understanding H. Economicus

CSGnet Archive CSG2000
1

[From Bruce Nevin (2000.08.04.1226 EDT)]

Rick, it seems to me that we are in complete agreement in virtually all of your reply. We differ perhaps only in the question of defining Leakage. The present specification of it (as a discrepancy) is not enough basis for giving people advice about the economy. For starters, there are some questions about where the money leaks to.

Rick Marken (2000.08.03.1500)--

> This is a problem because leakage is such a central concept
> to TCP's analysis and RSM's model derived from it.

I don't see what the problem is. I agree that leakage is hard
to measure. To measure it we would have to identify the money
that is being received as income (wages and profits) and is
never being spent on goods and services. Most of this money
is probably going into stocks and bonds (such as the bonds
the Fed sells to take money out of the economy). But it's hard
to tell which money is being "parked" in these instruments and
which is being left there to be drawn down for future consumption.

Maybe I'm all wet, but this is my understanding: except for "bonds the Fed sells to take money out of the economy," when you buy stocks or bonds your purchase does not withdraw your money from circulation. For instance, if you buy municipal bonds, the municipality that issued the bonds spends your money for goods and services. When a company issues stock, it receives money from stock purchasers which it then can spend to purchase goods and services. Leaving money in the bank does not remove it from circulation, since most of the bank's holdings are not kept on hand as cash, but rather invested in stocks, bonds, real estate, etc., with the cash flowing on to sellers of those goods and services. Suppose, like Uncle Scrooge, I sit on a pile of cash and live frugally. Unless I physically take the cash and store it under my mattress, or in the Fed's hidey hole (wherever and whatever that is), or in Uncle Scrooge's coin-filled swimming pool, the money is still circulating in the economy.

I also have a bit of difficulty blaming unions' collective bargaining. If the problem is uneven distribution of wealth, why is this not seen as their attempt to distribute wealth more evenly? An understandable attempt which is understandably resisted by those who prefer the inequalities to go in their favor. Why not rather (or equally) blame the latter for not saying "OK, we'll make our income as owners (or managers, or Controllers) more on a par with that of the worker bees, without introducing inflation." Maybe because if people are paid too much they stop producing? That's an argument just as well for paying the managers etc. less, isn't it?

Anyway, what I wanted to get at the meeting (but never got) was
suggestions for improving the model, including pointers to sources
of data that might be associated with variables in the model.

I regret that I had to leave for a meeting around the time Bill Williams' presentation was scheduled to begin, so I missed this part of your talk. But I'm still just trying to understand the analysis and the model. I'm not in any position to criticize it or suggest improvements based on economic data, etc. In particular, I want to understand what leakage is in practical, everyday terms. For me, that's the only way to verify whether proposed remedies are any less superstitious than Greenspan's manipulation of rates.

Here's a handy glossary that helps me keep track of things in your
"H. Economicus" paper. Since there is no Q distinct from Q' in the diagram, I suggest that you re-label Q' as Q to simplify things. I have done so here. For me at least, it makes it easier to read and easier to follow.

P' Selling price of goods and services Q. Consumer cost.

Q Goods and services produced at cost P and sold at price P'.

P'Q (1) Producer Income perceived by Composite Manager. Revenue.
                 (2) Demand perceived by Composite Controller.
                 (3) Cost to Composite Consumer to purchase Q.
                     GNP from Composite Consumer's point of view.

P Producer cost.

PQ Cost for Composite Producer to produce Q.
                 GNP according to the Fed.

PQ-P'Q Profit Margin.

Composite GNP
   Controller Controls Demand P'Q.
& Composite Controls Consumer Cost P'Q.
   Consumer

Composite GNP
   Manager Controls Profit Margin PQ-P'Q.

Leakage Dollars received by consumers (as wages or profit)
                 that are _not_ spent on goods and services. A disturbance
                 to control of P'Q.

You say that the Composite Controller fills the role of the Composite Producer and the Composite Consumer. They are both controlling P'Q, but are they controlling it according to the same reference variable? Demand and Cost are not identical!

The Consumer seeks lower cost. The Consumer varies Demand as means of controlling (a) optimal consumption of various desired or needed products, (b) minimal Cost, and (c) maximal available cash (budget). Factor the Giffen/Williams effect in where relevant.

