| Subject: | Re: [socialcredit] Calculations about the A + B theorem | | Date: | Friday, October 1, 2004 22:23:31 (-0700) | | From: | william_b_ryan <william_b_ryan @.....com>
|
| Subject: | Re: Calculations about the A + B theorem | | Date: | Friday, October 1, 2004 16:18:04 (+0200) | | From: | Per Almgren <info @........se>
|
My comments follow below at the appropriate places.
Per Almgren
At 17:02 2004-09-30, you wrote:
[ALMGREN] I refer to the staircase-similar diagram
that I sent some weeks ago.
-------------------------
-----------------------
[REPLY] It is apended below and also archived at
http://www.geocities.com/socredus/almgren/almgrenstep.gif
==>
[ALMGREN] If for some reason there is a need for
borrowing in each step in order to be able to pay out
money to the employees, subcontractors and owners as
prescribed within different contracts, we can name
this complementary financing X compared to the income
of size 1 from sold goods and services. The money
used for purchase from the preceding step is Y
compared to the total out-payment. This means that
private persons get 1 - Y of the total out-payment in
each step (just to make the calculations of this
example as simple as possible).
-------------------------
-----------------------
[REPLY] So the financial input to the logical firm
represented by the step is 1 + X. The financial
output is Y + (1 - Y) = 1. Have you not commenced
this train of logic with a contradiction? There does
not appear to be a "need for borrowing...in order to
be able to pay out money to the employees," etc.,
since the receipts from sales necessarily equals the
"total out-payment" as you have defined your terms.
This would seem to mandate that any conclusion you
may reach about the effects of interest on X couldn't
possibly derive from this model.
---------------
==>Almgren reply 10-01-04:
The retailers purchase from the next (wholesaler)
step is
( 1 + X ) x Y
and the sum of wages, salaries, dividends and interest
payments from the retailer to the consumers are
( 1 + X ) x ( 1 - Y ).
The wholesalers purchase from the following
(manufacturer) step is
( 1 + X ) x ( 1 + X ) x Y x Y and the sum of wages,
salaries, dividends and interest payments to the
consumers amounts to
( 1 + X ) x ( 1 + X ) x ( 1 - Y ) x Y and so on.
After rearranging for later summing we get
( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y )
where the leftmost parenthesis is the geometrical
factor which govern the size of the following steps.
Consumers income from the subsequent step will be
( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y ) ^ 2,
after that
( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y ) ^ 3, and so
on.
So there is no contradiction so far.
The adding of all consumers income from the different
steps and the rest of the calculation ought to be
quite clear in my former mail.
The out-payment from the first (retail) step is ( 1 +
X ) and the consumers purchase was of the amount 1.
Therefore the assumed borrowing need is X.
The retailers purchase from the next (wholesaler)
step is ( 1+ X ) x Y and the sum of wages, salaries,
dividends and interest payments from the retailer to
the consumers are
( 1 + X ) x ( 1 - Y ).
The wholesalers purchase from the following
(manufacturer) step is
( 1 + X ) x ( 1 + X ) x Y x Y and the sum of wages,
salaries, dividends and interest payments to the
consumers amounts to
( 1 + X ) x ( 1 + X ) x ( 1 - Y ) x Y and so on.
After rearranging for later summing we get
( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y )
where the leftmost parenthesis is the geometrical
factor which govern the size of the following steps.
Consumers income from the subsequent step will be
( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y ) ^ 2,
after that
( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y ) ^ 3, and so
on.
So there is no contradiction so far.
The adding of all consumers income from the different
steps and the rest of the calculation ought to be
quite clear in my former mail.
--
==>Ryan from the earlier message:
From a contradiction you may conclude anything at all.
You can just as easily conclude that the moon is made
of green cheese.
Care to comment?
-
==>Almgren continuing his reply 10-01-04:
Done. I can't see that my conclusion in the preceding
mail has been falsified.
Regards.
