# Nominal vs. Real Exchange Rates > AP Macroeconomics · Unit 6: Open Economy: International Trade and Finance > Source: https://www.owlsprep.com/study/ap-macroeconomics-u6-nominal-vs-real-exchange-rates/ This module covers the core distinction between nominal and real exchange rates, their calculation, purchasing power parity (PPP) applications, and the link between real exchange rates and net exports, tested in both AP Macro MCQ and FRQ. **Prerequisites:** Calculate percentage changes for prices; Understand what CPI and GDP deflator measure; Basic supply and demand in foreign exchange markets ## Learning objectives - Distinguish between nominal and real exchange rates - Calculate real exchange rates and PPP-implied nominal exchange rates - Interpret currency overvaluation and undervaluation - Relate real exchange rate changes to net exports ## Core Definitions: Nominal vs. Real Exchange Rates This topic makes up 10-15% of the total AP Macroeconomics exam score, appearing in both multiple-choice (MCQ) and free-response (FRQ) sections, often combined with questions about net exports, monetary policy, and purchasing power parity. **Nominal Exchange Rate** — The quoted market rate at which one currency can be exchanged for another. It measures how many units of one currency you get for a unit of another, and does not adjust for cross-country differences in price levels or purchasing power. *Notation:* $e$ *Example:* A bank quoting 1.09 USD per 1 EUR is a nominal exchange rate. **Real Exchange Rate** — Adjusts the nominal exchange rate for differences in aggregate price levels between two countries. It measures how many units of a domestic country’s basket of goods you need to buy one unit of a foreign country’s basket of goods, reflecting relative purchasing power. *Notation:* $R$ *Example:* A real exchange rate of 0.8 means the foreign basket costs 80% of the domestic basket's price. ## Nominal Exchange Rates The nominal exchange rate is the rate you see posted at currency exchange kiosks or quoted in financial news: it is the price of one currency in terms of another. AP Macroeconomics almost always uses the standard notation $e$, defined as the number of units of domestic currency you need to buy one unit of foreign currency. Less commonly, problems may define $e$ as the number of foreign currency units per unit domestic currency, so you must always check the question’s definition before calculating anything. An increase in $e$ (domestic currency per foreign) means the domestic currency has depreciated, while a decrease in $e$ means domestic currency has appreciated. **Worked example:** The US is the domestic country, and the Eurozone (EUR) is foreign. A bank quotes that 1 EUR trades for 1.09 USD. If a US tourist wants to buy a €140 dinner in Paris, how many USD do they need to exchange to pay for the meal, using standard AP notation? 1. Confirm the definition of nominal exchange rate per AP convention: $e$ = units domestic per 1 unit foreign. Here, $e = 1.09 \text{ USD}/\text{EUR}$. 2. To get the total USD cost, multiply the price in foreign currency by the nominal exchange rate. This cancels out the EUR unit: 3. $$140 \text{ EUR} \times 1.09 \frac{\text{USD}}{\text{EUR}}$$ 4. Calculate the result: $140 \times 1.09 = 152.60$. The tourist needs \$152.60 USD. > **Exam tip:** If a question defines $e$ as foreign per domestic (e.g. 0.92 EUR per 1 USD), flip the rate to get domestic per foreign before using the standard real exchange rate formula to avoid calculation errors. ## Real Exchange Rates: Calculation and Interpretation Nominal exchange rates only tell you about currency exchange, not about the relative cost of goods and services between countries, because price levels differ across countries. For example, a nominal depreciation of the domestic currency could be entirely offset by higher domestic inflation, leaving the relative cost of goods unchanged. The real exchange rate $R$ solves this problem. $$R = \frac{e \times P_f}{P_d}$$ Where $P_f$ = the foreign country’s aggregate price level (usually GDP deflator or CPI), and $P_d$ = the domestic country’s aggregate price level. If $R > 1$, the foreign basket is more expensive than the domestic basket; if $R < 1$, the foreign basket is cheaper. An increase in $R$ makes foreign goods more expensive, so exports rise and imports fall, increasing net exports. **Worked example:** Canada is the domestic country (CAD), and South Korea is the foreign country (KRW). The nominal exchange rate $e = 0.01$ CAD per 1 KRW. Canada’s GDP deflator (2015 base year) is 125, and South Korea’s GDP deflator (same 2015 base year) is 140. Calculate the real exchange rate, and state whether South Korean goods are relatively cheaper or more expensive than Canadian goods. 