Question

Suppose that we know that the velocity of money for Las Vegas is constant, the supply of money is growing at a rate of 6% per year, and the real GDP is growing at 3% per year. Also, the real interest rate in Las Vegas is is 2%. Show your work.

PART A. Solve for the nominal interest rate, i.

PART B. If the central bank decreases the money growth rate by 3% percentage points per year

(i.e. M = 3), determine the nominal interest rate. How does this compare to part A. What happens to the nominal interest rate, Delta i?

PART C. Suppose the growth rate of real GDP, Y, falls to 1% per year and that the growth

rate of the money supply is still 6%.

Determine the in?ation rate, Pi. How does this in?ation rate compare to part A?

Now, the central would like to maintain the level of in?ation found in part A. What must the

central bank do if it wishes to keep in?ation constant?

Answer 1

According to the quantity theory of money the following condition should hold.

=> m + v = p + y, where “m=growth of money supply”, “v=growth of velocity of money”, “p=growth of P” and “y=growth of output”.

A).

So, here “v = 0”, “”m = 6” and “y = 3”, => “p = 3”, by using the above relation.

Now, if “r=2%”, => i = r + p = 2% + 3% = 5%”. So, the nominal interest rate is “i=5%”.

B).

Now, the money supply decreases by “3%”, => “m = 6 -3 = 3” and “y = 3”, => “p = 0” by using the above relation.

=> m+ v = p + y,=> 3 = p + 3 => p = 0. So, here the nominal interest rate is equal to the real interest rate, => i=r=2%”, => ?i = 2 – 5 = (-3%), it decreases by “3%” .

C).

Growth rate of “Y” decreases by “1%”, => “y = 2”and “m=6”, => p = 4”.

So, here the rate of inflation is “4%” which is more than “part A” by “1%”.

Now, the central bank want to keep the “p=3” and “y=2”, => here the central bank should reduce the money supply by “1%”, => m =6 -1 = 5”. So, if “m=5”, => p = m-y= 5 – 2 = 3.

So, the central bank should reduce the money supply by “1%”.