Macroeconomics

The given equation is

Md/P = Y/(5.i)

Now, taking logerithm on both sides we get,

ln(Md) - ln(P) = ln(Y) - ln(5) - ln(i)

Taking differential on both sides we get,

dMd/Md - dP/P = dY/Y - 0 - di/i

Now, growth rate of nominal money is 1%. Hence,

dMd/Md = 0.01

Y and i remains constant. Hence,

dY/Y = di/i = 0

dMd/Md - dP/P = 0

or, 0.01 - dP/P = 0

or, dP/P = 0.01

or, (dP/P)×100% = 1%

or, πe = 1%

Hence, expected inflation (πe) is 1%.

Real interest rate (r) is fixed at 3%.

Hence, according to fisher's equation, nominal interest rate (i) is

i = r + πe = 3% + 1%

or, i = 4% or 0.04

The nominal interest rate is 4%.

Now, we are given that,

Y = 1000

Md = 5000

Putting the values of i, Md and Y in the given equation we get,

Md/P = Y/(5.i)

or, 5000/P = 1000/(5×4)

or, P = 100

The price level is 100.

Now, according to quantity theory of money, if velocity is V then,

Md.V = P.Y

or, 5000×V = 100×1000

or, V = 20

Velocity of money is 20.

(i) Nominal interest rate is 4% and velocity of money is 20.

(ii) The price level is 100.