Suppose the price level in South Korea is 120,000, the price level in the United States is 150, and the price level in Mexico is 600. Suppose the current nominal exchange rates are 1080 South Korean won per dollar and 5 pesos per dollar. Calculate the real exchange rates (rounded to two decimal places) between each pair of countries. Note that you will have to first calculate the nominal exchange rate between Mexico and South Korea before calculating the real exchange rate between those two countries. (4 points)
The Correct Answer and Explanation is:
To calculate the real exchange rate (RER) between two countries, we use the following formula: RER=(Nominal Exchange Rate×Foreign Price LevelDomestic Price Level)RER = \left( \frac{{\text{{Nominal Exchange Rate}} \times \text{{Foreign Price Level}}}}{{\text{{Domestic Price Level}}}} \right)RER=(Domestic Price LevelNominal Exchange Rate×Foreign Price Level)
Where:
- Nominal Exchange Rate refers to the exchange rate between the two currencies.
- Foreign Price Level is the price level in the foreign country.
- Domestic Price Level is the price level in the domestic country.
Step 1: Calculate the Real Exchange Rate between South Korea and the United States
First, we need to calculate the real exchange rate between South Korea and the United States.
The nominal exchange rate between South Korea and the U.S. is 1 USD = 1,080 won.
The price level in South Korea is 120,000, and the price level in the U.S. is 150. RERKR-Won to USD=(1,080×150120,000)=162,000120,000=1.35RER_{\text{KR-Won to USD}} = \left( \frac{{1,080 \times 150}}{{120,000}} \right) = \frac{{162,000}}{{120,000}} = 1.35RERKR-Won to USD=(120,0001,080×150)=120,000162,000=1.35
So, the real exchange rate between South Korea and the United States is 1.35.
Step 2: Calculate the Real Exchange Rate between the United States and Mexico
Next, we calculate the real exchange rate between the U.S. and Mexico. The nominal exchange rate between the U.S. and Mexico is 1 USD = 5 pesos.
The price level in Mexico is 600, and the price level in the U.S. is 150. RERMX-Pesos to USD=(5×600150)=3,000150=20RER_{\text{MX-Pesos to USD}} = \left( \frac{{5 \times 600}}{{150}} \right) = \frac{{3,000}}{{150}} = 20RERMX-Pesos to USD=(1505×600)=1503,000=20
So, the real exchange rate between the United States and Mexico is 20.
Step 3: Calculate the Nominal Exchange Rate between South Korea and Mexico
We now calculate the nominal exchange rate between South Korea and Mexico. Since we have the exchange rates between each country and the U.S., we can use the following relationship: Nominal Exchange Rate (MX-Won to Peso)=Nominal Exchange Rate (KR-Won to USD)Nominal Exchange Rate (USD to MX-Peso)\text{Nominal Exchange Rate (MX-Won to Peso)} = \frac{{\text{Nominal Exchange Rate (KR-Won to USD)}}}{{\text{Nominal Exchange Rate (USD to MX-Peso)}}}Nominal Exchange Rate (MX-Won to Peso)=Nominal Exchange Rate (USD to MX-Peso)Nominal Exchange Rate (KR-Won to USD) Nominal Exchange Rate (KR-Won to MX-Peso)=1,0805=216\text{Nominal Exchange Rate (KR-Won to MX-Peso)} = \frac{{1,080}}{{5}} = 216Nominal Exchange Rate (KR-Won to MX-Peso)=51,080=216
So, the nominal exchange rate between South Korea and Mexico is 216 won per peso.
Step 4: Calculate the Real Exchange Rate between South Korea and Mexico
Finally, we can calculate the real exchange rate between South Korea and Mexico. RERKR-Won to MX-Peso=(216×600120,000)=129,600120,000=1.08RER_{\text{KR-Won to MX-Peso}} = \left( \frac{{216 \times 600}}{{120,000}} \right) = \frac{{129,600}}{{120,000}} = 1.08RERKR-Won to MX-Peso=(120,000216×600)=120,000129,600=1.08
So, the real exchange rate between South Korea and Mexico is 1.08.
Summary:
- Real exchange rate between South Korea and the U.S.: 1.35
- Real exchange rate between the U.S. and Mexico: 20
- Real exchange rate between South Korea and Mexico: 1.08
These real exchange rates indicate the relative price levels of goods and services in the respective countries, adjusted for the exchange rates. The real exchange rate accounts for differences in inflation rates and price levels, providing a more accurate measure of purchasing power across countries.
