Free Liberal

Coordinating towards higher values

Piketty's Potlatch: r vs. β

by , Senior Editor, Free Liberal


This is Part III of “Piketty’s Potlatch”. See the Introduction and Part II.

From Part II: “Piketty’s Theorems”:



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

Where

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.



Let us hold ɑ – the total share of the economy that goes to capital – constant and consider two societies: one where r is high and β is low, and another where r is low and β is high.

For our low β society, let’s crank r up to a ridiculous 20% and for the high β society, turn r down to 3%, so we can really see what is happening. Let’s whip up a caveman retirement model: compound the return on prior year’s savings annually using r, and assume that you can retire when your passive income hits your wages less what you have been saving. For example, if you can save 10% of your wages, then you should be able to live off 90% of your wages in retirement. With our ridiculously high r society we get:

Saving Until Retirement with r=20% and Savings Rate=10%

YearEnd of Year SavingsRetirement Income
110.0%2.0%
222.0%4.4%
336.4%7.3%
453.7%10.7%
574.4%14.9%
699.3%19.9%
7129.2%25.8%
8165.0%33.0%
9208.0%41.6%
10259.6%51.9%
11321.5%64.3%
12395.8%79.2%
13485.0%97.0%

Thirteen years to retirement! Woohoo! Early retirement becomes the norm! Even if we drop that savings rate down to 5%, we get retirement in a mere 17 years.

Saving Until Retirement with r=20% and Savings Rate=5%

YearEnd of Year SavingsRetirement Income
15.0%1.0%
211.0%2.2%
318.2%3.6%
426.8%5.4%
537.2%7.4%
649.6%9.9%
764.6%12.9%
882.5%16.5%
9104.0%20.8%
10129.8%26.0%
11160.8%32.2%
12197.9%39.6%
13242.5%48.5%
14296.0%59.2%
15360.2%72.0%
16437.2%87.4%
17529.7%105.9%

So go ahead and party until you are 50, and then save a mere 5% and you can retire at 67. Or start young and save a bit more and you can join the aristocracy while you are still young enough to enjoy it.

But if too many people work and save young so they can enjoy a future four hour workweek, we wend our way back to the high β scenario. What happens when r drops down 3%. A 10% savings rate yields:

Saving Until Retirement with r=3% and Savings Rate=10%

YearEnd of Year SavingsRetirement Income
110.0%0.3%
220.3%0.6%
330.9%0.9%
441.8%1.3%
553.1%1.6%
664.7%1.9%
776.6%2.3%
888.9%2.7%
9101.6%3.0%
10114.6%3.4%
11128.1%3.8%
12141.9%4.3%
13156.2%4.7%
14170.9%5.1%
15186.0%5.6%
16201.6%6.0%
17217.6%6.5%
18234.1%7.0%
19251.2%7.5%
20268.7%8.1%
21286.8%8.6%
22305.4%9.2%
23324.5%9.7%
24344.3%10.3%
25364.6%10.9%
26385.5%11.6%
27407.1%12.2%
28429.3%12.9%
29452.2%13.6%
30475.8%14.3%
31500.0%15.0%
32525.0%15.8%
33550.8%16.5%
34577.3%17.3%
35604.6%18.1%
36632.8%19.0%
37661.7%19.9%
38691.6%20.7%
39722.3%21.7%
40754.0%22.6%
41786.6%23.6%
42820.2%24.6%
43854.8%25.6%
44890.5%26.7%
45927.2%27.8%
46965.0%29.0%
471004.0%30.1%
481044.1%31.3%
491085.4%32.6%
501128.0%33.8%
511171.8%35.2%
521217.0%36.5%
531263.5%37.9%
541311.4%39.3%
551360.7%40.8%
561411.5%42.3%
571463.9%43.9%
581517.8%45.5%
591573.3%47.2%
601630.5%48.9%
611689.5%50.7%
621750.1%52.5%
631812.6%54.4%
641877.0%56.3%
651943.3%58.3%
662011.6%60.3%
672082.0%62.5%
682154.4%64.6%
692229.1%66.9%
702305.9%69.2%
712385.1%71.6%
722466.7%74.0%
732550.7%76.5%
742637.2%79.1%
752726.3%81.8%
762818.1%84.5%
772912.6%87.4%
783010.0%90.3%

