# ECO102H1 Lecture 30: Lecture 30-The Multiplier

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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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

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###### ECO102H1 Full Course Notes

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## Document Summary

Autonomous expenditure independent of charges in y [gdp] Change in autonomous expenditure => shift in ae schedule => new intercept of ae. Example: :943424:8503/9:70: induced consumption expenditure is key. The multiplier: value: slope of ae schedule. = c + i = 10 + 0. 9y + 25 = 35 + 0. 9y. Observation: in this model, slope of ae schedule is mpc, so multiplier is 1___ T = taxes (note: t affects ae indirectly by influencing c) 2. 1 t = t * y where t = marginal tax rate. 2. 2 yd (disposable income) = y t. C = c0 (constant) + c1 (mpc) yd. = 10 + 0. 9 (y 0. 2 y) Thus: c = 10 + 0. 9 (y t) _: x = x predetermined by other forces. Exports do not depend upon real gdp: foreign versus domestic prices, exchange rate, imports, foreign versus domestic prices, exchange rate.