Fred,
> Julio, I think you are confusing the price of capital and the rate of
> interest. The price variable that is determined in marginal productivity
> theory is the *price of capital*, not the rate of interest. The rate of
> interest is one component of the price of capital, along with a
> depreciation component, and in disequilibrium an entrepreneur’s profit
> component (= 0 in LR equilibrium).
Not unusual to frame the production function in terms of joint
production. I alluded to this in a prior post. I think I said that
the output in the ditch digging operation could be, not just ditches,
but {ditches, worn shovels, tired/grumpy/experienced workers}. The
output vector can embed depreciation. Now, in equilibrium,
competition will enforce r = i(whatever), because (on the demand side)
r = MP_K, where the product already deducts depreciation so you don't
need to deduct it from K. There is *no* loss of generality.
But, back to the key question here: Why (on the supply side) do they
take i as given? To answer with a question: Why not? A theory
doesn't need to be about everything to add to our knowledge. We don't
need to know everything about everything to know a little something
about something. This MPT story is supposed to be about how the
profitability of capital invested in *means of production* is
determined. The theory says that, on the supply side, this
profitability has to be affected by the rent on wealth *ownership* in
general, i. And how this rent i is determined is not addressed
directly in this particular framework. Again, nothing wrong with
that.
Actually, if one can extract implications that are readily apparent,
then this actually highlights the true nature of capital, since the
story says that the profit extracted by the capitalists deploying
means of production in a given production process is nothing but a
particular form of rent extraction, a form of hijacking labor, on the
grounds of a monopoly of *ownership* over productive wealth. If i
(the income you fetch by merely holding financial claims, legal claims
over wealth, like $1) governs the profitability of means of
production, then it is clear that capitalists extort a portion of the
net product of social labor, not because capital as such (as a social
relation) "contributes" to output (it doesn't, *owning* wealth does
not contribute to producing anything; using wealth productively does,
but *owning* it doesn't), but because they are holding the productive
forces of social labor hostage.
> Assume for now that the Kd function can be derived in this way – letting go
> for now the impossibility of defining the MPK in all the cases in which
> production involves raw materials (or other intermediate inputs) (as
> Georgesen-Rogen acknowledged). Now Kd has to be combined with Ks in order
> to determine PK. What is the theory of Ks? I know of no such satisfactory
> theory in print. (Julio, if you know of one, please send me the reference.)
> Such a theory would presumably have to do with “capital goods rental
> firms”, i.e. firms that rent machines to other firms (another very
> unrealistic assumption of this theory; Julio, the unreality is not that the
> rental firms’ earnings are called rent, but that it is assumed that firms
> *rent
> *their machines rather than *purchase *them).
Again, refer to volume 3 of Capital, parts 5 (chs. 21-25, short
chapters) and 6 (chs. 37-38). Part 5 is about how capital, as a
social relation, has two intertwined aspects: (1) a socially
sanctioned monopoly of ownership over productive wealth, what economic
theorists now call "excludability," and (2) the direct control,
command, management, etc. over the production process, with labor as
an element subordinated to it. Although *in general* capital as the
dominant power we recognize it for historically cannot exist without
(2), *in particular* capital (i.e. individual capitals, a portion but
not the totality of social capital) need not involve itself with (2)
to appropriate a portion of the net output. There is a legal and
political apparatus that will see to it that you get that portion if
you only exercise (1), while keeping (2) out of sight. Then, in part
6, Marx frames land tenure as a monopoly of ownership over a crucial
piece of the productive wealth of society, its space/time and finite
natural resources. Marx shows that land rent (and its capitalization
or discounted present "value," the land price) is a form of i (plus
depreciation of physical structures, depletion of resources, etc.) as
well, i.e. unpaid labor, surplus value appropriated on the basis of
the socially-sanctioned power of the landowners to exclude others from
using this crucial means of production. What is the point here? The
point is that the capitalists *do* rent their machines and capitalist
farmers *do* rent their land, if from none other, from themselves.
Industrial and other capitalists routinely rent land and other means
of production (or legal claims over them) they do not own. But if
they own the machines or the land themselves, then competition will
make them impute a rental rate on them, as if they had a dual
personality, one as renters and other as entrepreneurs. They extract
gain (unpaid labor) with both hands. And this rental rate is i (plus,
if you wish, a machine depreciation rate, a resource depletion rate,
etc.). This is why I don't understand why you insist on claiming that
this is "unrealistic." This fact, which Marx studied meticulously, is
as real as the Atlantic Ocean.
>> > In Marx’s theory, on the other hand, the amount of profit depends on the
>> > difference between the new-value produced by workers and the wages paid.
>> New
>> > value in turn depends on the product of the MELT and the quantity of
>> > SNLT. That
>> > is:
>> >
>> > Profit = (MELT)(SNLT) – wages
>> >
>> > Thus an increase of wages results in a $ for $ reduction of profit.
>> >
>> > So I spoke too strongly when I said that MPK is independent of wages.
>> The
>> > MPK does vary inversely on wages, but is a completely different way from
>> > the relation between profit and wages in Marx’s theory.
