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ECON 1 – Section 20
Stabilizing Aggregate Demand:
The Role of the Fed
Nov. 13th, 2002
ECON 1 – Section 20 – Page 1
GSI: R. Estopina
Contact Details
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GSI: Ramon Estopina
Office Hours: Thursday 1:45-3:45 PM
Office: Evans 508-7
Email: [email protected]
Handouts (only sections 104 & 133) after
class in: http://www.ocf.berkeley.edu/~jaychen/econ1/
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Please read: Read before downloading!.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 2
GSI: R. Estopina
Section 20 Agenda
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Administrative Stuff (10 min)
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Recap Quiz (10 min)
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Example 26.4 (10 min)
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Problem 26.8 (10 min)
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Problem 26.9 (10 min)
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Re-cap (2 min)
Nov. 13th, 2002
ECON 1 – Section 20 – Page 3
GSI: R. Estopina
Administrative Stuff
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PS #4 due today !!! Leave them
on the table.
Remember, no class next
Monday!! -Midterm.
Review session probably Friday,
check Econ-1 website.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 4
GSI: R. Estopina
Review of Last Lecture - 11/6th
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Chapter 23 & 26:
Federal Reserve (Fed)
Federal Funds Rate (Federal Open Market Committee)
Discount Rate
Buying/Selling Bonds (Open Market Operations)
Relationship between Price of Bonds and Interest rate
Money D& S (equilibrium, shifts, stabilization by FED)
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Keynesian Model
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Keynesian cross, AD as function of r
FED fights inflation, FED fights recession
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Taylor Rule
Nov. 13th, 2002
ECON 1 – Section 20 – Page 5
GSI: R. Estopina
Recap Quiz - 1
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The interest rate that commercial banks
charge each other for very short-term loans
is called:
1) discount rate.
2) reserve rate.
3) real interest rate.
4) federal funds rate.
5) prime rate.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 6
GSI: R. Estopina
Recap Quiz - 2
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When the real interest rate rises, which of the
following is true?
1) C and Ip spending rise.
2) C and Ip spending fall.
3) C rises while Ip spending falls.
4) C falls while Ip spending rises.
5) C falls while Ip spending is unchanged.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 7
GSI: R. Estopina
Recap Quiz - 3
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To fight a recession, the Fed should do which
of the following?
1) Raise the real interest rate.
2) Lower the real interest rate.
3) Keep the real interest rate constant.
4) Allow the real interest rate to fluctuate
with the market.
5) Raise the nominal interest rate.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 8
GSI: R. Estopina
Recap Quiz - 4
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The Taylor rule is a(n)
1) rule the Fed is required to follow regarding monetary
policy.
2) example of a policy reaction function.
3) rule that helps Congress coordinate fiscal policy with
monetary policy.
4) guideline for individuals in making their portfolio
allocation decisions.
5) "rule of thumb" for solving the basic Keynesian model.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 9
GSI: R. Estopina
Recap Quiz - 5
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An increase in the interest rate by the Fed,
made with the intention of reducing an
expansionary gap, is called
1) expansionary monetary policy.
2) monetary loosening.
3) contractionary fiscal policy.
4) expansionary fiscal policy.
5) contractionary monetary policy.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 10
GSI: R. Estopina
Review Question
You hear a news report that
employment growth is lower
than expected.
 How do you expect that report
to affect market interest rates?
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Nov. 13th, 2002
ECON 1 – Section 20 – Page 11
GSI: R. Estopina
Review Answer
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Slow employment growth is indicative of a
possible recessionary output gap.
Typically the Fed responds to a slowing of
the economy by lowering the nominal
interest rate.
A weaker economy also reduces the
demand for money, which reduces the
nominal interest rate.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 12
GSI: R. Estopina
Another Review Question
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The Fed faces a recessionary gap.
How would you expect it to
respond?
How its policy change is likely to
affect the economy?
Nov. 13th, 2002
ECON 1 – Section 20 – Page 13
GSI: R. Estopina
Another Review Answer
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The Fed is likely to respond to a recessionary gap
with an expansionary monetary policy intended to
stimulate aggregate demand.
The first step is an open-market purchase of
government bonds, which puts additional money
into circulation and lowers the nominal interest rate.
The lower interest rate stimulates aggregate
demand (consumption and investment spending).
An increase in aggregate demand in turn raises
short-run equilibrium output, as firms produce
enough to meet the extra demand.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 14
GSI: R. Estopina
Important to remember:
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Equations of the day:
The real interest affects consumption ad
planned investment.
