It was just this fact that such tokens could just as easily function in place of the precious metals, that enabled fiat currencies, using paper money to be developed. The real relation between the Dollar and the Pound, Euro, Yen etc., therefore, is not what each represents in terms of gold, but how much abstract labour-time each represents. In other words, how much abstract labour-time, in the form of commodities, can I buy with $1 compared to what I can buy with £1 etc.
In a world of floating exchange rates, therefore, the determination of relative currency valuations is a function, not of their relation to quantities of gold – though even with wide fluctuations in the gold price, arbitrage should ensure its price in different currencies is the same – but of the relative levels of productivity in each currency area, which is the underlying value relation, which determines how much value is produced in an hour in country A as opposed to country B, as Marx discusses in Capital I – and the demand for and supply of each currency, which determines the market price. A currency like the dollar, that acts as world currency, will have high demand, because the majority of trade is denominated in it. To buy oil, you must obtain dollars, because oil is denominated in and bought and sold in dollars. To buy US commodities, or financial assets, you must first again obtain dollars. The demand for these financial assets, may also be a function of interest rates, so a country seeking to attract buyers of its currency will offer higher interest rates on its government bonds etc. But, as a fiat currency, the supply is simply a function of the liquidity created by the State, and the private banking and quasi-bank sector, mostly in the form of credit.
Its no wonder then that such money-dealing, alongside massive speculation in currency movements, has become a huge specialised business.
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