# CP007

**URL:** <http://discourse.iapct.org/t/cp007/2099>\
**Category:** CSG2001\
**Created:** [November 14, 2001, 4:33pm UTC](http://discourse.iapct.org/t/cp007/2099 "2001-11-14T16:33:59Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [November 14, 2001, 4:33pm UTC](http://discourse.iapct.org/t/cp007/2099/1 "2001-11-14T16:33:59Z")

</div>

[From Bill Powers (2001.11.14.0920 MST)]

Hi, Bill [Williams] --

> One of the things which I would not be surprized if the model displays is a  
> slight instablity-- maybe a mild limit cycle.

This will depend on lags (both integral and transport) and the gain around  
a loop. Since we know there will be lags, the main source of instability  
will be setting the gain too high without enough slowing: reacting too much  
and too fast to errors. Another factor which I suspect comes into play but  
which I've had no experience with: the statistical spread of lags and  
gains. One or two systems with long lags may not affect the overall economy  
quickly or strongly enough to produce a net positive feedback if most of  
the lags are shorter. Adding to the statistical spread is the fact that  
each little system's lag will start at a time that's randomly located  
relative to the time another system's lag starts (through there are some  
synchronizing effects such as seasonal variations and disasters). Also the  
linearity of the system will determine whether a small limit cycle will  
quickly grow to be a large one. If gain falls off with amplitude of  
changes, then runaway conditions can be self-limiting, oscillations  
occurring but limited to the amplitude where the positive-feedback gain has  
just fallen to 1.0 at the natural frequency of the system (if there is one).

It's good to keep all these details in mind, but we won't need them at  
first -- a simple linear system will do the trick. We need to keep these  
complications in mind for the time when our model refuses to behave like  
the real system.

> ... If investments take place primarily as a result of projecting past

behavior then

> the upper and lower transitions in the limit cycle would involve something

like

> reorganization of the thinking of those in a position to make investments.
> 
> In a static equlibrium there would be no net investment and
> 
> &nbsp;&nbsp;Income equal consumption or Y = C
> 
> During growth there would be increasing investment and
> 
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dI = dY - dC which could also be written as
> 
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dS = dY - dC THus the change in investment would by

definition

> be equal to the change in savings. And, the ratio of dC/dY which is  
> assumed to be a sort of psychological/cultural factor considered to be  
> relatively stable as long as the society's organization is relatively  
> consistant.

I think this idea can be carried further to show that it doesn't really  
work. I'm anticipating the model a bit here, but your observation is very  
helpful in getting started on it.

Investment is basically money given by the consumer to the producer in the  
hope of a later return as dividends or interest, or for a share of  
ownership with a return from profits-- instead of being payment for goods  
and services. Whatever amount of money is simply given to the producer as  
investment cannot be used for purchases, and in fact directly subtracts  
from purchases. So the total producer income is not changed by turning some  
consumer expenditures into investments.

The above is true if there is no backlog of consumer savings. If there is  
such a backlog, then producer income can be increased if consumers continue  
to purchase the same amount, and in addition transfer some of their savings  
to the producer as investment. This is what your differential equation  
above says. The added producer income is the invested money that can be  
used for maintenance or expansion of the means of production, because it is  
not needed to cover the current cost of production..

The problem here is that such gifts to the producer are made with the  
(unenforceable) expectation that they will be repaid with interest in the  
long run. At any given time, some old investments will be in process of  
returning a profit to past investors at the same time that some new  
investors are just starting to donate their savings to producers. If the  
repayment rate (dividends, interest) is just equal to the rate of new  
investment, the net investment in the whole economy will be zero, and  
growth of the whole economy, if any, will have to be due to factors other  
than investment.

So how can the economy as a whole grow? If the return on investment, over  
the long term, is greater than the amount invested (as the investors  
sincerely hope), then the producers, at any given time and on the average,  
are paying out to the investors more than they are getting from them as  
investments, so it is not possible for any net investment to result. In  
fact is it impossible, under conditions so far assumed, for producers to  
continue indefinitely paying more to consumers than they are getting back  
from sales to consumers: investments cost the producer money, to the extent  
that they produce any return to the investor above the original amount  
invested.

from another angle (and this is largely due to my father's thinking, though  
I don't think he worked it out quite right since he wasn't thinking in  
terms of a model):

I posited that consumers had a backlog of savings, so there could be  
investments without reducing purchases. But if we think of the long term,  
where could such a backlog come from? We have to remember that every penny  
that passes into the consumer's hands comes from one or more of the  
producers, either as wages or as capital income. In order for a consumer  
savings surplus to exist, the producers must have paid out to the consumers  
more money than the consumers spent on goods and services, for some length  
of time. This means that for some time, the producer must have paid out to  
the consumer more money than the producers' total income from sales of the  
same goods and services.

