In Chapter VII, Section 2 of Human Action, for the first time in his treatise Mises goes into some hardcore calculation using variables. (I say hardcore because it's been 10 years since I've been in a math class!)
I broke down his formula, but I'm having trouble understanding it. Perhaps the folks on here could aid me in understanding it?
To preface things, this is the chapter discussing Marginal Utility, and more specifically the distincting between objective use-value and subjective use-value. I'm pretty good on all that (for the most part), but the part below is what I find confusing:
(Here's a link to the PDF in case it didn't transcribe well: http://mises.org/Books/humanaction.pdf.)
2. The Law of Returns
Quantitative definiteness in the effects brought about by an economic good
means with regard to the goods of the first order (consumers’ goods): a quantity
a of cause brings about—either once and for all or piecemeal over a definite
period of time—a quantity α of effect. With regard to the goods of the higher
orders (producers’ goods) it means: a quantity b of cause brings about a quantity
β of effect, provided the complementary cause c contributes the quantity γ of
effect; only the concerted effects β and γ bring about the quantity p of the good
of the first order D. There are in this case three quantities: b and c of the two
complementary goods B and C, and p of the product D.
With b remaining unchanged, we call that value of c which results in the
highest value of
p
c
the optimum. If several values of c result in this highest
value of
, then we call that the optimum which results also in the highest
ACTION WITHIN THE WORLD 127
value of p. If the two complementary goods are employed in the optimal
ratio, they both render the highest output; their power to produce, their
objective use-value, is fully utilized; no fraction of them is wasted. If we
deviate from this optimal combination by increasing the quantity of C
without changing the quantity of B, the return will as a rule increase further,
sbut not in proportion to the increase in the quantity of C. If it is at all possible
to increase the return from p to p1 by increasing the quantity of one of the
complementary factors only, namely by substituting cx for c, x being greater
than 1, we have at any rate: p1 > p and p1c < pcx. For if it were possible to
compensate any decrease in b by a corresponding increase in c in such a way
that p remains unchanged, the physical power of production proper to B
would be unlimited and B would not be considered as scarce and as an
economic good. It would be of no importance for acting man whether the
supply of B available were greater or smaller. Even an infinitesimal quantity
of B would be sufficient for the production of any quantity of D, provided
the supply of C is large enough. On the other hand, an increase in the quantity
of B available could not increase the output of D if the supply of C does not
increase. The total return of the process would be imputed to C; B could not
be an economic good. A thing rendering such unlimited services is, for
instance, the knowledge of the causal relation implied. The formula, the
recipe that teaches us how to prepare coffee, provided it is known, renders
unlimited services. It does not lose anything from its capacity to produce
however often it is used; its productive power is inexhaustible; it is therefore
not an economic good. Acting man is never faced with a situation in which
he must choose between the use-value of a known formula and any other
useful thing.
He's proving the famous Law of Diminishing Returns. Wikipedia sums it up nicely:
The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant ("ceteris paribus"), will at some point yield lower per-unit returns.
In other words, say you are making bread in some imaginary world I made up for this example. You find that if you use one cup of water and a pound of flour you get a pound of bread. If use a cup of water and two pounds of flour you get 2 pounds of bread. If you use a cup of water and three pounds of flour you get 2 and a half pounds of bread, because the water doesn't interact as well with the flour when there is so much flour.
At one and two pounds of flour, [holding the amount of water fixed at one cup] you get a pound of bread per pound of flour. But at three pounds of flour, you got more bread than with two pounds, but not as much extra as before. That third pound of flour only added a half pound of extra bread.
The question is, is this true only in the imaginary world I set up? Mises is claiming that no matter what you are making that requires two or more ingredients [like the water and flour], at some point the same thing will happen. You will start getting less bang for your buck, as it were. Diminishing returns will set in.
This is quite an amazing claim, if you think about it. He's saying that no matter what you are making, bread, cars, computers, anything, and no matter what materials you are using, at some point diminishing returns will set in. And he makes this claim knowing nothing about the physics and chemistry and engineering involved.
His proof is in two steps. First, he points out that there must be an optimal mix. In our example, we found that for a cup of water [what he calls "b remaining unchanged"], one or two pounds of flour will give one and two pounds of bread, respectively. So we are getting one pound of bread per pound of flour in those two cases [what he calls p/c. In our case p is a pound of bread, c is a pound of flour]. If we assume you can't do any better than that, then the optimal mix occurs at one pound and at two pounds.
Then he proves that those optimal mixes have to stop happening at some point.
The fingers tire, tell me if this is enough for you to figure it out.
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Yes, very much, thank you. So I understand that in the example, there must be at least 2 variables: one being constant, the other fluctuating. I'll have to go back and re-read the selection, but it seems to me that if someone has a business that doesn't involve mutliple variables, let's say a table business. If a guy purchases tables, then refurbishes them or perhaps just rents them out as is, could Mises's Law of Returns be consistent?
I suppose that the given variables are the tables themselves and perhaps time that would rot the tables away, but I think I've missed the entire point.
I understand your summary, and thank you. I was just building on it with an abstract business model to see if it was relateable to all forms of business or only those that have fluctuating or multiple variables as opposed to a business with a static product for rent or sale.
It's not how many kinds of products are made that counts, it's how many products are used as his raw materials.
Even if all the business is making is refurbished tables, as long as refurbishing them requires at least two things, say an old table and paint, the law would apply.
If he rents them out as is, he is not producing something new out of raw materials, so the law is not talking about that.
Time doesn't count as one of the factors per se, although labor hours does.