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Chapter 27

Chapter 27 Mathematical Note EC140.docx

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Wilfrid Laurier University
Angela Trimarchi

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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