The basis of the initial formulation is to add together the capital in each sphere, which gives a figure for the total advanced capital, and to total the surplus value from each sphere. On that basis an average rate of profit can be determined as s/c+v. Marx and Engels describe the process by which this average rate of profit then acts to establish prices of production for commodities, around which market prices fluctuate, rather than the situation in pre-capitalist commodity production, where market prices fluctuated around the exchange value of commodities.
As Engels describes, in his Supplement to Capital III, it is the historical development of this process which explains why, as soon as capitalist commodity production begins, even on a fairly limited basis, in the 15th century, this brings to an end the exchange of commodities according to their exchange values, even where those commodities are not produced capitalistically. A capitalist producer will always seek to invest their capital where it can obtain the highest rate of profit. If we stick with the assumption that capital in each sphere turns over at the same rate, that will be where the organic composition of capital is lowest.
The process by which exchange values are then turned into prices of production, and by which the average rate of profit becomes established is fairly straightforward. As capital is accumulated in those spheres where the rate of profit is highest, the supply of commodities in that sphere will rise. This rise in supply, with no rise in demand, causes the prices of those commodities to fall below their exchange value. The supply of these commodities will continue to rise, and the price of them fall, so long as capital continues to enjoy a higher rate of profit in that sphere than in some other.
The reason that this process, as Engels says, means that all commodities cease to exchange at their exchange values, is also then quite straightforward. Suppose that cotton is produced by peasant producers. Its exchange value is, say £100 per ton. Cotton is an input, for peasant producers of yarn, and yarn is also an input for peasant producers of cotton cloth.
Suppose that cotton production offers capital the most profitable area for its investment. It provides capital with say 30% rate of profit, whereas the next most profitable sphere for investment would only return 25%. Capital then invests in cotton production. As other capitalists see the potential to obtain this 30% rate of profit, they too invest in this production. Consequently, the supply of cotton rises, and as it rises, the price of cotton progressively falls from £100 per ton, to £80, per ton, to £60 per ton.
At £80 per ton, the rate of profit for capital invested in this sphere might have fallen to say 27%, and when it falls to £60 per ton, the rate of profit will have fallen to 25%. If more capital is invested in cotton production, that would push the price below £60 per ton, and would reduce the rate of profit below 25%. But, capital can obtain 25% rate of profit, in the next most profitable sphere, say pottery manufacture, and so, rather than further capital accumulating in cotton production, it would begin to be invested in pottery manufacture, and the same sequence would unfold, in that sphere.
However, as the price of cotton falls, as a a result of increasing amounts of capital accumulating in that sphere, and the supply of cotton thereby continuing to rise, the peasant producers of yarn, now benefit from this lower price for their main material input. The peasant yarn producer, sees the price of yarn fall from £100 per ton to £80 per ton.
Suppose, the peasant producer of yarn originally laid out £20 for cotton, and added £20 of additional value by their labour. The exchange value of their output would then be £40. Now, capitalist production of cotton has caused its price to fall by 20%. The peasant yarn producer now only lays out £16 for their cotton, and continues to add £20 of value by their own labour. They sell their output of yarn, therefore, for £36, rather than £40. This is not a price of production for yarn, because yarn is not currently produced capitalistically. But, nor is it simply the exchange value of yarn, which continues to be £40, which is the value of the cotton consumed in its production, plus the value of the labour they add to it.
The £36 new price for yarn is a modified exchange value that arises, because the output of the capitalist cotton producer, is simultaneously the input of the peasant yarn producer, and as the price of cotton moves increasingly towards its price of production of £60 per ton, so this output price of cotton simultaneously modifies the input prices, and thereby also the output price of the peasant yarn producer. As Marx puts it,
“The foregoing statements have at any rate modified the original assumption concerning the determination of the cost-price of commodities. 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.”
