Exposition and refutation of the transformation problem of Bortkiewicz, dating from 1922: https://libcom.org/library/one-contr...lom-dvolajtski
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Many people have desperately tried to refute the Transformation Problem to defend the LTV. While most of them are ineffectual there has been a charge lead by Andrew Kliman that claims if one interprets Marx in the form of a single system while accounting for time nothing Marx said is false. Many have used this argument to solve the Transformation Problem but these attempts are in vain due to issues with this Temporal Single-System Interpretation of Marx. While the TSSI approach is certainly an interesting way of looking at Marx the model lacks a coherent equilibrium models which invalidates the attacks on the transformation problem by TSSI advocates, also TSSI is inconsistent due problems in its methodology and logic.
THE TSSI APPROACH
The TSSI approach claims to have proven all of the following;
All of Marx's aggregate value-price equalities are true
Values cannot be negative
Profit cannot be positive unless surplus value is positive
Value production is no longer irrelevant to price and profit determination
The profit rate is invariant to the distribution of profit
Productivity in luxury industries affects the rate of profit
Labor saving devices can cause the rate of profit to fall
These claims will be referred to as their respective letter in the above list. Because adherents to the TSSI system claim that the TSSI proves a-g thus proving Marx correct it is the best interpretation of Marx's original theories.
The TSSI approach is as follows; for any given “t” let pt be the price vector, λt be the value vector, and gt be the value-price deviation vector. Furthermore let (A, l) be technology where A is the input output matrix and l is the direct labor input vector. Both A and l are assumed to be to be constant for simplicity. Let xt be a vector of activities at “t” and τt denote the TSSI MELT (Monetary Expression of Labor Time). Let πrt be aggregate real profits. Finally let St be aggregate surplus value. With these TSSI advocates assert the following equations;
pt+1 = τt+1((ptA/τt)+gt+l)
λt+1 = (1/τt)ptA+l
gtxt = 0
πrt = [(pt+1/1+i)-ptA-ptbwl]xt
St = [λt+1-(ptA/τt)-(ptbwl/τt)]xt
pt+1=(1+rt)pt(A+bwl)
rt = (stxt)/(ptAxt+ptbwlxt)/τt
For TSSI to be proven wrong one or more of the equations links to the statement or the equation itself must be proven wrong thus vindicating the insolvency of the transformation problem.
METHODOLOGICAL FLAWS
DICHOTOMY OF CRITICISMS OF MARX AND TSSI
First there are methodological problems with the TSSI approach to Marxist theory. For the sake of argument equations 1-3 are to be held true, even though equation 3 is imposed, not derived from any meaningful train of thought. Even if equations 1-5 are to be held the TSSI rhetoric that criticisms of TSSI are criticisms of Marx are invalid, Marxists can and do reject TSSI. In saying that TSSI is the best interpretation of Marx TSSI advocates say that claims a-g adequately sum up Marx’s ideology despite never proving it.
INTERPRETATION AND THEORY
Kliman also argued that TSSI isn’t a theory but an interpretation of Marx, thus whether Marx is correct or not has no bearing on TSSI. This is false because if it were shown that Marx was empirically incorrect then TSSI as an interpretation is also false because it rests on Marx’s theory. Thus there should be a currently unstated premise that TSSI in claims a-g captures what is important and true in Marxian theory in the current day but this is noticeably lacking in the current form of TSSI.
EQUILIBRIUM MODEL FLAWS
Another issue of the TSSI approach is its lack of a clear equilibrium concept or distinction between dynamics and a static disequilibrium. The model also lacks coherent methodology for its equilibrium and disequilibrium models. Unless equilibrium is defined as static with market clearing disequilibrium has no bearing on equations 1-7 because it could be described as a dynamic equilibrium where the market clears at every stage. On top of this the vector pt+1 is determined on a universal uniform profit rate which is a long run aspect, according to TSSI advocates “this is a particular case”, but the TSSI approach holds that this particular case applies outside of the equilibrium by assuming the rate of profit is equal to the average. However if market prices don't 100% line up with the prices of production the assumption that the average is uniform is unjustified. This lack of coherent equilibrium models and the assumptions of pt+1 invalidate the TSSI solution of the transformation problem.
