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Macroeconomics. Use this equation and the quantity theory of money and fisher equation. Md Y = P 5i The following variables are: Y or GDP= 1,000 Money supply= 5,000 Growth rate of nominal money is 1% The real interest rate r is fixed at 3 percent by th investment and saving functions. Expected inflation rate is determined by the rate of nomeinal money growth i. Whats the nominal interest rate and the velocity for this economy? ii. Whats the price level
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.