# Lecture 30-The Multiplier

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Professor Thursday, February 4th, 2009.
The Multiplier
Autonomous Expenditure Ù Independent of charges in Y [GDP]
Induced Expenditure Ù Varies as Y [GDP] varies
Change in Autonomous Expenditure => shift in AE Schedule => new intercept of AE
Schedule
The Multiplier Concept
1. ¨< PXOWLSOLHU¨ Autonomous Expenditure
Example: ¨ \$XWRQRPRXV([SHQGLWXUH¨,
2. Induced consumption expenditure is key
Round #1 ¨I = 10 !¨< 
Round #2 ¨&PSF¨<   !¨Y = 9
Round #3 ¨&PSF¨<  !¨< 8.1
** mpc = marginal propensity to consume
Round #1 ¨ Autonomous Expenditure
Round #2 Induced Consumption Expenditure
Round #3 Induced Consumption Expenditure
** expenditure = income
=/[A[
450
C + I = AE
Y National Output
Aggregate
Planned
Expenditure
45°
¨I = 10
350
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1. Slope of AE schedule
AE = C + I = 10 + 0.9Y + 25 = 35 + 0.9Y
Slope = 0.9
2. Multiplier = 1 .
1 ± slope of AE schedule
= 1 .
1 ± 0.9
= 10
Observation: In this model, slope of AE Schedule is mpc, so multiplier is 1___
1 ± mpc
Extended Model
AE = C + I + G + X ± M
Government Sector
G = Government expenditure
T = Taxes
(Note: T affects AE indirectly by influencing C)
Foreign Sector
X = Exports
M = Imports
Government Spending and Taxes
1. Spending __
G = G political determinants
2. Taxes
2.1 T = t * Y where t = marginal tax rate
T = 0.2 Y numerical example
2.2 YD (Disposable Income) = Y ± T
C = C0 (constant) + C1 (mpc) YD
= C0 + C1 (Y ± T)
Consumption and Real GDP (National Income)
C = 10 + 0.9 YD Note: YD
T = 0.2 Y
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