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Homework answers / question archive / The reserve requirement, open market operations, and the money supply Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is checkable deposits

The reserve requirement, open market operations, and the money supply Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is checkable deposits

Economics

The reserve requirement, open market operations, and the money supply Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is checkable deposits. To simplify the analysis, suppose the banking system has total reserves of $400. Determine the simple money multiplier and the money supply for each reserve requirement listed in the following table. Reserve Requirement Money Supply (Percent) Simple Money Multiplier (Dollars) 2,000 400 20 5 10 A higher reserve requirement is associated with a smaller money supply. Suppose the Federal Reserve wants to increase the money supply by $200. Again, you can assume that banks do not hold excess reserves and that households do not hold currency. If the reserve requirement is 10%, the Fed will use open-market operations to buy $20.00 worth of U.S. government bonds. Now, suppose that, rather than immediately lending out all excess reserves, banks begin holding some excess reserves in response to uncertain economic conditions. Specifically, banks increase the percentage of deposits held as reserves from 10% to 25%. This increase in the reserve ratio causes the multiplier to fall to 4. Under these conditions, the Fed would need to buy $50.00 worth of U.S. government bonds in order to increase the money supply by $200. Which of the following statements help to explain why, in the real world, the Fed cannot precisely control the money supply? Check all that apply. The Fed cannot prevent banks from lending out required reserves. The Fed cannot control whether and to what extent banks hold excess reserves. The Fed cannot control the amount of money that households choose to hold as currency.

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We know that

Money multiplier=1/reserve requirement. So,

Money multiplier when reserve requirement is 20%=1/20%=1/.2=5.

Money supply will increase by as many times as money multiplier is. So,

Money supply when multiplie is 5=5*400=$2000

Money multiplier when reserve requirement is 10%=1/10%=10.

Money supply when multiplie is 10=10*400=$4000

From the formula of money multiplier, we can see that they have an inverse relationship. The higher the reserve requirement, smaller the money supply.

Since the multiplier is 10 for a 10% reserve requirement (assuming no currency drain and no excess reserves, as given in the question), it means that to increase money supply by 200, the increase in deposits would be 200/10=$20. And since the fed needs to increase the deposits, it means it needs to buy the bonds as it will give cash in lieu of the bonds.

An increase in reserve requirement would decrease the multiplier. The new multiplier would be =1/25%=4. So, the multiplier would fall to 4. Because the mutliplier is now 4, to increase the total money supply by 200, the Fed would need to buy bonds worth 200/4=50.

The correct options are B and C. The Fed cant stop banks from having excess reserves and neither can it stop people from holding currency (currency drain).