Question

Use commercial bank and Federal Reserve Bank balance sheets to demonstrate the effect of each of the following transactions on commercial bank reserves:

a. Federal Reserve Banks purchase securities from banks.

b. Commercial banks borrow from Federal Reserve Banks at the discount rate.

c. The Fed reduces the reserve ratio.

d. Commercial banks increase their reserves after the Fed increases the interest rate that it pays on reserves.

Short answer

a. Balance sheets if Federal Reserve Bank purchase securities

Federal reserves:

Assets	Liabilities and net worth
+Securities	+Reserves of commercial banks
Total (Increase)	Total (Increase)

Commercial banks:

Assets	Liabilities
-Securities +Reserves
Total	Total

b. Balance sheets if a commercial bank borrows from Fed

Federal reserves:

Assets	Liabilities and net worth
+Loans to commercial banks	+Reserves of commercial banks
Total	Total

Commercial bank:

Assets	Liabilities
+Reserves
Total	Total

c. Balance sheets after reducing the reserve ratio

Federal reserve:

Assets	Liabilities and net worth
	-Reserves of commercial banks
Total	Total

Commercial bank:

Assets	Liabilities
+loans
Total	Total

d. Balance sheets after Fed increases the interest rate on reserves.

Federal reserve:

Assets	Liabilities and net worth
	+Reserves of commercial banks
Total	Total

Commercial bank:

Assets	Liabilities
+Reserves
Total	Total

Step-by-step solution

Step 1. Explanation for part (a)

When federal reserve purchases securities from the commercial bank, they are added to the asset side of the Fed's balance sheet and are reduced from the asset side in the balance sheet of the commercial banks.

The reserves of the commercial banks are increased since the Fed makes payments for buying these securities. This adds to the liability of the Federal Reserve and assets of the commercial banks.

Step 2. Explanation for part (b) 

When commercial banks borrow from the Fed, the assets side of the federal reserve's balance sheet increases since the loans to commercial banks are assets for federal reserves as they will be paid back. Since the loans are borrowed at a discounted rate, the reserves of the commercial banks are increased.

Step 3. Explanation for part (c)

As the Fed reduces the reserve ratio, the amount which a bank needs to hold to support the withdrawals also gets reduced. The bank enhances the money supply by offering loans from this. Loans are considered to be an asset, and this will be reflected in the asset side of a commercial bank. Fed keeps these reserves with them as collateral of loans. Thus, they are shown on their balance sheet's liabilities and net worth side. Thus, since reserves have increased, it will also reflect in the Fed's balance sheet.

Step 4. Explanation for part (d)

Since commercial banks have increased their reserves due to increased interest rates offered by Fed on reserves rates, the reserves column on the assets side of commercial banks will increase. In contrast, commercial banks' reserve on the liabilities and net worth side of the Fed's balance sheet will also increase.