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Chapter 27

# Chapter 27 Mathematical Note EC140.docx

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Wilfrid Laurier University

Economics

EC140

Angela Trimarchi

Fall

Description

EC140 Mathematical Note – The Algebra of the Keynesian Model Week 3
Symbols used:
-Aggregate planned expenditure AE
-Real GDP Y
-Consumption expenditure C
-Disposable Income YD
-Investment I
-Government expenditure G
-Exports X
-Imports M
-Net taxes T
-Autonomous consumption expenditure a
-Autonomous taxes Ta
-Marginal propensity to consume b
-Marginal propensity to import m
-Marginal tax rate t
-Autonomous expenditure A
Aggregate Expenditure
-The sum of the planned amounts of consumption expenditure (C), investment (I), government
expenditure (G), and exports (X) minus the planned amount of imports (M)
AE = C + G + I + G + X – M
Consumption Function
-Depends on disposable income (YD)
C = a + bYD
-Disposable income equals real GDP minus net taxes (Y-T). So if we replace YD with (Y-T) the
consumption function becomes:
C = a + b(Y-T)
-Net taxes is written as:
T = a + tY
-Using that equation to replace T in the consumption function, the consumption function becomes:
C = a – bT + b(1-t)Y
a
Import Function
-Imports depend on real GDP
M = mY
Aggregate Expenditure Curve
-Use the consumption function and the import function to replace C and M in the AE equation. That is:
AE = a – ba + b(1-t)Y + I + g + x –My
-Collecting like terms:
AE = (a-ba + I + G + X) + [b(1-t) –m]Y
-The equation of the AE curve is:
AE = A + [b(1-t) – m]Y EC140

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