Lack of A Formal Proof
Marx's critics interpreting his models often argue he keeps assuming what he needs to explain, because rather than really "transforming values into prices" by some quantitative mapping procedure, such that prices are truly deduced from labour-values, he either (1) equates values and prices, or else (2) he combines both values and prices in one equation.
Thus, for example, either Marx infers a rate of profit from a given capital composition and a given quantity of surplus-value, or else he assumes a rate of profit in order to find the amount of surplus-value applying to a given quantity of capital invested. That might be fine if the aim is to just investigate what profit an enterprise or sector would receive on average, having produced a certain output value with a certain capital composition. But this manoeuvre of itself cannot contain any formal proof of a necessary quantitative relationship between values and prices, nor a formal proof that capitals of the same size but different compositions (and consequently different expenditures of labour-time) must obtain the same rate of profit. It remains only a theory.
Marx insists both that output prices obtained will necessarily deviate from values produced, but also that the sum of prices would equal to the sum of values in the pure case, yet, critics claim, he fails to show quantitatively how a distribution process could then occur such that price magnitudes map onto value magnitudes, and such that a uniform profit rate returns equal profits to capitals of equal sizes (a mapping relation is used here in the mathematical sense of a bijective morphism, involving one-to-one correspondence between value quantities and price quantities via mathematical equations). In that case, there is again no formal proof of any necessary relationship between values and prices, and Marx's manuscript really seems an endless, pointless theoretical detour leading nowhere. In modelling, simple logical paradoxes appear of the type that:
- in a static model, it is impossible to uphold the postulate of a uniform rate of profit and the postulate of total values=total prices at the same time;
- to find production-prices, a uniform rate of profit must be assumed, while at the same time to find a uniform rate of profit, production-prices must already be assumed;
- a price level must be assumed, rather than be deduced from labour-values.
All these conceptual and logical issues mentioned become crucial when attempts are made to model value and price aggregates mathematically to study capitalist competition. Different kinds of theoretical assumptions or interpretations will obviously lead to very different results.
Read more about this topic: Prices Of Production, Facts and Logic
Famous quotes containing the words lack of a, lack of, lack, formal and/or proof:
“Once one is caught up into the material world not one person in ten thousand finds the time to form literary taste, to examine the validity of philosophic concepts for himself, or to form what, for lack of a better phrase, I might call the wise and tragic sense of life.”
—F. Scott Fitzgerald (1896–1940)
“[The satirist] must fully possess, at least in the world of the imagination, the quality the lack of which he is deriding in others.”
—Rebecca West (1892–1983)
“The particular source of frustration of women observing their own self-study and measuring their worth as women by the distance they kept from men necessitated that a distance be kept, and so what vindicated them also poured fuel on the furnace of their rage. One delight presumed another dissatisfaction, but their hatefulness confessed to their own lack of power to please. They hated men because they needed husbands, and they loathed the men they chased away for going.”
—Alexander Theroux (b. 1940)
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“When children feel good about themselves, it’s like a snowball rolling downhill. They are continually able to recognize and integrate new proof of their value as they grow and mature.”
—Stephanie Martson (20th century)