In a foreign exchange market operating under a flexible exchange rate system, the daily qu… — JAMB UTME

In a foreign exchange market operating under a flexible exchange rate system, the daily quantity demanded of Euros ( $\text{EUR}$ ) in millions is given by $Q_d = 500 - 0.5E$ , while the daily quantity supplied of Euros in millions is given by $Q_s = 100 + 0.3E$ , where $E$ represents the exchange rate of local currency ( $\text{LCU}$ ) per Euro. What is the equilibrium exchange rate ( $E$ ) in local currency per Euro?

Answer: 500 LCU/EUR

Answer

The equilibrium exchange rate is

500

local currency units per Euro.

Under a floating exchange rate mechanism, the equilibrium exchange rate is determined at the point where the demand for foreign exchange equals the supply of foreign exchange (

Q_d = Q_s

). Setting

500 - 0.5E = 100 + 0.3E

yields

400 = 0.8E

, which calculates to

E = 500

local currency units per Euro.

Step-by-Step Solution

Equate the foreign exchange demand and supply functions to find market equilibrium.

500 - 0.5E = 100 + 0.3E

Equilibrium in a floating foreign exchange rate system is established where the market demand for foreign currency equals its market supply.

Rearrange the equation to gather constant terms on one side and exchange rate terms on the other side.

400 = 0.8E

Subtract

100

from both sides and add

0.5E

to both sides.

Divide the constant term by the combined coefficient of

E

to solve for the exchange rate.

E = 500

Dividing

400

0.8

yields the equilibrium exchange rate of

500

local currency units per Euro.

Key Concept

Determination of equilibrium exchange rate in a flexible foreign exchange market

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