CRR Hike versus Open Market Operations: How Much Money Is Really Destroyed
The Reserve Bank raises the cash reserve ratio from 4.0 per cent to 5.0 per cent. In this economy the public holds cash equal to 20 per cent of its bank deposits (currency–deposit ratio 0.2), banks keep no reserves beyond the statutory requirement, and there are no other leakages. Fresh high-powered money injected through the RBI's window into the system is ₹2,000 crore. Before the CRR change the money multiplier was 5.0 and the money stock supported by ₹2,000 crore of base money was ₹10,000 crore. A newspaper column argues that a 1 percentage point rise in the CRR is a trivial step, and that a far stronger instrument - an open market sale of ₹400 crore of government securities - would work faster. The finance ministry wants to know exactly how much the money supply changes in each case, and why the textbook formula 1/CRR badly misstates the answer.
1. Compute the money multiplier and the total money supply at a CRR of 5 per cent, showing deposits, currency with the public and bank reserves separately.
Read the worked answer
Multiplier. With c = 0.2 and r = 0.05,
m = (1 + c)/(c + r) = 1.2/(0.2 + 0.05) = 1.2/0.25 = 4.8
Levels from H = ₹2,000 crore.
- Deposits D = H/(c + r) = 2,000/0.25 = ₹8,000 crore
- Currency with public C = 0.2 × 8,000 = ₹1,600 crore
- Reserves R = 0.05 × 8,000 = ₹400 crore
Checks. C + R = 1,600 + 400 = ₹2,000 crore = H ✓ and M = C + D = 1,600 + 8,000 = ₹9,600 crore = 4.8 × 2,000 ✓.
The point worth noticing is that only ₹8,000 crore of the ₹9,600 crore money stock is deposits; the rest is currency that never entered the banking system and therefore cannot be multiplied.
2. By how much does the money supply fall when the CRR moves from 4 per cent to 5 per cent? Explain why using 1/CRR would greatly overstate the effect.
Read the worked answer
The two positions.
- At r = 0.04: m = 1.2/0.24 = 5.0 → M = 5.0 × 2,000 = ₹10,000 crore
- At r = 0.05: m = 4.8 → M = ₹9,600 crore
So the one percentage point hike destroys ₹400 crore of money supply, a fall of 4 per cent, on an unchanged base of ₹2,000 crore. The instrument works entirely through the multiplier.
Why 1/CRR is wrong here. 1/CRR gives 25 at 4% and 20 at 5%, implying deposits of ₹50,000 crore and ₹40,000 crore - a contraction of ₹10,000 crore, twenty-five times too large. The formula assumes that every rupee lent out comes straight back as a deposit and stays there forever. In reality the public keeps 20 paise of every rupee as cash, and that cash leaks permanently out of the deposit-creation chain; each rupee of base money therefore supports only ₹4 of deposits, not ₹20. The correct deposit multiplier is 1/(c + r), and the correct money multiplier is (1 + c)/(c + r).
3. An open market sale of ₹400 crore of securities is proposed instead. Quantify its effect measured from the post-CRR position and advise which instrument the RBI should use, and why.
Read the worked answer
Effect of the sale. The buyers pay the RBI, so high-powered money falls by the full ₹400 crore: H = 2,000 − 400 = ₹1,600 crore. With r still at 0.05, m = 4.8, so
M = 4.8 × 1,600 = ₹7,680 crore
That is a fall of ₹1,920 crore - nearly five times the ₹400 crore contraction produced by the CRR hike, because the base itself is cut and the cut is then multiplied.
Which is the better tool? They act on different parts of M = m × H.
- The CRR changes the multiplier. It hits every bank simultaneously, needs no market participation, and is durable and hard to reverse - a blunt, broad instrument that also acts as a tax on bank intermediation.
- OMO and repo change the base. They are market-driven, finely calibrated, quick to execute and easily reversed, but their size depends on how much the market is willing to buy or sell.
Judgement. For a decisive, durable tightening, the CRR is the appropriate instrument; for day-to-day liquidity management and signalling, OMO and the repo rate are better. The newspaper's claim that a CRR step is 'trivial' confuses the size of the announcement with its effect: ₹400 crore of deposits is destroyed per ₹2,000 crore of base money - the impact scales with the system, not with the 1 percentage point.