OWNERSHIP: Redress

["mark reiners" <markreiners@hotmail.com>]

While having no intention of returning to active engagement in this forum, 
for reasons stated at the end of my last submission in March, I have 
recently had sufficient time apart from other obligations to review some of 
the COG exchanges of the weeks since deciding to suspend my participation.  
In so doing, I have found an issue of profound theoretical import requiring 
clarifying redress.
There have been put forth both unsound claims for conventional analysis and 
unsound inferences drawn from them.  These have also been accompanied, one 
might add, by considerable undue self-congratulatory, credentials-based 
chest beating.  Both because I am convinced that these considerations go to 
the very core of why Binary critics are misguided in their increasingly 
strained or diversionary efforts to dismiss Binary theory, and in the 
interests of making sure that the COG/Ford Foundation records are not left 
without sound rebuttal to these errors of both claim and inference, I will 
briefly step out of the shadows to offer this redress.  The   redress will 
be on the relevant issues of the theory of Marginal Productivity, the 
Marginal Rate of Substitution (MRS) and Isoquant/Iso-cost analysis, and the 
erroneous claim that this analysis constitutes a basis of sufficient logical 
necessity to provide formal grounds for a dismissal of the foundational 
Binary productiveness propositions - not merely as "wrong", but as 
"hogwash", if memory serves.

Whether these claims stem my final submission, and thus were taking issue 
with my assertions in that installment regarding the limited relevance of 
substitution variability as providing any basis of logical necessity for 
invalidating the assertion of the perfect tracking of factor-shares with 
relative productiveness (within the parameters OF this variability), or that 
there is no a priori, universal way to characterize the L/K interface that 
would obtain for all production scenarios, - i.e., that each of these must 
be defined in a unique, scenario-specific manner - it is quite clear that a 
general argument is now being foisted off to the effect that these 
conventional MRS arguments provide some basis for invalidating Binary 
productiveness propositions generally.  In either case, they are incorrect.  
Just as an earlier participant was in error by previously asserting that 
symmetry arguments equate to a general claim of commutativity with respect 
to substitution, these more recent submissions are wildly misguided in 
uncritically subscribing to the MRS/Isoquant/Iso-cost characterization of 
production scenarios for reasons that I'll address shortly.  In fact, there 
is a subtle but deep connection between the failure of being able to 
substantiate and justify a general commutativity claim for symmetry, and the 
problems of the MRS/Isoquant/Iso-cost analysis.

Cutting immediately to the fundamental flaw in the MRS/Isoquant/ Iso-cost 
analysis, which renders it unsound as a general basis for dismissing Binary 
productiveness propositions, it will devolve onto a fallacious assumption 
inherent in this methodology that is either entirely unnoticed/overlooked or 
ignored by its practitioners.  In rushing to find justification for a 
wholesale formal dismissal of the foundational Binary productiveness 
propositions by invocation of the logic and mathematics of marginal 
productivity and the MRS/Isoquant/Iso-cost analysis, a both subtle yet 
glaring, as well as distinctly fatal, oversight is uncovered in the 
conventional wisdom.  When we examine the mathematics of MRS and the 
Isoquant/Iso-cost graphs representing them, the flawed assumption is hiding 
in plain sight.  It is blithely assumed, apparently on the basis of 
mathematical convention, that it is justified and/or relevant to treat the 
sloping line of the Isoquant, with respect to factors, as being comprised of 
a continuum; of being continuous, as opposed to being of a discrete or 
"quantum" nature.  This is profoundly important and it is wrong.  It will be 
illuminating to spell out why.

The analytic problem lies in the fact that the mathematics, and the 
assumption that the Isoquant slope may be legitimately treated as continuous 
with respect to factors, treats as perfectly relevant and meaningful as a 
basis for economic modeling the idea that factor substitution on a 
non-integer basis is sound.  The ontologic problem lies in the fact that it 
is NOT relevant to do so.  In short, for the MRS/Isoquant/Iso-cost analysis, 
and the theory of Marginal Productivity which largely rests on it, to be 
superior to and conceptually more sound than Binary Productiveness - indeed 
for it even to  simply be conceptually sound at all in itself - it must be 
able to operationally manifest and empirically substantiate what is implicit 
in the fact that the very MRS analysis implemented is based on the 
mathematical use of continuous functions.  In other words, for the theory of 
marginal productivity to be conceptually legitimate and real, it must be 
operationally possible and meaningful for factor substitution to be 
generally viable on a basis consistent with these continuous functions; 
i.e., it must be viable to actually physically substitute factors on a 
non-integer basis.  To reiterate with emphasis, the ontologic problem lies 
in the fact that it is NOT relevant to do so.  Why?

