Openness in Goods & Financial Markets

The Real Exchange Rate

coreExam · high

The real exchange rate ε = E·P / P* measures the price of domestic goods in units of foreign goods. E is the nominal exchange rate (foreign currency per unit of domestic), P is the domestic price level, P* is the foreign price level. Real appreciation (↑ε) means domestic goods become expensive abroad — exports fall, imports rise, NX shrinks.

Derivation

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Two Exchange Rates

| Concept | Symbol | Meaning | |---------|--------|---------| | Nominal | E | How much foreign currency one unit of domestic currency buys | | Real | ε | How much foreign goods one unit of domestic goods buys |

\varepsilon = \frac{E \cdot P}{P^*}

The BMW–Chrysler Example

With E = 1 USD/EUR, a BMW at 50,000 EUR costs 50,000 × 1 = 50,000 USD. A Chrysler costs 36,900 USD.

\varepsilon = \frac{E \cdot P_{\text{US}}}{P_{\text{EU}}} = \frac{1 \cdot 36900}{50000} = 0.738

You need 0.738 Chryslers to buy one BMW — US goods are cheaper in real terms.

Appreciation vs Depreciation

Real appreciation ( $\uparrow\varepsilon$ ): domestic goods become expensive relative to foreign. Exports fall, imports rise, $NX$ shrinks.
Real depreciation ( $\downarrow\varepsilon$ ): domestic goods become cheap. Exports rise, imports fall, $NX$ grows.

Decomposition

\frac{\Delta\varepsilon}{\varepsilon} \approx \frac{\Delta E}{E} + \pi - \pi^*

A country can have real appreciation without nominal appreciation if it has higher inflation than its trading partners.

Purchasing Power Parity (long run)

PPP: \ \varepsilon = \bar{\varepsilon} \implies \frac{\Delta E}{E} = \pi^* - \pi

Over decades, nominal exchange rates tend to adjust so the real rate is stable. In the short run, deviations are large and persistent.

Worked Example

E = 0.90 GBP/USD. P_UK = 100 (basket). P_US = 120 (basket). Compute ε. Then E rises to 1.00 GBP/USD (dollar appreciates nominally). Compute new ε.

Initial: ε = E·P/P* = 0.90 × 120 / 100 = 1.08. US goods slightly expensive: 1.08 UK baskets per US basket.
After nominal appreciation: ε = 1.00 × 120 / 100 = 1.20. Real appreciation of about 11%.
NX implication: at ε = 1.20, US exports fall (more expensive abroad) and imports rise (UK goods relatively cheap).

Initial ε = 1.08. After ↑E: ε = 1.20. ~11% real appreciation → NX falls.

Common Mistakes

—Confusing the direction: ↑ε is real appreciation (domestic goods expensive), not depreciation.
—Mixing the quoting convention: E as foreign/domestic vs domestic/foreign changes the sign of results.
—Forgetting inflation: if π > π* with E fixed, there is real appreciation even though nominal E is constant.
—Assuming PPP holds in the short run — it holds approximately over years/decades, not quarters.

Exam Cues

→Formula: ε = E · P / P*. Know the quoting convention assumed.
→Decomposition: Δε/ε ≈ ΔE/E + π − π*. Appears in EMS / Bundesbank-type questions.
→PPP in long run: ε constant → nominal depreciation offsets inflation differential.
→Mundell-Fleming (Ch 20): NX depends on ε, so real appreciation shifts IS left.