(Capital III, Chapter 9)
When capital has become fully invested in cotton production, so that any further investment would cause the rate of profit to fall below the average rate of profit of 25%, the price of cotton will have fallen to £60 per ton, which is its price of production, i.e. the cost of production, c + v, plus the average profit on the advanced capital. The market price of cotton may fluctuate above and below this level due to short term variations in supply and demand.
At this level, the peasant yarn producer's output will have fallen in value to £12 for cotton, and £20 value added by labour = £32. But, the peasant yarn producer, is, in turn, a provider of inputs to the weaver, who producer cotton cloth. Just as the price of production of cotton, simultaneously modifies the market value of yarn, so this modified market value of yarn simultaneously modifies the market value of cotton cloth.
If initially, the yarn producer consumed £20 of cotton, and added £20 of value by their labour, and sold this to the weaver, for £40, who, in turn, added £20 of value by their labour, to produce cloth with a value of £60, so the transformation of the value of cotton into a price of production, not only simultaneously modifies the market value of yarn, but also thereby the market value of cloth. The cloth producer sees the price they pay for yarn fall first to £36, which modifies the price of their cloth to £56, and then to £32, which reduces the price of their cloth to £52.
But, this continues to apply, when yarn production and cloth production themselves succumb to capitalist production. The only difference then is that instead of the price of their output being made up of the cost of their constant capital, plus the value added by labour, it too becomes a price of production comprising the cost of their constant capital, and their variable capital, plus the average rate of profit on their advanced capital.
In the same way as described above, therefore, if the rate of profit in yarn production was higher than in cloth production, capital would accumulate in the former, the supply of yarn would rise, pushing yarn prices down towards their price of production, at which point, only the average rate of profit would be produced.
The process, then by which this average rate of profit becomes established – never, as Marx points out, as an established fact, because it is a continual process, of moving towards it, as changes in social productivity continually change values, and the rate of profit – is then, a continual movement of capital away from spheres where the rate of profit is low, and into those where it is high. That movement reduces supply in the former, and raises supply in the latter. That raises the prices of commodities in the former, and reduces them in the latter.
However, on the basis of this understanding, its quite clear that in moving beyond the initial formulation of the question of the transformation of values into prices of production, the original assumption about equal amounts of capital being invested in each sphere, can no longer hold. If there are just two spheres of production A and I, then if the starting point is that there is £100 of capital invested in each, whilst the rate of profit in A is 25%, and the rate of profit in I is 20%, then, because the equalisation of the rate of profit involves a movement of capital to A from I, it cannot be the case that, as this process unfolds, both spheres continue to be the same size.
In Marx's initial model, the capital in each sphere is indicated in percentage terms, so that the total capital in each sphere totals to 100, and that continues to be the case once the values are transformed into prices of production. But, this representation of the capital in percentage terms, obscures the fact that in absolute terms, this process necessitates that the actual mass and capital in each sphere is thereby also changed. In the above, example, it might be the case that in order to bring about the average rate of profit of 22.5% ((25% + 20%)/2), the capital invested in A would have to rise from £100 to £120, thereby increasing the supply of A commodities, and reducing their price to the price of production, whilst the capital employed in I, would have to fall to £80, reducing the supply of I commodities, and so raising their price towards the price of production.
Yet, there is no way of determining on the basis purely of values, how much capital would need to be accumulated in A, in order to bring about the necessary reduction in price to reach the price of production. That would depend upon the price elasticity of demand in A. Similarly, the capital consequently withdrawn from I, that migrates to A, will cause a reduction in the supply of I commodities, but there is no way of knowing purely on the basis of values, what effect any given reduction in capital, and so supply will have on the prices of I commodities, because again that will be dependent upon the elasticity of demand for I commodities.
Marx himself makes this point in Theories of Surplus Value, Chapter XII. He writes, in respect of price changes resulting from a movement of capital in agriculture, between different classes of land,
“For the price of IV to rise to to £1 12s., the individual value of III, the demand would not have to rise by 75 tons. This applies especially to the dominant agricultural product, where an insufficiency in supply will bring about a much greater rise in price than corresponds to the arithmetical deficiency in supply.”
