Suppose many demand function is 1000+02y-1000(real money demand+inflation)
1)calculate velocity if y=2000,real money demand=0.06,and inflation is 0.04
To calculate velocity, we need to divide the nominal GDP by the money supply.
Given:
Demand function: 1000 + 0.2y - 1000 (inflation-adjusted money demand)
y = 2000 (real GDP or income)
Real money demand = 0.06
Inflation = 0.04
To find nominal GDP, we need to multiply the real GDP (y) by the price level (1 + inflation):
Nominal GDP = y * (1 + inflation)
Nominal GDP = 2000 * (1 + 0.04) = 2000 * 1.04 = 2080
The money supply is given by the real money demand and the price level:
Money Supply = Real Money Demand * (1 + inflation)
Money Supply = 0.06 * (1 + 0.04) = 0.06 * 1.04 = 0.0624
Now we can calculate velocity by dividing the nominal GDP by the money supply:
Velocity = Nominal GDP / Money Supply
Velocity = 2080 / 0.0624 = 33,333.33
Therefore, the velocity is approximately 33,333.33.
To calculate velocity, we need to use the quantity theory of money equation, which states that the velocity of money (V) is equal to the total nominal expenditure (P*Y) divided by the total money supply (M).
Here's how we can calculate the velocity:
1) Given:
Demand function (MD) = 1000 + 0.2Y - 1000(Inflation)
Y = 2000 (Real GDP)
Real Money Demand (MD) = 0.06
Inflation = 0.04
2) Calculate the Total Nominal Expenditure (P*Y):
Total Nominal Expenditure = P*Y
Since the inflation rate is not given, we need to calculate the price level (P) using the real money demand and inflation:
MD = (P * Y) / (1 + Inflation)
0.06 = P * 2000 / (1 + 0.04)
0.06 = P * 2000 / 1.04
P = 0.06 * 1.04 / 2000
P = 0.0000312
Total Nominal Expenditure = P * Y
Total Nominal Expenditure = 0.0000312 * 2000
Total Nominal Expenditure = 62.4
3) Calculate the Total Money Supply (M):
Total Money Supply = Real Money Demand / (1 + Inflation)
Total Money Supply = 0.06 / (1 + 0.04)
Total Money Supply = 0.06 / 1.04
Total Money Supply ≈ 0.0577
4) Calculate Velocity (V):
Velocity (V) = Total Nominal Expenditure / Total Money Supply
Velocity (V) = 62.4 / 0.0577
Velocity (V) ≈ 1079.72
Therefore, the velocity of money is approximately 1079.72.