Dear Professor Cram,

Could you please answer the following question for me?

Suppose that the public holds a cash/deposit ration of  c_p = 0.2, and the commercial banking sector holds a reserve/deposit ration of c_b = 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 c_b = 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+C_p)/(C_p + C_b).

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

For your question, we start with

C_p = 0.2 and  C_b = 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.