Question #14165

suppose real GDP is growing at 4 percent, the money supply is growing at 11 percent, the velocity of money is constant and the real interest rate is 6 percent.
a. what is the current inflation rate and nominal interest rate?
b.if the money supply growth rate increases to 15 percent, how will your answers in part (a) change?

Expert's answer

(i) M/P=Y/V

Y - growing by 3% so coeficient = 1.03

M - growing by 10% so coeficient = 1.10

V - constant =1

1.1/P=1.03/1

P=1.1/1.03≈1.068≈+6.8%

r-real interest rate

i-nominal interest rate

π-inflation

(1+r)=(1+i)/(1+π)

1.05=(1+i)/(1+0.068)

i=(1.05*1.068)-1

i≈0.1214≈12.14%

______ ______ ______ ______

(ii)

M/P=Y/V

Y - growing by 3% so coeficient = 1.03

M - growing by 15% so coeficient = 1.15

V - constant =1

1.15/P=1.03/1

P=1.15/1.03≈1.1165≈+11.65%

r-real interest rate

i-nominal interest rate

π-inflation

(1+r)=(1+i)/(1+π)

1.05=(1+i)/(1+0.1165)

i=(1.05*1.1165)-1

i≈0.1723≈17.23%

______ ______ ______ ______

i¹≈12.14%

i²≈17.23%

Δi=(17.23/12.14)-1≈

≈1.4195-1≈+41.95%

Nominal interest rate changed for ≈+41.95% or ≈+5.09 points.

Y - growing by 3% so coeficient = 1.03

M - growing by 10% so coeficient = 1.10

V - constant =1

1.1/P=1.03/1

P=1.1/1.03≈1.068≈+6.8%

r-real interest rate

i-nominal interest rate

π-inflation

(1+r)=(1+i)/(1+π)

1.05=(1+i)/(1+0.068)

i=(1.05*1.068)-1

i≈0.1214≈12.14%

______ ______ ______ ______

(ii)

M/P=Y/V

Y - growing by 3% so coeficient = 1.03

M - growing by 15% so coeficient = 1.15

V - constant =1

1.15/P=1.03/1

P=1.15/1.03≈1.1165≈+11.65%

r-real interest rate

i-nominal interest rate

π-inflation

(1+r)=(1+i)/(1+π)

1.05=(1+i)/(1+0.1165)

i=(1.05*1.1165)-1

i≈0.1723≈17.23%

______ ______ ______ ______

i¹≈12.14%

i²≈17.23%

Δi=(17.23/12.14)-1≈

≈1.4195-1≈+41.95%

Nominal interest rate changed for ≈+41.95% or ≈+5.09 points.

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