[From Bill Powers (2003.02.11.0922 MST)]
Bill Williams UMKC 10 Feburary 2003 7:10 AM CST--
>I think what Keynes had in mind was the loss of value of the sort
experienced when a >truck accumulates milage-- which seems real enough to me.
What I was referring to was his definition of "user cost". This is the
value the assets would have had if they had not been used to produce goods,
less an allowance for maintenance that might have been carried out, _minus_
the actual value of assets at the end of the same accounting period. But
the assets _were_ used for production; we can't put into the model
something that didn't happen. "User cost" (U) is different from
"supplementary cost" (V) which is what you refer to above -- physical
deterioration due to use, which is an actual cost if maintenance is carried
out (but, I would say, not if it isn't carried out and paid for). There is
a provision for that in Econ004. I don't know how to make a provision for
an alternate future in which the production and sales didn't happen and
some other level of maintenance of the unused machinery existed.
There are several basic problems with Chapter 6, though I'm sure I
misunderstood them once and may be doing it again. One problem is that
Keynes seems to be trying to express income in terms of a change in "value"
of an enterprise from the start to the end of an accounting period. But
this "value" is in part an aspect of the mechanical reality of sales and
manufacture, and in part a matter of perception, estimation, prediction,
and intention on the part of the entrepreneur. As a result, there are key
quantities, such as supplementary cost, which Keynes ends up saying are a
matter of accounting conventions and entrepreneur psychology. This is where
the "might-have-been" concepts enter: they are in the mind of the
entreprenuer as Keynes imagines him, and while they influence his actions,
they have no direct effect on the realities of what I am calling the
"plant" or the "household."
Your suspicions about the need for differential equations are supported by
my current understanding of the first page of Chapter 6. Keynes is not
distinguishing properly between rates and sums. This is because he is
thinking in terms of accounting periods like a week or a month, instead of
the very short dt that is required. Only when the calculations are done
very nearly continuously can you allow for changes in parameters (like
prices and wages) that take place during longer accounting periods. The
rate of change of "value" depends on the rate of sales times the price (A),
minus the rate of acquisition of new goods from other entrepreneurs, times
their price (A1), plus the rate of production at a certain cost per good
(factor cost F -- I got that wrong in the last post), times the duration of
dt to convert all these rates to quantities, all added to the initial
value. This gives a new initial value 1/1000 of a day later (or whatever
duration is assigned to dt). Now net income for any finite accounting
period is easily calculated: it is the sum of all the changes in net value
over all the time-slices of length dt -- the sum being, in the limit of
continuous calculation, the integral.So value is a cumulative variable,
while income and expenditures are rate variables. Keynes' verbodity and
rambling parenthetical style make it almost impossible to see the simple
relationships he is burying under all those words. The second paragraph of
ch. 6 shows Keynes struggling to describe an integral without, apparently,
knowing that such a concept exists.
>The task of translating from our model to Keynes and vice versa is a long
and hard one, >but I suppose it is necessary.
I'm not so sure that translation is what is required. There are some
things that Keynes got right. And, to ignore such items can be expected to
draw a charge of unnecessary originality.
Unless you're contradicting what you say later about not changing Keynes'
terminology, you misunderstand the direction of translation I propose. I am
perfectly amenable to using Keynes' symbols and terms, provided I can make
sense of them in a model. I'm willing, for example, to change Yk and Yw to
Fk and Fw in the equations for the plant-- factor costs instead of consumer
income. This just requires a statement that Yk = Fk and Yw = Fw, which
Keynes does, in effect say (factor costs for the entrerpreneur are income
for the others, he says). I already use G for the flow of goods, but the
equations could be rewritten so G means a flow of dollars -- all this would
mean is that buying a quantity of goods would require specifying the dollar
value, and the quantity of goods received by the purchaser would be G/P, P
being the price per unit good. Or we could express everything is dollars --
it makes no difference to the organization of the model, though it does
make what's happening harder to see.
