In a financial system where the Central Bank mandates a minimum cash reserve ratio of 10\%… — JAMB UTME

In a financial system where the Central Bank mandates a minimum cash reserve ratio of $10\%$ , commercial banks decide to voluntarily raise their total cash reserves to $15\%$ of deposits by holding excess reserves. Assuming public preference for holding currency remains constant, how will this decision impact the bank credit multiplier and the total volume of narrow money supply ( $M_1$ )?

A
The credit multiplier expands from $10$ to $15$ , causing an increase in the total volume of narrow money supply ( $M_1$ ).
The credit multiplier contracts from $10$ to approximately $6.67$ , causing a decrease in the total volume of narrow money supply ( $M_1$ ).Answer
C
The narrow money supply ( $M_1$ ) increases because commercial bank vault cash is added directly to currency in circulation outside banks.
D
The narrow money supply ( $M_1$ ) remains unchanged because voluntary excess reserve decisions alter broad money ( $M_2$ ) only.

Answer

The credit multiplier contracts from 10 to approximately 6.67, causing a decrease in the total volume of narrow money supply (M1).

The credit multiplier is inversely related to the total cash reserve ratio maintained by commercial banks (

K = \frac{1}{r}

). When banks voluntarily increase total cash reserves from

10\%

15\%

, the multiplier falls from

10

to approximately

6.67

. As banks retain more funds as reserves, their secondary lending capacity shrinks, reducing demand deposit creation and contracting the overall narrow money supply (

M_1

Step-by-Step Solution

Calculate the initial credit multiplier under the mandatory reserve ratio

Initial Multiplier =

\frac{1}{\text{Required Reserve Ratio}} = \frac{1}{0.10} = 10

The credit multiplier measures the total demand deposit expansion resulting from an initial deposit based on the cash reserve ratio.

Calculate the effective credit multiplier with voluntary excess reserves

Effective Multiplier =

\frac{1}{\text{Effective Reserve Ratio}} = \frac{1}{0.15} \approx 6.67

When banks hold additional excess reserves (5%), the total cash reserves ratio increases to 15% (0.15), reducing the fraction of deposits available for lending.

Analyze the impact on narrow money supply (

M_1

)

Narrow money supply (

M_1

) decreases.

M_1

consists of currency outside banks plus demand deposits. With a lower credit multiplier, commercial banks create fewer demand deposits, leading to a overall reduction in

M_1

Key Concept

Credit Multiplier and Money Supply Determinants

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