Compilation - PSET 2

Compilation - PSET 2 - Problem 1 Find the reduced form of...

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Unformatted text preview: Problem 1 Find the reduced form of the equation Clear @ Y D Given the National Income, we solve for the equation in terms of Y to get the reduced form, Doing this, we get : Solve @ Y C + C 1 H Y- t- t 1 * Y L + i + i 1 * Y + G + e- M- M 1 * Y, Y D :: Y fi e + G + C + i- M- C 1 t 1- C 1- i 1 + M 1 + C 1 t 1 >> e + G + C + i- M- C 1 t 1- C 1- i 1 + M 1 + C 1 t 1 : Reduced Form of the national income model From the reduced form equation, we can derive the relevant multipliers . We get the partial derivative of Y with respect to each relevant variable. By solving, we get : D @ Y, G D 1 1- C 1- i 1 + M 1 + C 1 t 1 Government spending multiplier D @ Y, C D 1 1- C 1- i 1 + M 1 + C 1 t 1 Consumption multiplier D @ Y, t D- C 1 1- C 1- i 1 + M 1 + C 1 t 1 Tax multiplier D @ Y, i D 1 1- C 1- i 1 + M 1 + C 1 t 1 Investment multiplier D @ Y, M D- 1 1- C 1- i 1 + M 1 + C 1 t 1 Imports multiplier Clear @ Y D To solve for the actual value of National income, we plug in values for the variables. By solving, we get : Solving for the equlibrium national income : Solve @ Y 260 + 0.7 * HH Y- 70- 0.3 * Y LL + H 3750 + 0.3 * Y L + 150 + 160- 10- H 0.20 * Y L , Y D 88 Y fi 10 392.7 << Solving for national income when i increased by 30. We increase the initial value of i by the specified increase. By simplifying , we get : Solve @ Y 260 + 0.7 * HH Y- 70- 0.3 * Y LL + H 3780 + 0.3 * Y L + 150 + 160- 10- H 0.20 * Y L , Y D 88 Y fi 10 465.9 << Clear @ Y D Solving for national income when componets of autonomous consumption decreased by 20. We decrease autonomous consumption , C by 20 to get the new value of Y. We get : Solve @ Y 240 + 0.7 * HH Y- 70- 0.3 * Y LL + H 3750 + 0.3 * Y L + 160 + 150- 10- H 0.20 * Y LD 8 Y fi 10343.902439024389` << When Y is equal to 10 465.9, G = 150 and T = 3209.7....
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Compilation - PSET 2 - Problem 1 Find the reduced form of...

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