CT7 September 2005 Q19

[alic3]

Hi,

This question is taken from the CT7 Revision Notes, and has been amended from the actual past paper.

"The proportion of deposits held by the banks for reserves is 0.3 and the broad money supply is 300 million. Assuming that the public deposits all its cash in the banking system, what is the value of the narrow money supply?"

The answer provided is 90 million.

I am trying to better understand the relationship between narrow money and broad money. From what I understand, broad money = narrow money + bank deposits, please correct me if this is wrong.

Working backwards from the answer, it seems that narrow money = broad money * proportion of deposits held by the banks for reserves.

(i) Why is this the case and does that mean that proportion of deposits held by the banks for reserves is not the reserve requirement or liquidity ratio?

(ii) How would this have changed if the public deposits only, say, 50% outside the banking system?

Thank you.

 

[Hemant Rupani]

Broad Money=(Narrow Money)*(Money Multiplier)
Money Multiplier=(1+c)/(r+c)...... where c=cash with public outside Bank r=reserve ratio

So,(Narrow Money)=Broad Money/(Money Multiplier)

1. As Assuming that the public deposits all its cash in the banking system, Money Multiplier will be same as Bank Multiplier 1/0.3
So, NM=300/(1/0.3)=90

2. If public deposits is 50% outside the banking system, then MM will be 1.5/0.8 and NM=300*0.8/1.5=160

 

[Margaret Wood]

The formula for the money multiplier is no longer in the CT7 syllabus. We just have the formula for the bank multiplier, ie b=1/L where L is the liquidity or reserve ratio.

This assumes, among other things, that all loans are redeposited in the banking system, ie the public does not keep any cash. If you are asked why the money multiplier that works in practice might be lower than the bank multiplier, the main reason is that in practice, people will hold some cash rather than redeposit all loans in the banking system.

 

[alic3]

Thank you both!