Exchange Rates – Determination under Fixed and Managed Systems
1. Measuring exchange rates
- Nominal exchange rate (E) – the price of one unit of foreign currency expressed in domestic currency.
$$E=\frac{\text{Units of domestic currency}}{\text{One unit of foreign currency}}$$
- Real exchange rate (RER) – adjusts the nominal rate for relative price levels, showing the purchasing‑power of the two currencies.
$$RER=\frac{E\times P^{*}}{P}$$
where P = domestic price level (e.g. CPI), P^{*} = foreign price level.
- Trade‑weighted exchange‑rate index – a weighted average of the nominal rates against a basket of the country’s major trading partners (usually USD, EUR, JPY). It measures overall export‑competitiveness.
Worked example (real exchange rate)
Suppose the nominal rate is £0.80 / US$1. UK CPI = 110, US CPI = 105 (base = 100). The real exchange rate is:
$$RER=\frac{0.80 \times 105}{110}=0.764\;\text{£ per US$ (real terms)}$$
Interpretation: after adjusting for price differences, a US$1 buys the equivalent of £0.764 in UK purchasing power.
2. Exchange‑rate regimes (Cambridge syllabus 11.2)
| Regime |
Key characteristics |
| Fixed (or pegged) |
Official parity is set by the government; the central bank intervenes continuously to keep the market rate at that level, using reserves and monetary‑policy tools. |
| Managed (or “dirty”) float |
The rate is determined by market supply and demand, but the central bank intervenes occasionally to smooth excessive volatility or to achieve macro‑economic objectives. |
3. Fixed‑rate system
3.1 How the peg is maintained
- Official parity declaration – the central bank announces a target rate (e.g. Eofficial=1.25 USD/£).
- Foreign‑exchange market intervention – buying foreign currency when there is excess demand for it, or selling foreign currency when there is excess supply.
- Use of foreign‑exchange reserves – reserves act as a buffer; a rapid fall in reserves signals pressure on the peg.
- Monetary‑policy adjustments – changing the domestic interest rate influences capital flows and therefore the pressure on the peg.
- Balance‑of‑payments (BoP) considerations – a persistent current‑account deficit must be financed by capital inflows or reserve draw‑down, otherwise a devaluation may become necessary.
3.2 Revaluation and devaluation
Revaluation: an official upward adjustment of the peg (the domestic currency appreciates).
Devaluation: an official downward adjustment of the peg (the domestic currency depreciates).
Both are used to correct a mis‑aligned BoP: a revaluation can curb inflation from cheap imports, while a devaluation can restore export competitiveness.
3.3 The “Impossible Trinity” (Mundell‑Fleming trilemma)
With a fixed exchange rate a country can simultaneously enjoy only two of the following three:
- Free capital mobility
- Independent monetary policy
- Fixed exchange rate
In practice most fixed‑rate economies sacrifice monetary‑policy independence.
3.4 Example calculation (reserve requirement to defend a peg)
Official parity: Eofficial=0.85 €/US$.
Market rate rises to Emarket=0.90 €/US$. The central bank must sell euros and buy dollars.
$$\Delta R=\frac{(E_{\text{market}}-E_{\text{official}})\times Q_{d}}{E_{\text{official}}}$$
where Qd is the quantity of dollars demanded at the market rate. ΔR is the amount of euro reserves that must be drawn down.
3.5 Summary of tools used under a fixed peg
| Tool |
How it works |
| Direct spot‑market intervention |
Buy foreign currency (to support domestic) or sell foreign currency (to defend the peg). |
| Open‑market operations (OMO) |
Change the domestic money supply, influencing interest rates and capital flows. |
| Reserve‑requirement changes |
Alter the amount of funds banks must hold, affecting credit and the money multiplier. |
| Capital controls |
Restrict inflows/outflows to reduce speculative pressure on the peg. |
4. Managed‑float system
4.1 Main determinants of the exchange rate
- Interest‑rate differentials – higher domestic rates attract foreign capital, increasing demand for the domestic currency.
- Relative price levels (Purchasing‑Power Parity) – if domestic inflation exceeds foreign inflation, the real value of the domestic currency falls, prompting a depreciation.
- Expectations and speculation – anticipated policy moves, political events or shocks can shift demand instantly.
- Capital‑flow dynamics – portfolio investment, FDI and short‑term “hot money” affect supply and demand for the currency.