1. Write the standard real exchange rate formula: $R = \frac{e P_f}{P_d}$. 2. Plug in the given values: $e = 0.01$, $P_f = 140$, $P_d = 125$. 3. Calculate the numerator first: $e \times P_f = 0.01 \times 140 = 1.4$. 4. Divide by the domestic price level to get $R$: 5. $$R = \frac{1.4}{125} = 0.0112$$ 6. Interpretation: $R = 0.0112 < 1$, so the South Korean basket of goods costs less in CAD terms than the identical Canadian basket. South Korean goods are relatively cheaper. > **Exam tip:** Always label the units for $e$ when you start a problem: this will help you catch any reversal of domestic/foreign before you lose points on an FRQ. ## Purchasing Power Parity and Currency Valuation Purchasing Power Parity (PPP) is a long-run exchange rate theory directly tied to the real exchange rate concept. PPP states that identical baskets of goods should cost the same in both countries when converted to the same currency, which means the real exchange rate should equal 1 in the long run, as arbitrage pushes prices and rates back to parity. $$1 = \frac{e_{PPP} P_f}{P_d} \implies e_{PPP} = \frac{P_d}{P_f}$$ If the actual $e > e_{PPP}$, the foreign currency is overvalued (it takes more domestic currency to buy one foreign unit than PPP predicts), so the domestic currency is undervalued. A common application is the Big Mac Index, which uses the price of a uniform good to calculate PPP-implied rates. **Worked example:** A Big Mac costs \$5.50 USD in the US (domestic) and 420 Mexican Pesos (MXN) in Mexico (foreign). What is the PPP-implied nominal exchange rate, expressed as USD per MXN? If the actual nominal exchange rate is 0.048 USD per MXN, is the Mexican Peso overvalued or undervalued? 1. PPP requires $R=1$, so the formula for $e_{PPP}$ (USD per MXN, domestic per foreign) is $e_{PPP} = \frac{P_d}{P_f}$. 2. Plug in the Big Mac prices: $P_d = 5.50$ USD, $P_f = 420$ MXN. 3. Calculate: 4. $$e_{PPP} = \frac{5.50}{420} \approx 0.0131 \text{ USD per MXN}$$ 5. Compare to actual $e = 0.048$ USD per MXN: actual $e$ is much larger than $e_{PPP}$, meaning 1 MXN buys more USD than PPP says it should. The Mexican Peso is overvalued. > **Exam tip:** Always double-check the required units for $e_{PPP}$ before writing your answer; reversing the ratio is the most common mistake on PPP FRQ questions. ## AP-Style Concept Check **Check your understanding** Test your calculation skills with this multiple-choice question: 1. Suppose the nominal exchange rate between the US dollar (domestic) and the Euro (foreign) increases from 1.10 USD per EUR to 1.155 USD per EUR. Over the same period, the US price level increases by 5%, and the Eurozone price level does not change. What is the approximate percentage change in the real exchange rate? - The real exchange rate decreases by 5% - The real exchange rate increases by 5% - The real exchange rate does not change (0% change) - The real exchange rate decreases by 10% *Answer:* The real exchange rate does not change (0% change) *Why:* Correct! The percentage change approximation is $\%ΔR = \%Δe + \%ΔP_f - \%ΔP_d$. The 5% increase in $e$ is exactly offset by the 5% increase in the US price level, so $R$ stays the same. **Worked example:** Japan is the domestic country (JPY), and the US is the foreign country (USD). Use the following data (same base year for both price indices): Nominal exchange rate = 140 JPY per 1 USD; Japan’s GDP deflator = 102; US GDP deflator = 110. (a) Calculate the real exchange rate (domestic baskets per foreign basket). (b) If PPP holds long-run, is the Japanese yen overvalued or undervalued? (c) Expansionary monetary policy raises Japan’s price level, holding $e$ and US prices constant. What happens to $R$ and Japan’s net exports? 1. (a) Confirm notation: $e = 140$ JPY per USD, $P_d = 102$, $P_f = 110$: 2. $$R = \frac{(140)(110)}{102} \approx 150.98$$ 3. (b) PPP requires $R=1$. $R ≈ 150.98 > 1$, so 1 USD buys more JPY than PPP implies, meaning the USD is overvalued and the Japanese yen is undervalued. 