In January 2012, one US dollar was worth 50 Indian rupees. Suppose that over the next year the value of the Indian rupee decreases to 60 Indian rupees to one US dollar. Suppose also that the price level of all goods and services in India, as measured in rupees, falls 20%, so that the Indian price index falls from a value of 100 to 80. At the same time, suppose that the US price level increases by 6%, to 106.
By what percentage did the value of the real exchange rate change over this period? Please give your answer to the nearest whole percentage point.
To find the percentage change in the value of the real exchange rate, we need to calculate the percentage change in the relative price levels between the two countries.
1. Calculate the relative price levels:
- Indian price level before: 100
- Indian price level after: 80
- US price level before: 100
- US price level after: 106
2. Find the percentage change in the Indian price level:
Percentage change in Indian price level = ((Indian price level after - Indian price level before) / Indian price level before) x 100
= ((80 - 100) / 100) x 100
= (-20 / 100) x 100
= -20%
3. Find the percentage change in the US price level:
Percentage change in US price level = ((US price level after - US price level before) / US price level before) x 100
= ((106 - 100) / 100) x 100
= (6 / 100) x 100
= 6%
4. Calculate the percentage change in the real exchange rate:
Percentage change in real exchange rate = Percentage change in Indian price level - Percentage change in US price level
= -20% - 6%
= -26%
Therefore, the value of the real exchange rate decreased by approximately 26% over this period.
To calculate the percentage change in the real exchange rate, we need to consider the changes in both nominal exchange rates and price levels in each country.
First, let's calculate the percentage change in the nominal exchange rate:
The initial exchange rate was 1 US dollar = 50 Indian rupees, and the final exchange rate was 1 US dollar = 60 Indian rupees.
Percentage change in the nominal exchange rate = [(Final exchange rate - Initial exchange rate) / Initial exchange rate] * 100
= [(60 - 50) / 50] * 100
= 20%
Now, let's calculate the percentage change in the price levels:
The initial Indian price index was 100, and it fell to 80.
The initial US price index was 100, and it increased to 106.
Percentage change in the Indian price level = [(Final price index - Initial price index) / Initial price index] * 100
= [(80 - 100) / 100] * 100
= -20%
Percentage change in the US price level = [(Final price index - Initial price index) / Initial price index] * 100
= [(106 - 100) / 100] * 100
= 6%
Now, we can calculate the percentage change in the real exchange rate:
Percentage change in the real exchange rate = Percentage change in the nominal exchange rate - Percentage change in the price levels
= 20% - (-20%)
= 40%
Therefore, the value of the real exchange rate changed by approximately 40% over this period.