The Controller seeks to make the quantity of goods and services equal the quantity that the Consumer is expected to demand. It is an anticipated, projected, imagined variable. Sometimes the reference level used by the Controller is set at a value different from Demand. For example, the Controller avoids flooding the market in order to maintain profit margin (e.g. the diamond racket), floods the market at low margin in order to overwhelm a competitor, raising prices and margins later when the competitor is gone (many familiar examples) and so on. Probably, then, the reference level used by the controller is set by the Manager, or at a higher level than both Manager and Controller.

Leakage enters the diagram as a disturbance without origin. Alpha leakage originates with the Fed as (apparently ill conceived) means of controlling Profit Margins PQ-P'Q. Sounds like the Manager is responsible for Alpha leakage, and could be shown as such in the diagram.

Suppose you include the Consumer as distinct from the Controller. Both Consumer and Controller control P'Q. They may conflict, at the very least because the Controller's estimate of the Consumer's Demand is inaccurate, and sometimes because of attempts to manipulate the market. If you include the Consumer as a second controller of P'Q, then you can show the Consumer doing something with available cash other than spending it on goods and services. Putting it under a mattress maybe. But maybe you can also show the Controller contributing to Leakage. Do static inventory, waste, and obsolescence contribute to Rho leakage?

Mapping from the aggregate roles in the diagram to roles of individuals in the economy is problematic. The Producer (Manager) controls the cost of goods and services P and P' as means of controlling profit margins. the Controller produces goods and services Q as means of controlling Consumer Demand P'Q. This value P'Q is simultaneously (1) Producer Income (Revenue) perceived by the Manager, (2) Consumer Demand perceived by the Controller, and (3) Prices paid by the Consumer. Whew! That is quite an indigestible lump!

The extent to which individual employees set reference levels for their production is (for most people) not directly related to perceived demand by consumers; this is quite explicitly the job of managers. Are managers in the ordinary business sense producers? A lot of us agree with Dilbert that maybe they're not.

The problem is that we're talking about aggregate entities that do not map neatly to familiar roles filled by individuals. This makes it difficult to advise people what changes they can make to reduce Leakage and improve the economy for all of us. Well, no, giving advise is easy. It makes it difficult to know whether the advise is sound or superstitious.

Your graphs show correlations that we don't hear much about, and your model behaves similarly. Surely it is on the right track. But if we want to go from modelling to recommending changes in human behavior, and changes in the aggregate even, that's a tall order!

         Bruce Nevin

···

At 05:57 PM 08/03/2000, Richard S. Marken wrote:

2

[From Rick Marken (2000.08.04.1030)]

Bruce Nevin (2000.08.04.1226 EDT) --

Rick, it seems to me that we are in complete agreement in
virtually all of your reply.

Yes. And you make some very helpful points that I will have to
consider as I continue working on the model economy. I just want
to make some quick clarifications. You say:

I also have a bit of difficulty blaming unions' collective
bargaining. If the problem is uneven distribution of wealth, why
is this not seen as their attempt to distribute wealth more evenly?

TCP does "blame" collective bargaining for inflation. But I think
he does that to show that he's not taking "sides". Collective
bargaining does cause inflation but only because management
raises prices immediately to cover any union won pay raise. This
is what causes inflation. So it's both the unions and management
together causing inflation. The union won pay raises would not
be inflationary if management lowered their own wages instead
of raising prices to compensate for the increased cost of
production caused by the workers' wage increase.

PQ-P'Q Profit Margin.

PQ-P'Q is not really profit margin. Profit is just a kind of
wage that is part of the cost of production, PQ. The composite
producer must receive, from the composite consumer, exactly
the same number of dollars it spent to produce Q. So P'Q (the
dollars received from the composite consumer) must equal PQ
(the dollars spent to produce Q). When P'Q = PQ, the composite
consumer is covering the composite consumer's expenses, which
include wages and profits.

The Consumer seeks lower cost.

Not at the aggregate level. The composite consumer must return
PQ dollars to itself, as composite producer, for producing the
Q being purchased. There is no lower cost to seek. the cost to
the composite consumer is precisely the cost to the composite
producer for producing Q.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
MindReadings.com mailto: marken@mindreadings.com
www.mindreadings.com

3

[Bruce Nevin (2000.08.04.1448 EDT)]

Rick Marken (2000.08.04.1030) --

PQ-P'Q is not really profit margin.

OK. I revised my little glossary (below).

> The Consumer seeks lower cost.

