Consider the equation %ΔM + %ΔV ≈ %ΔP + %ΔY. If the velocity of money does not change (%ΔV = 0), and the change in real GDP exactly keeps pace with the change in the money supply (%ΔM = %ΔY), what will happen to the price level (P)?

It will stay the same i.e %ΔP = 0

Explanation:

We are given the following formula,

%ΔM + %ΔV ≈ %ΔP + %ΔY

And told that,

%ΔV = 0

%ΔM = %ΔY

If that is the case therefore then the new formula should be written as follows,

%ΔM = %ΔY

This is because the % change in money supply is the only variable that is on the left side of the equation. For it to be equal to % change in real GDP on the right side of the equation then ONLY the % change in real GDP can exist on the right side. Which means that %ΔP has to be 0 as well.

For example, assume both %ΔM and %ΔY are 2 and %ΔP is 1

%ΔM = %ΔY

2 ≠ 2 + 1

The equation is not satisfied.

Now assume %ΔP = 0.

2 = 2 + 0.

Equation is satisfied.

Seeing as %ΔP is 0 that means there is no change in Prices so the Price Level stays the same.

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