Investment can be decomposed into planned investment

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Investment can be decomposed into planned investment and unplanned inventory investment: I = I P + unplanned inventory investment Planned Aggregate Expenditure: PAE = C + I P + G + NX Aggregate Expenditure: Y = C + I + G + NX Y - PAE = I - I P = unplanned inventory investment
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Economics 104 Fall 2010 4 A major component of planned aggregate expenditure: consumption , C . Consumption function: C = ¯ C + c · ( Y - T ) A model of aggregate consumption behaviour: ¯ C — the autonomous or exogenous component of consumption spending. c — the marginal propensity to consume (MPC) out of disposable income, Y - T . 0 < c < 1, the MPC is less than one. Basis reasoning: all else equal , a rise in disposable income leads to a rise in consumption expenditure but not by the full amount — some amount is saved. Aggregate saving: S = ( Y - T ) - C = - ¯ C + (1 - c ) · ( Y - T ) Planned aggregate expenditure: PAE = C + I P + G + NX = ¯ C + c · ( Y - T ) + I P + G + NX So planned aggregate expenditure is itself a function of output.
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Economics 104 Fall 2010 5 Short Run Equilibrium — where PAE is equal to actual expenditure, Y . PAE = ¯ C + c · ( Y - T ) + I P + G + NX PAE = Y Or, Y = ¯ C + c · ( Y - T ) + I P + G + NX
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Economics 104 Fall 2010 6 The Income-Expenditure Multiplier Principle: changes in autonomous expenditure give rise to larger changes in output. This is the multiplier effect . Recall the equilibrium condition: Y = ¯ C + c · ( Y - T ) + I P + G + NX For simplicity, assume that all other components of planned expenditure apart from consumption are autonomous : T = ¯ T ; I P = ¯ I ; G = ¯ G ; NX = ¯ NX Solve for Y , the endogenous variable: Y = 1 1 - c ( ¯ C - c · ¯ T + ¯ I + ¯ G + ¯ NX ) Since 0 < c < 1, any rise in the autonomous components causes a larger than increase in Y .
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