The very basis of the MRS/Isoquant/Iso-cost analysis is predicated on 
holding product quality, output and the nature of the L/K interface, defined 
by the technology in use, fixed as these factor amounts are altered.  The 
problem?  No actual level of output corresponding to either an incomplete or 
a completed production function is going to correspond to the implementation 
of a partial/fractional(less than integer/integer multiple) input of 
factor(s) since these are functionally of a clearly discrete, or "quantum", 
nature;i.e., a half, or a tenth, or .333… of a unit of L (labor, i.e., a 
human person) or K (capital tool: i.e., hammer, paint gun, metal press, 
robotic welder, etc.) is functionally meaningless.  Since the MRS/isoquant 
analysis requires that output (i.e., an executed production function) be 
held constant, the points comprising the sloping line of the Isoquant CANNOT 
be meaningfully continuous with respect to factors; they must necessarily be 
of a discrete/"quantum" nature, and NOT of a continuous nature.  As long as 
the line is envisioned as merely providing a source of graphic connection of 
these meaningful, discrete points of substitution, for the sake of visual 
convenience, clearly no harm is done.  When, however, on the basis of 
uncritical reliance on mathematical convention, the line, treated as a 
continuum, is used, instead, to conveniently rationalize the fabrication of 
an ontology that is not, in reality, there, great conceptual and modeling 
harm is done.

As just suggested, this all essentially places what turns out to be an 
impossible ontological and empirical burden on the conventional wisdom 
(except in the highly non-generic case of perfect substitution, which is, 
not insignificantly, of an integer/integer-multiple nature).  The reason 
this is so illuminates once again, if from a different perspective, the 
fallacious nature of an assumption that there is, necessarily, a 1:1 
relationship between cost/price dynamics, (remaining mindful of the 
distinction between product price and factor costs) and the entirely 
distinct production dynamics fixed by the engineering constraints which 
dictate the productive capabilities and limits of factors.  Contrary to the 
protestations of Binary critics and reflexive, uncritical adherents of the 
MRS/Isoquant/Iso-cost analysis, there is NO such relationship.  Further, 
attempts to force-feed such an imperative in the increasingly strained 
efforts to try to muster some definitive means by which to de-legitimize 
Binary productiveness leads to these revelations of the flawed nature of the 
MRS/Isoquant/Iso-cost analysis and the theory of Marginal Productivity that 
it is presumed this analysis substantiate.

There are any number of ways to illuminate this mathematically, but, since 
mathematics has been and so easily may be a source more of diversionary 
abstraction than conceptual illumination, suffice to say, initially, that it 
amounts to an unsound and unsupportable conflating as equivalent and 
inter-operable the two strata of causality mentioned above which are, in 
fact, hermetically distinct in operation.

As just indicated, arguing otherwise, as the Binary critics claiming that 
the MRS analysis constitutes a basis of logical and categorical necessity 
for dismissing Binary productiveness implicitly do, is effectively to assert 
that continuous price variability, which is what necessitates use of the 
continuum for the Isoquant, is a causal agent somehow capable by itself, per 
se, of actually altering the physical and/or engineering constraints of the 
participating production factors in some fashion - on the fly, as it were, 
and on a continuous basis, no less! - and thus magically allowing for factor 
substitution on other than an integer basis to be real.  This is 
transparently absurd.
In reality, the only thing that the methodology and results of the 
MRS/Isoquant/Iso-cost analysis allows us to properly infer is that 
such-and-such a result from an application of the mathematics (generally 
non-integer with respect to where this point will fall on the Isoquant of 
the factors) is the point of minimization of the cost function and, thus, 
that this point WOULD be the ideal point for substitution of factors.  It is 
NOT, in itself, anywhere nearly sufficient as a basis for inferring that 
substitution is actually physically viable at that ideal, cost-optimized 
point.  It does not and cannot supercede ontologic reality to insist that 
substitution IS, necessarily viable there.  That, however, is precisely what 
blind adherence to the theory of Marginal Productivity and the 
MRS/Isoquant/Iso-cost analysis require and, thus, why academically 
indoctrinated economists cannot get beyond their obstructed vision with 
respect to Binary productiveness.

