The currency used in the Duchy of Saxony is the ducet.Suppose the demand for the Saxonian ducet in the foreign exchange market equals 14,000 - 3,000e and the supply of ducets in the foreign exchange market equals 2,000 + 2,000e,where e is the nominal exchange rate expressed in dollars per ducet.If the ducet is fixed at $3 per ducet,then to maintain this fixed rate the Duchy of Saxony's international reserves must ____________ per period.

Question

Quizplus · Accepted Answer

To maintain a fixed exchange rate, the government must buy or sell its currency as needed in the foreign exchange market. When the demand for ducets exceeds the supply, the price of the ducet will rise above $3, which means that the Saxonian government must sell ducets and buy dollars to maintain the fixed rate.

From the demand and supply equations given, we can find the equilibrium exchange rate:

Demand = Supply
14,000 - 3,000e = 2,000 + 2,000e
5,000e = 12,000
e = 2.4

Since the fixed rate is $3 per ducet, the market exchange rate is below the fixed rate, which means the government needs to buy ducets (sell dollars) to maintain the fixed rate. The amount of dollars the government needs to buy can be found by multiplying the excess demand by the market exchange rate:

Excess demand = Demand - Supply
Excess demand = (14,000 - 3,000e) - (2,000 + 2,000e)
Excess demand = 12,000 - 5,000e

Excess demand at the equilibrium exchange rate:
Excess demand = 12,000 - 5,000(2.4)
Excess demand = 12,000 - 12,000 = 0

This means that at the equilibrium exchange rate, there is no excess demand or supply of ducets. However, since the fixed rate is higher than the equilibrium rate, there is excess demand for ducets, so the government needs to buy ducets with dollars to maintain the fixed rate. The amount of dollars needed per period can be found by multiplying the excess demand at the fixed exchange rate by the fixed exchange rate:

Excess demand at the fixed exchange rate:
Excess demand = 12,000 - 5,000(3)
Excess demand = -3,000

This means that the government needs to buy ducets (sell dollars) worth $3,000 to maintain the fixed exchange rate. Since the question asks for the change in international reserves per period, we know that the answer must be a change in dollars. Since the government needs to buy ducets with dollars, we know that the international reserves will decrease by $3,000 per period.

Therefore, the answer is (C) decrease by $9,000.

The Currency Used in the Duchy of Saxony Is the Ducet.Suppose