“Schmidt strayed into this bypath when quite close to the solution, because he believed that he needed nothing short of a mathematical formula to demonstrate the conformance of the average price of every individual commodity with the law of value.” (p 13)
“Sombart, as well as Schmidt, — I mention the illustrious Loria merely as an amusing vulgar-economist foil — does not make sufficient allowance for the fact that we are dealing here not only with a purely logical process, but with a historical process, and its explanatory reflection in thought, the logical pursuance of its inner connections.” (The Law Of Value and Rate of Profit, p 895)
Resolution of the transformation of exchange-values into prices of production is a lengthy and continuous process, which also involves the movement of capital from one sphere to another. A mathematical formula may be an approximation of the equilibrium market prices, that may result, at the end of that process, but it can never describe the actual process itself. For example, to know how much capital needs to move from sphere A to sphere B, to equalise profits, it is necessary to know how demand will react to any change in price. In other words, we need to know the price elasticity of demand in each sphere.
Suppose sphere A has a below average organic composition, and B above average. Capital moves from B to A. The price of A commodities falls. However, the elasticity of demand for A is high. As prices fall, demand rises sharply, soaking up the additional supply. Prices and profits remain higher than B. So, increasingly more capital has to move to A until a point is reached where elasticity falls, and demand no longer rises sharply with every fall in price. The consequence is that large amounts of capital have had to be removed from production of B before profit rates are equalised.
By contrast, if demand for A is inelastic, any fall in price will have little effect on increasing demand. A relatively small increase in supply will create the required fall in price to equalise profits, and so less capital will need to be withdrawn from B. That is part of the weakness of Marx’s presentation here. He says,
“Let us assume that the five different investments I to V of the foregoing illustration belong to one man.” (p 159)
He then goes on to describe how, for each of these capitals, the constant and variable capital would be known, and thereby the cost prices of each commodity. The owner would have to set the market prices of each commodity according to these cost-prices, because, at minimum, the market price must recover the cost of the capital consumed in production.
“But as regards the different quantities of surplus-value, or profit, produced by I to V, they might easily be regarded by the capitalist as profit on his advanced aggregate capital, so that each 100 units would get their definite aliquot part. Hence, the cost-prices of the commodities produced in the various departments I to V would be different; but that portion of their selling price derived from the profit added per 100 capital would be the same for all these commodities. The aggregate price of the commodities I to V would therefore equal their aggregate value, i. e., the sum of the cost-prices I to V plus the sum of the surplus-values, or profits, produced in I to V. It would hence actually be the money-expression of the total quantity of past and newly applied labour incorporated in commodities I to V. And in the same way the sum of the prices of production of all commodities produced in society — the totality of all branches of production — is equal to the sum of their values.” (p 159-60)
However, on the basis that I previously set out, its clear why this is simply not possible. If we take Department V, from Marx’s example, the exchange value of this commodity is indicated as 20. If we assume that on the basis of exchange values, demand and supply for V are in equilibrium at this price, then any variation from it must disturb that equilibrium. In fact, the price of production is indicated as 37, an almost doubling of the price. Consequently, the owner of this business could try to share out his overall profit, by increasing the market price of V in this way, but it would inevitably fail, because at this price, demand would likely collapse, and they would be left with large amounts of unsold production.
Similarly, with commodity III, if he reduces its price from 131 to 113, he will find that demand rises way above his output. The only way this could be resolved is by reducing the supply of V, and increasing the supply of III, with a consequent shift of capital from one sphere to the other.
In fact, Marx realised this, and in his historical explication of the process, he describes precisely this shift of capital from one sphere to another, and he also refers to the issue of demand elasticity. But, he does not incorporate it into his models. That is consistent with Marx's method, whereby he sets out the bare bones of a process, to highlight the main features, and then builds up the complexity around that skeleton, to bring it closer to reality. He intended to deal with all of these factors, like demand elasticity and so on later, in his analysis of competition. Similarly, he also understood that it was necessary to transform input prices simultaneously with output prices, because the latter, at the same time, comprise the former for some other capital. Yet, he did not do so, instead for now just noting the requirement to do so.
“We had originally assumed that the cost-price of a commodity equalled the value of the commodities consumed in its production. But for the buyer the price of production of a specific commodity is its cost-price, and may thus pass as cost-price into the prices of other commodities. Since the price of production may differ from the value of a commodity, it follows that the cost-price of a commodity containing this price of production of another commodity may also stand above or below that portion of its total value derived from the value of the means of production consumed by it. It is necessary to remember this modified significance of the cost-price, and to bear in mind that there is always the possibility of an error if the cost-price of a commodity in any particular sphere is identified with the value of the means of production consumed by it. Our present analysis does not necessitate a closer examination of this point.” (p 164-5)
In other words, if A is an input for B, the exchange value of A might be 100, whilst its price of production might be 50. But, when the producer of B, purchases A as an input, they buy it at its price of production, not its exchange value. For B, the price of production of A, is now its cost-price. If previously we had two firms, one capitalist, and one non-capitalist, so that A's output is priced as price of production, and B's is not:-
A
c 30 +v 10 + s 60; C = 40, s' = 600%, r' = 150%
B
c 100 + v 10 + 10; C = 110, s' = 100%, r' = 9.1%
we would now have
A
c 30 + v 10 + p 10 = 50; C = 40, r' = 25%
B
c 50 + v 10 + p 10 = 70; C = 60, p' = 16.6%
So, although B is not a capitalist firm, and its commodity is not priced in terms of a price of production, because it does not take part in the sharing out of the total surplus value, the price of its commodity is still affected by the fact that the producer of its input A is a capitalist firm, and the price of A's output falls, as a price of production, compared to its previous price, determined by exchange value. The price of B now falls from 120 to 70, as a result of the fall in the price of input A. Even though, B as a non-capitalist producer does not share in the total surplus value, and its output is not priced as a price of production, the rate of profit for B is still affected by this change. It rises from 9.1% to 16.6%, simply because its advanced “capital” has fallen from 110 to 60.
This is consistent with Marx's historical-logical method. If we consider yarn production, for a long time capitalist producers of yarn would have been able to take advantage of high market prices, determined on the basis of exchange value, to make high profits, because non-capitalist production remained dominant and determined market prices. Weavers would continue to buy yarn at that price, and it would continue to appear in their cost-price accordingly. It is only as capitalist production of yarn increases that the market price falls below the exchange value, as supply exceeds demand at the old price. At this new market price not only does demand for yarn rise, but this new market price becomes itself a component of the cost-price of the weaver, so the price of woven cloth falls, stimulating a rise in demand for cloth.
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