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# Appendix_C - The tax multiplier is the derivative of Y wrt...

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Appendix C: Include Exports and Imports Suppose X is exports and M is imports X = Xo, only autonomous M = Mo + mY , Mo is autonomous imports , and mY is induced imports , and m is the MPM or marginal propensity to import. At equilibrium in the open economy: Y = C + I + G + X – M If you do the algebra you end up with the following equation: Y = [ a – bTo + I + G + Xo – Mo]/(1 – b + bt + m) The government spending multiplier is derivative of Y wrt G which is 1/(1 – b + bt + m)
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Unformatted text preview: The tax multiplier is the derivative of Y wrt To which is -b/(1 – b + bt + m) Compare these multipliers with the multipliers in the closed economy in the previous slide. Appendix C, continued Note: Leakages and injections approach At equilibrium in the open economy Y = C + I + G + X – M or Leakages = Injections S + T + M = I + G + X Compare this with the leakages and injections approach in the closed economy where Leakages = Injections S + T = I + G...
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