'What is your name?' 'Billy Brown.' 'IT DOESN'T MATTER WHAT YOUR NAME IS!!!':
> 'Cost' and 'Value are two very different quantities.
I actually want to take issue with your definition of "production cost," since I think you are using it wrongly.
While the production cost of product X is not affected by the demand for product X, it IS affected by the price of capital, which, in turn, is affected by demand for capital.
Consider a case where I'm trying to build widgets, and widgets require
iron to build, along with $1 of labor to make the widget.
Now, you can read this in one or two ways. One way of looking at it is to
say that the cost to make a widget is the cost of the labor plus the cost
of the capital. If the iron needed for one widget costs $5, then, the
cost to make a widget is $6. This is what I'd normally think of if I
tried to specify a production cost. Note that it DOESN'T depend on the
demand for widgets, but it STILL depends on the cost of *capital*.
Now, you can read this in one or two ways. One way of looking at it is to say that the cost to make a widget is the cost of the labor plus the cost of the capital. If the iron needed for one widget costs $5, then, the cost to make a widget is $6. This is what I'd normally think of if I tried to specify a production cost. Note that it DOESN'T depend on the demand for widgets, but it STILL depends on the cost of *capital*.
Alternately, you *could* try to stick to your guns and say that "production cost" is $1 in this case, saying that it is, by definition, the cost of the labor necessary to make a widget. "Production cost" is a technical term, after all, so you can define it to be whatever you like, so long as the predictions come out right in the end.
> The two quantities are related only in the obvious sense that products
> whose cost is higher than their value will not be produced.
However, we notice that "production cost," when it is defined to be the cost of labor, does NOT validate the claim you make above. If iron costs $5 and the "production cost" is $1, but the market value of widgets is $3, I will not want to produce a widget, despite the fact that "production cost" is lower than market value.
Here you might object: "You forgot about the INDIRECT human labor involved in making the iron! If production cost is the cost of human labor required to create the iron PLUS the cost to turn that iron into a widget, the figures should work out in the end." However, this STILL doesn't make your claim above work out.
Suppose no one is willing to pay more than $7 for a widget. Suppose that the market value of iron is $5. According to MY definition of production costs, which includes labor and capital, the production cost is $6, so I'm making a $1/widget accounting profit.
Now suppose that the demand for widgets and the production cost of (iron + widgets) both remain constant, while the demand for IRON sharply increases, so that iron now costs $8.
By your definition of "production cost," the "production cost" of widgets remains the same as it was before (whatever it was). However, by MY definition of production cost, the production cost is now $1 of labor plus $8 of capital = $9, which is more than the market value of widgets. Clearly, in this case, I should not produce any widgets. But you asserted that "... products whose [production] cost is higher than their value will not be produced." But in this case the cost of labor has not changed, so if your claim about "production cost" as you have defined it is true, then I should not shut down.
So either your definition of "production cost" is wrong, your your claim about what when a firm should shut down is wrong. If your claim is wrong, then we would have to define some other kind of cost, perhaps the "total cost," which is given by "production cost + cost of capital," where if total cost is greater than market value, the product will not be produced. But this begs the question as to why we have invented this "production cost" term to begin with, when we already have a perfectly acceptable term in place: the cost of labor. Ockham's Razor tells me that, instead, we should take the simpler route, and say that "production cost" is the cost of labor plus the cost of capital, rather than creating a new entity, total cost, to make the same prediction.
-unless you love someone-
-nothing else makes any sense-