[OPE-L:7692] Re: Re: Absolute rents in Sraffaland and Marxland

From: Gil Skillman (gskillman@mail.wesleyan.edu)
Date: Fri Sep 20 2002 - 13:20:37 EDT

Hi Fred.  Some things are still not cleared up, though as you'll see I 
respond to your request to indicate the pure Sraffian treatment of the case 
of differential rent.

Where I wrote

> > But I dispute this characterization:  in the Sraffian framework, to the
> > contrary, the inclusion of absolute rent is accommodated *precisely* by
> > "adding another equation."

you ask

>And what equation would you add to this Sraffian framework?

You already know: staying strictly within the Sraffian framework, 
considering solely the existence of absolute, as opposed to differential 
rent, the extra equation comes from replacing the single price of 
production (or accounting, depending on context) equation with *two* 
equations, which implies that the additional variable, the rental rate, is 
matched by an additional equation.  I'll discuss below what happens if one 
adds the *additional* complication, beyond the scope of our original 
discussion, of differential rent.

As for the demand equation *I* would insist needs to be added to the basic 
system in order to reflect the existence of rent, I literally can't answer 
that yet, since it's still not clear to me from your answer below what 
makes that rent possible under your perspective.  More below.

Next, where I say

> >
> > As I stated in my previous post, so far as I can see absolute rent can 
> only
> > arise in one of two possible ways in the accounting equation for
> > gold:  either rent is a payment for scarce land, or it arises from the
> > exercise of monopsony power on the part of gold-producing capitalists,
> > resulting in the artificial depression of constant and variable capital
> > magnitudes below what would otherwise obtain.  I do not see that you have
> > introduced a third possibility, so is it legitimate to conclude, in light
> > of the above, that you're electing the latter alternative?  If not, how
> > exactly does the absolute rent arise, and why doesn't competition equate
> > the rate of return in the gold industry with the rate of return in other
> > sectors, in this case?

you write

>According to Marxs theory, the source of absolute rent in the gold
>industry is surplus labor, just like all forms of surplus-value.

That goes without saying, but it can't possibly answer the question at 
hand, since surplus labor is also the basis for profit in the sectors that 
don't enjoy absolute rent.  Therefore an additional condition is needed 
besides the recognition that profit, rent (and interest) are all 
manifestations of surplus value and thus surplus labor.  It's not clear to 
me yet what you understand that extra condition to be.

>   As I
>have already explained in several recent posts, under Marxs assumption of
>a lower than average composition of capital in the least productive gold
>mines, and the additional assumption of equal rates of surplus-value
>(i.e. no monopsony power in the labor market), the surplus-value produced
>in the gold industry is greater than the average profit, and the
>difference between the two is absolute rent.

Since we're speaking of *absolute* rent, we need not--and 
shouldn't--introduce the complication of having less or more productive 
gold mines, which speaks to the matter of differential rent. So the 
question is how it is that absolute rent arises on mines that are of equal 
productivity.  In particular:  what determines the level of absolute 
rent?  Is there some economic logic to its *quantitative* determination, or 
is its level randomly determined? Second, why doesn't capital mobility 
across sectors drive down the rate of return in the gold sector to that in 
other sectors, thus eliminating the absolute rent?

Specifically:  profit seeking capitalists in sectors receiving a lower rate 
of return than the gold industry would want to move into 
gold  production.  Were they to do so, it would reduce the aggregate supply 
in sectors they left, thus driving up the output price and the  rate of 
return in the sectors left behind.  However, remembering that C = Q*P in 
any case and that gold itself has no price, the resulting increases in 
commodity prices can only increase constant and variable capital costs in 
the gold industry, leading to a reduction in the rate of return.  In 
principle, capital mobility would ensure that this process continued until 
the intersectoral disparity in rates of return were eliminated.  What keeps 
that from happening in this case?

>  The average profit is equal
>to the general rate of profit (already determined prior to prices of
>production and rent) times the total capital invested in the gold
>industry.   In terms of equations:
>         surplus-value = new value ( = mL) - variable capital (taken as
>                                                                 given)

This assumes what must be proven, namely that an *inference* which has been 
demonstrated to hold only for the special and restrictive case that all 
commodities exchange at their respective values also holds in this more 
general setting.  As we know, Marx doesn't *define* surplus value in this 
way; it's rather the difference between the monetary magnitudes M' and M in 
the circuit of capital M-C-M', provided this corresponds to an augmentation 
in the total value produced.  Thus, by Marx's specification its the 
difference between two vector products of commodities *and their respective 
prices*: the first representing capitalist purchases, and the second 
representing capitalist sales.  In the special case of a commodity money 
system in which all commodities exchange at their respective values, this 
can be shown to translate into the expression you give above, where m 
equals the inverse of the value of the money commodity.

