Download Y = AE

Chapter 6
Output, Aggregate Expenditure, and
Aggregate Demand
MACROECONOMICS BY CURTIS,
IRVINE, AND BEGG
SECOND CANADIAN EDITION
MCGRAW-HILL RYERSON, © 2010
Learning Outcomes
2
This chapter explains
 AD & output (Y) in the short run
 Consumption, saving, & investment functions
 Export & import functions
 Aggregate expenditure & Ye in the short run
 The multiplier
 Leakages, injections, & Ye
 Equilibrium output & AD
Chapter 6
©2010 McGraw-Hill Ryerson Ltd.
AD & Output in the short Run
3
Assume:
 All prices & wages are fixed
 Interest
rates & exchange rates are fixed
 Business
produces output demanded
 Business
employs labour need for production
Chapter 6.1
©2010 McGraw-Hill Ryerson Ltd.
AE, AD, & Output with Constant Prices
4
P0
E
AS0
AD0
AE
Y = AE
AE(P0)
E
AE0
A0
45o
Y
Y0
Real GDP and Income
Aggregate Expenditure
GDP Deflator
P
Y
Y0
Real GDP and Income
Equilibrium Y0 @ Y = AE  POSITION of AD
Chapter 6.1
©2010 McGraw-Hill Ryerson Ltd.
Aggregate Expenditure (AE)
Components of AE:
 AE is planned aggregate expenditure
 From National Accounts (without govt):
AE ≡ C + I + X - Z
• With P constant:
(Y = AE)  equilibrium real GDP
Consumption, Saving, and Investment
6
 C ≡ planned consumption expenditure by
households
 Consumption Function:
 Relationship between C & disposable income (YD)
 Assuming no govt  YD = Y
• C Function argues that:
• Changes in Y cause Changes in C, e.g.
•
•
↑Y  ↑C & ↓Y ↓C, and
0 <∆C/∆Y < 1
Chapter 6.2
©2010 McGraw-Hill Ryerson Ltd.
The Consumption Function
Example of the C function:
Let C0 = constant > 0
Let 0 < c < 1 (a positive fraction)
Then argue:
C = C0 + cY,
C0≡ autonomous consumption
•
(consumption not related to current Y)
c = marginal propensity to consume
c = ∆C/∆Y ≡ MPC
• (cY = consumption determined by Y)
Chapter 6.2
©2010 McGraw-Hill Ryerson Ltd.
The Consumption Function
A numerical example:
C = C0 + cY, or
C = 20 + 0.8 Y
Y
C
∆C/∆Y
0
20
-50
60
0.8
100
100
0.8
150
140
0.8
200
180
0.8
• Autonomous C = 20
• MPC = ∆C/∆Y = 0.8
Chapter 6.2
S=Y–C
– 20
– 10
0
10
20
∆S/∆Y
-0.2
0.2
0.2
0.2
©2010 McGraw-Hill Ryerson Ltd.
The Consumption Function
9
A diagram to illustrate C = 20 + 0.8Y
C
C = 20 + 0.8Y
100
∆C = 40
60
∆Y = 50
∆C/∆Y = 40/50 = 0.8
C0 = 20
50
Chapter 6.2
100
Y
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The Consumption Function
10
Figure 6.2 The Consumption Function in Canada, 1961-2004
Real Consumption
Expenditure
700000
600000
500000
400000
∆C
300000
∆YD
200000
100000
100000
200000
300000
400000
500000
600000
700000
Real Disposable Income
The black regression line shows the relationship between C and Y
Chapter 6.2
©2010 McGraw-Hill Ryerson Ltd.
The Saving Function
11
Saving (S)