Not at the aggregate level. The composite consumer must return
PQ dollars to itself, as composite producer, for producing the
Q being purchased. There is no lower cost to seek. the cost to
the composite consumer is precisely the cost to the composite
producer for producing Q.

We can't apply these aggregate constructs to economic policy until we understand how the model relates to individual conduct. This is why interpreting the model is not at all simple and straightforward. The use of familiar labels like Manager, Controller, Consumer, Producer, invites a direct mapping to an individual manager, etc., but this extrapolation does not work. One way to deal with this is to insist against such mappings. On the other hand, though it might not be possible to make more distinctions of roles in the model, I have tried to indicate some such distinctions based on just such mappings. A couple more appear below.

P Producer cost of goods and services Q.
P' Selling price of goods and services Q.
Q Goods and services produced at cost P and sold at price P'.

P'Q (1) Producer Income perceived by Composite Manager. Revenue.
                 (2) Consumer Demand perceived by Composite Controller.
                 (3) Consumer Cost to purchase Q.
                     GNP from Composite Consumer's point of view.

PQ Cost for Composite Producer to produce Q.
                 GNP according to the Fed.

PQ-P'Q Profit Margin.

/Composite GNP

Controller Controls Demand P'Q.
               [This sounds like Marketing and Sales.]

Composite Controls Consumer Cost P'Q.

\ Consumer [Consumes goods & svcs as means to control other variables
                  and controls Cost as means of balancing own books.]

Composite GNP
   Manager Controls PQ-P'Q = 0. Balances books.
                  [This sounds like what a Controller or Comptroller does.]

Leakage Dollars received by consumers (as wages or profit)
                 that are _not_ spent on goods and services. A disturbance
                 to control of P'Q.

Also, I didn't mention that Cost Drivers, like Leakage, are a disturbance without origin. Since the model is limited to the economic environment, every factor has an origin in one or more of the players. Put another way, the environment for any one player is all and only the various players' outputs.

         Bruce Nevin

···

At 01:24 PM 08/04/2000, Richard S. Marken wrote:

4

[From Rick Marken (2000.08.04.1545)]

Bruce Nevin (2000.08.04.1448 EDT)--

We can't apply these aggregate constructs to economic policy
until we understand how the model relates to individual conduct.

I'm thinking that it just might be OK to build a model at the
aggregate level. But yours is an interesting point and I would
like to hear it discussed: is what I am doing a legitimate
modeling exercise? That is, is it reasonable to build an
"aggregate" control model like H. economicus where the functions
and variables are, in reality, implemented in collectives of people?
The environmental variables my the model -- variables like GNP, P'
savings, etc are measured at the collective level. It seems sort
of OK to me to build a model that controls these variables. But
I agree that it would be cool to derive the collective model from
the behavior of many individual models acting at the same time.
It's just that that kind of "aggregate" model seems like it might
be a very big project.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
MindReadings.com mailto: marken@mindreadings.com
www.mindreadings.com

5

[From ruce Nevin (2000.08.04.1448 EDT)]

Rick Marken (2000.08.04.1545) --

[...] is it reasonable to build an
"aggregate" control model like H. economicus where the functions
and variables are, in reality, implemented in collectives of people?

If you can use the model to define economic policies of the aggregate sort (I am reluctant to call aggregates a "level") in such a way that individuals know what to do to implement those policies, and how the policies affect them as individuals. My questions and suggestions mostly boil down to this: I don't see how to connect it with your life and mine.

For example, raising interest rates does not curb inflation. What does, in the model? Persuading unions to give up collective bargaining is a non-starter, as we've noted. Reducing leakage? Then we need to know how individuals contribute to alpha leakage.

If there are different ways of specifying the aggregate entities in the model
-- distinguishing the consumer from the producer and "controller", for example, in respect to their different ways of controlling P'Q (revenue, demand, cost of living) -- do the distinctions among these different models or versions of the model offer different "handles" for economic policy to tweak?

         Bruce Nevin

···

At 06:42 PM 08/04/2000, Richard S. Marken wrote:

6

[From Bill Powers (2000.08.05.1213 MNDT)]

Bruce Nevin (2000.08.04.1226 EDT)--

I'm horning in on "Leakage" discussion...

