Chapter 3 -- The
Simple Keynesian Model
Fundamental inflexibility
assumptions:
W -- inflexible
P -- inflexible
i -- inflexible
Overriding theme -- Production
Responds to Economic Activity
(focus on goods and services
expenditure)
Simplifying Assumptions
Business Saving = 0 (All private saving
is personal saving)
Taxes don’t depend upon income.
T = G (Balanced Budget)
NX = 0
Assumptions imply that the “Magic
Equation” is now S = I.
Causes of Consumption (C)
Disposable Income (YD = Y - T)
YD  C
Real GDP, or Total Income (Y)
Y  YD  C
Net Taxes (T)
T  YD  C
Consumer Confidence (CC)
CC  C
More Causes of
Consumption (C)
Real Interest Rate (r = i - e)
r  C
Nominal Interest Rate (i)
i  r  C
Expected Inflation Rate (e)
e  r  C
Real Wealth (A)
A  C
Measures -YD  C Relationship
Average Propensity to Consume
(APC)
APC = C/YD
Marginal Propensity to Consume
(MPC)
MPC = C/YD
Handling Multiple
Causes of Consumption
Causes of Consumption -Y, T, CC, i, e, A.
Autonomous Consumption (C0) -changes in C due to causes other
than Y.
Causes of Investment (I)
Business Confidence (BC)
BC  I
Business Taxes (BT)
BT  I
More Causes of Investment
Real Interest Rate (r = i - e)
r  I
Nominal Interest Rate (i)
i  r  I
Expected Inflation Rate (e)
e  r  I
Note: Investment does not depend
upon current income (Y)
Government Purchases of
Good and Services (G)
Government purchases of goods
and services is a policy variable,
controlled by the government 
no causing variables.
The previous properties imply that
I and G are completely
autonomous.
A Numerical Example
Y
5
25
45
65
85
105
125
T
5
5
5
5
5
5
5
YD
0
20
40
60
80
100
120
C
10
25
40
55
70
85
100
S
-10
-5
0
5
10
15
20
I G
10 5
10 5
10 5
10 5
10 5
10 5
10 5
The Saving-Investment
Relationship
Recall -- macro identity
S + (T - G) + -NX = I
With simplifying assumptions:
S=I
Why doesn’t S = I in numerical
example?
Intentions Versus Actual
Occurrences
Must distinguish between
intended, desired, planned S and I
versus actual or realized S and I.
Intended S and I -- strategies,
described by schedules and
graphs.
Actual S and I -- the numbers after
the period is over.
Planned Expenditure (EP)
Planned Expenditure (EP) -- The
total intended spending for various
levels of income.
In equation form,
EP = C + I + G.
Planned Expenditure in
the Numerical Example
Y
5
25
45
65
85
105
125
T
5
5
5
5
5
5
5
YD
0
20
40
60
80
100
120
C
10
25
40
55
70
85
100
S
-10
-5
0
5
10
15
20
I G EP
10 5 25
10 5 40
10 5 55
10 5 70
10 5 85
10 5 100
10 5 115
An Equilibrium Level
of Real GDP: EP = Y
Y
5
25
45
65
85
105
125
T
5
5
5
5
5
5
5
YD
0
20
40
60
80
100
120
C
10
25
40
55
70
85
100
S
-10
-5
0
5
10
15
20
I G EP
10 5 25
10 5 40
10 5 55
10 5 70
10 5 85
10 5 100
10 5 115
Why is Y* = 85 an
Equilibrium?
Example 1: Suppose Y = 105.
Intended
Actual
C = 85
C = 85
S = 15
S = 15
I = 10
I = 10 + 5 = 15
G= 5
G=5
EP = 100
Note -- Actual S = Actual I
Why is Y* = 85 an
Equilibrium? (Continued)
Example 2: Suppose Y = 65.
