Occasionally we post a blog not because people want it, but because we think they need it. Can we force anyone to read it? No, of course not. Do we think that everyone is going to understand it or even care about it? No. That, however, doesn't mean that we should remain silent. (Or that we should post illustrations when we can't think of any. . . .)
You’d think from the data coming out of the Bureau of Labor Statistics that human labor is the only factor of production. Not the most important factor, not the predominant factor — the only factor. Why? Because the Bureau of Labor Statistics defines “productivity” as “output” (i.e., production) divided by the number of hours of human labor that went into it. This means that “productivity” is the rate of production per hour of labor, regardless of any other inputs.
Granted, this has the advantage of simplicity . . . or simple mindedness; we always get those two confused.
The problem is that if you don’t factor anything other than labor into the equation, then the results that come from the equation won’t take anything else into account, either — “garbage in, garbage out” as the computer guys say.
Thus, what you end up with — mathematically speaking — is
P = O/L
where “P” is “Productivity,” “O” is “Output” or “Production,” and “L” is “Labor Hours.”
This means that
O = P x L
or Output equals Productivity (the rate of production) times the number of hours of Labor devoted to production — nothing else. According to this equation, as long as you input hours of human labor, you will have production . . . whether or not you add anything else into the process!
Mathematically speaking, that is.
And that — mathematically speaking — is nonsense.
Given the classical factors of production, then (land, labor, and capital), the equation for the rate of production should be somewhat more complex. We’ll start with “O” — output — for that is the same no matter what equation you use, e.g., whether you travel for ten hours at 100 miles per hour, or a hundred hours at 10 mph, you have still gone 1,000 miles, no more, no less.
We can, however, make things a little easier by using two factors in our equation instead of the classical three. We’ll use the Kelsonian “human” (labor) and “non-human” (capital), instead of land, labor, and capital. We also need a different word than “productivity” for the total package (the relationship between labor and capital) because “productivity” means the rate of production, not the proportion or relationship among the different factors. We’ll use “productiveness.”
We will therefore use x as the rate of labor productivity, and y as the rate of capital productivity. This means that Lx gives us the output attributable to labor, and Cy (we’re using “C” for “capital hours”) for the output attributable to capital (all the non-human factors of production). This gives us:
Lx + Cy = O
This is a straightforward
quadratic equation [oops — our memory is flawed; we just realized 02/19/2016 that it's a plain, old equation]. Once
you know how x and y relate to each other (their relative
productiveness), you can calculate how many labor or capital hours you will
need to produce a desired amount of output.
The solution will be a straight line on a graph.
This is the concept of “binary productiveness.” It is obviously more useful than the concept used by the Bureau of Labor Statistics and All the Best Economists.
There is just one problem: how do you calculate the relationship between labor and capital? We’ll give that a go on Monday.#30#