Example

Income-expenditure diagram AE AE = Y AE N H  550 D F 220 450 550 650 Y

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

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

It’s a bird It’s a plane No, it’s the multiplier effect!

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)

(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

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

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