C = 20 + 0.8Y
S=Y–C
+
S = -20 + 0.2Y
S = Y – (20 + 0.8Y)
0
S = -20 + 0.2Y
50
100
Y
-10
-20
MPS = ∆S/∆Y = 10/50 =0.2
–
Chapter 6.2
©2010 McGraw-Hill Ryerson Ltd.
Investment Expenditure
12
 Investment (I) planned
business spending on plant,
equipment & inventories
Investment
 I = I0 – bi0 (assuming i constant)
 Investment is autonomous,
 Based on business
I0
I = I0 – bi0
expectations of demand for
output & profit
 ∆i &/or ∆Expectations  shift
I function
Chapter 6.2
Real GDP and Income
Y
©2010 McGraw-Hill Ryerson Ltd.
The Export and Import Functions
13
Exports (X):
 Spending by residents of foreign countries on
domestic output
 X is autonomous: X = X0
 X depends on foreign Y, domestic & foreign P &
exchange rates
Chapter 6.3
©2010 McGraw-Hill Ryerson Ltd.
The Export and Import Functions
Imports (Z):
• Domestic spending on foreign output
• Z is embedded in C, I & X
• Z = Z0 + zY
Z0 = autonomous imports
z = ∆Z/∆Y, marginal propensity to import
• Z depends on Y, foreign Y, P & foreign P, &
exchange rates
Exports and Imports
15
Suppose:
X, Z
X = 100
Z = 40 + 0.2Y
Z = 40 + 0.2Y
X<Z
X0=100
100
X>Z
40
150
Chapter 6.3
300
450
Y
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Volatility of AE Components
16
• Consumption is the largest & most stable part of AE
• Investment & exports are volatile parts of AE
Chapter 6.3
©2010 McGraw-Hill Ryerson Ltd.
The AE Function
17
AE = C + I + X – Z
Suppose:
C = 20 + 0.8Y
I = 20
X = 50
Z = 10 + 0.2Y
AE = 80 + 0.6Y
Chapter 6.4
Y
C
I
X
Z
AE
0
100
150
200
20
100
140
180
20
20
20
20
50
50
50
50
10
30
40
50
80
140
170
200
∆AE/∆Y
0.6
0.6
0.6
©2010 McGraw-Hill Ryerson Ltd.
Aggregate Expenditure Functions
18
C = C0 + C Y
I = I0
X = X0Z0 +zY
AE = C0 + I0+Z0 + cY – zY
AE = A0 + (c –z)Y
AE = A0 + (c – z)Y
AE
AE1
∆AE
AE0
∆AE/∆Y = (c – z)
∆Y
A0
Y0
Chapter 6.4
Y1
Y
©2010 McGraw-Hill Ryerson Ltd.
Aggregate Expenditure Functions
19
C = 20 + 0.8Y
I = 20
X = 50
Z = 10 + 0.2Y
AE
AE = 20 + 20 + 50 – 10 + 0.8Y – 0.2Y
AE = 80 + 0.6Y
AE = 80 + 0.6Y
230
∆AE = 60
170
∆AE/∆Y = 60/100 = 0.6
∆Y =100
80
150
Chapter 6.4
250
Y
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Equilibrium Output
20
Short-run equilibrium:
 Y = AE
 Current output = current planned expenditure
 Business revenues cover costs & expected profit
 No unplanned ∆ inventories
Chapter 6.3
©2010 McGraw-Hill Ryerson Ltd.
Equilibrium Output: the 45o Diagram
21
Equilibrium: Y = AE
AE
Y = AE
Equilibrium
AE = A0 + (c – z)Y
450 line plots all
Y = AE
AEe
At intersection
AE & 450 line
Y = AE
AE1
Y1
A0
AE = A0 + (c – z)Y
AE1 > Y1 
Unplanned
↓ inventories
↑ Y  Ye
450
Y1
Chapter 6.4
Ye
Y
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Equilibrium Output
22

