Economics 0115
Homework #3: Answers
1.
Use the following data to construct balance sheets for the GFB
Bank, the Banking System, and the Federal Reserve Bank. Assume
that r = 10%.(Hint: MBR = TR of the Banking System.)
Go-For-Broke Bank
DD = $100,000
NW = $20,000
LL = $50,000
ER = $20,000
RR = $10,000
TR = $30,000
GS = $40,000
Banking System
DD = $10m
NW = $2m
LL = $5m
ER = $2m
RR =
TR =
GS =
RR = r(DD) = (0.1)($100,000) = $10,000
TR = RR + ER
TR = $10,000 + $20,000 = $30,000
A – L = NW
TR + LL + GS – DD = NW
$30,000 + $50,000 + GS - $100,000 = $20,000
GS = $40,000
RR = r(DD) = (0.1)($10m) = $1m
TR = RR + ER
TR = $1m + $2m = $3m
A – L = NW
TR + LL + GS – DD = NW
$3m + $5m + GS - $10m = $2m
GS = $4m
Figure 1-3
Federal Reserve Bank
A
GS = $3M
L
MBR = $3M
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 when ER = 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.
Suppose that the following data are available:
r = 12.5%, c = C/DD = 25%, and er = ER/DD = 2.5%
TR = $1.5B, C = $6.5B
a.
Compute the MS using the multiplier formula.
mm = (1.25)/(0.4) = 3.125
MS = mm(MB) = mm(TR + C) = 3.125($8B) = $25B
b.
Suppose that the inflation rate has been increasing and the
Fed wants to reduce it by contracting the money supply by
1%. What kind of open market operation must the Fed use and
how large must this open market operation be to accomplish
its goal? Calculate and explain.
-0.01(MS) = -$0.25B
Fed must sell GS to the banking system. This increases GS
in the banking system and decreases TRs by the same amount,
causing ER < 0, a contraction of loans and demand deposits,
and ultimately a decrease in the money supply. The
magnitude of this open market sale must be:
-$0.25B/3.125 = ΔMB = -$0.08B
Or an alternative calculation:
$24.75B = 3.125(X + $6.5B) = 3.125X + $20.3125B
$4.4375B = 3.125X,
X = $1.42B,
ΔX = -$0.08B
This means that the Fed must sell $80M in GS to the Banking
system (the minus means sell, plus means buy)
c.
During 1937, banks were holding large amounts of ER and the
Fed, fearing inflation if these were loaned out, raised the
reserve requirement to 20%. Banks, in their turn, wanting
to keep very large amounts of liquid reserve increased
their excess reserves even further to 5%. What effect would
this have on the complex multiplier and the money supply?
mm = 1.25/0.5 = 2.5
MB = TR + C = $8B
MS = 2.5($8B) = $20B
The Money Supply contracts by $5B or 20%. This actually
caused the recession of 1937-38.
d.
THINK ABOUT: Banks currently have been keeping huge
amounts of ER, in part because the Fed is now paying
interest on reserves, in part because there are no good
investment possibilities in the economy right now. What
does this do to the money multiplier? How will it affect
the Fed’s ability to affect the Money Supply through open
market operations?