Under chapter 7 of Human Action under the part "2. The Law of Returns", there are some parts I don't quite follow:

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

The producers goods could include raw materials right? And an optimum ratio of these materials could meet exact requirements for a product, for example if 10kg of wood is needed for every 1kg of Iron. Any increase in either single one in the ratio would be a waste, no?

This I do not understand at all, starting at wherever this x comes from:

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.

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

He wrote the phrase "as a rule" to hint that it's not always the case, the exceptions being the example you provided and the one he talks about later.

What he considers the usual is if you want to dig a ditch, and have people and shovels. then the optimal number of people is the number of shovels you have. If you add another person, more digging will be done, but since he has to use his bare hands, that last guy won't be as productive as the ones who have shovels.

This I do not understand at all, starting at wherever this x comes from:

In ordinary language, when you wanted to give an example of increasing the amount of something, you might say something like "Say I increased the amount of sugar in the batter from a teaspoon to a teaspoon and a half. Then it follows bla bla." When you want to be scientific, instead of saying from a teaspoon to a teaspoon and a half , you say "from one teaspoon to one teaspoon times some number X, X being greater than one."

What you gain in doing that is you are not limiting yourself to the case of a spoon and a half. You are also considering the case of upping the amount to a teaspoon and a third, or a quarter, or two teaspoons, any many other possiblities. You also gain sounding more impressive.

The point of the whole section you quoted is to prove that there is an optimum [meaning a value of C which will lead to diminishing returns if increased], something he only asserted until then, but didn't prove. After all, maybe p/c is a constant for all values of p and c. That is what he is disproving in that section you quoted.

My first point is also touched upon by an example by Mises afterwards:

In order to dye a piece of wool to a definite shade, a definite quantity of dye is required. A greater or smaller quantity would frustrate the aim sought. He who has more coloring matter must leave the surplus unused. He who has a smaller quantity can dye only a part of the piece. The diminishing return results in this instance in the complete use- lessness of the additional quantity which must not even be employed because it would thwart the design.

The end product is useless hence does not satisfy any increase in p?

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

He wrote the phrase "as a rule" to hint that it's not always the case, the exceptions being the example you provided and the one he talks about later.

What he considers the usual is if you want to dig a ditch, and have people and shovels. then the optimal number of people is the number of shovels you have. If you add another person, more digging will be done, but since he has to use his bare hands, that last guy won't be as productive as the ones who have shovels.

This I do not understand at all, starting at wherever this x comes from:

In ordinary language, when you wanted to give an example of increasing the amount of something, you might say something like "Say I increased the amount of sugar in the batter from a teaspoon to a teaspoon and a half. Then it follows bla bla." When you want to be scientific, instead of saying from a teaspoon to a teaspoon and a half , you say "from one teaspoon to one teaspoon times some number X, X being greater than one."

What you gain in doing that is you are not limiting yourself to the case of a spoon and a half. You are also considering the case of upping the amount to a teaspoon and a third, or a quarter, or two teaspoons, any many other possiblities. You also gain sounding more impressive.

The point of the whole section you quoted is to prove that there is an optimum [meaning a value of C which will lead to diminishing returns if increased], something he only asserted until then, but didn't prove. After all, maybe p/c is a constant for all values of p and c. That is what he is disproving in that section you quoted.

Thank you. I found out I accidentally thought he meant substituting c for cx and not the otherway around. I couldn't see my mistake and so I confused myself in the impressive sounding language.