[From Bill Powers (970405.0730 MST)]
Rick Marken (970404.0740 PST)--
Bill Powers (970403.1921 MST)--
What we're looking for is the equilibrium condition. This occurs
when the composite producer is paying out P'Q' dollars as the
total cost of production, and is receiving money in two forms:
(1) Sales receipts in the amount P'Q'(1 - alpha) and (2)
borrowing at the rate P'Q'*alpha.
It seems that there should be data on this. Maybe it's in TCP's
book.
I think there is a mistake in reasoning on page 99. Autoinflation does not
_increase the price_ of the output; it _decreases the output_ that is sold
at the _same_ price. In arriving at this point, TCP has assumed constant
dollars, which is why we do not see (dP/dt)/P in the final equations. See p.
94, top paragraph. So from the point of that assumption onward, P' is a
constant.
On page 100, this mistake becomes moot, because the conclusion is that
"... when the reduced output Q is expressed in terms of the 'ideal' dollar
P', it is equal to the fraction (1-alpha) of the quantity the nation is
capable of produing, zN."
Thus autoinflation doesn't show up as an increase in price -- that's
impossible when prices are being expressed in terms of constant dollars,
from which price inflation has been removed. It shows up as a decrease in
output by the fraction (1 - alpha). And that decrease is, of course, already
in the data TCP presents: it is simply Fig. 1-1, page 7.
There must be some measure of the borrowing done by the
aggregate producer (I suppose I should know what this measure is
since Linda works a for the Fed; unfortunately, she doesn't work
in the "giving away money" department;-)) This measure of borrowing
should be precisely equal to GNP*alpha, right?
Right, and it ought to be equal to one of the money-supply measures,
whichever one corresponds to total borrowing from the government. Or rather,
since this is a rate equation, the rate of change of this total, per year.
Money in the form of credit extended by one producer to another doesn't
count in this equation, because when we're speaking in composite terms,
internal redistribution of dollars does not provide any new money:
non-government money that changes hands increases the dollars available to
one producer at the expense of another, so in terms of the _composite_
producer, there is no change.
I suspect that I'm missing something here. Maybe my fixation on _government_
money is misplaced. Actually, all the composite producer needs is a way to
borrow enough more money every year to make up for leakage. In a way, any
promise to pay increases the money supply, if that promise can itself be
used in payment to someone else ("selling the paper"). I suppose that if
there's enough paper and bits flying around, there can be the appearance of
more money being available even if it doesn't come from Federal Reserve
affiliated banks.
It's really hard to think consistently in composite terms. I keep wanting to
think of transactions, forgetting that at the macro level, most transactions
cancel out.
I guess this isn't important right now. As long as the composite producer
has _some_ way to get new money into circulation to make up for leakage, we
probably don't have to be too concerned about what the source is. We know
there has to be a source; the equations have to balance.
If this seems OK, the basic model begins to look pretty simple. We can say
that z (per capita productivity) increases at a certain exponential rate,
and that N (population) increases at another exponential rate, so zN can be
computed open-loop. We then have the conditions
z = z0*exp(k1*t),
N = N0*exp(k2*t)
P'Q = (1 - alpha)zN
Borrowing = alpha*zN, and
Q = Q0*(k1 + k2 - alpha)
While this model isn't a control system, behind it there must be several
basic control systems working. In the composite producer, one of them
attempts to keep inventory as close to zero as possible by varying prices
and adjusting Wages and/or Kapital income, W+K; another varies borrowing so
as to be able to pay W+K. In the composite consumer, one control system
spends money in order to acquire goods/services. Another tries to maintain
an input of money by expending labor (in the case of Wages).
There are conflicting control systems, too. Generally, the owners of the
composite producer get their income from K, so they try to raise K and
(necessarily) reduce W. However, lowering W relative to K meets with great
resistance; the ratio remains quite constant, at around 60 K for 40 W. The
primary way around this is through taxation and not-for-profit activity,
which can swing the _effective_ ratio as far as 40 K for 60 W, after taxes
and donations.
This gets us into labor-management conflicts, management-government
conflicts, and conflicts involving all three, with labor and management
trying to influence government policies in their own favor. This largely
boils down to conflicts between those who receive Wage income and those who
receive Kapital income, with government providing one of the main
battlegrounds and the marketplace another.
I think that the TCP analysis establishes the basic macroeconomic
relationships with which all the human control systems have to deal. It's
like a description of the environmental laws we have to know in order to
model any control process. We can see that the basic requirement is that W +
K + borrowing - leakage has to equal P'Q' (all in terms of money flow rather
than exponential equations), or zN . If we take z and N as increasing at a
given rate, the other variables then have specific relationships.
Of course z and N do not HAVE to increase exponentially in a fixed way:
population control measures can affect the rate of growth of N, and
education and research can affect the rate of growth of z, and those things
may in turn be influenced by the overall state of the economy. However, I
think we have to build from the simple to the complex, and one way to avoid
intractible complexities at this stage of development is to assume z and N,
and their rates of growth, to be their historical values (which don't change
very fast).
Best,
Bill P.