Maybe I'm all wet, but this is my understanding: except for "bonds the Fed
sells to take money out of the economy," when you buy stocks or bonds your
purchase does not withdraw your money from circulation. For instance, if
you buy municipal bonds, the municipality that issued the bonds spends your
money for goods and services. When a company issues stock, it receives
money from stock purchasers which it then can spend to purchase goods and
services. Leaving money in the bank does not remove it from circulation,
since most of the bank's holdings are not kept on hand as cash, but rather
invested in stocks, bonds, real estate, etc., with the cash flowing on to
sellers of those goods and services. Suppose, like Uncle Scrooge, I sit on
a pile of cash and live frugally. Unless I physically take the cash and
store it under my mattress, or in the Fed's hidey hole (wherever and
whatever that is), or in Uncle Scrooge's coin-filled swimming pool, the
money is still circulating in the economy.

I agree with all of this.

Money that is taken out of circulation for some significant time but can be
returned to circulation is "rho" (reversible) leakage. Money that is taken
out of circulation permanently is alpha leakage. Since the 60s, most
leakage seems to have been alpha leakage, according to TCP.

So how does buying power ger removed _permanently_ from the American
economy? One simple answer is that it is transferred to another economy and
not spent on our goods and services (unfavorable balance of trade). In
1996, the balance of trade was a negative 2.3% of the GNP -- I'd guess
that's an appreciable part of the total leakage for that year, though I
don't have the exact figure.

Bad loans to Brazil are an example. It might also be that repaying bank
loans removes money from circulation (because money is created by loans,
and repaid loans simply cancel the debt without buying anything. Oddly,
defaulting on a loan leaves the money in circulation). Money in the
mattress, of course, disappears from circulation, permanently if the house
burns down.

I'm wondering about large family fortunes. The income from these fortunes
is, presumably, spent, but the principal probably can't be returned to
circulation through investment. Remember that investment is a steady 20% of
the composite producer's income, plus or minus 2%, in good times or bad. So
you can't just shove more money into investment: above 20-22%, nobody can
use it. It could be that large fortunes mostly just sit in banks or other
repositories, pulling interest but not circulating (this is what drives
banks to make foolish loans). That's rho leakage, of course; in principle,
the family fortune could be spent. In practice, of course, the idea is to
hang on to it.

I also have a bit of difficulty blaming unions' collective bargaining. If
the problem is uneven distribution of wealth, why is this not seen as their
attempt to distribute wealth more evenly?

That's not the point. The emphasis is on _collective_ -- industry-wide --
bargaining. If unions get a wage increase out of automakers, for example,
under collective agreements that apply to _all_ automakers, then there's no
competition to keep all the auto makers from raising the prices of cars,
loans, and so on exactly enough to cancel the industry-wide increase in
production costs. And that's exactly what they have always done. This
increases everyone else's expenses, so the wage increase demands cascade.
Prices rise across the board, with the result that the union workers have
not gained one penny in real income through all their decades of collective
bargaining. The historical record is perfectly clear about this; see
Chapter 6 of _Leakage_.

Here's an example, a table covering 1956 to 1966:

Year Wage cost index Price index
1956 100 100
1957 104 104
1958 106 106
1959 108 108
1960 111 110
1961 112 111
1962 112 112
1963 114 114
1964 116 116
1965 117 118
1966 121 121

See pp. 287-288 for explanation.

...Maybe
because if people are paid too much they stop producing? That's an argument
just as well for paying the managers etc. less, isn't it?

There's nothing in _Leakage_ saying that anyone should be paid less. The
argument is that people with large incomes need to spend more to hold down
leakage. If they don't spend it and leakage sends the economy down the
tube, TCP says the government should spend it for them. I sense some
Constitutional problems there. People who make immense amounts of money
have trouble spending even a fraction of it. Poor people spend everything
they have every week.

Best,

Bill P.

7

[From Rick Marken (2000.08.05.1900)]

Bruce Nevin (2000.08.04.1448 EDT)--

My questions and suggestions mostly boil down to this: I don't
see how to connect it [the H. economicus model] with your life
and mine.

The macro economy has daily effects on our lives: we see it in
the quality of the infrastructure that surrounds us, in the quality
of our community services (schools, parks, hospitals, police, etc),
in the quality of products available to us, in the cost of these
products to us, in our ability to get work to support our families,
etc. So macro level variables -- GNP, change in GNP, inflation -- do
have a connection to the quality of individual lives.

For example, raising interest rates does not curb inflation.
What does, in the model?