>>
>> Of course it is different (seemingly so), because the assumptions
>> about SNLT are different. In your equation, SNLT depends (I suppose,
>> following Marx) on the level of the productive force of labor and the
>> size of the social need for that commodity, two things you take as
>> given. In other words, SNLT is *exogenous* in explaining the
>> magnitude of surplus value. On the other hand, in the "neoclassical"
>> story, SNLT is *endogenous*, as the size of the social need expands
>> and contracts depending on prices (although, like in Marx, the
>> productive force of labor is also taken as given). So, the
>> "neoclassical" story accounts also for the feedback effect of wage
>> changes on profit via the adjustment of SNLT. However, if you're
>> willing to assume continuity, the effect in both stories turns out to
>> be the same, at the margin. This follows directly from the envelope
>> theorem:
>>
>> profit*(SNLT) = profit(wages, SNLT), where wages = wages(SNLT):
>> d profit*/d SNLT = d profit/d SNLT | wages=wages*(SNLT)
>>
> I don’t understand this argument at all. What is required to be proved is
> that the neoclassical MPK (aphysical characteristic of the production
> function) is equal to the Marxian [(MELT)(SNLT) – wages]. Where is the MPK
> in these equations? Where is the MELT?
MELT is an arbitrary constant, Fred. It depends on the (arbitrary)
choice of monetary unit. Truly irrelevant: Just let MELT=1. No loss
of generality. All I'm saying in these last equations is that, in the
MPT, profit is a function of SNLT. That is implied, of course. We
know that the neoclassicals do not use Marx's terminology or wield
Marx's conceptual understanding.
You claim that, unlike in Marx, in the MPT story, profits don't go
down if wages go up. I showed you that under the MPT story profits
(as a share) also go down if wages (as a share) go up. But do they
go down dollar for dollar, as they do in Marx? Not necessarily,
because in Marx some of the moving parts (SNLT) are assumed as given,
while in the MPT story, SNLT (or the output in which it is "embodied,"
which has a first-order effect on wages) is an endogenous variable.
The net output (and its value) is split into two portions under both
stories: the portion that goes to labor and the portion that goes to
capital. If you assume that the net output (and its value) is given,
then changes in the portion that goes to labor reduce 1-to-1 the
portion that goes to capital. But if the net output is allowed to
vary, then the 1-to-1 rule doesn't apply anymore, in general.
However, and here's where the envelope theorem applies, under the
right assumptions, the second order effect (from the parameter, wages,
to the endogenous variable, output or netput) can be made to vanish
about the "optimal" value of the "parameter," and you can have the
same 1-to-1 rule as in Marx. So, there: I'm showing the formal
equivalence between the two approaches. In words, if you make the
changes in net output small enough, then the marginal effect from
wages to net output goes to zero. Now, you may object and say, "But
Julio, you are mixing up use value and value categories." Well, in
this context (i.e. where the price of output is taken as given)
multiplying output levels times a given price is just scaling the
variable. Or, if you prefer, assume that the output price vector =
1$/unit. No loss of generality. "But" -- you may object again -- "I
am talking about *value*, socially necessary labor time, not about its
monetary form." Well, same logic: you can specify a correspondence
between output *and* its value (in monetary terms) *and* social labor
time (in hours or days or whatever). You can always normalize one
variable to simplify your analysis, provided you understand that other
things are expressed in terms of it. No loss of generality.
I don't know that I can be clearer than this.
Now, the Marxist and the neoclassical concepts, terms, etc. are
different and contradict each other in many levels. No kidding. But
*we* have to disentangle each of these levels and be able to translate
properly between the two frameworks. Like in any translation,
something may and will get lost in it. But that doesn't preclude the
need to do this translation as carefully as possible. I strongly
believe that serious engagement with virtually any product of the
human mind, even the most distorted and fantastic aberrant one, not
excluding religion, vampirism, or sorcery, can yield positive
knowledge of humanity and society. While we may feel good ridiculing
modern economics (and there are ways in which the prevailing economic
ideology is more harmful than religion), its influence is too large
for us to dismiss it or assume (rather than demonstrate) its
superficiality.
I guess Marxists are entitled to our own jargon, but so are the
neoclassicals. They would rather keep us this way. They do not want
to engage us. They would rather that we be a small bunch of crackpots
clinging to an aged set of theories and terms, speaking our own
private language, while theirs is the lingua franca of the social
sciences. Well, they have a point. They are in power. We are trying
to overthrow their thing. This is not to convince ourselves alone of
our righteous understanding. We are forced to engage them, and show
the world, not only them but anybody potentially or actually under
their spell, why and how our worldview is superior to theirs.
Ultimately, if these frameworks are entirely different at all levels,
then they cannot clash. To paraphrase Marx (the weapons of criticism
is no match for the criticism of the weapons), you cannot compare and
contrast Marx and the neoclassicals if they do not share the same
battle field, if they vibrate at different wave lengths. That is what
the radical critique of modern economics entails. Not just discarding
an idea because a term does not make sense to us prima facie. IMO,
that is too easy, and of too little use. We need to understand their
propositions in their merits and demerits, in the context of their
entire framework. I guess that if I were to summarize my main
objection to your critique of MPT, this would be it. You are
proceeding as if it were an obligation of the MPT people to translate
things for you neatly into Marxian jargon so you can see where they
match or not. Well, we cannot hold our breath for this to happen.(*)
We have to do the translation ourselves, and that requires a very
careful digestion of the MPT. It's not about showing how idiotic or
ideologically bent their views are. It is about us appropriating
whatever kernel of truth we may find in their stuff. Marx set the
example: He studied the bourgeois economics or political economy of
his time and knew it inside and out, which is why he became its most
formidable developer and critic.
(*) By the way, I was just watching yesterday the youtube video of a
lecture at the U of Chicago by Robert Lucas, and -- although in a very
simplistic, distorted manner and with a bit of nervous sarcasm --
Lucas made a few respectful references to Marx (though not about
today's Marxists). It is also of interest to note that Lucas was much
more tentative and slower than usual, especially with regards to his
own prejudices re. macro policies in the face of this depression
(which he kept calling "recession"). We all age, I guess. Anyway,
the serious thinkers among (or in) them cannot pretend that we don't
exist.
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