In other words, the minimization of a cost function, for any given level of 
product quality, output and associated technological L/K interface 
determining the shape of the Isoquant, only allows us to determine where the 
IDEAL point of substitution lies.  The fact that minimizing the cost 
function, given these constraint criteria, may analytically allow/require 
moving down the Isoquant on the basis of a continuous function does NOT mean 
that actual substitution is physically viable continuously.  It is this 
flawed inference that the Binary critics are blindly leaping to.  To 
reiterate, this would require a direct causal relation between continuous 
price variability and variability of the actual physical/engineering 
constraints of the factors themselves with respect to their productive 
capabilities!  The transparent absurdity of this thought should clarify what 
I meant earlier when I said that this amounts to asserting the conflation of 
two distinct types of causality.  However admittedly subtle a point, this 
profoundly important and fatal oversight in the conventional analysis is a 
nearly comic case constituting a defacto placement of the inferential cart 
before the causal horse, and it will not wash.  Thus, we find that the 
conventional theory of marginal productivity has ontologic, and empirical 
problems far more profound than those the Binary critics wrongly claim 
Binary theory suffers from.

There are other aspects of the Lagrangian optimization mathematical nature 
of the MRS/Isoquant/Iso-cost methodology that preclude us from inferring 
anything more than location of this minimized ideal, but it is not necessary 
or substantively more illuminating to invoke them.  Merely pointing out the 
insurmountably severe ontologic and empirical discrepancy noted already is 
quite sufficient for anyone examining this issue with anything remotely 
resembling unbiased vision.

Further, if the Binary critics concede that actual substitution of factors 
cannot violate ontology by occurring on other than an integer basis, then 
they are immediately compelled to also concede that the conventional 
descriptions of production/substitution scenarios are then necessarily 
subject to precisely the same elasticity variabilities with respect to 
factor costs and substitution viability which I asserted prevail in the 
Binary context in my final regular COG installments.   Doing so then puts 
both the conventional wisdom and the Binary critics in the untenable 
position of recognizing that that the Isoquant continuity assumption is 
violated.

(It is also important to remain mindful here that factor-shares tracking 
Relative Productiveness pertains to the issue of assigning returns to 
factors available from the sale prices of products generated BY the factors 
involved in production, while MRS/Isoquant/Iso-cost analysis pertains to 
optimizing the balance of factors USED in that process of production on the 
basis of THEIR costs.  These are clearly distinct.  While the complexities 
of market interactions allow feedback effects between product price and 
factor costs, these are generally of a highly indirect causal nature 
entailing no simple 1:1 correspondence or any basis for inferring that the 
latter provides grounds for logically dissallowing legitimacy of the 
former.)

In either case, the theoretical soundness of the Binary proposition that 
factor shares track productiveness (WITHIN the elasticity variability 
parameter enforce vis-à-vis factor-cost and the substitution viability 
defined by the particular productiveness profile at hand) remains unscathed 
by MRS/Isoquant/Iso-cost arguments. It does so because of the fact that, 
while substitution conditions require holding output, quality and the 
technological nature of the L/K interface fixed, satisfaction of these 
criteria does NOT hold fixed Relative Productiveness - which shifts in exact 
conjunction with factor adjustments made in substitution.  Therefore, the 
tracking of shares of final-product sale price to participating factors with 
Relative Productiveness cannot, as I have said before, FAIL to obtain 
precisely because the latter is defined in terms of the balance of factors 
used, given output.

Lest the Binary critics scramble for some way to cast my observations in 
terms of some mystical Binary delusion, I offer the following direct quote 
from the Encyclopedia Britannica (not a source known for pathologically 
indulging in blind cult allegiance, nor for editorially letting pass the 
espousal of "hogwash"):

"Substitution Problems

Another difficulty arises from the fact that marginal productivity assumes 
that the factors of production can be added to each other in small 
quantities. If one must choose between adding one big machine or none at all 
to production, THE CONCEPT OF THE MARGINAL PRODUCT BECOMES UNWORKABLE.  THIS 
"LUMPINESS" CREATES AN INDETERMINACY IN THE DISTRIBUTION OF INCOME. From the 
viewpoint of the individual firm, this objection to neoclassical theory is 
more serious than from the macroeconomic viewpoint since in terms of the 
national economy almost all additions to labour and capital are very small. 
A related problem is that of substitution among factors. The production 
function implies that land, labour, and capital can be combined in varying 
proportions, that every conceivable input mix is possible. But in some cases 
the input mix is fixed (e.g., one operator at one machine), and IN THAT 
SITUATION THE NEOCLASSICAL THEORY BREAKS DOWN COMPLETELY BECAUSE THE 
MARGINAL PRODUCT FOR EVERY FACTOR IS ZERO."