C  C  c(Y  T ) - ar
I  I  br
p
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Where a, b >0 and measure the strength
of the interest rate effect.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 15
GSI: R. Estopina
Important to remember (2)
Combined with the equations we know:
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AD  C  I  G  NX
p
GG
NX  N X
TT
AD  (C - cT  I  G  NX) - (a  b)r  cY
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Composed of:
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Autonomous AD, effect of r & Induced AD
Nov. 13th, 2002
ECON 1 – Section 20 – Page 16
GSI: R. Estopina
Important to remember (3)
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In equilibrium Y = AD, so:
Y  (C - cT  I  G  NX) - (a  b)r  cY
 1 
Y
[ C - cT  I  G  NX - (a  b)r ]
1 c 
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Vary scary, isn’t it?
Nov. 13th, 2002
ECON 1 – Section 20 – Page 17
GSI: R. Estopina
Example 26.4 (F&B page 707)
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In a certain economy, we have:
C  640  0.8(Y  T)- 400r
Ip  250 - 600r
G  G  300
NX  N X  20
T  T  250
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Where r is set by the Fed = 5%
Solve for the short-run equilibrium.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 18
GSI: R. Estopina
Example 26.4 (Conclusion)
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We know the definition of Aggregate Demand is:
AD = C + Ip + G + NX
Substituting the components:
And finally:
AD = [640 + 0.8(Y-250)-400(0.05)]
+ [250-600(0.05)] +300+20
AD = 960 + 0.8Y
In addition, from the short term equilibrium: Y=AD
So the previous equation will be:
Y = 960 + 0.8Y
Solving for Y:
Y = 960 / 0.2 = 4,800
Nov. 13th, 2002
ECON 1 – Section 20 – Page 19
GSI: R. Estopina
Problem 26.8 (F&B page 719)
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For the following economy, find at what
rate should the Fed set the real interest
rate to eliminate any output gap.
C  14,400  0.5(Y  T) - 40,000r
I p  8,000 - 20,000r
G  G  7,000
NX  NX  -1,800
T  T  8,000
Y *  40,000
Nov. 13th, 2002
ECON 1 – Section 20 – Page 20
GSI: R. Estopina
Problem 26.8 (cont’d)
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A) The relationship between aggregate demand
and output is given by:
AD  C  I p  G  NX
AD  14,400  0.5(Y  8000)  40,000r
8000  20,000r  7000  1800
AD  23,600  0.5Y  60,000r
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Autonomous aggregate demand equals
23,600 the part of aggregate demand that
does not depend on output nor on r.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 21
GSI: R. Estopina
Problem 26.8 (cont’d)
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To find short-run equilibrium output, use
the equation Y=AD and solve for Y:
Y  23,600  0.5Y  60,000r
0.5Y  23,600  60,000r
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Potential output Y*=40,000. To find the real
interest rate consistent with no output gap,
we set Y=40,000 in the equation for shortrun equilibrium output and solve for r.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 22
GSI: R. Estopina
Problem 26.8 (cont’d)
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So we have:
0.5(40,000)  23,600  60,000r
60,000r  3600
r  0.06
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So the real interest rate that eliminates
any output gap is 6%.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 23
GSI: R. Estopina
Problem 26.8 (cont’d)
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With Y*=Y as found before, now G
increases to 7,600.
What happens to the SR
equilibrium if the Fed leaves r
unchanged?
What should the Fed do to keep the
economy at full employment?
Nov. 13th, 2002
ECON 1 – Section 20 – Page 24
GSI: R. Estopina
Problem 26.8 (cont’d)
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Let’s solve for the new value of shortrun equilibrium output.
Recall for this economy:
AD  23,600  0.5Y  60,000r
Now there is an increase in government
purchases from 7000 to 7600 so
autonomous AD raises by 600, from
23,600 to 24,200.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 25
GSI: R. Estopina
Problem 26.8 (cont’d)
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And r = 6%, consequently:
AD  24,200  0.5Y  60,000(0.06)
AD  20,600  0.5Y
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Solving for output:
Y  AD
Y  20,600  0.5Y
0.5Y  20,600
Y  41,200
Nov. 13th, 2002
ECON 1 – Section 20 – Page 26
GSI: R. Estopina
Problem 26.8 (cont’d)
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So if the Fed keeps the interest rate at
6%, the increase in government
purchases raises output above potential
(an expansionary gap, remember
Y*=40,000).
To keep the economy at full employment
(and reduce inflation), the Fed has to
offset the increase in government
purchases with a higher real interest
rate.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 27
GSI: R. Estopina
Problem 26.8 (cont’d)
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Remember the process for
contractionary monetary policy:
Fed Increases interest rates by
reducing money supply (selling
bonds)…
 This will reduce C and I…
 Then AD Decreases…
 …and Decrease GDP and employment.
