Theories of Surplus Value, Part II, Chapter 8 - Part 33

The way Marx sets this out is, therefore, slightly misleading. An equilibrium condition of prices in this example would be arrived at where capital had effectively left spheres I and IV, and migrated to sphere III and V, although, in reality, as described above, this would be the result of accumulation taking place in III and V, and not in I and IV, or at least faster in the former than the latter.

Marx’s example is based on a percentage allocation, and so he retains the same figure of £1,000 of capital invested in each sphere. But, from his explanation of how these prices of production/average prices are formed, and an average rate of profit established, its clear that, in absolute terms, this is impossible.

If sphere I starts with £1,000 of capital, and so does sphere III, then its impossible for capital to move from I to III, so as to increase the supply of III, thereby reducing its price, and so reducing its profit to the average, and yet, at the end of that process, for I to still have £1,000 of capital invested the same as III. Either capital has relocated to bring about the average rate of profit, or it hasn't!

For the average price of I to rise from its exchange-value of £1100 to £1200, assuming no shift in demand, the supply of I must fall, which means less capital employed in that sphere, say a reduction to £900. Similarly, for the average price of III to fall from its exchange-value of £1300 to £1200, the supply of III must rise, which requires more capital to be advanced in this sphere, say to £1100, and similarly, capital might have to be reduced in sphere IV from £1000 to £950, whilst rising in sphere V from £1000 to £1050, so as to bring about the required reductions and rises in supply so as to modify average prices and establish an average rate of profit.

But, that would mean that the actual prices of production of the output in each sphere would not be £1200, in each case, but the cost price plus the 20% average profit, which is the definition of the price of production.

A more realistic picture of the actual situation might be something like this.

Sphere	£'s	Profit 20%	Price of Production
I	900	180	1080
II	1000	200	1200
III	1100	220	1320
IV	950	190	1140
V	1050	210	1260
Total	5000	1000	6000

Marx did not set it out this way for several reasons. Firstly, it requires that input prices be transformed simultaneously with output prices. As Marx says, in Capital III, although he realised that for a complete theory such a formulation was necessary, it was not required for his immediate task of explaining the basic mechanism by which competition transforms exchange-values into prices of production, via the reallocation of capital.

His task there was to show that the view of Ricardo and others, as with Rodbertus here, that market prices fluctuated around the exchange-value of commodities was wrong, and that, in fact, they fluctuated around this price of production, i.e. cost price plus average profit.

Marx also does not set out the situation as I have done above, because, as in other examples, he provides, he relates the situation to a purely proportional basis, for clarity of exposition. It is easier to see the equalisation of profit rates at 20%, and the movement of average prices if they are related in each case to a capital outlay of £1,000. It is just that the cost of this clarity of exposition also obscures the underlying reality of how that process of equalisation is effected.

The other reason that Marx could not provide such an explication, and the reason there can be no effective algebraic model for the resolution of the transformation problem is that it requires knowledge of the price elasticities of demand in each sphere. Marx certainly was aware of the concept of price elasticity of demand, as we will see later, but the mathematical tools for analysing it were only developed later by the marginalists.

But, without such knowledge, its impossible to arrive at a complete solution. For example, above I have arbitrarily chosen a figure of £900 as the amount of capital in sphere I as representing the extent to which supply would need to contract so as to cause the equilibrium/average price of I to rise to the price of production (cost price £900 + 20% = £1080. However, the actual amount by which supply would need to fall depends on the price elasticity of demand.

Suppose, Sphere I produces butter, and the previous situation represented a supply and demand for 1100 units. Capital leaves butter production and heads for sphere III. The capital invested in sphere I falls to £900, and now the supply of butter falls to 990 units. As a result of the reduction in supply of 110 units, the price rises from its previous price of £1 per unit to 1080/990 = £1.09 per unit.

However, assume Sphere I produces bread, and while consumers may switch from butter to margarine, in the event of a higher price of butter, there are fewer substitutes for bread. Consequently, any rise in the price of bread is likely to provoke a smaller reduction in demand, and so supply will need to fall by a smaller amount to cause the same rise in its price.

Suppose then that capital fell to £950, output would fall to 1045, and the price would rise to £1.09, giving a price of production for the output of £1140, which provides the 20% profit on the £950 of advanced capital. If instead, sphere I was involved in the production of some commodity which consumers could easily find substitutes for, if prices rose, then a much larger fall in supply would be required to bring about a rise in price to £1.09 per unit, to produce the average profit.

For example, supply of such a commodity might have to fall from 1100 units to 800 units. Where the £1,000 of capital was employed previously, this reduction in supply would require a capital of just £727. The 800 units would sell at the equilibrium price of £1.09, giving a return of £872, or 20% profit on the capital advanced.

Moreover, as I have set out elsewhere - The Transformation Problem and the Elasticity of Demand - it may not be possible for a condition of general equilibrium to be established on this basis, because there is nor reason why the amount of capital that must migrate into some particular sphere so as to raise supply, and reduce prices to the price of production, is equal to the amount of capital that must move from other spheres so as to reduce their supply and cause prices to rise to the price of production.

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