## Monday, February 22, 2016

### About That Labor Theory of Value, II: Determining Relative Contribution

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:
Lx + Cy = 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,
(Lx + Cy) x Mz = 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 Mz = 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 Lx + Cy and (Lx + Cy) x Mz both equal O, we can kick out Mz 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):
Lx + Cy = 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.
#30#