Per Almgren
----original message----
Date: Tue, 28 Sep 2004 22:08:59 +0200
To: socialcredit@elistas.com
From: "Per Almgren" <info@nordspar.se>
CC: Mats_h2001@yahoo.com
Subject: Calculations about the A + B theorem
Here come some simple calculation about the A + B
theorem. I am going to do it with more details in a
few weeks.
Regards
Per Almgren
-------------------------
-----------------------
Some preliminary and simple calculations regarding
the A + B theorem.
I refer to the staircase-similar diagram that I
sent some weeks ago. The diagram shows how the
money is distributed along the production chain and
stepwise paid out to private person.
If for some reason there is a need for borrowing in
each step in order to be able to pay out money to
the employees, subcontractors and owners as
prescribed within different contracts, we can name
this complementary financing X compared to the
income of size 1 from sold goods and services.
The money used for purchase from the preceding step
is Y compared to the total out-payment. This means
that private persons get 1 - Y of the total out-
payment in each step (just to make the calculations
of this example as simple as possible). This out-
payment consists of interest, dividends, wages and
salaries.
Of this total income the part P is used for
purchasing goods and services.
The model have the geometry of a constant factor Y
for the size of the purchase in each step and the
factor 1 + X regarding the size of necessary
borrowing.
The consumers purchasing power in step N will be P
x ( 1 - Y ) x (1 + X ) x ( Y x ( 1 + X ) ) ^N.
N=0 is the retailer step, N=1 the wholesaler step,
N=2 the manufacturer, N=3 the subcontractor and so
on towards approximately eternity.
If we sum this geometrical serial we find the sum
= P x ( 1 - Y ) x ( 1 + X ) / ( 1 - Y x ( 1 + X ))
The borrowed amount in each step will be X x ( Y x
( 1 + X ) ) ^ N and the sum of this serial is
X / ( 1 - Y x ( 1 + X ))
The retailers will sell for 1
This gives the equation
1 = P x ( 1 - Y ) x ( 1 + X ) / ( 1 - Y x ( 1 + X ))
If we solve for X we get X = ( 1 - Y ) x ( 1 - P )
/ ( Y + P x ( 1 - Y ))
This shows that if the private persons use all of
their earnings for purchasing goods and services
there wouldn't be any need for borrowing when P =
1. If they save some of their earnings or "invest"
them or lend them, it will be necessary for the
producing chain to borrow.
If we take away the interest on money, we will at
the same time eliminate a great part of the need
for borrowing.
Per Almgren
-
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<DIV>
<DIV>
<DIV>
<P>ALMGREN] If for some reason there is a need for <BR>borrowing in each step
in order to be able to pay out <BR>money to the employees, subcontractors and
owners as <BR>prescribed within different contracts, we can name <BR>this
complementary financing X compared to the income <BR>of size 1 from sold goods
and services. The money <BR>used for purchase from the preceding step is Y
<BR>compared to the total out-payment. This means that <BR>private persons get
1 - Y of the total out-payment in <BR>each step (just to make the calculations of
this <BR>example as simple as possible).<BR>--------------------------</P>
<P>==>Almgren reply 10-01-04:</P>
<P>The out-payment from the first (retail) step is ( 1 + <BR>X ) and the
consumers purchase was of the amount 1. <BR>Therefore the assumed borrowing need
is X.</P>
<P>The retailers purchase from the next (wholesaler) <BR>step is </P>
<P>( 1 + X ) x Y </P>
<P>and the sum of wages, salaries, dividends and interest<BR>payments from the
retailer to the consumers are</P>
<P>( 1 + X ) x ( 1 - Y
).<BR>---------------------------<BR>-------------------------<BR>----------------------</P>
<P>[Ryan reply 10-01-04] Alright, I now see what you <BR>meant by Y. It was
not at all clear from your initial <BR>post. Y is the coefficient representing
the <BR>percentage of the total outpayment going to the <BR>lower stage of
production in respect to that going <BR>to consumers. In terms of the A+B
theorem, the <BR>outpayment going to lower stages is termed B, and <BR>outpayment
to consumers is A. This is what you said <BR>in your earlier post:</P>
<P>"The model have the geometry of a constant factor Y <BR>for the size of the
purchase in each step..."</P>
