Exact Meaning of a Currency Devaluation

Martin 2

What is meant when one says that a currency was devalued by 25%? Is it necessary to specify the currency against which it was devalued, would the dollar or euro be assumed or some basket of currencies?
If 1 muster was equal to 1 euro and then the muster was devalued by 25% does that mean 1 euro now buys 1.25 musters or 1 muster now buys 0.75 euro? These are not the same as obviously in the second case 1 euro now buys 1.33 musters (i.e., 1/0.75).

I'm sorry if this seems like a very trivial question but I can't find a conclusive answer anywhere else on the web -perhaps because it's self evident to most people:)

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Économiste Monétaire

Usually, it's against a trade-weighted basket of currencies. A bilateral example: EUR/USD is 1.3225 today, so one Euro buys 1.3225 U.S. Dollars. A 25% devaluation of the Euro vis-à-vis the Dollar would mean an exchange rate of about 0.9919 ((0.9919 - 1.3225)/1.3225 = - 0.24998...).

Martin 2

Ok, so a 25% devaluation of the euro vis-à-vis the dollar means the euro would buy 25% less dollars (1.3225*0.75=0.9919) rather than the dollar would buy 25% more euros.

Thank you.

Économiste Monétaire

Correct. To get it in terms of a Dollar appreciation, take the change in the reciprocal of the EUR/USD quote. We can say that one Euro buys 1.3225 Dollars, or one Dollar buys 0.756144 Euro (= 1/1.3225). If the EUR/USD quote falls to 0.991875 after a 25% depreciation, then that means one Euro buys 0.991875 Dollars, or one Dollar buys 1.008192 Euro (= 1/0.991875). So the appreciation in Dollar is, (1.008191 - 0.756144)/0.756144 = 33.33%.