Eliminating leakage would eliminate one of the main causes of
inflation, according to H. economicus. The best Fed policy,
according to the model, is to do nothing at all to try to
control inflation. Just keep interest rates low.

Reducing leakage? Then we need to know how individuals
contribute to alpha leakage.

Yes. We have to discover where the income goes that is not being
returned to the composite producer. My guess is that it's being
held by _very_ wealthy people in non-productive instruments (like
stocks and bonds, which are productive instruments, in the sense
that the money received for purchase of the instrument goes for
capital investment, only when they are first issued).

...do the distinctions among these different models or versions
of the model offer different "handles" for economic policy to
tweak?

The main variable in the model to tweak will always be leakage.
If the H. economicus model is right then what keeps an economy
healthy and happy, giving maximum control and, thus, freedom,
to its individual members, is a circular flow of money in
which the amount of money flowing out of the composite producer
(as income to the composite consumer) is equal to the amount of
money flowing into the composite producer (as income to the
composite producer). This equilibrium does not happen by accident;
it requires control becuase there are disturbances to this
equilibrium.

The main disturbance to economic equilibrium is _leakage_, which
is probably a result of people not understanding the cooperative
nature of a money based econony. So particualrly clever, talented
or ruthless individuals are able to get a disproportionatly large
share of the money that represents the goods and services
produced by the econony. These people can't possibly spend all
this money themselves so they hoard it -- and it gets lost somehow
from the circular flow: leakage.

For the last 100 years or so, as the industrial economy really
took off, making it possible for a very small number of people
to get control of a very large proportion of GNP, leakage has
become a real problem. It has been delt with (equilibrium has
been maintained) mainly by adding money (unbacked by actual goods
and services) into the economy, which creates inflation. A better
way to reduce the effect of inflation would be to redistribute
income with "tweaks", like highly progressive taxation (including
a negative income tax). Of course, the "tweaks" would have to be
done carefully; we certainly don't want to screw up what works.
I would suggest that "tweaks" should always be considered
experimental; it the effect predicted by the model does not
happen almost immediately (given the noisiness of the data
I would give any tweak 6-12 months to prove itself) then I
would call off the tweak and try something else.

The important thing about the H. economicus model (I think) is
that it helps people see the economy in a new way; as a
collection of control systems acting cooperatively to produce
stuff for themselves and using money as the means of distributing
that stuff to individuals who have specialized in making one or an-
other component of that stuff. This new view of the economy suggests
new approaches to making the economy work better for everyone.

So, if you are interested in making the economy work better for
everyone, you can think of ways to achieve that goal in the context
of the h. economicus model of the economy. Of course, if making
tons of money for yourself is your main economic goal then it's
likely that you will reject the model ipso facto since the model
suggests that making tons of money for yourself deprives others
of the ability to control for the stuff they want and need.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: marken@mindreadings.com
mindreadings.com

8

[From Fred Nickols (2000.08.07.0640 EDT)] --

Bill Powers (2000.08.05.1213 MNDT)]

Bill, responding to Bruce Nevin, closed his response with this comment:

People who make immense amounts of money
have trouble spending even a fraction of it. Poor people spend everything
they have every week.

I had to laugh when I read that because it is Soooooooo true. I grew up
dirt poor and was never concerned with matters like saving or
investing. The problem at hand was how to get the next nickel, not what to
do with any extra. You learn to hustle at an early age in those
circumstances. Even today, after years and years of what some would call a
handsome income, I treat my money in ways that can only be termed
"cavalier." In short, I spend it. I'm not so well off as to have trouble
spending a fraction of it but I do manage to go through a pretty good chunk
of it.

(Apropos of Bill's comment, Who says there's no such thing as time
travel? Upon reading Bill's comment, I was immediately jerked back to
Burlington, Iowa in the early 1940s. That's almost a 60-year jump.)

In PCT terms, I wonder how reference conditions for spending and saving
patterns get established and then reorganized. Mine don't seem to have
been reorganized much.

···

--

Fred Nickols
The Distance Consulting Company
"Assistance at A Distance"
http://home.att.net/~nickols/distance.htm
nickols@att.net
(609) 490-0095

9

[From Bill Powers (2000.08.07.0734 MDT)]

Fred Nickols (2000.08.07.0640 EDT) --

In PCT terms, I wonder how reference conditions for spending and saving
patterns get established and then reorganized. Mine don't seem to have
been reorganized much.