<P>Using the terminology of A+B, this is saying that the <BR>ratio between A and
B is remaining constant through <BR>time. In other words, you are specifically
excluding <BR>the possibility of labor displacement from your <BR>model, where
the ratio of B is increasing to A. In <BR>terms of the theorem, for analytical
purposes, this <BR>special hypothetical condition where the ratio <BR>remains
constant is called quasi-steady state. The <BR>general condition prevailing in
the real world is <BR>however assumed in the theorem to be labor
<BR>displacement, which is empirically confirmable. <BR>Unless you can
demonstrate how you would factor in <BR>this increasing ratio, your model is
irrelevant to <BR>A+B completely. It would appear at this point that <BR>A+B
supplies the more complete model in terms of <BR>relevance to the real world. In
this respect, <BR>therefore, I fail to see how your model differs from <BR>the
orthodox model utilized by most
economists for <BR>the past two centuries.</P>
<P>It appears that the outpayment of all of the stages <BR>summed to
approximately infinity in your model equals <BR>the income of the consuming
sector as measured <BR>instantaneously. Is that correct? If so, this would
<BR>represent the critical departure from A+B. In terms <BR>of the theorem as
depicted in the diagram appended <BR>below also archived at<BR><A href="http://www.geocities.com/socredus/compendium/costs-flow.gif";>http://www.geocities.com/socredus/compendium/costs-flow.gif</A><BR>that
would be asserting that B is necessarily equal <BR>to A2. But the theorem is
predicated on the <BR>assumption that the general real world condition is B
<BR>greater than A2, and that with labor displacement the <BR>ratio of B is
increasing to both A1 and A2. B is <BR>equal to A2 only in the special
hypothetical <BR>condition of dynamic stasis. B is greater than A2 <BR>but
remains proportionate to A2 through time where B <BR>is increasing only where the
special condition of <BR>quasi-steady state prevails, the condition that
<BR>extends but encompasses dynamic stasis. The ratio <BR>A1+A2 to A1+B is
necessarily falling in the more <BR>general condition of labor displacement.</P>
<P>It also appears that your model is contingent on a <BR>constant quantity of
money (the kind that can fall <BR>into "hoards" and thereby exploited) and the
complete <BR>absence of credit money, like tally sticks tendered <BR>in trade a
millennium ago that contemplated future <BR>performance, or the more modern
variant in bank <BR>credits that function as money. If so, it would seem
<BR>your model is irrelevant to the real world as the <BR>archaeological and
historical records tell us has <BR>existed since the human race began trading.
See the <BR>papers at<BR><A href="http://www.geocities.com/new_economics/innes";>http://www.geocities.com/new_economics/innes</A><BR>If
not, it is incumbent on you to demonstrate how you <BR>would factor in a
continuously changing quantity of <BR>money to make it applicable to the real
world.</P>
<P>Later, I want to ask you some questions about JAK. <BR>But let's keep going
with this for awhile.</P>
<P>Bill</P>
<P> </P>
<P>----original message----<BR>Date: Fri, 01 Oct 2004 16:18:04 +0200 <BR>To: <A
href="mailto:socialcredit@elistas.com">socialcredit@elistas.com</A> <BR>From:
"Per Almgren" <<A
href="mailto:info@nordspar.se">info@nordspar.se</A>><BR>CC: <A
href="mailto:Mats_h2001@yahoo.com">Mats_h2001@yahoo.com</A> <BR>Subject: Re:
Calculations about the A + B theorem </P>
<P>My comments follow below at the appropriate places.</P>
<P>Per Almgren</P>
<P>At 17:02 2004-09-30, you wrote:</P>
<P>[ALMGREN] I refer to the staircase-similar diagram <BR>that I sent some
weeks ago.<BR>-------------------------<BR>-----------------------<BR>[REPLY] It
is apended below and also archived at<BR><A href="http://www.geocities.com/socredus/almgren/almgrenstep.gif";>http://www.geocities.com/socredus/almgren/almgrenstep.gif</A><BR>==><BR>[ALMGREN]
If for some reason there is a need for <BR>borrowing in each step in order to be
able to pay out <BR>money to the employees, subcontractors and owners as
<BR>prescribed within different contracts, we can name <BR>this complementary
financing X compared to the income <BR>of size 1 from sold goods and services.