4. (c) A higher Japanese price level increases $P_d$ (the denominator of the $R$ formula). Holding $e$ and $P_f$ constant, $R$ decreases. Lower $R$ means US goods are cheaper relative to Japanese goods, so imports rise and exports fall, decreasing Japan’s net exports. ## Common pitfalls - **Wrong:** Using $e$ defined as foreign per domestic directly in the standard formula $R = \frac{e P_f}{P_d}$ that expects $e$ as domestic per foreign. - Why it fails: Different sources use different notation conventions, so students rely on memorization instead of adjusting to the problem’s given definition. - Correct: If $e$ is foreign per domestic, convert it to domestic per foreign by taking the reciprocal $1/e$ before plugging into the formula. - **Wrong:** Interpreting a rise in $R$ as meaning domestic goods are more expensive, leading to a conclusion that net exports fall. - Why it fails: Students mix up what $R$ measures: it is the relative price of foreign goods, not domestic goods. - Correct: Remember that higher $R$ = foreign goods more expensive = exports rise, imports fall = higher net exports. - **Wrong:** Claiming that a nominal depreciation of domestic currency always causes a real depreciation. - Why it fails: Students assume nominal and real exchange rates always move together, ignoring differences in inflation between countries. - Correct: Always check inflation differentials: if domestic inflation is higher than the rate of nominal depreciation, the real exchange rate can appreciate even as nominal depreciates. - **Wrong:** Plugging price indices with different base years directly into the real exchange rate formula. - Why it fails: Different base years create misleading relative price level calculations. - Correct: Rebase both indices to the same base year by dividing each index by its base year value before plugging into the formula. - **Wrong:** Calculating $e_{PPP}$ as $\frac{P_f}{P_d}$ instead of $\frac{P_d}{P_f}$, leading to wrong over/undervaluation conclusions. - Why it fails: Students reverse the ratio when they forget that $e_{PPP}$ is derived from setting $R=1$. - Correct: Derive $e_{PPP}$ quickly by starting from $R=1 = \frac{e P_f}{P_d}$ and rearranging to solve for $e$ before plugging in numbers. ## Cheatsheet | Category | Formula | Notes | | --- | --- | --- | | Nominal Exchange Rate (Standard AP) | $e = \frac{\text{Domestic Currency Units}}{\text{1 Foreign Currency Unit}}$ | Always confirm notation in the question | | Real Exchange Rate | $R = \frac{e \times P_f}{P_d}$ | $P_f$ = foreign price level, $P_d$ = domestic price level | | Percentage Change in $R$ | $\%ΔR \approx \%Δe + \%ΔP_f - \%ΔP_d$ | Approximation for small changes, common in MCQ | | PPP-Implied Nominal Exchange Rate | $e_{PPP} = \frac{P_d}{P_f}$ | Derived from setting $R=1$ for identical baskets | | Foreign Currency Overvaluation | $\text{Actual } e > e_{PPP}$ | $e$ = domestic per foreign | | Foreign Currency Undervaluation | $\text{Actual } e < e_{PPP}$ | $e$ = domestic per foreign | | Effect of Higher $R$ on Net Exports | $↑R → ↑NX$ | Higher $R$ means foreign goods are more expensive | ## What's next Mastery of nominal vs. real exchange rates is the foundational building block for all open economy analysis in AP Macroeconomics, required to correctly predict how changes in currency markets and price levels affect trade flows, aggregate demand, and macroeconomic equilibrium. Next, you will apply these concepts to analyze how fiscal and monetary policy influence exchange rates and net exports in the open economy AD-AS model and open economy loanable funds market. Without correctly distinguishing between nominal and real changes and interpreting their effects, you will struggle to earn full points on FRQs about open economy policy, and this topic also feeds into the larger course concept of how international interactions affect domestic inflation and unemployment. - [The Foreign Exchange Market](https://www.owlsprep.com/study/ap-macroeconomics-u6-the-foreign-exchange-market/) - [Effects of Policy and Shocks on the Foreign Exchange Market](https://www.owlsprep.com/study/ap-macroeconomics-u6-effects-of-policy-and-shocks/) - [Changes in Exchange Rates and Net Exports](https://www.owlsprep.com/study/ap-macroeconomics-u6-changes-in-exchange-rates-and/) --- From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ap-macroeconomics-u6-nominal-vs-real-exchange-rates/