Holy Wage Slavery, Batman! It takes 78 years to reach financial freedom with a 10% savings rate. You could still retire in less by living off the principal (by buying an annuity when you are too feeble to work), but then there is no legacy to leave your children. Joining the financially free aristocracy is looking like an arduous multi-generational enterprise – or a rare perk for those who strike it big launching the next big dot com business. Maybe Dr. Piketty is onto something. Maybe it is time to hold a big old potlatch. Confiscate the savings of the super-rich and build a giant Clinton Monument. or something.

Not so fast. An economy with a high r is an economy with low wages as Adam Smith pointed out centuries ago. All those high dollar assembly lines which created the broad middle class in the middle of the 20th Century require outrageous interest payments to the few who have saved. Ask your local small business owner how much he pays in interest today. A society with an r of 20% means 20% after taking account for risk. Given the high failure rates for small businesses, we might be talking 50% or more, especially for the young just getting started.

If wages are a mere 20% higher in the low r society, you could save 25% and still live off the exact same amount of money as the lower wage worker in the high r society.

Saving Until Retirement with r=3% and Savings Rate=25%

YearEnd of Year SavingsRetirement Income
125.0%0.8%
250.8%1.5%
377.3%2.3%
4104.6%3.1%
5132.7%4.0%
6161.7%4.9%
7191.6%5.7%
8222.3%6.7%
9254.0%7.6%
10286.6%8.6%
11320.2%9.6%
12354.8%10.6%
13390.4%11.7%
14427.2%12.8%
15465.0%13.9%
16503.9%15.1%
17544.0%16.3%
18585.4%17.6%
19627.9%18.8%
20671.8%20.2%
21716.9%21.5%
22763.4%22.9%
23811.3%24.3%
24860.7%25.8%
25911.5%27.3%
26963.8%28.9%
271017.7%30.5%
281073.3%32.2%
291130.5%33.9%
301189.4%35.7%
311250.1%37.5%
321312.6%39.4%
331376.9%41.3%
341443.3%43.3%
351511.6%45.3%
361581.9%47.5%
371654.4%49.6%
381729.0%51.9%
391805.9%54.2%
401885.0%56.6%
411966.6%59.0%
422050.6%61.5%
432137.1%64.1%
442226.2%66.8%
452318.0%69.5%
462412.5%72.4%
472509.9%75.3%

This gets us down to 47 years to financial freedom. This is still rather long, but I think the difference in wages would be much greater. Methinks a doubling in the high savings society is easily attainable. This would allow a 55% savings rate with the exact same standard of living.

Saving Until Retirement with r=3% and Savings Rate=55%

YearEnd of Year SavingsRetirement Income
155.0%1.7%
2111.7%3.3%
3170.0%5.1%
4230.1%6.9%
5292.0%8.8%
6355.8%10.7%
7421.4%12.6%
8489.1%14.7%
9558.8%16.8%
10630.5%18.9%
11704.4%21.1%
12780.6%23.4%
13859.0%25.8%
14939.7%28.2%
151022.9%30.7%
161108.6%33.3%
171196.9%35.9%
181287.8%38.6%
191381.4%41.4%
201477.9%44.3%
211577.2%47.3%

This gives us 21 years to financial freedom – well within the career path of a blue collar worker. But can we expect such financial discipline from the average worker?

The answer is probably no, but keep in mind that both scenarios are intentionally extreme to expose the dynamic.

So which scenario is more progressive? For that we probably need to consult the data, or dig more deeply into the theory. For now I invite you to look at the low β societies that exist today, those low capital societies where interest rates on the street are astronomical. Do you see people making the transition from laborer to loan shark in 13 years?

I see real slavery.

I’ll take low interest rates and billionaires building spaceships.


Potlatch Alternatives

All this talk of β vs. r and even ɑ vs. the return on labor could well be moot. If The People own a big chunk of the means of production, we could have an egalitarian society even with a high ɑ. This would be a society with slack, where we get to enjoy modern technology and not have to work so hard…

Read the rest here.

About

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.