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Yes, somebody could use bitcoin to transfer wealth just as you described. How the currency conversion rate is determined is by supply and demand, just like any other thing that people buy. If lots of people buy bitcoin, demand increases, and vice versa. Price fluctuates based on changes in demand. The supply increases slowly and steadily from mining. So the exchange rate isn't determined by any one person or party, it's determined by the behavior of anyone selling or buying bitcoin.