Fred,
> 1. *quantity and quality*
I tried my best to explain my view on this, but I obviously didn't get
my point across.
> Thus, according to marginal productivity theory, the quantity of profit is
> independent of wages; but according to Marx’s theory, the quantity of
> profit varies inversely with wages. Thus an increase of wages has no
> effect on the quantity of profit according to marginal productivity theory,
> but causes a reduction of profit according to Marx’s theory.
But the marginal productivity theory cannot (repeat, *cannot*) claim
such a thing, i.e. that the quantity of profit is independent of
wages. How could it? Precisely, the cost function is the dual of the
production function (linearly transformed, just "scaled" by the input
price vector). The conditions of the class struggle are embedded in
the cost function via the production function and/or input prices
(e.g. the wage rate).
If I say, "Let gravity acceleration be constant, then the
instantaneous speed of an object in free fall depends on the distance
from the point where it is released and the time elapsed from its
release," you cannot take this as me saying that the speed of the
object is *independent* of gravity. No. I'm assuming gravity
constant for the time being. I'm assuming that we're staying on the
surface of this planet to conduct our experiments. Similarly, the
textbooks usually say, "Let the labor market be "perfectly
competitive." Therefore, the wage rate is exogenous. Under these
conditions, competition makes the profit per unit of means of
production dependent on the marginal output generated by such unit."
This does *not* mean that the profit per unit of means of production
is *independent* of the wage rate. Obviously, if the wage rate
changes, the entire cost function shifts and, consequently, the
marginal product of "capital" goes down (under the usual assumptions
of technological convexity). Same "prediction" as Marx's.
> I think you are conflating fixed proportions between inputs (e.g. machines
> and labor) with fixed proportions between raw material inputs and output.
> Most
> of the literature on fixed proportions is about different inputs, rather
> than raw material input and output. I don’t think there is much
> variability between machines and labor, but I think there is even less
> (i.e. little or none) between raw material inputs and output.
I'm not sure why you're saying this. Maybe because, in my posts, I
implied that fixed proportions between inputs lead to discontinuities
in the profit function. Again, there's a mathematical duality between
the input space and the output space (the same space, if you take the
economy as a whole and, as I justified earlier, you are willing to
view society is a device by which humans reproduce themselves). If,
in the input space, you have fixed proportions between inputs, then
the marginal rates of input substitution (the pairwise ratios of
marginal outputs) are going to be undefined or flip from, say, zero to
infinity. This implies that, in the output space, the marginal rates
of transformation between outputs (the pairwise ratios of the marginal
costs) will be messed up as well. FWIW. Not sure it addresses your
point.
By the way, some readers here will appreciate the fact that Soviet
economists contributed significantly to the modern understanding of
duality (e.g. Evgeni Slutsky, Leonid Kantorovic, etc.).
> Michael P. mentioned Georgesen-Rogen, who is one of the few who has
> discussed raw materials in marginal productivity. In the article by GR
> that I have read (“Coefficients of Production and the Marginal Productivity
> Theory”, *Review of Economic Studies*, 1935-36), he calls raw materials
> “limitational inputs” – by which he means that an increase of these inputs
> is a *necessary condition* for the increase of output (i.e. fixed ratios
> between these inputs and output). And he concludes that when we take these
> limitational inputs into account “we can no longer make use of the concept
> of physical marginal product.” (p. 46)
All one needs to get around GR's objection is to redefine a few
concepts. Note that we are disagreeing about the general validity of
abstractions here. We're not talking about concrete practical
applications, which -- as I said -- may require particular
modifications to the abstract models. But the same proviso applies to
any other general theory.
Suppose you say that "home heating with an oil furnace" is the output.
It's easy to redefine output more generally as "home heating,"
period, and bypass the issue. Now, the production function has as its
inputs gas, oil, electricity, and boilers powered by various
alternative energy sources, etc. There's now plenty of
substitutability between them. I imagine you objecting that there's
an oil furnace installed, "fixed" for the time being? Well, again,
extend the period of time and what may appear "fixed" starts to
"circulate." In my first hefty reply to you, I argued about how human
societies reduce all inputs and outputs to the ultimate input/output
-- the productive force of labor. If, for example, I redefine output
as "home comfort" instead of "home heating," then we can have home
heating along with many other substitutable inputs (e.g. sweaters,
etc.) as the arguments in this redefined production function.
> Julio, please explain in further detail how an increase in the working day
> shifts the production function and how it affects the quantity of profit
> produced.
Okay. Arbitrary example: Let "labor" be a variable input in some
apple production function, measured in worker-day units, with working
days defined as 8 hours/day. If L = 1 worker-day, Q = 16 apples.
Technology, etc. are all fixed. Now, change the working day to 10
hours/day. With L = 1 worker-day, say, Q = 20 apples (or 18 with
decreasing returns to labor hours). Etc. The entire production
function shifts upwards. Similarly, if the intensity of labor
increases.
> So Clark was wrong about his own theory and you are right about his theory?
> Seems unlikely to me.
