Suppose a bottle of wine costs 25 euros in France and 20 dollars in the United States. If the exchange rate is

Question

Suppose a bottle of wine costs 25 euros in France and 20 dollars in the United States. If the exchange rate is 1.25 euros per dollar, what is the real exchange rate?

Answer 1

Whatever the previous answer says is correct and it implies that the question is not permissible in the sense that the data given is not adequate to workout the correct solution. Since the question is not scientifically put, it cannot have a true scientific answer about the real exchange rate.
However, the question is interesting and therefore may deserve a straight forward answer, even at the cost of scientific rigour.The answer is : the real exchange rate is 1.25 euros per US dollar, the same as the nominal exchange rate given in the question. The reason is that with 20 dollars one can buy a bottle of wine in the US or convert that into euros at the nominal exchange rate and get 20*1.25 or 225 euros which is exactly equal to the cost of a boltle of wine in France. If the bottles of wine are of equal quality in both the countries, we can say that the nominal exchange rate reflects the purchasing power of the two currencies correctly. Hence, it is also the real exchange rate. The simplifying assumption is that the prices of the bottles of wine represents the general price level for the commodity baskets in the US and France.

Answer 2

Not at all clear. The idea of purchasing power parity is to compare currencies based on what they will buy:

http://en.wikipedia.org/wiki/Purchasing_power_parity

but you clearly can't apply it to the price of a bottle of wine without a lot more work. For example, the transportation costs for a locally produced bottle will be different from one imported (is it a California wine? a French wine? or an Australian wine?) Is the wine seen as being of the same class? (For a long time the French looked down on non-European wines so wouldn't pay much for them. The result was relatively lower prices for them compared with places where they were appreciated.)

The Economist has a "Big Mac" index, but clearly a Big Mac is more representative (being made of local ingredients, by local labor, etc.) than wine, and even so, they realize that it is not very accurate.