It will be a little harder to maintain the distinction between flows and
sums. If G is used for value as Keynes does, it is not a rate variable, and
we need a symbol for the amount of G that changes hands during a
transaction. I use V (for inVentory) to mean what Keynes evidently means by
G, and G to represent the rate at which goods are removed from V and sent
to the consumer's inventory. We'll just have to be creative.
Anyway, what did Keynes get right? I'm still trying to figure that out. It
looks to me as though he counts as investment the cost of maintaining
deteriorating machinery (V), which according to his I guess famous
conclusion, income = consumption + investment, is part of "Savings." It's
also pretty hard to figure out which side of the dividing line he's
standing on when he refers to A - A1 as "consumption." Gross proceeds from
sales minus the cost of buying new equipment from other entrepreneurs is
"consumption"? He mentions elsewhere that consumption for a consumer is
measured in goods, but for an entrepreneur it is measured in dividends
declared. This is pretty discouraging to a person who is honestly trying to
figure out what he means.
There's the classic reviewers two sentence comment. "There's much that's
good in this paper and there's much that's new. Unfortunately what's good
isn't new and what's new isn't good." The issue I think is what is effort
you are putting into this intended to accomplish?
As a practical matter to communicate to the profession there isn't any
alternative to using the Keynesian symbols.
OK, as I say, I'm willing to do that. But I want to establish the right
entities in the model, and for that I need to distinguish between what is
actually going on and what the manager or entrpeneur only imagines might
happen, and to keep the physical bookkeeping distinct from accounting
conventions which may represent the system in variable ways, but do not
affect what is actually going on.
When Schumpeter at Harvard published a book on Macro economic theory in
the 1940's he was considered the grand old man of the profession. When
the book was reviewed, all the reviewers first translated what he'd said
into Keynes' language and then they explained what was wrong with it.
>you can be relatively sure, that if you use non-standard terminology and
symbols people >aren't going to pay what have to say much attention. Again,
I'm not responsible for >this, its just the way the market for economic
ideas is, for now and for the forseeable >future.
All right, but we have to be careful not to be cowed out of saying what we
believe to be true. It's hard not to think of people who react in the ways
you describe as retarded, and I should think that in any open discussion
they would be ashamed to act that way. But if they'e not, then we just have
to work on two levels: one level, developing a competent model that fits
the behavior of the economic system, and the second level, disguising the
model so these touchy creatures think it says what they believed all along.
If that's really the situation, the main thing for us to do is keep them
from preventing us from doing our work. We don't particularly need to value
their opinions.
So let's use Keynes' terminology; as I said, you misunderstood the
direction in which I proposed to translate. I remember when I had just
learned algebra how upsetting it was to see the solution of the quadratic
equation written with v, L, M, and N instead of y, A, B, and C. So I can
understand a person's having a hang-up over the notation instead of the
underlying meaning. However, I was 14 or 15 -- it's harder to understand in
an adult.
>Economics is an extremely conservative profession. Either you make your
peace with >this, or you can beat your head against a wall, or maybe if you
are extremely clever >you can upset the applecart. But, upsetting the apple
cart is only going to be of value >if you have an audience that is looking
for that sort of thing. For now I feel that I >can say much of what needs
to be said using the Keynesian symbols.
I think we've exhausted that subject: Keynsian symbols it is. You may have
to help me out a little.
>I thought we'd reached an understanding that as far as some basic first
principles there isn't a difference of any signficance between our views.
So, why are we having this discussion about Keynes? My recomendation of
Keynes, and the Keynesian sysmbols is based on the same advice I give
someone who wanted to sing clasical opera-- you'd better plan on learning
Italian.
I'm just trying to understand what he meant by saying income = consumption
+ investment, which you accept as a given truth in your model. To make that
equation factually true we have to have some very specific meanings for
those three terms, and my present effort is to try to grasp what those
meanings are. I can't create a model using Keynesian symbols until I know
how the quantities are calculated. It is not at all easy to find out what
Keynes means by them, If you know, just tell me and save me all this work.
Best,
Bill P.