The determination of the equilibrium foreign exchange rate

International Trade and Globalisation – Foreign‑Exchange Rates

Objective

To understand how the equilibrium foreign‑exchange (FX) rate is determined in the foreign‑exchange market and to analyse the effects of changes in that rate.

Key Definitions (Cambridge wording)

Why do economic agents buy or sell foreign currency? (Cambridge order)

• Trade transactions – importers need foreign currency to pay for overseas goods and services; exporters receive foreign currency from sales abroad.
• Investment flows – investors buy foreign assets (stocks, bonds, real estate) and must obtain the foreign currency; foreign investors sell that currency when they repatriate profits, interest and dividends.
• Speculation – traders anticipate future movements in the FX rate and buy (or sell) now to profit from expected appreciation or depreciation.
• Government intervention – central banks may buy or sell foreign currency to influence the rate or to maintain a fixed peg.
• Tourism / holiday spending – households travelling abroad need foreign currency to pay for accommodation, transport, and other expenses.

Demand for Foreign Currency

The demand curve is downward‑sloping because, ceteris paribus, a lower price of foreign currency (i.e. a cheaper foreign currency) makes imports, travel and foreign investment relatively cheaper, increasing the quantity demanded.

Determinants that shift the demand curve (right‑ward = increase, left‑ward = decrease)

• Higher domestic income (Y_d) → more purchases of imported goods.
• Lower foreign income (Y_f) → foreign demand for domestic exports falls, reducing the need for foreign currency.
• Relative price change (terms of trade) – if foreign goods become cheaper, demand for foreign currency rises.
• Expectations of future depreciation of the domestic currency → agents buy foreign currency now.
• Higher foreign interest rates (i_f) relative to domestic rates → capital inflows increase demand for foreign currency.
• Speculative expectations of a rise in the foreign currency’s value.

Supply of Foreign Currency

The supply curve is upward‑sloping because a higher price of foreign currency (i.e. a more valuable foreign currency) encourages exporters and foreign investors to sell their foreign earnings for the domestic currency.

Determinants that shift the supply curve (right‑ward = increase, left‑ward = decrease)

• Higher domestic production / export levels (X) → more foreign earnings to convert.
• Increased foreign direct investment (FDI) or portfolio‑investment inflows → brings foreign currency into the domestic market.
• Higher domestic interest rates (i_d) relative to foreign rates → attract foreign capital, increasing supply.
• Government intervention – central bank sells foreign reserves (adds to supply) or buys reserves (removes supply).
• Expectations of future appreciation of the domestic currency → exporters may hold off selling, reducing supply.
• Speculative expectations of a fall in the foreign currency’s value.

Diagram – Axes and Labels

When drawing the foreign‑exchange market diagram, label the axes exactly as the syllabus requires:

• Vertical axis (P): FX rate – price of one unit of foreign currency in domestic currency (e.g. £ per $).
• Horizontal axis (Q): Quantity of foreign currency.

Equilibrium Determination

Equilibrium occurs where the quantity of foreign currency demanded equals the quantity supplied.

Linear‑equation model (used in IGCSE)

\[

QD = a - bP \qquad\qquad QS = c + dP

\]

• \(Q_D\) – quantity demanded.
• \(Q_S\) – quantity supplied.
• \(P\) – FX rate (price of foreign currency).
• \(a, b, c, d\) – positive constants that capture the determinants listed above.

Step‑by‑step checklist for solving the equilibrium rate

1. Write down the demand and supply equations.
2. Set them equal: \(a - bP = c + dP\).
3. Collect the \(P\) terms on one side: \((b + d)P = a - c\).
4. Solve for \(P\): \(P^{*} = \dfrac{a - c}{b + d}\).
5. Substitute \(P^{*}\) back into either the demand or supply equation to find the equilibrium quantity \(Q^{*}\) (optional for exam).

Illustrative Example 1 – Solving a linear system

Demand and supply for US dollars (USD) in the United Kingdom:

\[

QD = 500 - 2P \qquad\qquad QS = 100 + 3P

\]

1. Set \(QD = QS\): \(500 - 2P = 100 + 3P\).
2. Bring the \(P\) terms together: \(500 - 100 = 3P + 2P\) → \(400 = 5P\).
3. Solve for \(P\): \(P^{*} = 80\).

Interpretation: 1 USD = £0.80. This is the equilibrium rate where UK importers’ demand for dollars equals the amount exporters and investors are willing to sell.

Illustrative Example 2 – Effect of a right‑ward demand shift

Domestic income rises, shifting demand to:

\[

Q_D' = 620 - 2P

\]

Supply remains \(Q_S = 100 + 3P\).

1. Set \(QD' = QS\): \(620 - 2P = 100 + 3P\).
2. Re‑arrange: \(620 - 100 = 3P + 2P\) → \(520 = 5P\).
3. Solve: \(P' = 104\).

Result: 1 USD = £1.04. The dollar has appreciated (the pound has depreciated) because higher domestic income increased demand for foreign currency.

Impact of Shifts – Diagrammatic Interpretation

When the demand curve shifts right, the equilibrium moves up the supply curve – the foreign currency becomes more expensive (appreciates).

When the supply curve shifts right, the equilibrium moves down the demand curve – the foreign currency becomes cheaper (depreciates).

Consequences of Changes in the Exchange Rate

• Appreciation of the domestic currency

  • Imports become cheaper → consumer‑price inflation may fall.
  • Exports become more expensive for foreign buyers → export demand falls.
  • Current‑account deficit may shrink (or surplus may grow).

• Depreciation of the domestic currency

  • Imports become more expensive → imported inflation may rise.
  • Exports become cheaper for foreign buyers → export demand rises.
  • Current‑account deficit may widen (or surplus may shrink).

• Both movements affect household purchasing power, firm profitability and the attractiveness of the country for foreign investment.

Summary Table of Determinants

Key Take‑aways

• The equilibrium FX rate is where the quantity of foreign currency demanded equals the quantity supplied.
• A floating exchange rate is set entirely by market forces; appreciation means the domestic currency strengthens, depreciation means it weakens.
• Demand‑side determinants: domestic income, foreign income, relative prices, expectations, and foreign interest rates.
• Supply‑side determinants: export earnings, foreign‑investment inflows, domestic interest rates, expectations, and government intervention.
• Any shift in these determinants moves the equilibrium rate, influencing import prices, export competitiveness, inflation and the balance of payments.
• For the exam you must be able to:

  1. Draw the demand‑supply diagram with correctly labelled axes (P on vertical, Q on horizontal).
  2. Identify the direction of a shift and state whether the foreign currency appreciates or depreciates.
  3. Solve a simple linear system (set QD = QS, isolate P) and interpret the result.