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Pretty often I hear someone saying stuff like "The pound is worth more than the US Dollar" or "The Kiwi Dollar is worth less than the Euro".

Well, technically it is correct that 1 pound buys me more than 1 USD, and that 1 EUR buys me more than 1 NZD.

But I always found these statements to be meaningless, because it doesn't tell me anything at all about how the economies of the two countries compare. In addition, couldn't a country decide (I think Russia did it in the 90s) that from now on, to redefine the currency so that wages and prices and everything money-related gets scaled by the same factor?

So if I tell you that "1 unit of currency X buys you 2 units of currency Y", can you deduce anything of interest from that statement?

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No. An exchange rate tells you the exchange rate, that's all. Changes in exchange rates are a little more interesting because they suggest economic changes (or anticipation of such), but since the exchange rate is the composite of many economic forces, determining what changes may be in action from an exchange rate change is not really possible.

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Relative changes in rates are significant.

Why? Exchange rates encourage cross-border trade. For example, I live in an area that is now popular with Canadian tourists, mostly due to the favorable exchange rates.

Changes in exchange rates between trading partners can affect trade balance as well. The US "strong dollar" policy made US exports expensive and imports cheaper, which encouraged more imports.

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