[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
Income equal consumption or Y = C
During growth there would be increasing investment and
dI = dY - dC which could also be written as
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.