Suppose money demand function is 1000+0.2y-1000(real money demand+inflation)
What is velocity if y=2000,real money demand is 0.06, and inflation is 0.04
To find the velocity, we can use the equation of exchange:
M * V = P * Y
Where:
M = money supply
V = velocity of money
P = price level (inflation)
Y = real GDP
We are given:
Y = 2000
Real money demand = 0.06
Inflation = 0.04
Substituting these values into the money demand function:
1000 + 0.2(2000) - 1000(0.06 + 0.04) = M * V
Simplifying:
1000 + 400 - 1000(0.1) = M * V
1400 - 100 = M * V
1300 = M * V
We don't have the exact value of the money supply, so we can't obtain the exact velocity. However, we do know that the velocity is equal to 1300 divided by the money supply (M).
To find velocity, we need to use the quantity equation, which relates money supply (M), velocity of money (V), price level (P), and real output (Y). The quantity equation is:
M * V = P * Y
In this case, the money demand function is given as:
1000 + 0.2Y - 1000 (real money demand + inflation)
We are given Y = 2000 (output), real money demand = 0.06, and inflation = 0.04.
To find the money supply (M), we can rearrange the money demand function as follows:
1000 + 0.2Y - 1000 (real money demand + inflation) = M
Plugging in the given values:
M = 1000 + 0.2(2000) - 1000 (0.06 + 0.04)
M = 1000 + 400 - 1000 (0.1)
M = 1000 + 400 - 100
M = 1300
Now we can substitute the values of M, Y, P, and solve for velocity (V):
M * V = P * Y
1300 * V = P * 2000
Given that inflation = P = 0.04, we substitute these values:
1300 * V = 0.04 * 2000
1300 * V = 80
Divide both sides of the equation by 1300:
V = 80 / 1300
V ≈ 0.0615
Therefore, the velocity (V) is approximately 0.0615.