- Government/central‑bank intervention – occasional buying or selling of foreign currency, or signalling future policy, to smooth excessive volatility.
4.2 Central‑bank intervention tools (managed float)
- Direct spot‑market intervention (buy/sell foreign currency).
- Indirect intervention via open‑market operations that change the domestic money supply.
- Foreign‑exchange swaps or forward contracts – used to signal future policy stance and to manage short‑term liquidity.
- Reserve‑requirement adjustments – affect the amount of money banks can create, influencing interest rates and capital flows.
4.3 Mundell‑Fleming framework (small open economy, imperfect capital mobility)
In a managed float the equilibrium exchange rate is found where the IS, LM and BP curves intersect.
- A rise in the domestic interest rate shifts the LM curve leftward, attracting capital inflows and causing an appreciation (E falls).
- A deterioration in the current account shifts the BP curve leftward, putting upward pressure on E (depreciation).
4.4 Effects of an exchange‑rate change
- Marshall‑Lerner condition – a depreciation improves the current‑account balance if the sum of the absolute values of the export and import price elasticities exceeds one.
$$|\varepsilon_{X}|+|\varepsilon_{M}|>1$$
- J‑curve effect – after an initial depreciation the current account may worsen in the short run (quantities adjust slowly) before improving as export volumes rise and import volumes fall.
4.5 Diagram suggestions (for exam practice)
- Supply‑and‑demand for foreign currency in a managed float, showing a leftward shift of the supply curve after a central‑bank intervention that supports the domestic currency.
- IS‑LM‑BP diagram for a small open economy, highlighting the effect of an interest‑rate increase on E.
- J‑curve diagram (current‑account balance vs. time after a depreciation).
- Marshall‑Lerner illustration: export‑price elasticity, import‑price elasticity and the resulting change in the current account.
5. Comparison of Fixed and Managed Systems
| Aspect |
Fixed exchange rate |
Managed float |
| Primary determinant of E |
Official parity set by the government; maintained by reserves and intervention. |
Market supply and demand; central bank intervenes only occasionally. |
| Monetary‑policy autonomy |
Limited – must align with parity maintenance. |
Greater – can target inflation or output while allowing some exchange‑rate flexibility. |
| Capital mobility |
Often restricted (capital controls) to protect the peg. |
Generally free; capital flows directly affect E. |
| Reserve requirements |
High – large reserves needed to defend the peg. |
Lower – reserves used mainly for occasional smoothing. |
| Vulnerability to speculative attacks |
High if reserves are low or the parity is mis‑aligned. |
Lower; flexibility absorbs shocks. |
| Typical policy objectives |
Exchange‑rate stability, trade predictability. |
Price stability, economic growth, controlled volatility. |
6. Policy implications and exam‑style questions
- Explain how a rise in the domestic interest rate would affect the exchange rate under a managed float. (Use the interest‑rate differential and capital‑flow channel.)
- Discuss the pros and cons of defending a fixed peg when a country experiences a large current‑account deficit.
- Analyse the likely short‑run effect on the exchange rate of a sudden increase in foreign‑exchange reserves.
- Using the Marshall‑Lerner condition, evaluate whether a 10 % depreciation will improve the current account of a country whose export elasticity is 0.4 and import elasticity is 0.7.
- Describe the J‑curve phenomenon and illustrate it with a suitable diagram.
Suggested diagrams for answers
- Supply‑and‑demand for foreign currency (managed float) showing an intervention‑induced shift.
- IS‑LM‑BP diagram for a small open economy under a managed float.
- J‑curve diagram (current‑account balance vs. time after depreciation).
- Marshall‑Lerner illustration with export and import elasticities.
7. Summary
Fixed exchange‑rate regime: The government sets an official parity and must use foreign‑exchange reserves, monetary‑policy adjustments, and often capital controls to keep the market rate at that level. Revaluation (appreciation) and devaluation (depreciation) are official adjustments to the peg.
Managed‑float regime: The exchange rate is primarily determined by market forces—interest‑rate differentials, relative price levels (PPP), expectations, and capital flows—while the central bank intervenes intermittently to curb excessive volatility or to achieve broader macro‑economic goals. The choice between regimes involves trade‑offs among exchange‑rate stability, monetary‑policy independence and the need for reserves, as captured by the impossible trinity.