Yes, Clark was wrong about his own theory. It happens often. It's
not just me saying it, but even if it were only me, that would not
make him any righter. The earlier interpretations of marginal
productivity theory have been amended in various ways since Clark's
times. And not only Clark's belief that each class gets its "natural"
desert. Also the original confusion about zero profits deemed general
but shown since to be limited to "linearly homogenous" production
functions ("constant returns to scale"). Etc.
> I don’t understand what a theory of deserts has to do with a theory of
> profit.
With all due respect, Fred, but it's you who mixed things up. Cf.
your papers. You frame the marginal productivity theory as a theory
of deserts, as the argument that workers deserve to be exploited, etc.
I am the one who's tried to show that this is totally unwarranted on
the theory's premises. And I believe this is not the way any serious
conventional economist todays interprets the theory. Cf. any
advanced micro textbook.
> I am criticizing how Krugman and other neoclassical economists interpret
> marginal productivity theory, because that is the dominant interpretation
> and it is an invalid theory and an ideological weapon.
Not really. You premised your criticism of Krugman on marginal
products, production functions, etc. being "illegitimate" concepts,
etc. But if you're wrong and these concepts are "legitimate," then
your criticism of Krugman lacks substance.
> An empirical test of marginal productivity theory is not possible because
> marginal products are not observable separately from the prices of labor
> and capital. That is one of the main problems with this theory and my
> first criticism of Krugman in my post on the Economist’s View blog.
Obviously, I have failed to convince you that it is *not* the prices
of labor and capital as *social forms* that are involved, but instead
the *material contents* of such forms: material "quantitatively
specified proportions" or "essential determinations of value," which
Marx in Capital (for the most part) postulated as given. I can only
advise you and other readers to re-read what I wrote on my blog re.
the CCC and to think about it carefully.
> This is an important point, which I would like to emphasize. The price
> variable that is supposed to be determined by the marginal productivity
> theory of capital is the *price of capital*, i.e. the price of capital
> goods – sometimes call the “rental rate” because it is usually assumed that
> firms *rent *their capital goods rather than purchase them (another very
> unrealistic assumption of this theory).
How do you believe that the price of machines is determined in a
capitalist society? Do you think that it has nothing to do with the
capitalist demand for machines? If, like Marx, you believe that the
*necessity* of social labor time devoted to machine production depends
(on the one hand) on the magnitude of the (capitalist) "social need"
for machines, then you need to specify what drives capitalist
acquisition of machines, what makes the (capitalist) social need for
machines to increase or decrease. Here's a hint: Capitalists do not
care about machines for their own sake. Machines are simply devices
for them to extract unpaid labor from workers. Competition will make
the capitalists acquire machines only insofar as their spending on
them yields a return at least equal (or, approximately so, adjusting
for the lumpiness of machines regarded at a certain scale) to the
return on other inputs. If the return on the machines is greater,
then they will acquire machines. If not, they will favor other
inputs.
Now, I don't see why the "rent" part puzzles you and seems unrealistic
to you. Doesn't Marx explain "land" price as capitalized rent (the
"discounted present value" of land rents)? Where does Marx get his
discount rate? What is his argument? Landlords in a capitalist
society view holding land like they would regard holding machines or
any other type of productive wealth. Holding it only makes sense to
them if the return on their land (the "rental rate") is the same they
would get by holding the land price as loaned capital. (And, of
course, if the land comes along with other goodies, you have to take
into consideration the "depreciation," "depletion," or "amortization"
of said goodies. (An understanding of this is also in Marx, by the
way: cf. Capital 3, part 6. The "land" rental rate = interest rate.
Opportunity cost. And I use quotation marks, because "land" here is
-- again -- shorthand for any type of owned wealth under capitalism.
Yes, the interest (as opposed to the "profit of enterprise") is a
rent.
I could go on and on. This is Marx's volume 3, and many of his
arguments were not completely settled. I am no Marx, but I believe
that we can do better with hindsight. But I'll leave that discussion
for later.
> The price of capital (goods) (*PK*) consists of two components: an
> explicit *depreciation *component (this period’s cost of the capital goods)
> and an implicit *interest *component, which is the “opportunity cost” o the
> rental firms of investing in these capital goods, rather than in
> alternative investments. The depreciation component is equal to the
> product of the price of the capital goods when purchased (*PG*) and the
> depreciation rate of these capital goods (*d*), and the interest component
> (the “opportunity cost”) is equal to the product of the price of the
> capital goods when purchased and the rate of interest prevailing in the
> economy (*r*). Algebraically:
>
> *PK** *= *dPG* + *rPG*
>
> Thus we can see that the "price of capital" (goods) is not an actual market
> price, but is instead a hypothetical price constructed with the assumption
> of an implicit “opportunity cost” of the capital goods rental firms. It is
> not clear why anyone would want to explain this unreal price, which no one
> ever observes in capitalist economies.
Why would anyone want to explain value (an "unreal price"), which no
one ever observes in capitalist economies? Goose and gander. This is
just to show how some of your arguments are tantamount to rejecting
abstractions because they cannot fully account for the concrete.
> The emperor has no clothes!
The last word on this discussion should be yours, Fred.
Comradely.
PS re. this thread: Michael Perelman, if that's okay, please cc me
your comments or post them on the list for everybody to read. I
cannot find them on the archives.
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