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Nov. 13th, 2002
ECON 1 – Section 20 – Page 28
GSI: R. Estopina
Problem 26.8 (cont’d)
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To see how much the real interest rate
must rise, note that after the increase in
government purchases aggregate demand
is given by:
AD  24,200  0.5Y  60,000r
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Solving for output:
Y  AD
Y  24,200  0.5Y  60,000r
0.5Y  24,200  60,000r
Nov. 13th, 2002
ECON 1 – Section 20 – Page 29
GSI: R. Estopina
Problem 26.8 (cont’d)
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We want to know the value of r that sets Y at
its full-employment level of 40,000. To find that
rate, we set Y=40,000 in the previous equation
and solve for r:
0.5(40,000)  24,200  60,000r
60,000r  4,200
r  0.07
Nov. 13th, 2002
ECON 1 – Section 20 – Page 30
GSI: R. Estopina
Problem 26.8 (cont’d)
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So to keep the economy at full
employment when government
purchases increase, the Fed should raise
the real interest rate from 6% to 7%.
The increase in r is consistent with the
effects of an increased government
deficit in the market for saving and
investment (Chapter 22).
Nov. 13th, 2002
ECON 1 – Section 20 – Page 31
GSI: R. Estopina
Problem 26.8 (Conclusion)
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In other words,
Expenditure line
(r=6%)
Expenditure line
(r=7%)
40,000
Nov. 13th, 2002
41,200
ECON 1 – Section 20 – Page 32
GSI: R. Estopina
Problem 26.9 (F&B page 720)
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Supposing the Fed follows the Taylor
rule, find the real int. rate (r) and the
nominal int. rate (i) that the Fed will set
in each of the following situations:
A) Inflation or 4% and a expansionary
gap equal to 1% of potential output.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 33
GSI: R. Estopina
Problem 26.9 (cont’d)
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Remember Taylor rule:
 Y * Y 
r  0.01  0.5
  0.5
 Y* 
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Fed sets r, so it decreases as relative
income gap grows, and increases as
inflation increases.
Fed’s goals:
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Y = Y*
Low  (inflation rate)
Nov. 13th, 2002
ECON 1 – Section 20 – Page 34
GSI: R. Estopina
Problem 26.9 (cont’d)
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Taylor rule is an example of a Policy
reaction function.
It describes how the action a
policymaker takes depends on the state
of the economy
Ideally policymakers should try to react
in such a way as to optimize economic
performance
Nov. 13th, 2002
ECON 1 – Section 20 – Page 35
GSI: R. Estopina
Problem 26.9 (cont’d)
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A) Inflation of 4% and a expansionary
gap equal to 1% of potential output.

(Y * Y )
Y*
r
i=r+
0.04
-0.01
0.035
0.075
4%
-1%
3.5%
7.5%
Nov. 13th, 2002
ECON 1 – Section 20 – Page 36
GSI: R. Estopina
Problem 26.9 (cont’d)
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B) Inflation of 2% and a recessionary
gap equal to 2% of potential output.

(Y * Y )
Y*
r
i=r+
0.02
0.02
0.01
0.03
2%
2%
1%
3%
Nov. 13th, 2002
ECON 1 – Section 20 – Page 37
GSI: R. Estopina
Problem 26.9 (cont’d)
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C) Inflation of 6% and no output gap.

(Y * Y )
Y*
r
i=r+
0.06
0
0.04
0.10
6%
0%
4%
10%
Nov. 13th, 2002
ECON 1 – Section 20 – Page 38
GSI: R. Estopina
Problem 26.9 (Conclusion)
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D) Inflation of 2% and a recessionary
gap equal to 5% of potential output.
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(Y * Y )
Y*
r
i=r+
0.02
2%
0.05
5%
-0.05
-0.5%
0.015
1.5%
Can the Fed set a negative real
interest rate?
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It’s possible for the Fed to set a negative
r, by setting the nominal rate below .
Nov. 13th, 2002
ECON 1 – Section 20 – Page 39
GSI: R. Estopina
Problems for next sections !!!
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For next section:
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Chapter 27: Problems 2, 4, 6 & 8.
Remember: This is not mandatory.
It won’t be graded. Only for those
of you that need improvement in
Exam grades.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 40
GSI: R. Estopina
Next class
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Next Class:
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Section 21 – Wednesday, Nov 20th
No class next Monday. Midterm Exam.
Due PS#4 !!!!
If you want more practice, work on Next Sections
Problems (although you probably have enough).
Read ch. 27.
You can download handouts this afternoon.
Thank you for coming on time !!!
Enjoy the long weekend & C-U Wednesday !!.
Nov. 13th, 2002
ECON 1 – Section 20 – Page 41
GSI: R. Estopina