Demand-side Equilibrium
(Keynesian Equilibrium)
Consumption function in the DI-C
Space
C
C
C = constant + coefficient * DI
0
DI (Disposable Income)
Consumption function
in the Y-C Space
C
C
C = constant + coefficient * Y
0
Y (GDP)
Consumption Function in the Y-C
space
 The
equation form:
C = constant + coefficient * Y
 To convert from the old form
C = a + b DI
= a + b (Y - T)
= a+bY-bT
where T is a (lump-sum) tax, and
DI = Y - T
Consumption function
in the Y-C Space
C
C
C = ( a – bT) + b Y
a – bT
0
Y (GDP)
Consumption Function in the Y-C
space
T
is assumed to be a lump-sum tax,
it is a constant.
 DI = Y – T
 If T= 0, then C = a + bY, same as
before
 If T increases, then the C function
line will shift
 Note the C function does not shift in
the DI-C space
Other components in AE
 AE
= C + I + G + (X - IM)
 In addition to C, there are
components: I, G, and X-IM
Investment (I)
 Investment
is the business firms'
purchase of new physical assets
(including adding in inventories, and
house construction).
 It very volatile.
Shifters of I
 Business
confidence and
expectations
 Growth of demand (sales)
 Interest rate
 Product innovation
 Tax incentive
Government expenditure G
 Government
expenditure is the
purchases of goods and services by
all government levels.
 Determined by the government
Net Exports: X - IM
 Gross
exports minus imports
 Shifters of net exports:
– Other countries' income: affects X
– Our income: affects IM
– Relative prices of exports and imports
The Circular Flow of Expenditures
and Income
Rest of the
World
Financial System
3
2
Investors
Consumers
4
1
Government
5
6
Firms
(produce the
domestic product)
Flow in the circular flow diagram
As the flow circulates around the
circular flow system, will the volume
grow larger, smaller, or keep the
same level?
Keynesian answer
 Depends
on AE and Y
 If AE > Y,
Y increases, flow grows
bigger.
 Reasons: When AE > Y
– Spending greater than output
– Inventory falls
– Firms find sale is strong, and increase
output
Keynesian answer
 If
AE < Y, Y falls, flow becomes
smaller.
Reasons: When AE < Y
– Spending less than output
– Unintended inventory increases
– Firms find sale is slow and cut the
production
Keynesian answer
 When
AE = Y, remains the same
level
 Reasons: Firms found the current
output just satisfies the demand. So
keep the same output level.
 Keynesian equilibrium condition:
AE = Y
The Keynesian Equilibrium
 Denote
Y* (at Y*, AE=Y)
 Also called “Demand-side
equilibrium”
 The output is determined by
spending, or the demand.
 It is stable
 It does not imply full employment
 So recession can be prolonged
Construct the AE schedule
 The
Aggregate Expenditure Schedule
(AE)
 The AE refers to the relationship
between AE and GDP (Y)
 AE = C + I + G + (X - IM)
 It tells you what the total spending
is at different income Y level
The AE function
AE= C+I+G+X-IM
AE
C+I+G
C+I
C
X-IM
G
I
0
Y (GDP)
The AE function
AE
AE
7500
AE0
0
Y0
8000
Y (GDP)
The 45 degree line
 Property
 Any
point on the 45 degree line has
the equal distance to the vertical axis
and horizontal axis.
The 45 degree line
AE= Y
AE
AE1
45 degree
0
Y1
Y (GDP)
Graphical illustration of the
Keynesian Equilibrium
 It
is the intersection of the AE line
and the 45 degree line.
Keynesian equilibrium
AE=Y
$
AE
0
Y*
Y
The Determination of Equilibrium
Output
Copyright © 2003 South-Western/Thomson Learning. All rights reserved.
Income-Expenditure Diagram
Output exceeds spending
7,200
45° AE=C+I+G+ (X-IM)
6,800
6600
Real Expenditure
6,400
E
6,000
Equilibrium
5,600
5400
5,200
4,800
0
Spending exceeds
output
4,800 5,200 5,600
6,000 6,400 6,800 7,200
Real GDP
Equation form for
the Keynesian equilibrium
A Model Economy is described as
follows:
C = 100 + 0.9 DI
I = 150
G = 200
X - IM = -50
T=0
Solve for the Keynesian equilibrium Y*
Equation form for
the Keynesian equilibrium
 Consumption
function
C = 100 + 0.9 DI
Assume T = 0
C = 100 + 0.9 (Y - T)
= 100 + 0.9 Y

I = 150

G = 200

X - IM = -50
Approach
Solve for the equilibrium level Y*
 Find the AE schedule equation
 Utilize the equilibrium condition, AE
=Y
 Solve for the equilibrium Y: Y*
Step 1
 Add
together to get AE,
AE = C + I + G + X - IM
AE = 100 + 0.9 Y + 150 + 200 - 50
= 400 + 0.9 Y
Step 2
 Using
the Keynesian equilibrium
condition
Y = AE = 400 + 0.9 Y
Step 3
 Solve
for equilibrium Y:
Y* = 1/(1-0.9) X 400
= 10 X 400
= 4000
Potential GDP Yp
versus
Demand-side equilibrium Y*
 Potential
GDP, Yp, is the full
employment GDP
 Y* does not have to equal Yp
 Y* < Yp: recessionary gap.
– Why a prolonged recessionary gap?
 Y*
> Yp: inflationary gap.
Recessionary Gap
AE=Y
$
AE
Recessionary gap
0
Y*
Yp
Y
Recessionary gap
 Y*
< Yp: recessionary gap.
 Recessionary Gap: when the
Keynesian equilibrium output is less
than potential GDP
 Implies prolonged high
unemployment
 Implies a prolonged recession
 Why prolonged?
Inflationary Gap
AE=Y
$
AE
Inflationary gap
0
Yp
Y*
Y