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:

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.

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.