Intended
Actual
C = 55
C = 55
S= 5
S= 5
I = 10
I = 10 + -5 = 5
G= 5
G= 5
EP = 70
Note -- Actual S = Actual I
Why is Y* = 85 an
Equilibrium? (Finally)
Example 3: Suppose Y = 85.
Intended
Actual
C = 70
C = 70
S = 10
S = 10
I = 10
I = 10
G= 5
G=5
EP = 85
Note -- Actual S = Actual I
Properties of Equilibrium
No unintended inventory
accumulation or depletion.
All intentions are realized.
Intended Saving = Intended
Investment (only at equilibrium).
EP = Y
Equilibrium and the
Natural Level of Real GDP
Fundamental Prediction of
Keynesian models -- Y* is not
necessarily equal to YN.
Classical Prediction: Selfcorrecting economy  Y* = YN.
(Business cycle represents
deviations from equilibrium)
Keynesian Prediction -State of the Economy
Y* < YN (sluggish economy)
Y* > YN (accelerating inflation)
Y* = YN (desired state of
economy)
If Y*  YN, then one needs
economic policy to achieve a new
equilibrium closer to YN.
The Keynesian Prescription
Achieve a new equilibrium by
shifting the Ep curve.
If Y* < YN, seek to increase
expenditure, described by shifting
the EP curve upward.
If Y* > YN, seek to decrease
expenditure, described by shifting
the EP curve downward.
Shifting the EP Curve
Key -- Change Autonomous
Consumption, Autonomous
Investment, or Government
Purchases (or, later,
Autonomous Net Exports).
Change C0 -- change T, CC, i, e, A
Change I0 -- change BC, BT, i, e
Change G0.
Economic Policy
Purpose -- to move Y* closer to YN.
Method -- change autonomous
expenditure (C0, I0, G0).
If economy is sluggish (Y* < YN),
increase autonomous expenditure.
If economy has accelerating
inflation (Y* > YN), decrease
autonomous expenditure.
Strategies for Policy
Expansionary Policy -- Policy
designed to address a sluggish
economy (Y* < YN).
Contractionary Policy -- Policy
designed to address an
overstimulated, or accelerated
inflation economy (Y* > YN).
Quantitative Effects -Changes in C0, I0, or G0
Y
5
25
45
65
85
105
125
T
5
5
5
5
5
5
5
YD
0
20
40
60
80
100
120
C
10
25
40
55
70
85
100
S
-10
-5
0
5
10
15
20
I G EP
10 5 25
10 5 40
10 5 55
10 5 70
10 5 85
10 5 100
10 5 115
Note: MPC = C = 25 - 10 = 0.75
YD
20 - 0
Example -- If autonomous
government purchases are
changed by 5, how much will Y*
change as a result?
Solution -- Numerical
Example
Y
5
25
45
65
85
105
125
EP
25
40
55
70
85
100
115
EP’ (G0 = 5)
30
45
60
75
90
105
120
The Multiplier Effect
The Multiplier Effect -- Given an
initial change in autonomous
consumption, autonomous
investment, or government
purchases of goods and services,
the resulting change in equilibrium
output will be a multiple of the
initial change.
The Multiplier Effect
in Equation Form
Y* = m (C0, I0, G0, or NX0),
where m = the multiplier.
m = 1/(1 - MPC)
Our Example: (G0 = 5  Y* = 20)
(20) = (4)(5)
MPC = 0.75  m = 1/(1 - 0.75) = 4
Tracing the Effect on Y*:
G0 = 5, with MPC = 0.75
Round
1
2
3
...
Y*
Added
Spending
5
5(0.75)
5(0.75)2
...
20
Added
Income
5
5(0.75)
5(0.75)2
...
20
Properties: Multiplier Effect
The multiplier varies positively
with the MPC, i.e. MPC  m.
Applies for either increases or
decreases in C0, I0, G0, or NX0.
Applies to changes both policyinduced and otherwise.
Changes in autonomous net taxes
(T0) have a multiplier effect, but not
the same multiplier.
