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By using total derivative prove that percentage change in money supply will be equal with the...

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

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

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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, YF. Hence, (dY/Y) = 0.

Hence, we obtain:

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

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