital, alas, can be regressive. If you have it, you can invest the income therefrom to buy more. Positive feedback ensues. In this manner the rich get paid merely for being rich. For this reason I have been shouting across the Internet for the past decade that modern liberals need to part ways from Keynes…”

Read the rest of the introduction.

Piketty takes a very macro approach to the problem of wealth distribution. He starts with an accounting identity he calls “The First Fundamental Law of Capitalism:” [page 52]

ɑ = r * β


ɑ = share of the national income going to investors

r = rate of return on investment

β = the capital to income ratio – how many years of the national income does it take to equal the value of total capital stock.

As someone who likes to boil down big problems by looking at use cases, my impulse is to focus on r. It is the rate that laborers and entrepreneurs pay the owners of capital for financing tools, facilities and cash flow. A world in which consumers pay lower credit card rates and business owners pay less interest for tools and office space strikes me as a progressive one. Adam Smith had a similar view back in 1776:

It generally requires a greater stock to carry out any sort of trade in a great town than in a country village. The great stocks employed in every branch of trade, and the number of rich competitors, generally reduce the rate of profit in the former below what it is in the latter. But the wages of labour are generally higher in a great town than in a country village. In a thriving town the people who have great stocks to employ frequently cannot get the number of workmen they want, and therefore bid against one another in order to get as many as they can, which raises the wages of labour, and lowers the profits of stock. In the remote parts of the country there is frequently not stock sufficient to employ all the people, who therefore bid against one another in order to get employment, which lowers the wages of labour and raises the profits of stock.1

As Piketty acknowledges, capital has a diminishing rate of return [page 212]. More savings means lower r. And so I oppose Keynes’ pro consumption bias for progressive reasons.

Piketty, on the other hand, focuses on β. His reasoning is quite novel – at least to me. With a high β, you have to be really stinking rich to get a big share of ɑ. Even if we hold ɑ constant (by lowering r through more savings) the high β society is a society dominated by aristocrats.

He then introduces his second theorem which is no mere accounting identity [page 166]:

β = s / g


s = the national savings rate

g = the economy’s growth rate

We are back to a call for overconsumption without Keynes’ pseudoscience. Even if we stick to the Supply Side belief that growth requires savings, the Law of Diminishing Returns does inform us that s / g shrinks if we reduce s, since the available savings will go to higher return activities. While I’m not absolutely certain that Piketty’s theorem is true, it does seem plausible, unlike Keynes’ Paradox of Thrift.

So should we hold a massive national potlatch to get rid of that surplus savings?

My gut says, “No.” I’d rather have a high β society where startup entrepreneurs have access to cheap capital, and billionaires have fun building spaceships, floating islands, and expensive electric cars.

But let’s look a bit deeper at the problems of a high β society…

1 Chapter IX of the Wealth of Nations

Piketty’s Potlatch continues

Part III: r vs. β

Part IV: Potlatch Alternatives


Dr. Carl Milsted, Jr. is a Senior Editor of Free Liberal and is a member of its founding committee. He is the author of Holistic Politics and the Enhanced Precision Political Quiz, an online version of the popular Nolan quiz.