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).

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.

• $C$ = 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).

• $R$ = 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:

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.

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:

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