In other words, Marx is basically describing a situation where, for a commodity that is a necessity, the staple food commodity, the price elasticity of demand is relatively inelastic. As supply falls short of demand, the price rises, but the rise in price does not choke of demand by a corresponding proportion. In order to bring demand and supply into balance, therefore, the price will need to rise by a proportionally greater amount than where the price elasticity of demand is relative elastic, so that any given rise in price would cause a proportionally greater reduction in demand.
Marx well understood the concept of elasticity of demand, long before it was theorised by the marginalists. For example, he also writes in Theories of Surplus Value,
“The same value can be embodied in very different quantities [of commodities]. But the use-value—consumption—depends not on value, but on the quantity. It is quite unintelligible why I should buy six knives because I can get them for the same price that I previously paid for one.” (TOSV3 p 118-9)
Unfortunately, at the time Marx was writing, he did not have the analytical tools that the marginalists later developed to be able to measure such elasticities.
Unfortunately, at the time Marx was writing, he did not have the analytical tools that the marginalists later developed to be able to measure such elasticities.
Suppose we take an economy with the two spheres A and I above. In I, its capital is comprised:
c 50 + v 50 + s 25 = 125.
A's capital is comprised:
c 60 + v 40 + s 20 = 120.
In that case, the rate of profit in I is 25%, and in A 20%. The average rate of profit is 22.5%. In order for both capitals to obtain this average rate of profit, capital must leave A, and migrate to I. The supply of I commodities will then rise, reducing their price to the price of production, and similarly the supply of A commodities will decline raising their price to the price of production.
In order to examine this, its necessary to also consider the actual mass of capital employed, rather than just its percentage composition, and to consider the actual volume of output. For ease of calculation, we can assume that these initial proportional relations are also absolute amounts of capital. In other words, in I, £50 of constant and variable capital is employed, and in A £60 of constant capital, and £40 of variable capital. (It doesn't matter whether this is £'s, $'s, or €'s, or whether this represents thousands, millions or billions)
We can also assume that the actual output of I is 125 units, and of A is 120 units. In that case, the price per unit of I commodities is £1, and also the price per unit of A commodities is £1. However, we know that the rate of profit in I is above the average, and is below the average in A. Put another way, if both spheres are to produce the average rate of profit, the unit price of I commodities must fall, and the unit price of A commodities must rise.
If we examine the value composition of a unit of output in each sphere, it is, in I:
c 50/125 + v 50/125 + s 25/125 = c £0.40 + v £0.40 + s £0.20 = £1.
In A, it is:
c 60/120 + v 40/120 + s 20/120 = c £0.50 + v £0.33 + s £0.17 = £1.
In order for I to obtain the average rate of profit of 22.5%, the unit price of its commodities must fall. The price of production for each unit will be:
c £0.40 + v £0.40 = k £0.80 + p £0.18 = £0.98.
Similarly, for A to obtain the average rate of profit, the unit price of its output will have to rise:
c £0.50 + v £0.33 = k £0.83 + p £0.19 = £1.02
But, as Marx says, above, how much supply of I will have to rise to reduce the unit price from £1.00 to £0.98, will depend upon what type of commodity I is, and what the price elasticity for it is. If I is a “dominant agricultural product, where an insufficiency in supply will bring about a much greater rise in price than corresponds to the arithmetical deficiency in supply”, then similarly, it may not require a large rise in supply, in excess of demand, to cause the price to fall by the required amount.
Suppose, however, that, in order to reduce the price of I from £1.00 per unit to £0.98 per unit, the supply must rise by 10% to 137.5 units. In that case, where previously in I, the capital employed consisted of £50 of constant capital and £50 of variable capital, this would also now have to be increased in absolute terms by 10%, to effect this 10% increase in the supply of I commodities. The actual situation in sphere I would then be:
c 55 + v 55 = k £110.00 + p £24.75 = £134.75.
