[OPEL:6213] RE: Historical, real and current costs (Example 1)

andrew kliman (Andrew_Kliman@CLASSIC.MSN.COM)
Mon, 23 Feb 98 09:33:37 UT

A reply to the PIAF:

From: owner-ope-l@galaxy.csuchico.edu on behalf of Duncan K. Foley
Sent: Sunday, February 22, 1998 9:58 PM
To: ope-l@galaxy.csuchico.edu
Subject: RE: [OPE-L] Historical, real and current costs (Example 1)

Let me first note that I am replying only to this post, and not to "RE:
[OPE-L] Historical, real and current costs: general," which was posted by
Duncan at the same time. It is important to point this out because the latter
post contains a new suggestion about computing the simultaneist MELT at a
single *point* in time.

Heretofore, up to and including the post to which I am replying, Duncan has
always maintained that the MELT is defined over an *interval* of time. The
response below defends my contention that this, Duncan's original definition
of the MELT, deals improperly with inflation and deflation. If and when we
reach agreement over this, I will then be happy to consider the new
suggestion, but it seems best to deal with the original theory first.

Duncan writes: "Andrew contrasts what he calls the 'TSS' definition of the
MELT ... with the "New Interpretation" MELT ...."

Yes, except that the latter, I believe, is also the MELT of the simultaneous
single-system interpretations.

My first example showed that this latter interpretation of the MELT
necessitates the conclusion that a drop in the price level can imply that
workers exploit capitalists, whereas the capitalists would have exploited the
workers under the original price level. One assumption of that example was:

(3) The price of corn is:
(a) $4/bu. from Jan. 1, 1996 through Dec. 30, 1997, inclusive.
(b) $3.92/bu. on Dec. 31, 1997 (the price drops by 2%).

Duncan writes: "Perhaps Andrew meant to write that the price is $4/bu from
Jan 1 1996 through December 31, 1996, and $3.92/bu from Jan 1, 1997 through
December 31, 1997."

No. The price is constant throughout all of 1996 and all but the last day of
1997. It then falls by 2%.

Duncan: "But if this is not what he meant, there is a problem. This type of
assumption, read literally, is not acceptable in a period model. In a period
model you want to specify a single price for each period. ...

"(If Andrew really wants to have the price drop on the _last day_ of 1997,
then what we'd better do is move to a model in which the period is the day.
But then Andrew has to tell us a lot more about the time structure of
production, the time profile of wage payments, the time profile of sales, and
so forth, before we can analyze the model.)"

I wasn't aware until now that the New Interpretation depended on a period
model in this sense. I thought it was meant to be applicable to actual firm-
or aggregate-level (such as the NIPA) accounts. These are generally
constructed on annual or quarterly bases, and prices certainly do change
during the course of a quarter or year.

My example shows that the simultaneist MELT yields erroneous conclusions under
such circumstances. Hence, the simultaneist MELT yields erroneous conclusions
when applied to real-world data. Duncan's comment here -- and those which
follow -- seem implicitly to accept the validity of this point.

The only remaining question -- and a new one to me -- is whether the
simultaneist MELT is valid in an abstract "period model." I note that, even
if the answer were "yes," this MELT would lack operational significance, since
again, in the real world, data are constructed for periods during which prices
do change. I personally am not overly concerned about this, but I mention it
due to Duncan's expressed interest in operational theories.

Yet the answer to this question is "no." I do not agree that "In a period
model you want to specify a single price for each period." First of all, of
course, the TSS conception is that each period contains at least two prices
for each commodity, the input price and the output price. I realize, however,
that this way of putting the point will not be persuasive to those who reject
the TSS conception.

So let me come to the crucial analytical issue. As Duncan notes (elsewhere),
the simultaneist MELT is a flow-based measure. In other words, rather than
measuring the money/labor-time relation at a *point* in time, it attempts to
do so over some *interval* of time. Now, for an interval of time of any
length, prices at the *beginning* of the interval can always differ from
prices at the *end* of the interval.

