Question

Suppose V is constant, M is growing 5% per year, Y is growing 2% per year, and r = 4. a. Solve for i. b. If the Central bank increases the money growth rate by 2 percentage points per year, find Δi. c. Suppose the growth rate of Y falls to 1% per year. - What will happen to π ? - What must the Fed do if it wishes to π constant?

Answer 1

According to quantity theory of money:

MV = PY

Where M is money supply; V is velocity; P is price level; Y is real GDP.

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(a)

MV = PY

=> Growth rate of M +Growth rate of V = Growth rate of P + Growth rate of Y

Given information

V is constant. So, growth rate of V will be zero.

Growth rate of M = 5%

Growth rate of Y =2%

=> Growth rate of M +Growth rate of V = Growth rate of P + Growth rate of Y

=> 5% + 0 = Growth rate of P + 2%

=> Growth rate of P = 5% - 2%

=> Growth rate of P= 3%

Hence, the inflation rate is  3%

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According to fisher effect.

Nominal interest rate (i) = Real interest rate (r) + inflation rate

=> i = r + inflation rate

=>i = 4% + 3%

=> i = 7%

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(b)

Central bank increases the money growth rate by 2 percentage points per year,

=>Growth rate of M = 5% + 2% = 7%

and Growth rate of Y = 3%

=> Growth rate of M +Growth rate of V = Growth rate of P + Growth rate of Y

=> 7% + 0 = Growth rate of P + 2%

=> Growth rate of P = 7% - 2%

=> Growth rate of P= 5%

Hence, the inflation rate is 5%

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New inflaton rate is 5%

According to fisher effect.

Nominal interest rate (i) = Real interest rate (r) + inflation rate

=> i = r + inflation rate

=>i = 4% + 5%

=> i = 9%

New nominal interest rate is 9%.

Change in nominal interest rate (Δi) = New nominal interest rate - original nominal interest rate

=> Δi = 9% - 7%

=> Δi = 2%

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(c)

(i)

Suppose growth rate of Y falls to 1%.

Growth rate of Y = 1%

and Growth rate of M = 5%

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=> Growth rate of M +Growth rate of V = Growth rate of P + Growth rate of Y

=> 5% + 0 = Growth rate of P + 1%

=> Growth rate of P = 5% - 1%

=> Growth rate of P= 4%

Hence, the inflation rate is 4%

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New inflaton rate is 4%

Original inflation rate is 3%

Change in inflation ( Δπ) = 4% - 3%

=> Δπ = 1%

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(ii) In that case to prevent inflation from rising. Fed must reduce the money growth rate by 1 percentage point per year.