Obviously, there is only one way for this to happen other than a transfer  
of savings from producer to consumer, which has an obvious limit. The  
producers must create new money, either by printing it themselves or by  
borrowing it. Since they're not allowed to print it, any consumer savings  
(or, by the same reasoning, producer savings) can arise only from the  
creation of debt.

Therefore, the only place growth can come from (or at least be paid for) is  
the creation of debt (which includes consumer debt, but let's not rush on  
too far). Investment, in the long run, has nothing to do with growth. The  
encouragement of Investment is quite understandable as an encouragement to  
donate savings to producers, thus assuring that producers have as much as  
possible of the total money supply. Producers cannot, however, continue  
indefinitely paying more than their total income just so consumers can have  
savings that they can invest, nor can producers continue indefinitely  
paying more than the amount invested as a return on investment, nor can  
producers afford indefinitely to charge less for their goods than the total  
cost of producing them and maintaining the plant. The inference is the  
same one my father drew, though perhaps not for exactly the same reasons:  
the only possible long-term macroeconomic steady state is one in which the  
costs of production exactly equal the income from production, and by the  
same token the consumers' receipts from wages and capital income exactly  
equal the cost of buying goods and services. There can be a short-term  
imbalance while both consumers and producers build up a prudent level of  
savings, but this money has to come from the same place where all money  
comes from: borrowing.

As I say, I'm anticipating the model here, but this has given me some ideas  
about how to start building it. I think the best way (as it looks now) is  
to start with big chunks, producer and consumer, which we can later begin  
to break down so that there is more than one of each, and each major entity  
can have internal structure -- that is, so there can be competing producers  
and consumers. There may be some hidden snags, but if there are we won't  
find out what they are until be build the model and try to get it to run.

I'm copying this to CSGnet, as an invitation to other modelers to join in  
or offer alternatives.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Richard\_Marken2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/edb3f5/32.png) [@Richard\_Marken2](http://discourse.iapct.org/u/Richard_Marken2)\
**Post date:** [November 14, 2001, 5:27pm UTC](http://discourse.iapct.org/t/cp007/2099/2 "2001-11-14T17:27:35Z")

</div>

[From Rick Marken (2001.11.14.0927)]

Bill Powers (2001.11.14.0920 MST)--

> I'm copying this to CSGnet, as an invitation to other modelers to join in  
> or offer alternatives.

Mmmm. Delicious. I'll start savoring it this weekend. It'll be nice to get back  
to the model.

Best

Rick

> **···**
>
> --  
> Richard S. Marken, Ph.D.  
> The RAND Corporation  
> PO Box 2138  
> 1700 Main Street  
> Santa Monica, CA 90407-2138  
> Tel: 310-393-0411 x7971  
> Fax: 310-451-7018  
> E-mail: rmarken@rand.org

---

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**Author:** ![Bruce\_Gregory](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/4bbf92/32.png) [@Bruce\_Gregory](http://discourse.iapct.org/u/Bruce_Gregory)\
**Post date:** [November 14, 2001, 7:18pm UTC](http://discourse.iapct.org/t/cp007/2099/3 "2001-11-14T19:18:10Z")

</div>

[From Bruce Gregory (2001.1114.1418)]

> Bill Powers (2001.11.14.0920 MST)

I am uncertain as to why you think the economy can be modeled as a control  
system. It seems to be a far cry from real living control systems. I  
suspect that it would better be modeled as the unintentional side effect of  
large numbers of agents controlling quite different perceptions. (The  
President's exhortation to "shop till you drop" has not produced a  
remarkable rush to shopping malls despite the general agreement that "it  
would be good for the economy.")

Nevertheless, I wish you well. It will be a real coup if you pull it off.  
Fully worthy a Nobel Prize, I would think. There is no danger that the  
success of the model would be ignored, since it would solve a problem that  
so many are obsessed with.

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [November 15, 2001, 4:55pm UTC](http://discourse.iapct.org/t/cp007/2099/4 "2001-11-15T16:55:16Z")

</div>

[From Bill Powers (2001.11.15.0907 MST)]

Bruce Gregory (2001.1114.1418)]

> I am uncertain as to why you think the economy can be modeled as a control  
> system.

I don't. I intend to model it as a collection of living control systems  
interacting with each other through natural properties of the environment  
and social conventions adopted by most of the actors (such as paying for  
goods you take from a store).

As I would model it, the basic driving force in the economy is the set of  
reference signals in the whole population, which define what inputs people  
want from their environment. In the current American system, the main means  
of getting things (not all things, but most of the critical ones like food  
and clothing) is to give money to producers who produce those things. And  
the only ways to get money honestly are (1) by trading one's time and  
effort for it, which is to say working for wages, and (2) owning some part  
of the means of production or holding paper that entitles you to a share of  
the income from production (like the pension money I live off of now). I'm  
sure there are still significant sectors of the economy in which money does  
not figure, but the model can easily be set up to accomodate them (the  
price of some goods is then labor without any money changing hands).

