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I've found a formula derivation in my international economics book, but I can't understand how it was derived.

It says

$ E P X = P^* IMP $

where E is the exchange rate, P is the level of national prices, X represents export, P* is the level of foreign prices, IMP represents import.

Then it derives it as:

$ e + p + x = p^* + imp $

saying that now it's expressed in terms of average annual variations. In a note, it says that this means that we're rewriting the first formula in terms of natural logs and differentiating it with respect to time. Please, could you give me a hint (or an explaination, if it's not too long) about the meaning of this derivation?

Thank you in advance and sorry for my awkward English

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up vote 1 down vote accepted

In general:

$$\log(a b) = \log(b) + \log(b)$$ So in your case: $$\log(EPX) =\log(E)+\log(P)+\log(X)$$ Which your textbook wrote as: $$e+p+x$$

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Thank you very much! – Luigi May 5 '12 at 14:10

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