Question

The Economist magazine uses the price of a Big Mac to determine whether a currency is undervalued or overvalued. In July \(2012,\) the price of a Big Mac was \(\$ 4.33\) in New York, 15.65 yuan in Beijing, and 6.50 Swiss francs in Geneva. The exchange rates were 6.37 yuan per U.S. dollar and 0.98 Swiss francs per U.S. dollar. Source: The Economist, July 25,2012 a. Was the yuan undervalued or overvalued relative to purchasing power parity? b. Was the Swiss franc undervalued or overvalued relative to purchasing power parity? c. Do you think the price of a Big Mac in different countries provides a valid test of purchasing power parity?

Short answer

The yuan was undervalued, and the Swiss franc was overvalued. Big Mac prices provide a rough but not fully accurate test of PPP.

Step-by-step solution

Calculate the implied exchange rate for yuan

Find the implied exchange rate by dividing the price of a Big Mac in Beijing by the price in New York.\[ \text{Implied Exchange Rate for Yuan} = \frac{15.65 \text{ yuan}}{4.33 \text{ USD}} \ \text{Implied Exchange Rate for Yuan} = 3.61 \text{ yuan per USD} \]

Compare implied exchange rate to actual exchange rate for yuan

Compare the implied exchange rate with the given actual exchange rate to determine if the yuan is undervalued or overvalued. The actual rate is 6.37 yuan per USD. Since \[ 3.61 < 6.37 \], the yuan is undervalued because it takes more yuan to buy 1 USD than the implied rate suggests.

Calculate the implied exchange rate for Swiss francs

Find the implied exchange rate by dividing the price of a Big Mac in Geneva by the price in New York.\[ \text{Implied Exchange Rate for Swiss Francs} = \frac{6.50 \text{ CHF}}{4.33 \text{ USD}} \ \text{Implied Exchange Rate for Swiss Francs} = 1.50 \text{ CHF per USD} \]

Compare implied exchange rate to actual exchange rate for Swiss francs

Compare the implied exchange rate with the given actual exchange rate to determine if the Swiss franc is undervalued or overvalued. The actual rate is 0.98 CHF per USD. Since \[ 1.50 > 0.98 \], the Swiss franc is overvalued because it takes fewer Swiss francs to buy 1 USD than the implied rate suggests.

Evaluate the validity of using Big Mac prices for PPP

The price of a Big Mac in different countries may not provide a completely valid test of purchasing power parity (PPP) due to differences in local costs such as labor, rent, and raw materials. Additionally, cultural and consumer preference variations can affect pricing. However, it offers an accessible and consistent product for a general comparison across countries.

Key concepts

currency valuation

The concept of currency valuation involves determining whether a currency is overvalued or undervalued relative to another currency based on certain economic indicators. In the problem, we use the price of a Big Mac as a basic gauge to assess the value of different currencies. By comparing the prices of a Big Mac in various currencies and the corresponding exchange rates, we can infer if the actual value of the currency aligns with what it *actually* buys in practical terms. This method can spotlight discrepancies by showing whether too many or too few units of foreign currency are needed for the same item compared to a baseline, usually the US dollar.

exchange rates

An exchange rate reflects how much one currency is worth in relation to another. When we talk about exchange rates in the exercise, we're referring to the amount of yuan or Swiss francs needed to buy one US dollar. For example, the exchange rate of 6.37 yuan per USD means you need 6.37 yuan to purchase a single US dollar. Comparing these rates to our implied rates from the Big Mac prices shows if a currency is over or undervalued. These comparisons provide a clearer picture when these rates significantly deviate from our calculations.

Big Mac Index

The Big Mac Index is a fun, yet insightful tool created by The Economist to compare the purchasing power parity (PPP) of different currencies. Since a Big Mac is a uniformly produced good sold worldwide, its price in different currencies can act as a simple measure of currency valuation. This index reveals imbalances by showing whether the cost of a Big Mac in one country is higher or lower than in another when translated into a common currency, usually the US dollar. For instance, if a Big Mac costs 15.65 yuan in Beijing and $4.33 in New York, the implied exchange rate can be derived and then compared to the actual market rate.

economic comparison

When we conduct an economic comparison using the Big Mac Index, we dive into how different economies impact the cost of a standard good—here, a Big Mac. By evaluating labor, rent, and raw material differences, we understand that local economies can influence prices significantly. These comparisons also factor in consumer preferences and cultural factors, which can further affect the local cost of the same item. Therefore, while the Big Mac Index is a catchy way to visualize currency value differences, it’s not a perfect test of purchase power parity due to those varying contributing factors. However, it provides an engaging entry point for deeper economic analysis across international borders.