Fallacy of Composition: Production Function
There
surely is a production function at each workshop of a factory but not on the level
of factory rightly managed; not to mention at the whole firm to the aggregate industry
all the way to the macro-economy.
The operation of the workshop is mechanic,
but management of the firm is organic: That’s fortunate (+) to some while
unfortunate (-) to others. With regard to the production function, some (+) take
the organic economy as the economy; while others (-) take a certain mechanic workshop
out of indefinitely many nationally for the whole economy.
An interesting question: Would
there be such a thing as organic “equation” or “function” as called in mathematics
and macroeconomics? As for the rest of us, at least: Well, never in Here on
Earth. We have yet to discover what
over There in Eternity.
14)
The Production Function
Visiting a workshop of the widget maker, we would find a certain fixed number
of real machines as in a certain month
(T-1), the accounting period of widget business. When the machines fixated
at the workshop are running at more or less normal capacity, we would discover
the law of diminishing marginal products
of labor, sometimes veiled with the name “the law of diminishing returns.”
You know what? The firm does not only have multiple
factories but also multiple workshops per factory. Would the law of same “name”
and “fame” hold true across multiple workshops or across many factories of the
same firm? Again the answer depends on whom you ask the question of.
Rest
of Us. Absolutely positively no, primarily
because the marginality presupposes multiple units of the same kind in the
given context. The law would seldom bind when we move to another workshop of
the same factory. Insult to injury (雪上加霜, xuě shàng
jiā shuāng): The firm can have many different
accounting periods depending upon items; the law never applies across so many periods
per year, the standard accounting
period as for GDP (Y).
The manager, junior or senior, of
the factory is seldom so dumb as to stick all through the year to the workshop
where the law applies at the very first. Furthermore, she pays the keenest
attention to the market so as not to be single-mindedly stuck to the physical
output; certainly, the quantity is no more than a means to the end of monetary income.
Macroeconomists:
The law of diminishing returns shall apply equally legitimately from the workshop
to the factory to the firm to the industry to the economy.
In the first place of
macroeconomics, all that matters is the “real quantities” without monetary prices. The aggregate scale
of production would not affect the market price. In the second place, what is
true at each workshop must always be true all across the nation. As a result, we
have the production function, that is, Y=
f(L, K). A rose on the purple dress of silk (錦上添花, jǐnshàngtiānhuā):
The function is nicely differentiable and gracefully subject to integration (cf. the Cobb-Douglas production
function).
When in Cambridge, all in all:
1) We
are never concerned about demand side because the aggregate demand would
conveniently be identical to the aggregate supply, effectively or
ineffectively. We neglect the annoying AD “everywhere except for in the” AS-AD model.
It’s the “real quantities” of GDP (Y)=
AS, stupid.
2) As
Robert Solow famously talked about, the economy is so tightly bound with the
law of diminishing returns as to eventually
fall in the stationary state, static (Y*),
comparative static (Y1 vsY2 in the year) or of Golden rule (Y***** of five carats).
3) All
that matters at the end of the day is: “It’s the supply side, your Excellency!”
as Arthur Laffer would possibly like to suggest.
Did
We Know: Whether for stability in “the short
run” or for betterment in “the long run” the economy when in Cambridge grows as
vertically (L-1) as a tree does?
Yes of course: In the first to last
place of macroeconomics, the time dimension is dead, or otherwise has long faded
away into oblivion (T0). Down with the time dimension!
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