When people work for wages, they are being part of some producer, creating  
the goods or services that the producer creates, and at the same time  
providing income for themselves as consumers. When they are not working  
(and some never work), they become consumers and spend those wages to  
purchase the products that they or others have been producing. Some  
people, those who live on capital income, get money from the producers  
without having to help create the product. Some get their money by  
providing a service, such as lending or holding money, or singing better  
than the average person can, so the product is not "goods".

There is certainly a feedback loop between producers and consumers, but its  
gain is close to unity and there is no reference signal adjustable from  
outside (and nobody to adjust it). We just model the interactions between  
producers and consumers directly and don't worry about what to call the  
loop. What we call it won't affect the way it works.

I'm considering creating two physical entities, plants and households,  
which contain all the environmental stuff involved like money, goods, means  
of production, and places to store things, natural wear and tear, and so  
forth. Basically these are just records in which certain types of data are  
stored; they don't \_do\_ anything by themselves.

Then we create the agents involved: the consumers who want things and work  
to get them, and managers whose goals have to do with production and profit  
and in general furthering the welfare of producers. Consumers are  
concerned with the data related to households, such as savings, income,  
depreciation and consumption of goods, and acquisition of goods (which  
includes services if we like). Managers are concerned with the data related  
to plants, such as inventory, prices, number of workers, productivity, wage  
and capital costs of production, and distribution of unearned income to  
owners and holders of other claims on income. Managers and consumers  
interact (1) where wages are paid as part of the cost of production, and  
(2) where goods are sold in return for producer income.

So far this seems perfectly straightforward, involving no magical rules  
that float in the air and no other arbitrary abstractions such as a law of  
supply and demand. The agents are simply human beings controlling for  
various variables (as you suggest), some of them managing the process of  
producing goods and services and all of them controlling for household  
variables. If we take everything important into account, the model ought to  
behave like the real thing. If it doesn't, we've left out something and  
need to find out what it is, and include it.

> Nevertheless, I wish you well. It will be a real coup if you pull it off.  
> Fully worthy a Nobel Prize, I would think. There is no danger that the  
> success of the model would be ignored, since it would solve a problem that  
> so many are obsessed with.

So does PCT, but most people seem to have no trouble with ignoring it. I  
don't think I'm in danger of getting a Nobel Prize for anything.

Best,

Bill P.

---

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**Author:** ![Bill\_Williams\_UMKC](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/48db29/32.png) [@Bill\_Williams\_UMKC](http://discourse.iapct.org/u/Bill_Williams_UMKC)\
**Post date:** [November 15, 2001, 8:27pm UTC](http://discourse.iapct.org/t/cp007/2099/5 "2001-11-15T20:27:02Z")

</div>

[From Bill Williams 15 November 2001 CST 2:00]

> [From Bill Powers (2001.11.15.0907 MST)]

> So far this [the proposed model of the economy] seems perfectly  
> straightforward, involving no magical rules that float in the  
> air and no other arbitrary abstractions such as a law of supply  
> and demand.

If we're going to do this in public, it seems to me that shots at orthodox  
economic theory such as the above ought to be accompanied by an explicitly  
stated explaination of why constructs such as the law of supply and demand  
are faulty. While I am in agreement with you in finding fault with the  
orthodox conception of supply and demand, neither the notions of supply and  
demand, nor the system of which they are a part appear to me to be either  
"arbitrary" or "abstractions"

When you say that what you've proposed so far "seems perfectly straightforward"  
and you use the adjective "easy" to describe the task of putting this thing  
together, I can't aggree. I'm still trying to find a systematic way of  
approaching the task of addressing a number of what I perceive to be  
contradictions in the assertions contained in the previous previous CP007  
posting. It seems to me that if the task were genuinely "easy" it would have  
been carried out sometime ago. Closer to home you've had a long standing  
interest in economic problems and have undertaken some more or less extensive  
attempts to construct a PCT model of the economy. THe succes of those efforts  
can be judged by the fact that you are starting this effort from scratch rather  
than from the basis of work already carried out. I think your suggestion that  
the task be approached systematically "step by step" is a good starting point.

But, I am going to tell you emphatically now, that if you are going approch this  
with the attitude that it is "easy" I'm not going to have anything to do with  
it. When I was a flight instructor and I had a student with an attitude problem  
I'd tell them that I didn't have any interest in explaining to the FAA why one  
of my student had killed himself. Let some other instructor have the pleasure.  
THe boss didn't like me sending business someplace else. I was meanspirited  
enough to gloat when the student made a smoking hole in the ground.

