Question

Assume that the following data characterize the hypothetical economy of Trance: money supply = \(200 billion; quantity of money demanded for transactions = \)150 billion; quantity of money demanded as an asset = \(10 billion at 12 percent interest, increasing by \)10 billion for each 2-percentage-point fall in the interest rate.

a. What is the equilibrium interest rate in Trance?

b. At the equilibrium interest rate, what are the quantity of money supplied, the quantity of money demanded, the amount of money demanded for transactions, and the amount of money demanded as an asset in Trance?

Short answer

a.The equilibrium interest rate in Trance is 4%.

b.The quantity of money demanded and supplied is $200 billion,

The amount of money demanded for transactions is $150 billion.

The amount of money as an asset is $50 billion.

Step-by-step solution

Equilibrium interest rate

The quantity of money demanded as an asset increases by $10, interest rate decreases by 2%. In the question, the total money supply is $200 billion. And from the supply-demand equilibrium

$$\begin{gathered} Q_s=Q_d \\ =Money{D}_T+MoneyasAsset \\ 200=150+Assetmoney \\ So,Asset(demandofmoney)=50 \end{gathered}$$

From the given data, the quantity of money demanded as an asset is 10 at a 12% interest rate and increases by 10 at every 2% fall in interest rate.

Thus, to obtain $50 billion of money (so that money supplied is equal to money demanded) as an asset, the equilibrium interest rate should be 4%.

Various quantities of money at the equilibrium rate of interest

The quantity of money supplied at an equilibrium interest rate of 4% is $200 billion. The quantity of money demanded at this rate is also $200 billion.

The quantity of money demanded for transactions are $ 150 billion. And the amount of money demanded as an asset is $50 billion at an equilibrium interest rate of 4% in Trance.