Economics 0115                  Berger                     Homework #3: Answers

1.     Use the following data to construct balance sheets for the GFB Bank, theBanking System, and the Federal Reserve Bank. Assume that r = 10%.(Hint:MBR = TR of the Banking System.)

Go-For-Broke Bank            Banking System

DD = \$100,000                DD = \$10m

NW = \$20,000                 NW = \$2m

LL = \$50,000                 LL = \$5m

ER = \$20,000                 ER = \$2m

2. Using the data from Q.1., show how the Go-For-Broke Bank and the Banking    System achieve lending equilibrium. How many new DDs are created from       new LLs? Explain.

For the Banking System, the multiplier is m = 1/r = 1/.1 = 10 and ER = \$2m. Multiplying the two together gives \$20m in new DDs created from   new loans.

3.   Using only the balance sheet for the Banking System from Q.2 when       ER =  0, show what happens to the Banking System's balance sheet

when the Fed raises the reserve ratio to 20%. (Hint: What will

the balance sheet look like when ER = 0 again?)

4.  Using only the balance sheet for the Banking System from Q.2 when       ER = 0, show what happens when the Fed purchases \$1m in GS from a bank  in the Banking System. (Hint: What will the balance sheet look like whenER = 0 again?)

5.  Using only the balance sheet for the Banking System from Q.2 when       ER = 0, show what happens when the Fed purchases \$1m in GS from a bank  in the Banking System and simultaneously raises the minimum  legal      reserve ratio to 20%.(Hint: What will the balance sheet look like when  ER = 0 again?)

Note that the order in which these policy actions are

calculated can be reversed: the legal reserve ratio could be

raised first and then the purchase of \$1m in GS by the Fed

could be performed. The result will be the same as shown in the

last balance sheet for the Banking System.

6.   Assuming that r = 10% and c = 25%, do the following:

NOTE: 1) Round to the second decimal place.

2) ΔDD = ΔLL/(1+c) and ΔLL – ΔDD = ΔC

3) ΔER at the end of the round is equal to 9/10 of the ΔDDs.(Why?)

4)  ΔMS = ΔDD + ΔC. (Why?)

EXPLANATION: The complex money multiplier here is mm = (1+0.25)/

(0.1+0.25) = 1.25/0.35 = 3.57. ΔLL = \$5 at round 1 is then multiplied  by 3.57 to get the total increase of \$17.85 in the money supply and    also the increase in loans.  Since c = C/DD = ΔC/ΔDD = 1/4, and the    currency multiplier = 0.25/0.35 = 0.71 then currency increases by      (0.71)(\$5) = \$3.55; the DD multiplier is 1/0.35 = 2.86 (2.86 + 0.71 =  3.57) and DDs increase by 2.86(\$5) =\$14.30. Once these numbers are     established then the preceding line (All others) can be calculated by  subtraction. Note that 62.7% of the total increase in the money supply comes in the first 3 rounds, 73.1% in the first 4 rounds, 80.6% in the first 5rounds, and 86% in the first 6 rounds.

7.   Repeat the above example without any cash leakage. Compare the

two examples. What do you find? Explain.                                                                                                                Assume r = 10%

Since r = 10%, m = 10. ΔER = \$5 at round 1 so \$5 times 10 is a

\$50 increase in MS. Notice that approximately 47% of total new DD have been created by the end of round 6.

A comparison of these two examples show that the multiplier is

larger when there is no cash leakage. When reserves do not leak

out of the banking system as currency but go to other banks to

increase their reserves, more money can be created through the

lending process.