Define 'money multiplier'.

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Q. Define 'money multiplier'.

Yanam CbseCBSE Class XII Board 2019Subjective· 1mImportance★★★★★

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Concept understanding — Money Multiplier Determinants

The Money Multiplier: From a ₹100 Note to a River of Credit

Imagine you find a crisp ₹100 note on the street. You deposit it in your bank account. What happens next? That ₹100 doesn't just sit in a vault. The bank, keeping only a fraction aside as required by the RBI, lends out the rest — say ₹90. That ₹90 goes to someone who pays a shopkeeper, who deposits it in their bank. That bank again keeps a fraction and lends out, say ₹81. The cycle repeats.

Your single ₹100 note has now created deposits worth ₹100 + ₹90 + ₹81 + … — a total far larger than the original amount. This multiplying effect is the money multiplier in action.

The Precise Meaning

The money multiplier ( $m$ ) tells us the maximum amount of money the banking system can create from each rupee of fresh reserves (like your ₹100 deposit). It is the ratio of the total money supply ( $M$ ) to the monetary base ( $H$ , also called high-powered money — currency held by the public plus reserves of banks).

m = \frac{M}{H}

Where:

$M$ = total money supply (currency with public + demand deposits)
$H$ = high-powered money (currency with public + cash reserves of banks)

What Determines the Multiplier? (The NCERT Story)

The multiplier is not a magic number. It depends on two key behavioural ratios that the NCERT textbook emphasises:

1. The Currency-Deposit Ratio ( $c$ )

This is the proportion of money people prefer to hold as cash rather than in bank deposits.

c = \frac{C}{D}

$C$ = currency held by the public
$D$ = demand deposits with banks

If people trust banks and find digital payments easy, $c$ is low — more money stays in the banking system, and the multiplier is larger. If people panic and hoard cash (like during a bank run), $c$ rises, and the multiplier shrinks.

2. The Reserve-Deposit Ratio ( $r$ )

This is the fraction of deposits banks keep as reserves (both required by RBI and extra as precaution).

r = \frac{R}{D}

$R$ = total reserves of banks (vault cash + RBI deposits)
$D$ = demand deposits

The RBI sets a minimum Cash Reserve Ratio (CRR) — say 4%. If banks keep exactly that, $r = 0.04$ . If they keep more (excess reserves), $r$ is higher.

The Formula That Connects Everything

From the definitions, NCERT derives the money multiplier in terms of these two behavioural ratios:

m = \frac{1 + c}{c + r}

Let's see why this makes sense:

The numerator $1 + c$ reflects that total money supply $M = C + D = cD + D = D(1 + c)$
The denominator $c + r$ reflects that high-powered money $H = C + R = cD + rD = D(c + r)$
Dividing: $m = \frac{D(1 + c)}{D(c + r)} = \frac{1 + c}{c + r}$

What This Tells Us (The "Why It Matters")

If $c = 0$ (no cash holding, all money in banks): $m = \frac{1}{r}$ . With a 10% reserve ratio, the multiplier is 10 — each rupee of reserves creates ₹10 of deposits.
If $c$ is large (people prefer cash): the multiplier falls. Cash "leaks" out of the banking system and stops the chain of lending.
If $r$ is large (banks keep more reserves): the multiplier falls. Less money is available to lend.

Watch out

The multiplier is a maximum theoretical value. In reality, banks may not lend all excess reserves, and borrowers may not spend all borrowed money immediately. The actual multiplier is usually smaller.

A Simple Numerical Example (NCERT Style)

Suppose:

$c = 0.2$ (people hold ₹20 cash for every ₹100 in deposits)
$r = 0.1$ (banks keep 10% of deposits as reserves)

Then:

$m = \frac{1 + 0.2}{0.2 + 0.1} = \frac{1.2}{0.3} = 4$ …

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The money multiplier is the ratio of the total money supply (M) to the monetary base (H), showing how much commercial banks expand the money supply through credit creation from a given amount of high-powered money.

The money multiplier is one of the most elegant concepts in macroeconomics because it reveals how the banking system, as a whole, can create money out of thin air — but only within strict limits set by the central bank and the public’s behaviour.

Think of it this way: the central bank (RBI in India) prints currency and holds reserves — this is called high-powered money or the monetary base ( $H$ ). But the actual money supply in the economy ( $M$ ) is much larger than $H$ . Why? Because when a bank receives a deposit, it keeps a fraction as reserves and lends out the rest. That loan becomes someone else’s income, which gets deposited in another bank, which again lends out most of it, and so on. This chain multiplies the initial base money into a larger total money supply.

The money multiplier ( $m$ ) captures this expansion effect:

m = \frac{M}{H}

Where:

$M$ = total money supply (typically M1 or M3)
$H$ = high-powered money (currency with public + reserves of banks)

Now, what determines the size of this multiplier? It depends on two key behavioural ratios:

Currency-deposit ratio ( $c = \frac{C}{D}$ ) — how much currency people prefer to hold relative to deposits. If people hoard more cash, less money stays in the banking system for lending, so the multiplier falls.
Reserve-deposit ratio ( $r = \frac{R}{D}$ ) — the fraction of deposits banks keep as reserves (both required and excess). A higher reserve ratio means banks lend less, reducing the multiplier.

Watch out

A common mistake is to think the money multiplier equals $1/r$ (the simple deposit multiplier). That is only true in a world with no currency holding by the public. In reality, $c > 0$ , so the actual money multiplier is smaller.

The full formula for the money multiplier (using M1 = currency + demand deposits) is: …

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