The determination of the equilibrium foreign exchange rate

International Trade and Globalisation – Foreign Exchange Rates

Objective

To understand how the equilibrium foreign exchange rate is determined in the foreign‑exchange market.

Key Concepts

• Foreign exchange rate (FX rate): The price of one currency expressed in terms of another.
• Spot market: Market for immediate delivery of foreign currency.
• Demand for foreign currency: The amount of foreign currency that buyers wish to obtain.
• Supply of foreign currency: The amount of foreign currency that sellers are willing to provide.
• Equilibrium FX rate: The rate at which the quantity of foreign currency demanded equals the quantity supplied.

Demand for Foreign Currency

The demand curve slopes downwards because, ceteris paribus, a lower price of foreign currency (i.e., a cheaper foreign currency) encourages more imports, travel, and investment abroad.

Factors that shift the demand curve:

• Changes in domestic income – higher income increases demand for imports.
• Changes in foreign income – higher foreign income raises demand for domestic exports, reducing demand for foreign currency.
• Relative price changes – if foreign goods become relatively cheaper, demand for foreign currency rises.
• Expectations of future exchange rates – expectation of depreciation makes buyers want to purchase foreign currency now.
• Interest rate differentials – higher foreign interest rates attract capital, increasing demand for foreign currency.

Supply of Foreign Currency

The supply curve slopes upwards because a higher price of foreign currency (i.e., a more expensive foreign currency) encourages more exporters and foreign investors to sell foreign currency for the domestic currency.

Factors that shift the supply curve:

• Domestic production levels – higher output raises export earnings, increasing supply of foreign currency.
• Foreign investment inflows – foreign direct investment (FDI) brings foreign currency into the domestic market.
• Government interventions – foreign‑exchange reserves sold or bought by the central bank.
• Expectations of future exchange rates – expectation of appreciation leads exporters to hold off selling foreign currency, reducing supply.
• Interest rate differentials – higher domestic interest rates attract foreign capital, increasing supply of foreign currency.

Equilibrium Determination

In the foreign‑exchange market, equilibrium is reached where the quantity of foreign currency demanded equals the quantity supplied.

Mathematically, let:

\$QD = f(P, Yd, Yf, Ee, if - id)\$

\$QS = g(P, X, If, id - if)\$

where:

• \$Q_D\$ = quantity of foreign currency demanded
• \$Q_S\$ = quantity of foreign currency supplied
• \$P\$ = foreign exchange rate (price of foreign currency in domestic currency)
• \$Y_d\$ = domestic income
• \$Y_f\$ = foreign income
• \$E_e\$ = expected future exchange rate
• \$if\$, \$id\$ = foreign and domestic interest rates
• \$X\$ = exports
• \$I_f\$ = foreign investment inflows

Equilibrium condition:

\$QD(P^*) = QS(P^*)\$

Solving for \$P^*\$ gives the equilibrium foreign exchange rate.

Illustrative Example

Suppose the demand and supply for US dollars (USD) in the UK are represented by the following linear equations:

\$Q_D = 500 - 2P\$

\$Q_S = 100 + 3P\$

where \$P\$ is the price of 1 USD in pounds (£) and \$Q\$ is measured in millions of dollars.

Set \$QD = QS\$ to find equilibrium:

\$500 - 2P = 100 + 3P\$

\$400 = 5P\$

\$P^* = 80\$

Thus, the equilibrium exchange rate is £0.80 per USD.

Impact of Shifts

Consider a rise in UK domestic income, shifting the demand curve rightward. Holding supply constant, the new equilibrium will be at a higher \$P\$, meaning the USD appreciates relative to the pound.

Summary Table of Determinants

Key Take‑aways

• The equilibrium foreign exchange rate is set where demand equals supply for a given currency.
• Both macro‑economic variables (income, interest rates) and expectations influence the position of the demand and supply curves.
• Changes in any determinant cause the equilibrium rate to move, affecting the relative price of imports, exports, and capital flows.
• Understanding these mechanisms helps explain short‑run exchange‑rate volatility and informs policy decisions.