Chapter 6.4
©2010 McGraw-Hill Ryerson Ltd.
Adjusting to Short-Run Equilibrium
23
Suppose Y ≠ AE
Unplanned ∆ inventories
•
Y > AE  unplanned inventory ↑ ↓Y
•
Y < AE  unplanned inventory ↓ ↑ Y
•
∆Y  Y = AE
Chapter 6.4
©2010 McGraw-Hill Ryerson Ltd.
Equilibrium Output and Employment
24
 In equilibrium Ye = AE
 However if:



(Ye < YP) ≡ Recessionary gap & high
unemployment
(Ye > YP) ≡ Inflationary gap & low
unemployment
(Ye = YP) ≡ ‘full employment’
Chapter 6.4
©2010 McGraw-Hill Ryerson Ltd.
The Multiplier
25

Chapter 6.5
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The Multiplier: ∆Ye /∆A
26
Y=AE
Example ∆ A0 = ∆(C0 + I0 + X0 - Z0)
AE
A0 + (c – z)Y
A1 + (c – z)Y
ΔA
∆Ye = ∆A/(1 – c + z)
= ∆A x multiplier
A0
A1
ΔYe
45
o
Ye’
Chapter 6.5
Ye
Real GDP
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Multiplier
27

Y
The multiplier 
A
Chapter 6.5
©2010 McGraw-Hill Ryerson Ltd.
The Size of the Multiplier
28
A Numerical example:
Initial case
Increased A: ∆X = 10
Consumption: C = 20 +0.8Y
C = 20 +0.8Y
Investment:
I = 20
I = 20
Exports:
X = 50
X = 60
Imports:
Z = 10 + 0.2Y
Z = 10 + 0.2Y
Equilibrium: Y = 80 + 0.6Y
Ye= 200
Y = 90 + 0.6Y
Ye= 225
∆Y/∆A = 25/10 = 2.5 = 1/(1 – 0.6)
Chapter 6.5
©2010 McGraw-Hill Ryerson Ltd.
Leakages & Injections
29
An alternative view of equilibrium Y:
 From Y = AE
Y = C + I + X – Z, which gives
Y – C = I + X – Z , but Y – C = S
 Thus S + Z = I + X gives Ye
 S & Z are leakages from AE
 I & X are injections into AE
 Injections = Leakages
Chapter 6.6
 equilibrium Y
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Leakages & Injections
30
Equilibrium Y: S + Z = I + X
S + Z, I + X
S+Z
I0 + X0
I+X
S1 + Z1
0
Y1
Y
Ye
At Ye: S + Z = I + X
S0 + Z0
At Y1: S1 + Z1 < I + X
Leakages < planned I + X
Unwanted
Chapter 6.6
↓ Inventories  ↑Y
©2010 McGraw-Hill Ryerson Ltd.
AE & AD Model
31
Key model concepts:
 Autonomous expenditure:
Independent of current income
 A0 = C0 + I0 + X0 + Z0

 Induced expenditure
 Determined by current income
 MPC & MPZ  (c – z)∆Y = ∆AE
Chapter 6.7
©2010 McGraw-Hill Ryerson Ltd.
AE & AD Model
32
Key model concepts:
• Equilibrium Y = A0 x multiplier
• Induced expenditure  multiplier
• ∆A x multiplier  ∆Y > ∆A
• Volatility in A  Business cycles in Y
Chapter 6.7
©2010 McGraw-Hill Ryerson Ltd.
Equilibrium Y & AD
33
The AD function:
 Ye from Y = AE positions the AD curve
 ΔA  horizontal shift in AD = ΔA x multiplier
 Fluctuations in AD from fluctuations in A 
business cycles in Y
 A diagram to illustrate
Chapter 6.7
©2010 McGraw-Hill Ryerson Ltd.
Equilibrium Y & AD
34
AE
Y=AE
P
AE1
AE0
ΔA
A1
P0
AS
AD’
A0
ΔY
AD0
ΔY
450
Ye
Ye’
Y
Ye
Ye’
Y
• ∆A ∆Y = ∆A x multiplier  shift AD = ∆A x multiplier
Chapter 6.7
©2010 McGraw-Hill Ryerson Ltd.
Chapter Summary
35
 Aggregate demand determines Y at constant P
 Equilibrium Y = AE positions AD
 AE ≡ planned (C + I + X – Z)
 AE = autonomous expenditure + induced expenditure
 C linked to YD by MPC = ∆C/∆YD, 0 < MPC < 1
 S = Y – C, MPS = ∆S/∆Y, MPS = 1 – MPC
Chapter 6
©2010 McGraw-Hill Ryerson Ltd.
Chapter Summary
36
 Imports (Z) linked to Y: MPZ = ∆Z/∆Y. 0 < ∆Z/∆Y <1
 Equilibrium Y = AE  equivalently, S + Z = I + X.
 AE > Y  unplanned fall in inventories 
↑Y
 AE < Y  unplanned rise in inventories 
↓Y
 The multiplier ≡ ∆Ye/∆A = 1/(1 – slope AE)
 ∆A
 ∆Y  shift AD  ∆Ye in AD/AS
 ∆A  ∆AD  business cycles in Y
Chapter 6
©2010 McGraw-Hill Ryerson Ltd.