So give it some thought regarding how you are intend to approach this. With the  
attitude you display now I think the project is doomed.

I should have initial changes to the previous CP007 posting ready later to day,  
maybe we can start from there.

Best  
&nbsp;&nbsp;Bill Williams

> **···**
>
> \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_  
> Do you want a free e-mail for life ? Get it at [http://www.email.ro/](http://www.email.ro/)

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [November 16, 2001, 3:08am UTC](http://discourse.iapct.org/t/cp007/2099/6 "2001-11-16T03:08:53Z")

</div>

[From Bill Powers (2001.11.15.1913 MST)]

Bill Williams 15 November 2001 CST 2:00 --

> > So far this [the proposed model of the economy] seems perfectly  
> > straightforward, involving no magical rules that float in the  
> > air and no other arbitrary abstractions such as a law of supply  
> > and demand.
> 
> If we're going to do this in public, it seems to me that shots at orthodox  
> economic theory such as the above ought to be accompanied by an explicitly  
> stated explaination of why constructs such as the law of supply and demand  
> are faulty. While I am in agreement with you in finding fault with the  
> orthodox conception of supply and demand, neither the notions of supply and  
> demand, nor the system of which they are a part appear to me to be either  
> "arbitrary" or "abstractions"

Well, you know more about orthodox economics than I do, but I don't think  
this law can be classified as an observation, can it? Anyway, I would count  
it as an abstraction relative to such statements as "sales equal  
purchases," and other simple observations at a lower level of abstraction  
-- that is, closer to actual transactions. If there is actually a general  
principle or law of supply and demand, we should be able to see it in a  
working model, as a consequence of the more detailed interactions. We don't  
need to start by assuming it, whatever it is.

> When you say that what you've proposed so far "seems perfectly  
> straightforward" and you use the adjective "easy" to describe the task of  
> putting this thing together, I can't agree.

What I was describing to Bruce G. seemed straightforward to me. Modeling  
just the part I was speaking of looked fairly easy. I got a good bit of it  
done this morning before I ran out of steam. Maybe there are pitfalls  
awaiting me -- in fact there usually are in this modeling game. If so, I  
haven't seen them yet.

> I'm still trying to find a systematic way of  
> approaching the task of addressing a number of what I perceive to be  
> contradictions in the assertions contained in the previous previous CP007  
> posting.

I admitted then that I was getting ahead of the modeling, guessing how it  
would turn out to behave. I could be wrong -- maybe investment will turn  
out to have a lot to do with growth. Fortunately, we don't have to know the  
answer to build the model; the model will tell us the answer once we get it  
right. We can let the consumers give some of their money to producers and  
see if the producers can really pay it back with interest without creating  
more debt (i.e., without requiring that somebody's savings go negative).

> It seems to me that if the task were genuinely "easy" it would have  
> been carried out sometime ago.

Not necessarily. Look at the time and energy that have been expended on  
"modern control theory" models, which will \_never\_ work as an explanation  
of even so simple a behavior as tracking a target. The control-system model  
gives a quantitative explanation in just a few lines of code. What's easy  
under one approach can be impossibly difficult under another.

> Closer to home you've had a long standing  
> interest in economic problems and have undertaken some more or less extensive  
> attempts to construct a PCT model of the economy. The success of those  
> efforts can be judged by the fact that you are starting this effort from  
> scratch rather than from the basis of work already carried out.

I think your point might be that I considered those previous efforts  
straightforward and easy, and see where it got me. You're right, of course:  
they weren't straightforward enough, so they proved not to be easy. So far  
the basic elements I'm trying to work with now look a lot more  
straightforward this time, with the task of turning the design into a model  
being correspondingly easier. I've always found that most of my  
difficulties come from making overelaborate assumptions and otherwise  
overcomplicating a problem. I'd rather have a simple model that works than  
a correct-looking one that doesn't even run. It's far easier to make  
helpful changes in a model that at least does something that we can criticize.

> I think your suggestion that the task be approached systematically "step

by step" is \>a good starting point.

Fine, that's how I'm trying to approach it. I'm looking forward to seeing  
your critique. Just remember that I was only guessing about what the model  
would show when we get it to run. I'll drop any guesses in a flash if they  
don't prove out.

> But, I am going to tell you emphatically now, that if you are going

approach this

> with the attitude that it is "easy" I'm not going to have anything to do with  
> it.

Well, shoot, what am I going to do with two Nobel Prizes? Don't you want at  
least one of them?

> So give it some thought regarding how you are intend to approach this.

With the

> attitude you display now I think the project is doomed.

I'm not the only one with an attitude, pal. Shadenfreude is an attitude, too.

But yes, let's get on with the details. This was beginning to sound like  
CSGnet for a moment, there.

Best,

Bill P.