If the dollar value of a British pound depreciates by 10% along with a 10% increase of the U.S. price level, what can we say about the value of the dollar/pound real exchange rate? (Credit Arlyn Rubash, Chapter 21 Exam)

For some reason this question tripped me up when I took the Chapter 21 Assessment – twice.

First, to define the dollar/pound real exchange rate: The dollar/pound real exchange rate measures the relative price of British and U.S. goods. (Credit Grinblatt/Titman textbook)

To use an example:

Assume the dollar pound exchange rate is 2.00 $/pound

Assume that an item being purchased in the United States costs $100.

This year, it would cost 50 pounds to purchase (50 pounds x 2 dollars/pound = $100).

Next year, if the dollar value of the British pound depreciates 10% the exchange rate would become 1.8 $/pound (2.0 x .9).

Next year, if there is a 10% increase in U.S. prices the cost of the item would become $110 (100 x 1.1).

Thus, next year, it would cost 61.11 pounds to purchase the item (61.11 pounds x 1.8 dollars/pound = $110).

Or, if the dollar value of a British pound depreciating means that the pound becomes more valuable, it would be as follows:

Next year, if the dollar value of the British pound depreciates 10%, the exchange rate will become 2.2 dollars/pound (2.0 x 1.1 = 2.2).

Next year, if there is a 10% increase in U.S. prices the cost of the item would become $110 (100 x 1.1 = $110)

Thus, next year, it would again cost 50 pounds to purchase the item (50 pounds x 2.2 dollars/pound = $110).

This question confused me, but hopefully the example above, combined with the clarification that the depreciation means that the pound became more valuable helps everyone understand.