On the basis of these objectively determined quanta, the relations that produce various ratios – rate of surplus value, rate of profit, annual rate of profit – also continue to be objectively determined, as Marx sets out in Capital III, even when the prices of commodities are based on prices of production rather than exchange value.
Moreover, although the rate of interest, and rent are now seen to be based not on some objectively determined metric, but as resulting from these subjective preferences that produce different levels of demand and supply, nor are these prices arbitrary either. They move between upper and lower bounds which are set by objective conditions. On the one hand, the fact that the owner of land or capital will not loan it for free, and on the other that the borrowers of capital or land will not pay such a high price for it that it wipes out their profit.
Moreover, Marx's theory of value itself involves a certain degree of subjectivity, which interacts with the objective determination of values. For example, the measurement of value is determined by the quantity of abstract labour. With the development of a money commodity as the general commodity, then, as Marx sets out in Capital I, the labour involved in the production of this money-commodity similarly becomes the representative of general or abstract labour. But, labour is always expended as concrete labour, and any amount of expended concrete labour may represent more or less abstract labour. In other words, as Marx describes it, some particular concrete labour may represent complex, rather than simple, labour, and thereby create a greater mass of value in a given time.
The concrete labour of a tailor, for example, may represent twice as much abstract labour as that of a machine minder. But, as Marx points out, the determination of this multiple of complex to simple labour is not objectively determinable a priori. Whether an hour of labour by a tailor produces 2,3,4 or more times as much value as an hour of labour by a machine minder is only determined a posteriori, in the market, by the consumers of their products, and that is a subjective assessment by those consumers.
Similarly, as Marx sets out in Theories of Surplus Value Part 3, supply is a function of value, whereas demand is a function of use 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.”
And use value is a matter of subjective preference. The level of demand for any particular commodity, is a result of the sum of these subjective preferences at a particular price. Indeed, the level of aggregate demand itself is the result of the summation of such preferences, for all commodities, as against the preference for the general commodity money.
“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)
That does not change the objective determination of the value of the commodity, but the level of demand for any commodity does, in turn, affect the conditions under which the commodity itself is produced, and consequently the labour-time required for its production. If the demand for motor cars amounts to just a few hundred vehicles per year, there is no point advancing billions of pounds of capital to mass produce cars, which could not then be sold. Cars may be instead hand-built, or produced on small-scale assembly lines, and the cost of production, per car, will be relatively high. But, if the demand for cars extends into the millions per year, it becomes possible to produce on a mammoth scale, to utilise large-scale factories, industrial robots and so on, so that the labour-time required for production drops massively, causing the value of a car to fall, which, in turn, then leads to increased levels of demand, though as Marx states above, not necessarily a proportional increase of demand compared to the fall in price.
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