Question

The U.S. price level is $115,$ the Japanese price level is $92,$ and the real exchange rate is 98.75 Japanese real GDP per unit of U.S. real GDP. What is the nominal exchange rate?

Short answer

The nominal exchange rate is 79.113.

Step-by-step solution

Understand the Given Data

Note down the given values: U.S. price level (P_US) is 115, Japanese price level (P_Japan) is 92, and the real exchange rate (RER) is 98.75 Japanese real GDP per unit of U.S. real GDP.

Use the Real Exchange Rate Formula

Recall the formula for the real exchange rate: $$RER=\frac{NominalExchangeRate\times P_{U}S}{P_{J}apan}$$Where:- RER is the real exchange rate- Nominal Exchange Rate is the nominal exchange rate we need to find- P_US is the U.S. price level- P_Japan is the Japanese price level

Rearrange the Formula to Solve for the Nominal Exchange Rate

Rearrange the formula to solve for the nominal exchange rate: $$NominalExchangeRate=\frac{RER\times P_{J}apan}{P_{U}S}$$

Plug in the Given Values

Substitute the given values into the rearranged formula: $$NominalExchangeRate=\frac{98.75\times 92}{115}$$

Calculate the Nominal Exchange Rate

Perform the calculation:$$NominalExchangeRate=\frac{98.75\times 92}{115}=\frac{9098}{115}=79.113$$

Key concepts

real exchange rate

The real exchange rate tells us how many times one country's goods are worth in terms of another country's goods. It connects the physical quantity of goods between countries, and is often expressed as a ratio of the real GDPs. Think of it as how internationally effective your country's resources are compared to another country. This measure is crucial because it accounts for differences in price levels between countries.
The real exchange rate uses both the nominal exchange rate and the relative price levels of two countries. It gives a depiction of the purchasing power between two currencies. The formula often used is: $$RER=\frac{NominalExchangeRate\times PriceLeve{l}_{US}}{PriceLeve{l}_{Japan}}$$ Using this formula, you can determine how competitive a country's goods will be in terms of international trade.

price levels

Price levels indicate the average amount of money that goods and services cost in an economy. It is a critical component in calculating the real exchange rate. By comparing price levels between countries, you can gauge price competitiveness. For example, in the original exercise, we’re given U.S. price level as 115 and Japanese price level as 92. This means, on average, goods are more expensive in the U.S. than in Japan.
Price levels are often influenced by factors such as inflation, monetary policies, and economic conditions. An increase in the price level in a country is usually a result of inflation, which reflects how the general cost of goods and services in that country has increased.
The formula for price levels in terms of real exchange rate goes as follows:
$$RER=\frac{NominalExchangeRate\times PriceLeve{l}_{US}}{PriceLeve{l}_{Japan}}$$By understanding this formula, we get insights on how changes in price levels can impact the real exchange rate and ultimately international competitiveness.

currency conversion

Currency conversion is the process of exchanging one currency for another. It's a crucial aspect of international trade and finance. To find the nominal exchange rate, as seen in the exercise, you need to convert prices from one currency to another. The nominal exchange rate tells you how many units of one currency you can get for another.
In the given problem, to find the nominal exchange rate, we used the real exchange rate along with the price levels of both countries. The formula: $$NominalExchangeRate=\frac{RER\times PriceLeve{l}_{Japan}}{PriceLeve{l}_{US}}$$By plugging in the values, we found that the nominal exchange rate between USD and JPY is approximately 79.113.
Understanding currency conversion is vital for many reasons such as traveling, investing abroad, or understanding the value of goods priced in a different currency.

international economics

International economics involves understanding how countries interact through trade, monetary policy, and currency exchange. It revolves around the theories and principles that explain how economies operate on a global scale.
An essential part of international economics is appreciating how exchange rates and price levels influence trade and investments between countries. This becomes apparent in the exercise, where knowing the real exchange rate, price levels, and nominal exchange rate forms a complete picture.
Studying international economics helps understand global financial markets, the balance of payments, and the impact of international trade policies. By grasping these concepts, you can better comprehend how global events influence your local economy, and how economic well-being of countries are interconnected globally.