The money <BR>used for purchase from the preceding step is Y <BR>compared to the
total out-payment. This means that <BR>private persons get 1 - Y of the total
out-payment in <BR>each step (just to make the calculations of this <BR>example
as simple as
possible).<BR>-------------------------<BR>-----------------------<BR>[REPLY]
So the financial input to the logical firm <BR>represented by the step is 1 + X.
The financial <BR>output is Y + (1 - Y) = 1. Have you not commenced <BR>this
train of logic with a contradiction? There does <BR>not appear to be a "need for
borrowing...in order to <BR>be able to pay out money to the employees," etc.,
<BR>since the receipts from sales necessarily equals the <BR>"total out-payment"
as you have defined your terms. <BR>This would seem to mandate that any
conclusion you <BR>may reach about the effects of interest on X couldn't
<BR>possibly derive from this model.<BR>---------------</P>
<P>==>Almgren reply 10-01-04:</P>
<P>The retailers purchase from the next (wholesaler) <BR>step is </P>
<P>( 1 + X ) x Y </P>
<P>and the sum of wages, salaries, dividends and interest<BR>payments from the
retailer to the consumers are</P>
<P>( 1 + X ) x ( 1 - Y ).</P>
<P>The wholesalers purchase from the following <BR>(manufacturer) step is</P>
<P>( 1 + X ) x ( 1 + X ) x Y x Y and the sum of wages, <BR>salaries, dividends
and interest payments to the <BR>consumers amounts to</P>
<P>( 1 + X ) x ( 1 + X ) x ( 1 - Y ) x Y and so on.</P>
<P>After rearranging for later summing we get</P>
<P>( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y )</P>
<P>where the leftmost parenthesis is the geometrical <BR>factor which govern the
size of the following steps.</P>
<P>Consumers income from the subsequent step will be<BR>( 1 + X ) x ( 1 - Y ) x
(( 1 + X ) x Y ) ^ 2,</P>
<P>after that</P>
<P>( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y ) ^ 3, and so <BR>on.</P>
<P>So there is no contradiction so far.</P>
<P>The adding of all consumers income from the different <BR>steps and the rest
of the calculation ought to be <BR>quite clear in my former mail.<BR> <BR>The
out-payment from the first (retail) step is ( 1 + <BR>X ) and the consumers
purchase was of the amount 1. <BR>Therefore the assumed borrowing need is X.</P>
<P>The retailers purchase from the next (wholesaler) <BR>step is ( 1+ X ) x Y
and the sum of wages, salaries, <BR>dividends and interest payments from the
retailer to <BR>the consumers are</P>
<P>( 1 + X ) x ( 1 - Y ).</P>
<P>The wholesalers purchase from the following <BR>(manufacturer) step is</P>
<P>( 1 + X ) x ( 1 + X ) x Y x Y and the sum of wages, <BR>salaries, dividends
and interest payments to the <BR>consumers amounts to</P>
<P>( 1 + X ) x ( 1 + X ) x ( 1 - Y ) x Y and so on.</P>
<P>After rearranging for later summing we get</P>
<P>( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y )</P>
<P>where the leftmost parenthesis is the geometrical <BR>factor which govern the
size of the following steps.</P>
<P>Consumers income from the subsequent step will be<BR>( 1 + X ) x ( 1 - Y ) x
(( 1 + X ) x Y ) ^ 2,</P>
<P>after that</P>
<P>( 1 + X ) x ( 1 - Y ) x (( 1 + X ) x Y ) ^ 3, and so <BR>on.</P>
<P>So there is no contradiction so far.</P>
<P>The adding of all consumers income from the different <BR>steps and the rest
of the calculation ought to be <BR>quite clear in my former mail.<BR>--</P>
<P>==>Ryan from the earlier message:</P>
