A point about GDP

In macro,  GDP is abbreviated as Y.  Supposedly,  Y can be broken into consumption and savings as

(1 )   Y = C + S

However, this is grossly untrue because that formula omits  rental income which banks collect on excess credit.  I define excess credit as credit which is created beyond real demand.

Real demand, r  is the sum of a’/a +b’/b + d   which are, respectively, the investment demand for productivity growth,  labor force growth  and capital depreciation.  In the US,  r is about

0.045  or 4.5%.  When banks charge interest above this they receive a rental income  of

(2)  R = Y*( i – r) = c Y.

So,  (1)  needs to be rewritten

(3)  Y = C + S + R

That this is no small matter can be shown easily.   First,  divide (1) through by Y to get

(1a)   1 =  C/Y + S/Y  =  u  +  (1-u)

Doing the same for (3) we get

(3a)  1 ≠  u + (1-u) + c  = 1 + c     ,   c = R/Y

If  we want to normalize (3a) so that  Y still equals 1,  we get

1 = u/(1+c) + (1-u)/(1+c) + c/(1+c)

Repetition of this normalization, after a few years leads to the formula

(3b)   1 =  u*exp(-ct)  +  (1-u)*exp(-ct) +c*exp(ct)

In other words,  the workers and savers share is a decaying exponential, and the bankers share is a growing exponential.   If you are thinking that I have made a math error.  look at these figures:

US VelocityUS Money Velocity 1881-1966Screen Shot 2013-03-09 at 5.05.34 PM

Velocity, V, in the Quantity Theory of Money is given by the formula

V = pQ/m    where p is price level, Q is real output  and m is money.  To get a handle on the enormity of the crime which is committed via excess credit,  imagine a horizontal line drawn at

V = 4.5 from 1880 to the present.  The rectangular area enclosed between V = 4.5 and V = 1 is the total wealth produced in the US from 1880 to now.  The area above the velocity curve is the banker’s share, and the area below the velocity curve is the wealth allotted to the worker and savers.

The third figure shows the declining worker share since about 1945.  Remember,  the worker’s share is only the share of output below the velocity curve.  The savers, which are merchants can pass along some of their loss to the workers via higher prices.

My personal fantasy is to see 100 gallows erected around the reflecting pool at the Washington Monument whereon 100 bankers would be hanged per day for 100 days so as to teach future bankers an important lesson.

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