Money Multiplier, OMO and CRR in an Inflation Episode
Consumer price inflation has been running at 6.8%, above the upper tolerance limit, and the monetary policy committee is deciding between raising the cash reserve ratio and selling government securities in the open market. The banking system's position is: currency held by the public ₹800 crore, net demand and time liabilities (deposits) ₹3,200 crore, and total cash reserves with the central bank ₹144 crore, of which the statutory minimum is 4.5% of deposits. Banks are holding almost no excess reserves, and credit demand from firms is described as moderate. One deputy governor argues that selling ₹50 crore of securities to banks will 'remove ₹50 crore of money from the economy and is therefore too small to matter'. Another argues that the CRR route is 'certain and immediate'. The committee has asked for the arithmetic of both channels before voting, and for a view on which instrument fits the current situation.
1. Calculate the currency-deposit ratio, the reserve-deposit ratio, the money multiplier and the money supply, and verify the money supply from its components.
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- Currency-deposit ratio c = C/D = 800/3,200 = 0.25
- Reserve-deposit ratio r = R/D = 144/3,200 = 0.045, which equals the statutory minimum, consistent with the statement that there are almost no excess reserves.
- Money multiplier m = (1 + c)/(c + r) = 1.25/0.295 = 4.24 (approximately)
- High-powered money H = C + R = 800 + 144 = ₹944 crore
- Money supply M = m × H = 4.237 × 944 ≈ ₹4,000 crore
Check: M = C + D = 800 + 3,200 = ₹4,000 crore. The two routes agree, which confirms that the multiplier formula and the data are consistent.
2. Work out the effect of the ₹50 crore open market sale on reserves, high-powered money, currency with the public and deposits.
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Banks pay for the securities out of their balances with the central bank, so reserves fall by ₹50 crore: R = 144 - 50 = ₹94 crore. The public is not a party to the transaction, so C stays at ₹800 crore and H = 800 + 94 = ₹894 crore, a fall of ₹50 crore.
With c and r unchanged, ΔM = m × ΔH = 4.237 × (-50) ≈ -₹212 crore. So the deputy governor's '₹50 crore' understates the effect roughly fourfold.
Splitting the fall: since C/D = 0.25, deposits fall by 212/1.25 ≈ ₹170 crore and currency with the public by 0.25 × 170 ≈ ₹42 crore (as borrowers repay and draw down balances, both cash and deposits shrink). New money supply ≈ 4,000 - 212 = ₹3,788 crore.
Caveat: this is an upper bound. It assumes banks lend out every rupee of remaining excess reserves and that the public's cash habit does not change. With moderate credit demand, the realised fall will be smaller.
3. Which instrument should the committee use, and what does this case show about the limits of the money multiplier?
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The deputy governor's arithmetic is wrong but the CRR advocate's confidence is misplaced.
Case for the OMO sale: it is reversible, can be sized in small steps, can be repeated, and does not impose a levy on banks. It acts on high-powered money, which is then multiplied, so ₹50 crore is not trivial.
Case against a CRR hike here: banks already hold no excess reserves, so a CRR increase forces them to contract by calling in loans - quick in the deposit ledger, slow and costly in the loan book - and it hits every bank regardless of its liquidity position. It is a blunt instrument with a lag.
Judgement: use the OMO sale first for fine-tuning; reserve the CRR for a large and persistent liquidity overhang.
Limits of the multiplier: m = 4.24 is a maximum, not a forecast. If banks hold excess reserves or credit demand is weak, the realised expansion is smaller; if inflation fears make the public hold more cash, c rises, m falls, and the same H supports less M. Use the multiplier to judge direction and rough size, never as a precise prediction.