<P>From a contradiction you may conclude anything at all. <BR>You can just as
easily conclude that the moon is made <BR>of green cheese.</P>
<P>Care to comment?<BR>-</P>
<P>==>Almgren continuing his reply 10-01-04:</P>
<P>Done. I can't see that my conclusion in the preceding <BR>mail has been
falsified. </P>
<P>Regards.</P>
<P>Per Almgren</P>
<P> </P>
<P>----original message----<BR>Date: Tue, 28 Sep 2004 22:08:59 +0200 <BR>To: <A
href="mailto:socialcredit@elistas.com">socialcredit@elistas.com</A> <BR>From:
"Per Almgren" <<A
href="mailto:info@nordspar.se">info@nordspar.se</A>><BR>CC: <A
href="mailto:Mats_h2001@yahoo.com">Mats_h2001@yahoo.com</A> <BR>Subject:
Calculations about the A + B theorem <BR> <BR>Here come some simple
calculation about the A + B <BR>theorem. I am going to do it with more details in
a <BR>few weeks.</P>
<P>Regards</P>
<P>Per Almgren<BR>-------------------------<BR>-----------------------</P>
<P>Some preliminary and simple calculations regarding <BR>the A + B theorem.</P>
<P>I refer to the staircase-similar diagram that I <BR>sent some weeks ago. The
diagram shows how the <BR>money is distributed along the production chain and
<BR>stepwise paid out to private person.</P>
<P>If for some reason there is a need for borrowing in <BR>each step in order to
be able to pay out money to <BR>the employees, subcontractors and owners as
<BR>prescribed within different contracts, we can name <BR>this complementary
financing X compared to the <BR>income of size 1 from sold goods and
services.</P>
<P>The money used for purchase from the preceding step <BR>is Y compared to the
total out-payment. This means <BR>that private persons get 1 - Y of the total
out-<BR>payment in each step (just to make the calculations <BR>of this example
as simple as possible). This out-<BR>payment consists of interest, dividends,
wages and <BR>salaries.</P>
<P>Of this total income the part P is used for <BR>purchasing goods and
services.</P>
<P>The model have the geometry of a constant factor Y <BR>for the size of the
purchase in each step and the <BR>factor 1 + X regarding the size of necessary
<BR>borrowing.</P>
<P>The consumers purchasing power in step N will be P <BR>x ( 1 - Y ) x (1 + X )
x ( Y x ( 1 + X ) ) ^N.</P>
<P>N=0 is the retailer step, N=1 the wholesaler step, <BR>N=2 the manufacturer,
N=3 the subcontractor and so <BR>on towards approximately eternity.</P>
<P>If we sum this geometrical serial we find the sum <BR>= P x ( 1 - Y ) x ( 1
+ X ) / ( 1 - Y x ( 1 + X ))</P>
<P>The borrowed amount in each step will be X x ( Y x <BR>( 1 + X ) ) ^ N and
the sum of this serial is<BR>X / ( 1 - Y x ( 1 + X ))</P>
<P>The retailers will sell for 1</P>
<P>This gives the equation</P>
<P>1 = P x ( 1 - Y ) x ( 1 + X ) / ( 1 - Y x ( 1 + X ))</P>
<P>If we solve for X we get X = ( 1 - Y ) x ( 1 - P ) <BR>/ ( Y + P x ( 1 - Y
))</P>
<P>This shows that if the private persons use all of <BR>their earnings for
purchasing goods and services <BR>there wouldn't be any need for borrowing when P
= <BR>1. If they save some of their earnings or "invest" <BR>them or lend them,
it will be necessary for the <BR>producing chain to borrow. </P>
<P>If we take away the interest on money, we will at <BR>the same time eliminate
a great part of the need <BR>for borrowing.</P>
<P>Per Almgren<BR>-</P>
<P><BR> </P></DIV></DIV></DIV><p>
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