However, this inference from Marx's more fundamental definition of surplus 
value has not been demonstrated to generalize to less restrictive initial 
conditions.  To begin with, it obviously wouldn't hold in the case of fiat 
money, in which the value of money is effectively zero and thus m is 
undefined.  But second, it wouldn't generally hold in the case that 
commodity prices and values diverge (even with commodity money), for the 
simply reason that in that case it no longer holds that each commodity's 
price is just equal to m times its labor value, where m is again understood 
to represent the inverse of the value of money.

>         absolute rent = surplus-value - average profit ( = r Kg)
>No additional equation is needed to determine absolute rent in the gold
>industry.  Certainly no additional equation derived from an alternative
>physical "technique" to produce gold, as you suggest above.  Such physical
>techniques play no role in Marxs theory of surplus-value and absolute

The basis on which you reach this conclusion is not yet clear, since it's 
not known yet what determines the magnitude by which the rate of return in 
the gold industry exceeds the average profit rate, and especially it's not 
known why capital mobility doesn't lead to this differential being 
erased.  Furthermore, I don't see the basis for this even on your own 
terms, since "a lower than average composition of capital in the least 
productive gold mines" surely speaks to differences in physical input 

>Right, the other determinant is the money-value-added per hour (m); i.e.
>         S = m Ls

Agreed, if this is understood as an inference based on Marx's more 
fundamental definition of S, under the restrictive condition that all 
commodities exchange at their respective values.  This inference has not 
been shown to obtain under the more general conditions we're discussing, 
remembering that in any case C = Q*P and V=w*L, whether or not these 
relationships are made explicit in a given setting.

>My point is that with lands of unequal quality, which is the general case,
>there is BOTH differential rent on the more productive gold mines AND
>absolute rent on the least productive gold mines.  And I would like to
>know how Mainwaring and you determine absolute rent in this more general

I understood the sense of your earlier comments to be that only *absolute* 
rent was the transhistorical and thus the general case, and absolute rent 
need not presume mines of unequal quality.  Therefore it would seem 
preferable for us to agree on the significance of Mainwaring's 
representation for the case of pure absolute (intensive) rent, which 
demonstrates that the addition of a variable representing the absolute 
rental rate is matched by the addition of an equation, leaving the 
inconsistency problem intact.

Your question is thus whether this conclusion extends to the more 
complicated case of differential rent, based on mines of unequal 
quality.  Yes it does, as demonstrated in Mainwaring's equations 
(12.1)-(12.X).  In this more general setting, the number of equations for 
the differential rent-producing sector is augmented by a number of 
equations precisely equal to the number of distinct rental rates for the 
inframarginal land.  Thus, for example, if there are two levels of rent 
corresponding to three gradations of quality (the marginal land of course 
receiving no rent), the pure Sraffian approach would be to write

  Pk = (1+r)[(Sum over i:)PiEio] + wLio + aoTo
  Pk = (1+r)[(Sum over i:)PiEi1] +wLi1 + a1T1
  Pk = (1+r)[Sum over i:)PiEi2]   +wLi2

Thus in this case two new equations are added to go along with the two 
levels of differential rent.

> > But for what it's worth, in the Sraffian framework an
> > additional equation would have to be added for each additional level of
> > differential rent, so my original inconsistency conclusion continues to 
> hold.
>Yes, and an additional equation is also added to explain absolute rent is
>this case.  This equation is that absolute rent = 0, which is no
>explanation at all.  At least that is what Sraffa and Kurz do.  What
>equation does Mainwaring add in this case?

See above.

>   And what equation do you add?

That would depend on what explanation you give for the persistence of 
absolute rent in the face of capital mobility.  Once I know that, I can 
tell you.  Basically I want to make sure we're on the same page before 
trying to address your question.   But in any case, the pure Sraffian 
treatment, which at least has the benefit that it avoids your "mixing 
metaphors" critique, demonstrates that the inconsistency problem in the 
commodity money scenario is not eliminated by presence of absolute, or for 
that matter differential, rent.



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