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Lecture 30

Lecture 30-The Multiplier

5 Pages
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Department
Economics
Course Code
ECO102H1
Professor
Jack Carr

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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
www.notesolution.com
The Multiplier: Value
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
www.notesolution.com

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Description
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. ¨ C = 10 + 0.72 Y I = 25 G = 17 X = 24 => X ± M = NX = 24 ± 0.1 Y M = 0.1 Y Extended Model: Numerical Example Equilibrium National Income: Y = 200 Y C = 10 + 0.72 * Y I = 25 G = 17 X ± M = 24 ± 0.1 * Y. AE = C + I + G + X ± M 100 82 25 17 14 138 200 154 25 17 4 200 300 226 25 17 -6 262 www.notesolution.com Student Exercise 1. Why is Y = 300 not the equilibrium level of national income (output)? 2. At Y = 300, is desired inventory investment equal to actual inventory investment? The Multiplier 2.1 ¨,  !¨ Multiplier = ___1 ___ = 2.63 1 ± 0.62 Extended Model AE = C + I + G + X ± M = 76 + 0.62 Y Autonomous Expenditure = 76 Comparing the Simple Model and the Extended Model Example Simple Model C + I ± AE Multiplier = 10 Extended Model C + I + G + X ± M Multiplier = 2.63 76 200 AE Y National Output Aggregate Planned Expenditure 45° www.notesolution.com Why the difference? 1. Technical answer: slope of AE schedule is different 2. Intuitive answer: at each round, induced expenditure is smaller in extended model Why is multiplier smaller? ¨ Autonomous Expenditure Round #1 ¨I = 10 !¨ shift in AE Schedule => new intercept of AE Schedule The Multiplier Concept 1. <2:O9L5OL07 Autonomous Expenditure Example: :943424:8[503L9:70, 2. Induced consumption expenditure is key Round #1 I = 10 < Round #2 25. < Y = 9 Round #3 25. < <8.1 ** mpc = marginal propensity to consume Round #1 Autonomous Expenditure Round #2 Induced Consumption Expenditure Round #3 Induced Consumption Expenditure ** expenditure = income www.notesolution.com
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