The price of production of I's output then is £134.75, and this now represents 137.5 units, with a unit price of £0.98.
The capital employed in I has then risen by £10, but this implies that the capital employed in A falls by £10. The capital employed in A would then be:
c 54 + v 36 = k £90.00 + p £20.25 = £110.25
The total capital employed then remains £200 as under prices determined by exchange values; and similarly the total profit is £45, as before, and the total prices of commodities is £245, the same as the total value of commodities.
However, there is a problem here. The increase in the capital in I was determined on the basis of the need for the unit price of I commodities to fall to £0.98 per unit, and, in turn, on the basis that to effect this reduction, supply would have to rise by 10%, requiring £10 of capital to be transferred from A to I. But, there is no reason why £10 of capital having been removed from A, and causing a 10% reduction in the supply of A commodities will result in the price of A commodities rising from £1.00 to £1.02, which is what is required for capital employed in A to obtain the average rate of profit.
Exactly how, the price of A will respond to a 10% reduction in supply, will again depend on the elasticity of demand for A commodities, just as the elasticity of demand for I commodities, determined that the supply of those commodities would have to rise by 10% to effect the fall in price from £1 per unit to £0.98 per unit.
It could be argued that the elasticity of demand for A and I, as the only two commodities, mutually influence each other. But, that would be to make a variant of the error of Say's Law. In fact, in a money economy, A and I here are, of course, not the only commodities, because in addition to them is the general commodity money. If 10% of capital is withdrawn from the production of A, the supply of A commodities will fall by 10% from 120 to 108. But, unless we know what the elasticity of demand for A commodities is, its impossible to know what effect this reduction in supply will have on the price of A commodities.
On the one hand, if demand for A is relatively inelastic, the initial demand for 120 units may require the price to rise substantially, in order to choke it back to the 108 units of supply. If, in order to reduce demand to the available 108 units of supply, the price per unit rises not to £1.02, but to £1.05, then that would mean that there would be insufficient monetary demand required to buy the 137.5 units of I, at the price of production of £0.98. That would mean that the unit price of I commodities would have to fall below £0.98.
In that case, in terms of realised profits, A would be making a higher rate of profit than I, which would lead to a flow back of capital from I to A, increasing the supply of A, and reducing the supply of I, whilst raising the price of I and lowering the price of A.
On the other hand, if the demand for A is relatively elastic, the demand may be cut from 120 units to 108 units, even if the price rises to only £1.01. At that price, capital employed in A will still make less than average profits. In order to raise the price per unit to £1.02 it may be necessary to reduce supply by a larger amount. Suppose that at a price of £1.02 per unit for the 108 units supplied, demand falls to just 100 units, there would then be an overproduction of A, and the immediate consequence would be a fall in the market price of A.
Capital would be withdrawn from A, so as to reduce supply to 100 units, so that demand was met. It could be that this capital would migrate to the production of I, but as set out above, that in turn depends upon there being sufficient demand for the resultant increased demand for I commodities, which again depends upon the elasticity of demand for I.
Alternatively, it could be that the consequence is that capital is simply withdrawn. Consumers faced with the higher price of A commodities might reduce their demand from 120 to 100, but they may not increase their demand for I commodities correspondingly. Instead they might decide to simply hold on to money.
As Marx puts it in Theories of Surplus Value,
“At a given moment, the supply of all commodities can be greater than the demand for all commodities, since the demand for the general commodity, money, exchange-value, is greater than the demand for all particular commodities, in other words the motive to turn the commodity into money, to realise its exchange-value, prevails over the motive to transform the commodity again into use-value.” (TOSV2 p 505)
In other words, the actual process whereby the price of production of commodities is determined, and that capital is reallocated from one sphere to another to bring about such prices of production, and consequently an average rate of profit, across all spheres of production, is far more complicated once the analysis moves from the abstract level of pure value relations, and the consequences for supply, to include the effects of competition and demand, which thereby effects the determination of actual market prices.
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