The Guv has seen to it that you will get at least a pittance of social
security (and your pittance will be a lot more than most other people's, I
would guess). Also, I presume that you're in some sort of retirement plan
-- if not, please start socking it away _immediately_ or you will be very
sorry. If you really need to reorganize, I suggest imagining your future as
vividly as possible, until terror sends you to the nearest phone to set up
a retirement plan. Being "cavalier" about money doesn't necessarily mean
being stupid about it, does it?

I got unstupid at about the age of 50, with Mary's help (she was able to
put over 30% of her income as a municipal employee -- a librarian -- into a
retirement plan, so by the time I retired, only 15 years later, we squeaked
through with enough to live decently, though not lavishly by many people's
standards). What being poor did for me, in the thirties, was to help me
figure out interesting things to do that didn't cost much if anything.
That's probably why I'm a theoretician now. Ideas are cheap.

Best,

Bill P.

10

[From Bill Powers (2000.08.07.0746 MDT)]

Rick Marken (2000.08.05.1900) and other interested parties --

I got out TCP's book last night and began trying to understand it again,
with a view to working with your modeling effort. There are some sticky
places where I think we need to reconsider some of his analysis --
particularly in modeling the effect of leakage. He wasn't used to modeling,
and didn't know how to deal with loops containing delays, so he tried to
make everything instantaneous. That's not necessary. Also, I think his
autoinflation doesn't really happen. All that happens is that people get
fired, or have their wages reduced, when leakage gets large enough to
cancel growth. This would all become clearer if his circular flow diagram
included growth factors. We can probably fix that.

Let's look at the part he got right first.

The basic equation with no leakage is

(1) PQ = zN,

where P is mean price, Q is quantity of goods or services produced per
year, z is productivity in PQ (dollars) per capita, and N is the
population. PQ or zN is the total amount of production expressed as a
quantity of money. I'm ignoring the primes for now so I write PQ instead of
P'Q'.

First, take the time derivative of both sides of the equation. The time
derivative of x times y is x(dy/dt) + y(dx/dt), so we have

(2) P(dQ/dt) + Q(dP/dt) = z(dN/dt) + N(dz/dt)

Now divide the left side of (2) by PQ and the right side by zN. Since PQ =
zN, this is equivalent to dividing both sides by the same number, a legal
operation on an equation. The first term on the left will be P(dQ/dt)/PQ,
which is(1/Q)(dQ/dt). The whole equation then becomes

(3) (1/Q)(dQ/dt) + (1/P)(dP/dt) = (1/N)(dN/dt) + (1/z)(dz/dt)

These are derivatives of logarithms, because d/dt(log(x)) = (1/x)(dx/dt).

Defining zdot, Ndot, and Pdot as the respective logarithmic derivatives, we
obtain

(4) (1/Q)dQ/dt) = zdot + Ndot - Pdot.

When we express all quantities in constant dollars referred to a specific
year (to remove effects of inflation), Pdot becomes zero becaused the price
is forced to be a constant, and its time derivative is therefore zero. This
simplifies the equation to

(5) (1/Q)dQ/dt) = zdot + Ndot (in constant dollars)

The left side is the derivative of log(Q), so we have

(6) d/dt[log(Q)] = zdot + Ndot, or, integrating,

(7) Q = Qo{exp[(zdot + Ndot)(t - to)]}

Q is the production rate at time t and Qo is the rate at time "to" (that's
t-naught), the time to which we refer all prices. This equation describes
the basic exponential growth of production when nothing else interferes and
Ndot and zdot are constant.

Equation 7 says that productivity and population growth rates completely
determine the rate of increase of production (remembering that production
itself is the rate at which goods and services are produced, so we are
talking about changes in the rate of production).

We can change equation 7, which describes a flow of goods and services, so
it dewscribes a flow of money, just be multiplying by Po, the average price
at time to, the time to which we are reducing the value of the dollar to
remove the effects of inflation.

(8) PoQ = PoQo{exp[(zdot + Ndot)(t - to)]}

In the circular flow case, this describes the amount of money circulating
at time t. Equation 8 thus describes not a constant circular flow, but a
growing circular flow (provided zdot + Ndot remains positive).