(Emphases above are mine.  Further, strong exception might be taken, from a 
Binary perspective, on the equivication that this problem is less 
significant macro-economically. The reason is that it is precisely because 
conventional wisdom ignores the microeconomic distributional implications 
noted, allowing the rationalization which precludes serious consideration of 
universalization of capital ownership. This then frustrates the Binary 
prediction of massive, positive-feedback growth effects, which are clearly 
of a distinctly macro-economic character.)

All of these considerations further reveal what is completely ignored in the 
MRS/isoquant methodology: namely, what is it that determines/ defines the 
"quantum" (or "lumpiness" in Britannica's terms) of a given production 
function?  In Binary analysis this is immediate, though unique to every 
distinct production function and L/K interface: the relative productiveness 
profile of the factors cooperating to generate the output of the specified 
production function.
One may anticipate some grasping at straws by critics in terms of claiming 
that there is nothing to prohibit consideration of production functions 
fixed at something less than completion.  Even a moment of  reflection, 
however, will immediately lead to the realization, as already noted above, 
that this does absolutely nothing to change the fact that the participating 
factors are participating in the full functionality mandated by their 
"quantum", all/nothing nature.  One can drive a nail a tenth, or a third, or 
a half of the way to plane, (i.e., an incomplete production function) but a 
tenth, or a third, or a half OF a unit of labor (person) or capital (hammer, 
e.g.) will be useless to drive the nail at all.

Even recognizing that price/cost and demand fluctuation, because of the 
virtual infinity of distinct causal forces that may effect them, will 
effectively be manifest continuously - i.e. may generally fall between the 
integer/integer multiple Isoquant points designating physically and 
ontologically viable points for real substitution of the factors - does not 
change the fundamentally discrete/"quantum" ontology and functionality OF 
the factors.  Hence, this straw will not hold.  What this latter 
circumstance WILL do is something else.  Though it will explicitly compel 
introduction of the vastly less convenient or tractable hornet's nest of 
non-linear mathematics, this has the advantage of being far more pertinent 
to the reality of the complexity of the underlying causal dynamics than is 
the convenient use of continuous functions where the results are at complete 
odds with ontologic reality.

The above constitutes the fundamental flaw of conventional 
MRS/Isoquant/Iso-cost analysis and of the theory of Marginal Productivity.  
While it is true that the interaction of the discrete with the continuous 
will inconveniently complicate the tractability of the mathematics, (as it 
does far and wide at the interface of classical and quantum physics) and 
lead to the kind of non-linearities and elasticity variabilities that I 
touched on in my last submission, that is entirely incidental. This fact is 
no basis for pretending that waving the wand of a mathematical convention 
and ignoring reality justifies concluding that the mathematics is more real 
than the reality it should be in the service of modeling.  This was the 
point which John Medaille intuitively and appropriately made in his brief 
response to the flawed assertion of the Binary critic that he was sure that 
his MRS/Isoqaunt explication would turn out to allow some triumphant, 
general claim justifying dismissal of Binary productiveness propositions as 
"hogwash".  They are conceptually distinct, yes.  "Hogwash"?  Not by a LONG 
shot!  This should help to clarify that the real source of the "hogwash" 
lies elsewhere.  The dismissiveness will not hold precisely because the 
MRS/Isoquant/Iso-cost analysis is, itself, fundamentally flawed with this 
oversight.

As an aside of both conceptual and historical import, it is worth noting the 
highly germane analogy that it was precisely such a problem with a 
discrepancy between the discrete (or "quantum") and the continuous, 
appearing in the Blackbody radiation problem in physics just over a hundred 
years ago, which compelled the formulation of a discrete/"quantum" analysis 
of the spectrum.   This, in turn, is what led to the quantum revolution of 
physics.

