Last Thursday we
fiddled around a bit with the concept of “productivity” as defined by the
Bureau of Labor Statistics and most economists.
Briefly, the idea is that labor is the source of all production. At best, capital only “enhances” labor. Just as the pictures we didn't put into this blog are supposed to enhance understanding.

The problem is
that the formula for productivity, P = O/L (Productivity equals Output per
Labor Hour) accounts

*only*for labor, nothing else. No materials, supplies, or capital, whether enhancing labor or as a discrete factor of production. According to the formula, labor is the sole input and factor of production.
Consequently we derived
a more complete formula, one that takes capital into account:

**L**

*x*+ C*y*= O
where C is the capital factor,

*x*is the rate of production per labor hour, and*y*is the rate of production per capital hour. That’s as far as we went.
The next step is
to determine the relative rates of production for capital and labor, but before
we do that, there’s a problem that crops up.
Our formula is a great advance on the standard formula, but it still
leaves something out: all the non-labor and non-capital inputs to production,

*i.e.*, the materials, supplies, utilities, and so on.
Part of the
problem here is that, traditionally, such things have been grouped under
“land,” thereby giving “land” a double meaning: an input to production as well
as a factor of production. Including
land under capital as a non-human factor of production solves part of this
problem, but it still leaves the fact that our formula does not include
whatever it is on which labor and capital expend their energies.

We need to add
another term in our equation. We’ll call
it “M” for materials, and define it as anything other than labor and capital
used in production. We will use

*z*for the rate at which materials are used per hour. This gives us,**(L**

*x*+ C*y*) x M*z*= O
We forget what
this kind of equation this is called, but it looks as if it’s on three axes
instead of two, making it a bit more complicated. Still, what we added doesn’t change anything. It actually helps us figure out how labor and
capital relate to each other.

That’s because M
is the only thing we can know with absolute certainty on the input side of the
equation. Assuming our accounting is
accurate, we know

*exactly*how much non-labor and non-capital input went into one hour’s worth of production just by isolating M and considering it alone, i.e., assuming that*z*= O/M, or M*z*= O.
For example,
let’s assume that 20 units of M costing $5,000 are used up in one hour to
produce 100 units of output. For every
20 units of M, we get 100 units of O. The
equation tells us that z, the rate of material usage, is 100/20, or 5.

The equation also
tells us something else: we can take M out of our equation! Why?
Because we can take it for granted — but only as long as we say so in
our assumptions, and recognize that improvements in C — the technology — will
change M. As long as everything else
stays the same, however — the standard “ceteris paribus” assumption in
economics — we can ignore it, at least for the purposes of determining the relative
contribution of labor and capital.

Since L

*x*+ C*y*and (L*x*+ C*y*) x M*z*both equal O, we can kick out M*z*as long as everything else stays*exactly*the same. Our math isn’t good enough, but somehow M, C, and L combine to give us O, as long as everything stays the same, it’s all fixed — which means the relationships between all the factors remain fixed.
So, we were right
the first time — at least as long as nothing changes

*and*we’re only interested in determining the relative contributions of labor and capital. The formula is (or should be):**L**

*x*+ C*y*= O
We’re not back at
square one, though. Our little exercise
gave us a valuable piece of information: the cost of an input, the next best
thing to the physical input, gives us a basis for determining its relative
contribution to production: its productiveness.
We can’t calculate the actual physical contribution, because capital and
labor have a synergy that is certainly absent from labor alone, and may be
absent from capital alone (assuming a completely automated production process).

To get our data,
we go once again to our accounting records.
We find that to produce the 100 units of O in our example we put in 1
labor hour at $25 per hour and 1 capital hour at $50 per hour. Plugging these into our equation, we get 25x
+ 50y = 20, or, for every labor input there are two capital inputs. The productiveness of capital is twice that
of labor.

That being the
case, the owners of capital should receive twice what the owners of labor
receive for every unit of output sold.

There’s a
problem, however. Our analysis assumes
that there is no interference in the cost of capital or of labor; that the cost
reflects the true value of each of the inputs, which we know is not the case.

Why? Because when
owners of capital have the upper hand, they use their power to take what
belongs to the owners of labor, and when owners of labor have the upper hand,
they use their power to take what belongs to the owners of capital. A free market, the best means of determining
just wages (return to labor), just prices (“return” to “output”), and just
profits (return to capital) isn’t operating because market participants aren’t
coming from genuinely equal bargaining positions.

What is the solution? Obviously, to put owners of labor and owners
of capital on the same footing, or as near the same as possible. This gives them equal bargaining positions which
is essential to the functioning of a free market and thus of determining the
true value of anything.

Since owners of
capital are already owners of labor simply as human beings, the only way to put
owners of labor and owners of capital on the same footing is to turn owners of
labor into owners of capital.

And that is the
whole point of Capital
Homesteading.

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