1. Example

2. Income-expenditure diagramAE
AE = Y AE N H 
550 D F
220
450
550
650 Y

3. Assume that Potential GDP is $650 AE = Y AE
Recessionary gap AE
Assume that Potential GDP is $650
AE = Y AE
The recessionary gap at full employment is the difference between Y and AE, or vertical distance NH N H 
550 D F
220
450
550
650 Y

4. AE AE = Y Let Ia = 100 AE 2 1 320 Y 220 550 750 Y
Change in autonomous I AE
AE = Y
Let Ia = 100 AE 2
How did a $100 change in autononous spending bring about a $250 change in real income (or GDP)? 1
320 Y
220
550
750 Y

5. It’s a bird
It’s a plane
No, it’s 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. (1 - c + m)Y = Ia .Thus, we have:
Rearrange (3) to obtain
(1 - c + m)Y = Ia .Thus, we have: 1
Y =
 Ia
Referring back to our numbers, we have
1 - c + m
Notice that the multiplier (k) is 2.5

8. Multiplier round by round
Note that :  Y = cY + m Y + Ia

9. The multiplier effect works both waysAE
AE = Y
Let Xa = -40 AE
AE0 
The multiplier effect works both ways 0
220
180
450
550 Y