Suppose that in society consumer preferences are such that the owners of potatoes like carrots so much that they are prepared to exchange 1kg. of potatoes for only 1 kg of carrots. But, 1 kg of carrots requires only ½ day to produce, compared to potatoes, which requires 1 day to produce 1 kg. For observant producers, they will see an opportunity for profit. They will switch all of their production from potatoes, or any other commodity, to carrots. In 100 days, they will now produce 200 kg. of carrots, which they will be able to exchange for 200 kg of potatoes, where previously they would only have been able to obtain 100 kg of potatoes, from their labour. As the supply of carrots rises, and rises, whilst the supply of potatoes continues to fall, this changed relation of supply to demand will bring about a fall in the market price of carrots measured in potatoes.
At any carrot price of potatoes less than 2:1, there will be advantage in producing carrots rather than potatoes, and supply of carrots will then continue to rise relative to potatoes. What determines that, however much the relative preference for carrots, as opposed to potatoes, the locus around which their rate of exchange is 2:1? It is that this is the relation of the amount of labour-time required to produce carrots as opposed to potatoes.
Suppose that 1 kg of potatoes exchanges for 1 gram of gold, which also requires 1 day of labour to produce. Commodity producers who divert all of their production into carrot production may have no great desire for potatoes themselves, but, now, 1 day of their labour produces 2 kg. of carrots, which exchanges for 2 kg. of potatoes. But, 1 day of their labour produces only 1 kg of potatoes. So, again, commodity producers would have an incentive to spend 100 days producing 200 kg. of carrots, which they exchange for 200 kg. of potatoes, which they then subsequently exchange for 200 grams of gold, which acts as money, and is readily exchangeable for any other commodity.
Now, the carrot producer has obtained 200 grams of gold, whereas previously, in producing potatoes, they would only have obtained 100 grams of gold. Even if the various producers of these commodities did not notice these disparities, the merchants who, increasingly, are the means by which the exchanges are effected, certainly would, and would recognise the potential for profits in arbitraging these differences. The merchant would be quite happy to give 1 gram of gold to the carrot producer, in exchange for 2 kg. of carrots, and then to sell these 2 kg. of carrots to the potato producers for 2 grams of gold. They have then doubled their holding of gold from 1 gram to 2 grams. They are then in a position to use these 2 grams of gold to buy 4 kg. of carrots and so on.
Competition, between merchants, for these profits might first drive up the gold price of carrots, so that 2 grams of gold had to be paid for 2 kg. of carrots, but, then there is the question of the gold producers to consider. In order to obtain gold to buy carrots, the merchants must sell carrots and potatoes to the gold producer. If the gold price of carrots rises, the merchants demand for gold will rise, and so the price they have to pay for gold in terms of carrots and potatoes will rise. If the competition between merchants pushed up the price of carrots so that the merchant profit disappeared, and carrot producers accumulated gold, the merchants would themselves have an incentive to use their capital to produce carrots, raising the supply and pushing down the price.
Only on the basis that 1 kg. of potatoes exchanges for 1 gram of gold, which also exchanges for 2 kg. of carrots will a sustainable position arise, and this is determined by the fact that 1 day of labour is required for the production of 1 kg of potatoes, 1 gram of gold, or 2 kg. of carrots. Of course, it can be objected, as Bohm-Bawerk does, that the labour used in producing potatoes differs from that used in producing gold, which, in turn, differs to that used in producing carrots. That is true, but all that means, as Marx makes clear, is that the measure of this quantity of labour is undertaken not in units of each specific type of concrete labour, but in terms of a common, average, abstract unit of labour-time. We do not measure length by actual human feet, each of which differs in length, but by an average foot, settled upon and agreed as a standard unit of measurement.
And, the same is true of metres, the definition of which has been varied over time, in order to obtain an ever more accurate and invariable standard of measurement, which has become necessary, as space travel, has made even the slightest discrepancy meaningful over astronomical distances.
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