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