Question

In December \(2016,\) you needed 83 percent more pesos to buy one U.S. dollar than you had needed in December 2004\. Over the same time period, the consumer price index in Mexico increased 57.8 percent, and the consumer price index in the United States increased 26.7 percent. Are these data consistent with the theory of purchasing power parity? Briefly explain.

Short answer

No, these data are not consistent with the theory of Purchasing Power Parity. The exchange rate increased by more than the change in relative price levels of the two countries, which contradicts with the theory of PPP.

Step-by-step solution

Find the increase in the exchange rate

We first find the increase in the exchange rate. The exercise tells us that we need 83 percent more pesos to buy one U.S. dollar. In other words, the exchange rate has increased by 83 percent.

Calculate Change in Relative Prices

Next, we need to calculate how much the price level has changed in Mexico relative to the United States. The change in relative price levels can be calculated by subtracting the percent change in the CPI in the United States from the percent change in the CPI in Mexico. Therefore, we subtract 26.7 percent from 57.8 percent to get 31.1 percent.

Compare the increase in the exchange rate with the change in relative prices

Lastly, we compare the increase in the exchange rate with the change in relative prices. We found that the exchange rate increased by 83 percent and relative prices increased by 31.1 percent. Since the exchange rate increased by more than the relative price levels, these data are not consistent with the theory of Purchasing Power Parity. According to PPP, the exchange rate should adjust to compensate for the changes in relative buying power of the two countries, meaning that the increase in the exchange rate should be similar to the change in relative prices.

Key concepts

Exchange Rate

The exchange rate is a crucial concept in understanding how currencies are traded globally. It represents the value of one currency in terms of another. In the scenario given, we see that in December 2016, it required 83% more Mexican pesos to purchase one U.S. dollar compared to December 2004. This means the exchange rate between the Mexican peso and the U.S. dollar had increased significantly over this period.

Exchange rates can fluctuate due to various factors including economic stability, inflation, interest rates, and geopolitical events. A higher exchange rate indicates that a currency has weakened compared to the other currency. In the context of purchasing power parity (PPP), exchange rates should theoretically adjust to reflect changes in the relative price levels or inflation rates of two countries. When exchange rate changes are not aligned with relative price levels, it may suggest variations from PPP predictions.

Consumer Price Index

The consumer price index (CPI) measures the average change over time in the prices paid by consumers for a market basket of goods and services. It is an indicator of inflation and is used to gauge the cost of living. In the given problem, the CPI in Mexico increased by 57.8% from December 2004 to December 2016, while the CPI in the United States rose by 26.7% over the same period.

Understanding these figures is key when evaluating currency value through PPP. If the CPI rises in one country more than in another, it suggests that consumers experience higher inflation pressures, decreasing purchasing power domestically. This is important as PPP suggests that over time, currencies should adjust to equalize the cost of a basket of goods in any two countries. In this case, the different CPI changes suggest varying levels of inflation, which should ideally be reflected in the exchange rate adjustments. However, as the solution shows, the disparity between CPI changes and the exchange rate increase was substantial.

Relative Prices

Relative prices involve comparing the price levels of two different countries. In the context of PPP, it means comparing the general price level change using CPI in both countries. To find the relative price change, we subtract the U.S. CPI increase (26.7%) from the Mexican CPI increase (57.8%), obtaining 31.1%. This means that, relatively, goods and services in Mexico became more expensive compared to those in the United States from 2004 to 2016.

The theory of PPP suggests that exchange rates should reflect these relative price changes. Ideally, if Mexico's relative prices increased by 31.1%, the exchange rate should have mirrored this change to keep the purchasing power between the currencies equal. However, the exchange rate increased by 83%, indicating a deviation from the expected parity. This tells us there are other influences affecting the exchange rates beyond just changes in price levels.