Question

1. By using total derivative prove that percentage change in money supply

   will be equal with the percentage change in price level (MV=PY)!

Answer 1

Money supply may be related to the aggregate economy by using the equation of exchange:  

MV = PY

Taking logarithm on both sides, we get,

Applying total derivative, we get,

In the long run it is assumed that velocity of money is constant, so that (dV/V) = 0.

Also, in the long run, output is at the full employment level, Y_F. Hence, (dY/Y) = 0.

Hence, we obtain:

that is, percentage change in money supply will be equal with the percentage change in price level.