The contentiousness with which the conventional economic wisdom is resisting 
(or ignoring) the Binary analysis strongly suggests that we are currently 
confronted with a similarly momentous crisis in economics - to the apparent 
obliviousness of academics and economists clinging to the fundamentally 
flawed MRS/Isoquant/Iso-cost analysis, and theory of Marginal Productivity.  
It is also of considerable interest and import to note that even the MIT 
Dictionary of Modern Economics points out that, "Iso-product curves are 
typically drawn as being convex to the origin because of THE ASSUMED 
substitutability of inputs…".  (Emphasis mine.)  These considerations 
emphatically serve to illuminate, at the very least, how deeply ambiguous 
the exact defining conditions of this assumption really are generally, and 
how blatantly and irreparably flawed they are specifically for wide swaths 
of the potential production horizon.

In conclusion, until I see GE, General Motors, AT&T, etc., etc. employing 
OTHER than integer increments of labor or capital - i.e., until I see them 
hiring one/sixteenth of a laborer or one/forty-second of a robotic welder or 
painter - I will continue to infer that the MRS/Isoquant analysis is as 
analytically artifactual with respect to characterizing production scenarios 
and substitution processes, as well as issues of distribution, as the 
epicycles of Ptolemy are to characterizing celestial orbits.  Until such 
time, I will also continue to emphatically contend that Binary 
productiveness is the FAR more sound - and, YES, paradigmatically distinct, 
as WELL as revolutionary - conceptual basis for such characterization and 
analysis by virtue of it reasoning instead, (consistent with ontologic 
reality) that it is the degree of contribution to output of participating 
factors that is appropriately incremental, but on a quantum basis defined by 
the productiveness profile of the specific L/K interface unique to each 
production function/scenario, and NOT continuous increments OF the 
participating factors, per se.

These considerations should help to make blazingly clear why the latter is 
utterly ridiculous.  What it should also serve to illuminate is that the 
actual locus of the "hogwash" that Binary critics generally seem just a tad 
too anxious to lay at the door of Binary theory lies, instead, in swallowing 
hook, line, sinker and complete fishing pole the MRS/Isoquant/Iso-cost 
analysis as gospel.  Apparently doing so for no better reason than the fact 
that it appears in economics textbooks.  It should serve to clarify that the 
locus of the "hogwash" is, in reality, acting on the uncritical reflex of 
assuming that conventional, textbook mathematical methodologies are 
themselves free of assumptions (in this case that a distinction between 
continuous or discrete mathematics is a matter of indifference - it is not) 
and that they may be blindly relied upon to provide some mystically 
unassailable, commanding Oracular claim to incontestable truth.  It should 
serve to clarify that the locus of the "hogwash" lies in elevating such 
methodologies to the level of laws passed down on stone tablets and Divinely 
inscribed with lightning.  THESE are more accurately identified as the 
sources of the "hogwash", NOT the Binary explications with respect to 
escalators, donkeys and sacks, or holes and shovels.  Those simply have 
against them the strike of not yet appearing in textbooks, nor yet having 
been adopted and sanctified as the conventional wisdom.

It should also serve to help put the lie to the vacuous assertion of other 
Binary critics that there remains some vast chasm of unresolved issues 
between recognizing that capital is responsible for most of the production 
and the proposition that it should thus be garnering a commensurate share of 
returns from that production.  Bull feathers and Turkey hooves!  We may even 
hope that it will help to remove the tortured mantle from these critics - 
though I elect not to hold my breath - of persisting with this tiresome and 
rather increasingly ridiculous martyr's pose of righteously standing against 
the onslaught and saving the World from the scourge of the "holes" in Binary 
theory.  I reiterate: the "holes" are not in Binary theory, they are in the 
inadequate understanding OF the theory by far too often inappropriately 
snide, pompous, and/or dismissive Binary critics.
There is a GREAT deal more that could be said about the problematic 
assumption that mathematical convention can always be blindly relied upon 
for argument salvation.  Many of these considerations enter into some of the 
most cutting edge research in both complexity theory, pure mathematics and 
even quantum physics - dealing, for instance, with how to analyze behavior 
of dependent variables when the conditions of dependency of those variables 
may, themselves, defy stable pre-definition due to contingency on 
self-organizing dynamics that are a global property of the system, and thus 
not amenable to reductionistic isolation - but, though related to some of 
our concerns here, this would take us WAY too far afield.
Sincerely,
MARK REINERS

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