Fallacy of Composition: Cobb-Douglas Function
Particularly celebrated as a production function is the caption.
To
Begin. There in the market as of economics are two hands, supply and
demand; the former represents the household while the latter the firm. In macroeconomics, however, the aggregate
households are the aggregate firms. Therefore, the aggregate income earners are
the aggregate income payers. In other words, each of us is and all of us are
the earner on one hand and the payer on the other hand, no questions allowed.
There in the economy are no such things as labor incomes vs capital incomes. It’s the gross national income, stupid! In the first place, each of us and all of us are us in commonwealth. In the second place, we wear a hat each, subject to varying colors across (L-3); namely, consumer, producer, demander-cum-buyer, supplier-cum-seller, employee-cum-income earner, employer-cum-income payer, saver, investor, laborer, capitalist, debtor, creditor, private person, public human and the like.
There on the other side are
numerous businesses, professions and disciplines; accordingly, production
technology is one, economics is another, business administration is still another,
political science is yet another, mathematics is obviously another, financial accounting
is no doubt another and so on so forth. There surely is jargon, or “the names”
(名, ming) of Confucius,
specific to each profession or discipline. Typically, the income in “economics” is
one the income out of “financial accounting” is another.
15)
The Cobb-Douglas Production Function
We somehow have the so-famed “Cobb-Douglas
production function”: F(K, L)= A∙Kα∙L1-α. Amazingly, this
function is created on the basis of the shares from the national income accounting
of capital income (α; about 30% in the US) vs labor income (1- α). In effect, this function combines technology
with accounting. No wonder, it is the magnum opus of Mathematician and Politician.
Even
better, the mathematical equation of technology is so discreetly conceived as
to be differentiable and as to beget among others the so-called “Solow residual.”
Viola, there comes Politico-Mathematics!
Or, Techno-Accounting!
Exogenous to Cambridge. None of us on Earth, as non-macroeconomist, can
even think about the real aggregate machines (K); none, either, the real aggregate laborers (L).
Insult
to injury: How many hours per week do
each and all machines and each and all laborers run on the job? Is that naught
(0), one (1), two (2), three (3), or 40, 84 or 500 hours? What a “constant” are
the weekly working hours in the short run to the long run? How about the
productivity of each and all machines or laborers? Some of us must care, but who?
From
Here to Eternity, all of us never do nor shall know what each and all of them in
and out of the production function are like. Nevertheless, the rest of us are
so very much well aware that each and all the residuals are accounted for at the CPAs’ convenience.
Furthermore,
the so-called “bottom line” of “income statement” catches incomes of all the
capitalists with various names such as proprietor, entrepreneur and
shareholder. Oh yah, baker, butcher and brewer not alienated, either. Are the share-owners
of the bottom line domestic, national or alien? Are they us or them?
Are you game?
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