An economics book has the following example:
In the USA, a Big Mac sells for 1 USD, while in Germany it sells for 3 EUR.
The "fair" FX relation would therefore be 1 USD = 3 EUR. At the FX market, however, the FX relation is 1 USD = 2 EUR.
The author now concludes that the EUR is undervalued. But I think that's wrong, the EUR is overvalued here, isn't it?
Your conclusion is correct here. Since at the current FX rate you can buy the burger cheaply at an equivalent rate of 2 EUR in the US. So basically, if you live in Germany and want to buy a Big Mac, you are better of buying the Big Mac from the US since via the FX rate you will still have 1 EUR left(if you started with 3 EUR) and hence this will increase the demand of the USD in the foreign exchange market and hence
USD should appreciate in the future => USD in undervalued => EUR is overvalued.
You are right. The EUR is overvalued. Or, to put it differently, a change in the exchange rate from 1/3 to 1/2 means that the EUR appreciated (or increased its value) with respect to the USD. Equivalently, the USD depreciated with respect to the EUR. You need more USD to buy a Big Mac in Germany.
