Question

Suppose that the money demand function is (M/P)d = 800 - 50r, where r is interest rate in percent. The money supply M is 2,000 and the price level P is fixed at 5. a. Graph the supply and demand for real money balances. b. What is equilibrium interest rate? c. What happens to the equilibrium interest rate if the supply of money is reduced from 2000 to 15000? d. If the central bank wants the interest rate to be 4 percent, what money supply should it set?

Answer 1

A)

In the graph the downward sloping curve shows the money demand function. That is $(\frac{M}{P})^{D}=800-50r$ With M=2000 and P=5. So the real money balances is $(\frac{M}{P})^{S}=400$ . We know that real money supply is independent with the rate of interest. So it will represented on vertical axis.

That is:

B)

When we get the equilibrium rate of interest when the demand for money and real balances of money are intersect each other. That is

$400=800-50r$

$400=50r$

$r=\frac{400}{50}=8$

so the rate of interest is 8%

C)

In this case the real money balnces reduced to 2000 to 1500 then the new real balances is $(\frac{M}{P})^{S}=300$ . Then the new equilibrium rate of interest is solved by

$300=800-50r$

$500=50r$

$r=\frac{500}{50}=10$

When money supply reduced from 2000 to 1500 the rate of interest increased from 8% to 10%

D)

If the central bank set the interest rate at 4 percent then $(\frac{M}{P})^{S}$ equal to $(\frac{M}{P})^{D}$ Then

$\frac{M}{P}=800-50r$

Here the price level is 5 and interest rate is 4 percent. Then,

$\frac{M}{5}=800-50\times 4$

$\frac{M}{5}=800-200$

$\frac{M}{5}=600$

$M=600\times 5=1300$

If the central bank set interest rate at 4.Then nominal money supply increased from 800 to 1300.

Answer 2

Money demand or the demand for money refers to the optimal or desired holdings of financial assets in the form of money. The money is either kept as cash in hand or in the form of bank deposits. Money supply refers to the total amount of money in circulation or in existence in a country. It can be affected by the Federal Bank, which is not under control of the government and is an independent body. money supply through open market operations, changes in discount rates s and changes in required reserve ratios. Suppose the money demand function is given as follows: M800-50r The nominal money supply is 2,000 and the price level is fixed at 5. Thus, the real money balances are 400 The following graph shows the supply and demand for real money balances:

Interest rates Money Supply 16% Money demand 400 800 Real Money Balances The equilibrium interest rate is calculated as follows:

800-50r 50r = 400 7-8% 400 Hence, the equilibrium rate of interest is 8% Suppose the nominal supply of money is reduced from 2,000 to 1,500. The real money supply is now 300 (MP). The new equilibrium interest rate is calculated as follows: (MAY-(%" 800-50r 300 50r 500 E-10%] Thus, the new equilibrium interest rate is 10%

If the Fed wants an interest rate of 4%, then the level of nominal money supply should be 800-50ir 4, 000-250(4%) = M M 4,000-1,000 M 3,000 Hence, the Fed should set the nominal money supply at 3,000