Y

1
Example
2
Income-expenditure diagram
AE
AE Y
AE
N
H
?
550
D
F
220
0
550
450
650
Y
3
Recessionary gap
AE
Assume that Potential GDP is 650
AE Y
AE
The recessionary gap at full employment is the
difference betweenY and AE, or vertical
distance NH
N
H
?
550
D
F
220
0
550
450
650
Y
4
Change in autonomous I
AE
AE Y
Let ?Ia 100
AE
?2
How did a 100 change in autononousspending
bring about a 250 changein real income(or
GDP)?
?1
320
?Y
220
0
550
750
Y
5
Its a bird
Its a plane
No, its the multiplier effect!
6
Deriving the multiplier
Let k denote the spending multiplier. We can show
that
To see why, we will do some algebra

• Y C I G X - M. Therefore
• ?Y ?C ?I ?G ?X - ?M. Assume that
• ?Ca ?Ga ?Xa 0. Hence, we can say
• ?Y c?Y ?Ia - m?Y (3)

7
Rearrange (3) to obtain

• (1 - c m)?Y ?Ia .Thus, we have

1
?Y
? ?Ia
Referring back toour numbers,we have
1 - c m
Notice thatthe multiplier(k) is 2.5
8
Multiplier round by round
Note that ? Y c?Y m ?Y ?Ia
9
AE
AE Y
Let ?Xa -40
AE
AE0
?
The multiplier effect works bothways
?0
220
180
0
550
450
Y