Money Supply and Money Multiplier with public holding cash and banking reserves

Dear Professor Cram,

Could you please answer the following question for me?

Suppose that the public holds a cash/deposit ration of  cp = 0.2, and the commercial banking sector holds a reserve/deposit ration of cb = 0.2.  The monetary base is given by H = 50.

Find the value of the money multiplier and the total amount of money in the economy. How does the money multiplier change if the central bank raises the reserve requirement to cb = 0.3? Briefly explain the economic reasoning for this change in the money multiplier.

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The Multiplier (M) for money is (1+Cp)/(Cp + Cb).

When Cp=0 the formula reduces to its simpler form of the inverse of reserves, or 1/ Cb.

For your question, we start with

Cp = 0.2 and  Cb = 0.2 so the multiplier is (1+0.2)/(0.2+0.2) = 1.2/0.4 = 3

The total money in the economy is M·H = 3·50 = 150

When the banking reserve requirement is increased to 0.3 the multiplier drops:

(1+0.2)/(0.2+0.3) = 1.2/0.5 = 2.4

This will reduce the total amount of money in the economy.

I hope this helps.

Good studying.