To illustrate this, let me adopt Duncan's suggestion that we adopt "a model in
which the period is the day." Prices at 12:01 am can differ from prices of
11:59 pm.

If we shrink the period still further, to a minute, say, then prices at second
1 can differ from prices at second 60. And so on.

Thus, the problem with Duncan's "period model" proposal is that he wants it to
do two contradictory things: (1) pertain to an interval of time but (2)
ensure that prices remain constant throughout this interval of time. It
cannot be done.

Duncan wishes to specify analytical periods such that prices remain constant
during period t and change from period t to period t+1. I would presume he
would also want to leave no gaps between periods. Then his proposal doesn't
work. The end of period t *is* the start of period t+1. Hence, when its
price changes, a commodity will have two different prices at one and the same
time. For instance, at the midnight which divides Dec. 30 and Dec. 31, 1997,
one and the same bushel of corn will be worth both $4 and $3.92.

There is one way, however, to specify the MELT so as to ensure that prices
(and thus the money/labor-time relation) remain constant for a specific
measurement of the MELT. Define it so as to pertain to a single point in
time. This is precisely what the TSS interpretation of the MELT does.

Duncan: "Here I have a problem. If the money wage continued to be $396/200hrs
$1.98/hr in 1997, and the price of corn dropped to $3.92/bu, ...."

No. Again, I meant my price assumption literally. The price of corn dropped
after all of the wages accrued (and perhaps even were paid, and perhaps even
were all used to buy and consume corn at $4/bu.)

Duncan: "Here Andrew apparently wants to stick to the literal dating he
proposed above, imagining that the workers buy corn at $4/bu throughout 1996
and all of 1997 except the last day. As I've pointed out above, this isn't
actually consistent with the treatment of the year as a period, in which
prices and wages have to remain constant by definition."

Duncan must mean here that it isn't consistent with a "year" being the length
of a period in an abstract model in which prices do not change during the
period. A year is certainly a period, and firm- and aggregate-level accounts
are constructed on the basis of that period, even though prices and wages
change during it.

Duncan: "Of course, real economies do not function in terms of nice, neat
periods of a year or a month, or even a day or a minute, so we'd better be
sure our analysis is independent of the length of the accounting period."

I'm not entirely sure what "function in terms of" means, or what "analysis ...
independent of the length of the accounting period" means. By the latter,
Duncan may be concerned with mapping analytical periods (defined such that
prices do not change during the period) onto accounting periods. I don't
think this is possible given the conditions he specifies for a "period model."
Only an analytical period having a time-interval of zero length can ensure
that prices do not change within the period. An accounting period of any
finite length will then contain an infinity of analytical periods.

Duncan: "If we shift over to a model where the accounting period is a day, we
have 730 days (366 in 1996, which was a leap year + 364 from Jan 1, 1997
through December 30, 1997) during which the price of corn was $4/bu, the wage
was $1.98/hr and the value of labor-power was .99 (hours of social labor/ hour
of labor-power), and one day (December 31, 1997) when the price of corn was
$3.92, the wage was still $1.98, and the value of labor-power was 1.01 (hours
of social labor per hour of labor-power)."

Not quite. If the start-of-day price on Dec. 31, 1997 is $3.92, then the
end-of-day price on Dec. 30, 1997 is also $3.92. But the start-of-day price
on Dec. 30, 1997 is $4. So the price of corn must have changed sometime
during Dec. 30, 1997. Assume that the time of change was 9 pm, and that this
was also the time when the output of Dec. 30 was sold. Assume that the wages
of that day all accrued before, say, 5 pm, the end of the workday.

(To get fancy, and speak of wage payments and consumption as well, we can
imagine that each worker received her pay for that day sometime after 5 pm,
took the money to the company store, and bought, cooked, and ate the corn,
finishing the last bit no later than 8:59 pm.)

Then you have the same problem as before. The simultaneist conception of the
MELT necessitates the conclusion that the decline in the price of corn implies
that workers exploit the capitalists, whereas the capitalists would have
exploited the workers given the original price.

Andrew Kliman