Changing G0 Versus
Changing T0, MPC = 0.75
Added Spending
Round
G0 = 5
T0 = -5
1
5
5(0.75)
2
5(0.75)
5(0.75)2
3
5(0.75)2
5(0.75)3
...
...
...
______________________________
Y*
20
15
The Net Taxes Multiplier
Y* =
-MPC T0
1 - MPC
The Net Taxes Multiplier is smaller
than the regular multiplier (less of
an impact on Y* for the same initial
change).
Tax or transfer policy is not as
powerful as G policy, but less
likely to overshoot YN.
Application:
The Obama Stimulus Plan
The Obama Stimulus Plan – A $787 B
stimulus package passed in February
2009, to address sluggish US economy.
-- Tax Cuts = $288 B
-- Extended unemployment benefits,
education and health care = $224 B
-- Federal contracts, grants, and loans
= $275 B (Infrastructure
improvements = $83 B)
The Simple Keynesian
Model -- The Algebra
The model in equation form.
(1) EP = C + I + G,
(2) C = C0 + b(Y - T),
(3) I = I0,
(4) G = G0,
(5) T = T0,
(6) At equilibrium, EP = Y*.
Solving for Y*
Substitute equations (2), (3), (4),
(5), and (6) into (1)
 Y* = C0 + b(Y* - T0) + I0 + G0.
Solve for Y*
 Y* = 1 {C0 + I0 + G0} + -b T0.
(1 - b)
(1 - b)
Removing the
Simplifying Assumptions
Investment depends upon current
output or income (Y).
I = I0 + dY,
d = marginal propensity
to invest
Income Tax
T = T0 + tY,
t = marginal tax rate
Causes of Net Exports
(NX = Exports - Imports)
Foreign output or income (Yf)
Yf  Exports  NX
US output or income (Y)
Y  Imports  NX
Barriers to Trade
Real exchange rate (e)
e  NX
A Model for Net Exports
in Equation Form
NX = NX0 - fY
NX0 = Autonomous Net Exports
(made up of causes other
than Y)
f = marginal propensity to import
The Model Without the
Simplifying Assumptions:
What Results Are The
Same?
Answer -- All the qualitative
results are the same!!
Same Results
Equilibrium occurs where Ep = Y.
True equilibrium, guided by unintended
inventory changes.
Y* may be <. >, or = YN.
Need for policy if Y* is different from
YN .
Policy – change autonomous
expenditure (expansionary or
contractionary).
More of the Same Results
Same options as before
(C0, I0, G0).
Multiplier effect exists.
Tax multiplier is smaller than the
autonomous spending multiplier.
The Model Without the
Simplifying Assumptions:
What Results Are Different?
More possibilities for policy.
-- autonomous net taxes (T0)
-- marginal tax rate (t)
-- trade policy (NX0)
Different multipliers for
autonomous spending and net
taxes.
The Expanded
Simple Keynesian Model
(1)
(2)
(3)
(4)
(5)
(6)
(7)
EP = C + I + G + NX,
C = C0 + b(Y - T),
I = I0 + dY,
G = G0,
NX = NX0 – fY,
T = T0 + tY,
At equilibrium, EP = Y*.
More Realistic Multipliers
Substitute equations (2)-(7) into (1),
solve for Y*.
Y* =
1
[C0 + I0 + G0 + NX0]
(1 – b(1–t) – d + f)
-b
[T0].
(1 – b(1–t) – d + f)
The Economy and the
Federal Budget
Recall that the Federal Budget is
given by
Budget = T - G.
Substitute income tax function for
T (with Y = Y*):
Budget = (T0 + tY*) - G.
Note that Y*  Budget
The Economy and the
Balance of Trade
Recall that the Balance of Trade
(BOT) is approximated by Net
Exports (NX).
Also recall that the Net Exports
equation is (Y = Y*):
NX = NX0 - fY*.
Note that Y*  BOT