Now let's do this whole derivation again to include leakage. Let leakage L
be defined as a fraction k of the current rate of money flow, so that

(9) L = k(PQ)

Going all the way back to equation (1), which is what TCP should have done
but didn't, we now modify the expression for the amount of money (PQ)
produced each year: we have

(10) PQ = zN - L, or

(11) PQ = zN - k(PQ), or

(12) PQ = zN/(1 + k)

Equation (5) now becomes

(13) (1/Q)(dQ/dt) = (zdot + Ndot)/(1 + k) (in constant dollars)

and equation (8) becomes

(14) PoQ = PoQo{exp[(zdot + Ndot)/(1 + k)][t - to]}

The units of PQ, zdot, Ndot, and k depend on the units of time. If dt = 1
year, all these numbers are expressed in units per year, and so on.

Notice that k (which is TCP's alpha + rho) does not simply subtract from
the sum of zdot and Ndot. As k increases, there is a negative effect on the
total exponent, but it results from dividing by k instead of subtracting it.

For small values of k, however, 1/(1+k) is nearly equal to 1 - k. Suppose k
is 0.01. Then 1/1.01 is 0.990099, whereas 1 - 0.01 is 0.99. If k is as
large as 0.1, 1/(1 + k) = 0.90909 while 1 - k is 0.9 -- only 9% different.

I think TCP knew this but forgot it, as he forgot many of the steps he used
in reaching his conclusions by the time the book was submitted for
publication.

I think I'd better stop here because I suspect that I didn't do the
integration just right to get equation 14. I'll try to slog it through, but
it would be really neat if Richard or Wolfgang or some other smart person
would check over this whole derivation so far and tell us the right answer.

For purposes of simulation you can use, from equation (13),

dQ/dt = Q*(zdot + Ndot)/(1 + k), and

Q = Q + (dQ/dt)*dt, or
Q = Q + Q*[(zdot + Ndot)/(1+k)]*dt (program step)

That will give the correct integration. Remember that zdot, Ndot, and k
have to be given in terms of the size of dt. If leakage is 0.1 per year,
it's 0.00833 per month, and so on.

I'll pause here for replies.

Besst,

Bill P.

11

[From Bruce Gregory (2000.0807.1407)]

Fred Nickols (2000.08.07.0640 EDT)]

In PCT terms, I wonder how reference conditions for spending and saving
patterns get established and then reorganized. Mine don't seem to have
been reorganized much.

They are established in the same way any reference conditions are established, by
reorganization. They are changed by reorganization when they are no longer
effective in maintaining intrinsic variables at their reference levels.

BG

12

[From Bruce Gregory (2000.0807.1451)]

Bill Powers (2000.08.07.0734 MDT)

If you really need to reorganize, I suggest imagining your future as
vividly as possible, until terror sends you to the nearest phone to set up
a retirement plan.

Were it only that easy to reorganize! I suspect that you must be failing to
control a variable (other than in imagination) for reorganization to take place.
If your approached worked, people who chronically imagine diasters would
reorganize very rapidly. That doesn't seem to happen.

BG

13

[From Bill Powers (2000.08.07.1407 MDT)]

Bruce Gregory (2000.0807.1451)]

If your approached worked, people who chronically imagine diasters would
reorganize very rapidly. That doesn't seem to happen.

I think it's possible that they do reorganize rapidly. Too-rapid
reorganization is not effective in an e-coli-type reorganizing system; the
bias tends to get wiped out by constant reorganization at the maximum rate.
You have to be in the range where you reorganize less often when things are
getting better.

You know the old saying, though: He who keeps his head when all around are
losing theirs probably hasn't grasped the situation.

Best,

Bill P.

14

[From Rick Marken (2000.08.07.1320)]

Bill Powers (2000.08.07.0746 MDT)

Thanks for the re-analysis of some of the leakage equations.
I'll look it over and comment more completely once I've
had time to look at it more carefully. But I think I disagree
with

(10) PQ = zN - L, or

Leakage doesn't decrease the money _produced_; it decreases
the component of PQ that is _returned_ to the producer of
PQ (I bought an economics text and economists call this
quantity E, for expenditure). So leakage, L, is the
difference between PQ and E: L = PQ - E. So PQ = E + L
and E = PQ - L.

If PQ = zN then E = zN - L and the control problem is to
design an economy that keeps PQ = E under conditions
where L is varying.