LOGICAL FLAWS
TAUTOLOGICAL EQUATIONS
The justifications of claims a-g lack a real backing and tautologically follow from the equations, instead of proving a-g Kliman is able to merely restate them in a mathematical form thanks to arbitrary assumptions. For example claims a and c rest on equation 3 but 3 is never proven, simply imposed. Claim b follows from the assumption that pt >= 0. Claims d-f rely on claim 7 because the price rate of profit is defined as the average value rate of profit. All claims rest on the assumption that the MELT is positive at all times despite it's un-determinability as claimed by some TSSI advocates.
OKISHIO’S THEOREM AND FMT
TSSI is flawed on logical grounds in other places as well. To prove claim G TSSI advocates must disprove Okishio’s theorem and to prove claim C they must disprove the FMT. However the TSSI refutations are hardly true refutations, the FMT and Okishio’s theorem are mathematically true. The refutations don't mathematically refute the theorems, they only show that once assumptions are violated the theorems don't hold. But these criticisms are hardly their own, they have been known of for decades. In order for actual criticisms adherents to the TSSI would have to construct a theoretical relevant model in which Okishio’s theorem and the FMT do not hold instead of picking at the assumptions of the theorems.
THE MELT
The best example of logical flaws in the TSSI approach is the treatment of the monetary expression of labor hours, or MELT. Kliman fails to put forward a coherent definition without contradicting it later. Even if the definition of the MELT was consistent the assumption that τt = 1 is imposed without explanation. However Kliman put forward this definition of the MELT; “the ratio of a unit of money to the amount of labor commanded by a unit of money”, in mathematical terms;
τt+1 = (pt+1xt)/(λt+1xt)
However this is just a fancy way to put forward equations 1-3, it's by no means a coherent definition like Kliman implies. On top of the fact that the ratio Kliman puts forward is by no means a definition it assumes that liquidity preference is nil which contradicts Marx's original theory which invalidates TSSI as a true approach to Marx.
Kliman put forward another definition of the MELT which is
Price = MELT × Labor commanded
However this mystical “labor commanded” isn't defined by any writings on TSSI and instead one is supposed to blindly accept this, however through the ith equation of equation 1 we can determine this “labor commanded”, thus the definition of the MELT is as follows
pit+1 = τt+1[(Σpj,taji/τt)+gi,t+li,t]
Where the bracketed statement is labor commanded, however this is just another rewrite of previous equations, not a coherent definition of the MELT.
In all of Klimans definitions of the MELT the words may seem correct but he fails to provide a definition of the MELT that isn't rewriting previous equations leading to circular definitions. One can combine equations 1-3 to create
τt+1 = (τtpt+1x)/(ptAx+τtlx)
But this still doesn't properly define the MELT due to the rewriting’s circular nature.
TSSI advocates try to reconcile this with saying that the MELT has to be determined dynamically. This doesn't solve anything though because they still say it can be expressed by the previously stated ratios. But this distinction between the determination and expression doesn't solve anything because there is no adequate way to determine the MELT at t=0. While Kliman tries to avoid this by saying that the MELT isn't physically observable they run into the problem that a theoretical construct could do this. This approach is rejected because it would require an independent definition of the MELT that doesn't rewrite equations. Kliman goes on to state that τ0 can be expressed but not determined unless there in knowledge of everything before τ0. However the definitions of the MELT put forward require knowledge of τt-1 to know τt which leads to a problem of infinite regress unless this doesn't hold at τ0.
CLAIM “C” AND EPISTEMOLOGY
Finally TSSI attacks on NI about claim C say that in NI positive profit with negative surplus value is possible due to a negative NI MELT. This section will assume for argument's sake that the MELT as put forward by TSSI adherents is a coherent theory. This is an issue when the TSSI MELT is equal to the NI MELT in a stationary economy. One could attack this by saying that it's only equal in a special case. However according to TSSI epistemological theory a single example is enough to disprove generality even if the example was arbitrarily constructed. Thus positive profit and negative surplus value is possible in TSSI interpretations. To solve this one must either reject TSSI epistemology or claim C, however in doing so they invalidate the TSSI approach.
CONCLUSION
As seen above the TSSI model lacks coherent equilibrium models, and has severe methodological and logical problems which leads to the conclusion that While the TSSI approach is certainly an interesting way of looking at Marx the model lacks a coherent equilibrium models which invalidates the attacks on the transformation problem by TSSI advocates, also TSSI is inconsistent due problems in its methodology and logic.
Exposition and refutation of the transformation problem of Bortkiewicz, dating from 1922: https://libcom.org/library/one-contr...lom-dvolajtski