In a foreign exchange market, the daily demand for US Dollars (\text{USD}) in Nigeria is r… — JAMB UTME

In a foreign exchange market, the daily demand for US Dollars ( $\text{USD}$ ) in Nigeria is represented by the function $Q_d = 250 - 0.25 E$ , and the daily supply of US Dollars is represented by $Q_s = 50 + 0.25 E$ , where $Q$ is the quantity in millions of US Dollars and $E$ is the exchange rate in Naira per Dollar ( $\text{NGN/USD}$ ). If the monetary authority fixes the exchange rate at $\$1 = \text{NGN } 350$ , how many millions of US Dollars must the central bank release from its foreign reserves daily to clear the market deficit and defend this pegged rate?

Answer: 25 million USD

Answer

The central bank must supply 25 million US Dollars from its reserves daily.

At the fixed exchange rate of

\text{NGN } 350

per US Dollar (which overvalues the Naira relative to the free-market equilibrium of

\text{NGN } 400

), foreign currency demand (

162.5\text{ million USD}

) exceeds foreign currency supply (

137.5\text{ million USD}

). To prevent the exchange rate from depreciating towards equilibrium, the monetary authority must inject the shortfall of

25\text{ million USD}

directly from its foreign reserves.

Step-by-Step Solution

Substitute the pegged exchange rate (

E = 350

) into the foreign exchange demand equation to find

Q_d

Q_d = 250 - 0.25(350) = 162.5\text{ million USD}

Determines the total foreign currency demanded by importers and investors at the fixed exchange rate.

Substitute the pegged exchange rate (

E = 350

) into the foreign exchange supply equation to find

Q_s

Q_s = 50 + 0.25(350) = 137.5\text{ million USD}

Determines the private market supply of foreign currency from exporters and foreign inflows at the fixed exchange rate.

Subtract market supply from market demand (

Q_d - Q_s

) to calculate the foreign exchange shortfall.

\text{Market Deficit} = 162.5 - 137.5 = 25\text{ million USD}

Under a fixed exchange rate system, the central bank must intervene by selling reserves equal to the market deficit to prevent the currency from depreciating.

Key Concept

Central Bank Intervention in Fixed Exchange Rate Systems

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