By the way, in the economics text I bought (_Introduction
to Economics_ by S. Cassler, HarperCollins, 1992) there is
a beautiful drawing of a circular flow model of the macro
economy (p. 59, Figure 4.1). So TCP's circular flow analysis
is not so far out after all. What is missing from the
conventional macroeconomic analysis of the circular flow is
any realization that maintenance of economic equilibrium (the
necessary match between PQ -- what the composite producer
pays for production of Q -- and E -- what the composite
producer receives as payment for Q) must be a _control
process_. The current economic thinking seems to assume
that economic equilibrium (PQ = E) is maintained (against
disturbances such as leakage) by external forces that
bring the system back to equilibrium, just as restoring
forces bring a pendulum back to plumb after it is
disturbed by a push.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
MindReadings.com mailto: marken@mindreadings.com
www.mindreadings.com

15

[From Bill Powers (2000.08.07.1631 MDT)]

Rick Marken (2000.08.07.1320)--

...I think I disagree
with

(10) PQ = zN - L, or

Leakage doesn't decrease the money _produced_; it decreases
the component of PQ that is _returned_ to the producer of
PQ (I bought an economics text and economists call this
quantity E, for expenditure).

Think of equation 10 as a program statement. The _next_ value of PQ
(received from sales) is equal to the previous value of zN (paid to
consumers) minus the leakage. The next time around, there will be only zN -
L available to pay out.

But I'm not happy with my derivation. If z and N are constant, growth rate
comes out to be zero with or without leakage, whereas intuitively leakage
should make it negative. I have to be leaving something out.

Part of the problem is that wages account for only part of total production
costs. But on re-examination, I don't like the way TCP introduces leakage;
his way requires introducing new money into the system at the same rate as
the leakage, to keep the circular flow constant. But why should the flow of
money remain constant? One explanation would be that the composite producer
is trying to maintain the same income in dollars and does so by raising
prices. However, raising prices can't by itself increase the number of
circulating dollars; if the circulating dollars decrease, production simply
has to decrease; there isn't enough money after leakage to buy it all at
existing prices, so how could raising the price provide enough money? The
only way the composite producer could replace the lost dollars would be by
borrowing them from a bank that is empowered to create new money -- that
is, from the government. And in that case, why should leakage have any
effect at all? The lost dollars are simply replaced, and the composite
consumer will never know about it. The same number of dollars as before is
available, so there is no need to change either prices or Q.

My inclination, since TCP was quite a smart man, is to assume that he saw a
relationship intuitively that he simple failed to be able to derive
formally. A hint is contained in this:

"Thus, thinking of a shift from the ideal to the actual mode of operation,
we see that the dollar outlay for production stays the same while the
output diminishes." (p. 97)

If, indeed, there is some control system attempting to keep the dollar
outlay for production constant, TCP might have been on the right track.
Unfortunately, it's hard to see why a workforce that is being paid the same
(in part with newly created money) should suddenly start producing less, as
if its productivity had suddenly gone down. This kind of reasoning about
parts of the system as if they were not influenced by the rest of the
system is just not effective. I'd be very happy if someone could explain
this to me as TCP evidently understood it, but right now I can't see the
sense in it.

It's probably worthwhile to keep looking for the missing derivation. But a
better interim approach might be to try to put together a simulation using
nothing but the rock-bottom clearly correct relationships that don't need
any arm-waving or intuitive jumps to see. The relationships we need might
just fall out of such a simulation. If they don't, that means there are
assumptions or facts that need to be brought forward to make the model
complete.

There is one basic fact that tells us leakage exists: people spend less on
goods and services every year than they receive through wages and capital
income. We also know that capital expenses -- maintenance, expansion, and
such investment expenses -- amount to a very steady 20 (+/- 2) percent of
total expenditures by the composite producer. We know that capital income
amounts to about 60% of total income, and 40% after redistribution --
again, with very little variation.

At the macro level, as TCP says, the bookkeeping is pretty simple, and
nothing like as complex as it is in microeconomics. We know that PQ is the
money that comes into the composite producer during each dt of the
simulation. If we simulate all the destinations of this money with
reasonable throughness, recognizing that the whole product, neither more
nor less, must be sold and that the only money with which it can be bought
is capital or wage income (and perhaps borrowing which creates new money),
we should have a pretty complete picture of the main interactions in the
macroeconomy. As we learn to think in terms of composite, whole-nation,
timeless entities, correcting mistaken ideas that the nation is just a
scaled-up family, we should be able to carry on from the start TCP gave us
and come up with a convincing and useful model.

So far I haven't said anything very useful. Maybe soon.

Best,

Bill P.