Open Market Operations, Excess Reserves and the Money Multiplier
An economy has currency held by the public of ₹400 crore and demand deposits of ₹800 crore. Banks hold reserves of ₹80 crore with the central bank and have no excess reserves. The required reserve ratio is 10 per cent and the public's currency–deposit ratio is 0.5. The central bank buys government securities worth ₹48 crore from commercial banks and pays by crediting their reserve accounts. Banks initially do nothing with the new reserves because they are worried about bad loans. A policy adviser claims that the purchase will increase the money supply by ₹120 crore, while a bank manager says the money supply will not change at all. You are asked to evaluate both claims using the money multiplier, and to explain how a rise in the public's currency–deposit ratio would change the outcome.
1. Calculate the currency–deposit ratio, the reserve–deposit ratio, the money multiplier, the monetary base and the initial money supply.
Read the worked answer
Currency–deposit ratio c = C / D = 400 / 800 = 0.5.
Reserve–deposit ratio rr = R / D = 80 / 800 = 0.10.
Money multiplier m = (1 + c) / (rr + c) = (1 + 0.5) / (0.10 + 0.5) = 1.5 / 0.6 = 2.5.
Monetary base (high-powered money) H = C + R = 400 + 80 = ₹480 crore.
Money supply M = C + D = 400 + 800 = ₹1,200 crore.
Check: M = m × H = 2.5 × 480 = ₹1,200 crore. The figures are consistent.
2. Evaluate the adviser's claim that the purchase will raise the money supply by ₹120 crore and the manager's claim that it will not change at all.
Read the worked answer
The open market purchase raises bank reserves by ₹48 crore, so H becomes 480 + 48 = ₹528 crore.
If the multiplier stayed at 2.5 and banks lent out every possible rupee, the maximum money supply would be 2.5 × 528 = ₹1,320 crore, an increase of ₹120 crore. The adviser's figure is therefore an upper bound, not a guaranteed outcome.
The manager is right in the short run if banks hold the new reserves as excess reserves and do not lend. Reserves are not part of the public's money supply; only currency and deposits are. If deposits do not rise, M stays at ₹1,200 crore even though H has risen.
The actual change lies between zero and ₹120 crore. It depends on whether banks lend, whether borrowers spend, and whether recipients keep the proceeds as deposits rather than cash. The adviser treats a maximum as a prediction; the manager ignores the possibility of later lending.
3. Suppose the public's currency–deposit ratio rises to 0.8 while the monetary base is ₹528 crore. Recalculate the multiplier and money supply, and explain what this shows about the adviser's estimate.
Read the worked answer
With c = 0.8 and rr = 0.10:
m = (1 + 0.8) / (0.10 + 0.8) = 1.8 / 0.9 = 2.0.
Money supply = 2.0 × 528 = ₹1,056 crore.
This is actually below the initial ₹1,200 crore, even though the monetary base has risen. The reason is that a higher currency–deposit ratio means the public is holding more cash and banks have a smaller deposit base from which to create credit. The leakage into cash reduces the multiplier.
The adviser's estimate of a fixed ₹120 crore increase assumes a stable currency–deposit ratio and full lending. Once either assumption fails, the estimate is unreliable. A central bank purchase adds reserves, but it cannot force the public to hold deposits or banks to lend.