Question

Suppose that the money demand function is (M/P)d=1000-200r where r is the interest rate in percent. The money supply M is 1200 and the price level P is 2.

a. Graph the supply and demand for real money balances.
b.What is the equilibrium interest rate?
c. Assume the price level is fixe
d. What happens to the equilibrium interest rate if the supply of money is raised from 1200 to 1600?
d. If the Fed wishes to raise the interest rate to 5 percent, what money supply should it set?

Answer 1

The equilibrium interest rate with a money supply of 1200 and price level of 2 is 2.5%. If the money supply increases to 1600, the interest rate falls to maintain equilibrium. To raise the interest rate to 5%, the Fed would theoretically reduce the money supply to zero, which is impractical, indicating a significant reduction would be needed.

Step-by-step explanation:

To address the student's question regarding the money demand function and the effects of changes in money supply, we need to evaluate each part of the question:

• Graphing the supply and demand for real money balances would show a downward-sloping demand curve based on the money demand function (M/P)d = 1000 - 200r, and a vertical supply curve at M = 1200 since the supply is given and fixed.
• The equilibrium interest rate can be found by setting the real money demand equal to the real money supply, which is (1200/2). Solving for r in the demand equation 500 = 1000 - 200r gives us r = 2.5% as the equilibrium interest rate.
• When the money supply is increased from 1200 to 1600, with the price level fixed, the new real money supply would be (1600/2). To achieve the new equilibrium, the interest rate would decrease because the higher money supply would reduce the interest rate needed to equate demand and supply.
• If the Fed wishes to raise the interest rate to 5 percent, we would set the demand for real money balances equal to the new desired interest rate and solve for M in the equation (M/P)d = 1000 - 200(5). The money supply needed would be M = P*(1000 - 200*5) = 2*(1000 - 1000) = 0, which is theoretically not plausible. In practice, however, the Fed would need to significantly reduce the money supply below the initial value to approach the desired higher interest rate while considering other market dynamics and the liquidity trap.

Answer 2

Answe and Explanation:

b) To find out the equilibrium interest we will equate the money demand function with the money supply:

1000 - 200(r) = 1200/2

r = 2%

c) If the price is fixed and if the supply of money of is increased from 1200 to 1400 then the supply of real balances will be 1400/2 = 700

The equilibrium interest would be:

1000 - 200(r) = 700

r = 1.5%

Thus, it shows that when the supply of money is increased and the price is fixed then the interest rate would fall from 2% to 1.5%

d) The supply of real balances would be 1600/2 = 800

Hence, the interest rate will be:

1000-200(r) = 800

r = 1%

As proved above, an increase in the money supply would decrease the interest rate keeping the price fixed.

e) If the Fed keeps the interest rate at 5% then,

1000 - 200(5) = Money supply/2

Money supply = 0

Reduce the money supply if the interest is increase from 2% to 5%

a) Picture is attached.