measurement of exchange rates: distinction between nominal and real exchange rates

Exchange Rates – Measurement, Determination and Economic Effects (Cambridge IGCSE/A‑Level)

1. Measuring Exchange Rates

1.1 What is an exchange rate?

An exchange rate is the price of one country’s currency expressed in terms of another’s. It is the “price” that traders pay in the foreign‑exchange (FX) market.

1.2 Nominal exchange rate ( e )

• Definition: the amount of domestic currency required to purchase one unit of foreign currency.
• Cambridge notation: e = domestic currency / foreign currency (domestic‑per‑foreign).
• Reminder: if the rate is quoted the other way round (foreign per domestic) you must invert it before using the formula for the real exchange rate.
• Formula: $$e = \frac{\text{Domestic‑currency units}}{\text{Foreign‑currency unit}}$$
• Example: If £1 buys €1.20, then e = 1.20 € / £. The pound is the domestic currency, the euro the foreign currency.

1.3 Real exchange rate ( R )

• Definition: the relative price of a typical basket of domestic goods to a comparable basket of foreign goods, after adjusting for price‑level differences.
• Cambridge notation: $$R = \frac{e \times P^{*}}{P}$$ where
  • e = nominal exchange rate (domestic per foreign)
  • P^{*} = foreign price level (e.g., foreign CPI index)
  • P = domestic price level (e.g., domestic CPI index)
• Interpretation
  • R = 1 → identical purchasing power in both countries (PPP equilibrium).
  • R > 1 → domestic goods are relatively expensive (real appreciation).
  • R < 1 → domestic goods are relatively cheap (real depreciation).

1.4 Relationship between nominal and real rates

1. Holding price levels constant (ceteris paribus), a change in e moves R in the same direction.
2. If price levels change, R can shift even when e is unchanged – the “inflation‑differential” effect.
3. Time dimension
   • Short‑run: A nominal depreciation improves competitiveness only if domestic inflation is lower than foreign inflation.
   • Long‑run: Persistent inflation erodes the real effect; the real exchange rate tends toward PPP equilibrium.

1.5 Numerical illustration – nominal vs. real

Real exchange rate:

$$R = \frac{e \times P^{*}}{P}= \frac{0.75 \times 110}{100}=0.825$$

Interpretation: R < 1 – the pound is undervalued in real terms; UK goods are relatively cheap for US consumers.

2. Determination of Exchange Rates

2.1 Floating (market‑determined) rates

In a floating system the exchange rate is set by supply and demand in the FX market.

• Key determinants (Cambridge syllabus)
  • Interest‑rate differentials (uncovered interest parity)
  • Relative price levels (inflation differentials)
  • Expectations about future rates (speculative flows)
  • Relative income and output (trade‑balance effects)
  • Risk premium and capital‑flow considerations
• Ceteris paribus: All other factors are held constant when analysing the effect of one determinant.

2.2 Fixed and Managed‑float regimes

• Fixed rate: Government (or central bank) commits to a specific e and intervenes to keep it at that level.
• Managed float (or “dirty float”): The rate is largely market‑determined but the authority may intervene occasionally to smooth excessive volatility.
• Policy tools
  • Buying/selling foreign reserves
  • Changing domestic interest rates (monetary policy)
  • Capital controls or exchange‑rate bands

2.3 Policy‑option checklist (when each tool is used)

2.4 Revaluation, Devaluation, Appreciation and Depreciation

3. Impact of Exchange‑Rate Movements on the External Economy

3.1 Current‑account effects – the Marshall‑Lerner condition

• The condition states that a real depreciation improves the current account iff the sum of the export‑price elasticity (εₓ) and the import‑price elasticity (εₘ) exceeds one: $$\varepsilon_x + \varepsilon_m > 1$$
• Why it matters:
  • The price effect of a depreciation makes exports cheaper and imports more expensive.
  • Only when the volume response (captured by the elasticities) is large enough does the net export revenue rise.
  • The condition must hold both before and after the depreciation for the improvement to be sustained.
• In the short run elasticities are often low, so a depreciation may initially worsen the trade balance.

3.2 Short‑run dynamics – the J‑curve

After a real depreciation the current‑account balance may first fall (imports are sticky) and later improve as export volumes rise and import volumes fall, producing a “J‑shaped” trajectory.

4. Linking Exchange Rates to Core Economic Concepts

• Margin‑decision: Firms compare marginal revenue from exporting (price in foreign currency × expected exchange rate) with marginal cost (including domestic input prices). A real depreciation raises marginal revenue, encouraging export expansion.
• Equilibrium / Disequilibrium: In the FX market equilibrium, supply = demand at the prevailing e. Fixed‑rate regimes impose a price ceiling or floor; if market pressure differs, excess demand or supply creates disequilibrium.
• Efficiency: An appropriately valued real exchange rate allocates resources to their most productive uses (comparative advantage). Over‑valuation leads to too many imports and under‑utilised export capacity.
• Equity (distributional effects): Appreciation benefits import‑dependent consumers but harms export‑oriented workers; depreciation has the opposite distributional impact.
• Progress & Development: Developing economies often pursue a slightly undervalued real exchange rate to stimulate export‑led growth, but must balance this against inflationary pressures and external vulnerability.

5. Further Numerical Example – Marshall‑Lerner Test

Assume a 10 % real depreciation. Export‑price elasticity = 0.4, import‑price elasticity = 0.7.

Check the condition:

$$\varepsilon_x + \varepsilon_m = 0.4 + 0.7 = 1.1 \; > \; 1$$

Because the sum exceeds one, the real depreciation is expected to improve the current‑account balance in the medium term, provided the elasticities remain unchanged.

6. Summary – Key Points to Remember

• The nominal exchange rate (e) is the market price of one currency in terms of another; it must be quoted as domestic‑per‑foreign for the real‑rate formula.
• The real exchange rate adjusts the nominal rate for relative price levels: R = (e × P*) / P.
• Changes in e affect R ceteris paribus; inflation differentials also shift R.
• Exchange‑rate regimes:
  • Floating – determined by market forces.
  • Fixed / Managed float – set by government intervention, using tools such as reserve operations, interest‑rate changes, or capital controls.
• Policy actions (revaluation, devaluation, appreciation, depreciation) are used to influence competitiveness, inflation, and the external balance; the checklist above links each tool to typical objectives and real‑world cases.
• The Marshall‑Lerner condition tells us when a real depreciation will improve the current account; it must hold both before and after the move.
• In the short run a depreciation may cause a temporary deterioration of the trade balance – the J‑curve effect.
• Real‑exchange‑rate movements intersect with margin‑decision, market equilibrium, efficiency, equity and development – all core concepts in the Cambridge syllabus.