Question

Suppose the velocity of money (V) is constant, Money supply (M) is growing at 5% per year, output (Y) is growing at 2% per year and interest rate (r) is 4%. Using the knowledge of the quantity theory of money and the Fischer effect;

a) Solve for i (nominal interest rate)

b) If the Central Bank increases the money supply by 2 percentage point per year, find the change in nominal interest rate

c) Suppose the growth rate of Y falls to 1% per year, what will happen to inflation? What can the Central Bank do if it wishes to keep inflation constant?

Answer 1

Suppose V is constant, M is growing 5% per year, Y is growing 2% per year, and r = 4.

a)

We first find $\pi = 5 -2$

$\pi=3$

Therefore, $i = r + \pi$

$= 4 + 3$

$= 7$

b)

$\Delta i = 2$

It is just the same as the increase in the money growth rate.

$π=5−2$

$π=3$

Hence, $i = r + \pi$

$=4+3$

$= 7$

c)

The central bank does nothing $\Delta \pi =1$. For the central bank to prevent inflation from rising, it must reduce the money growth rate by $1\%$ point per year.