Question

Suppose the money demand function

Mᵈ =Y(8-0.5i)

where i is the interest rate, as a percentage. The initial money supply M is 2000 and the nominal income $Y is 500.

a. What is the equilibrium interest rate?

b. Suppose the reserve ratio is 10%. The public hold 20% of money in currency. What is quantity of central bank money?

c. If the central bank wants to change the interest rate to 4 percent, what new money supply will it set?

d. Graph the supply of and demand for money and show the change in part c.

e. How does the central bank reduce the interest rate through open market operation? How much the central bank needs to transact to achieve the target in part c?

f. Starting from the situation in parts a and b, suppose the introduction of an electronic payment system eliminates the need of holding currency and makes the money demand more sensitive to interest rate so that
​​​​​​​Mᵈ =Y(8-0.6i).
The nominal income $Y is still 500. If the central bank keeps the interest rate at the level in part a, how would the quantities of money and central bank money change?

Answer 1

To target a 4% interest rate, the central bank must adjust the money supply according to the basic quantity equation of money, with a constant nominal income of 500. Contractionary policies can reduce the money supply, while an example increase of $100 billion in supply would expand nominal GDP by $300 billion, assuming a constant money velocity of 3.

Step-by-step explanation:

If the central bank wants to adjust the interest rate to 4%, it needs to consider the basic quantity equation of money, which states that the money supply multiplied by the velocity is equal to the nominal GDP (money supply × velocity = nominal GDP). Keeping the nominal income (Y) constant at 500, the central bank can leverage this equation to calculate the new money supply necessary to target the desired 4% interest rate.

To determine the change in quantities of money and central bank money when keeping the interest rate at 4%, one must consider that the central bank's actions would reflect a contractionary monetary policy if they intend to raise the interest rate. This type of policy typically reduces the money supply and consequently the quantity of central bank money. Additionally, factors such as deposit insurance, the economic cycle, and changes in the discount rate may affect these quantities.

Using the information provided about an increase of $100 billion in money supply with a velocity of 3, the nominal GDP would expand by $300 billion ($100 billion × 3). This provides an idea of how changes in the money supply can significantly influence the nominal GDP, given the velocity of money as a constant factor.