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>> Deriving the Multiplier Algebraically appendix 11 This appendix shows how to derive the multiplier algebraically. First recall that in this chapter planned aggregate spending, AE Planned is the sum of consumer spending, C, which is determined by the consumption function, and planned investment spend- ing, I Planned . Rewriting equation 11-9 to express all its terms fully, we have: (11A-1) AE Planned = A + MPC × YD + I Planned Because there are no taxes or government transfers in this model, disposable income is equal to GDP, so equation 11A-1 becomes (11A-2) AE Planned = A + MPC × GDP + I Planned The income–expenditure equilibrium GDP, Y *, is equal to planned aggregate spending: (11A-3) Y * = AE Planned = A + MPC × Y * + I Planned in income–expenditure equilibrium Just two more steps. Subtract MPC × Y * from both sides of Equation 11-12:
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(11A-4) Y * MPC × Y * = Y * × (1 MPC ) = A + I Planned Finally, divide both sides by (1 MPC ): (11A-5) Y* = Equation 11A-5 tells us that a $1 autonomous change in planned aggregate spending—
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This note was uploaded on 04/10/2008 for the course ECONOMICS 103 taught by Professor Sheflin during the Spring '08 term at Rutgers.

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