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Compilation - PSET 2

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

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Problem 1 Findthereducedformoftheequation Clear @ Y D GiventheNationalIncome, wesolvefortheequationintermsofYtogetthereducedform, Doingthis, weget: Solve @ Y C 0 + C 1 H Y - t 0 - t 1 * Y L + i 0 + i 1 * Y + G + e - M 0 - M 1 * Y, Y D :: Y fi e + G + C 0 + i 0 - M 0 - C 1 t 0 1 - C 1 - i 1 + M 1 + C 1 t 1 >> e + G + C 0 + i 0 - M 0 - C 1 t 0 1 - C 1 - i 1 + M 1 + C 1 t 1 :ReducedFormofthenationalincomemodel Fromthereducedformequation, wecanderivetherelevantmultipliers.We getthepartialderivativeofYwithrespecttoeachrelevantvariable. Bysolving, weget: D @ Y, G D 1 1 - C 1 - i 1 + M 1 + C 1 t 1 Governmentspendingmultiplier D @ Y, C 0 D 1 1 - C 1 - i 1 + M 1 + C 1 t 1 Consumption multiplier D @ Y, t 0 D - C 1 1 - C 1 - i 1 + M 1 + C 1 t 1 Taxmultiplier D @ Y, i 0 D 1 1 - C 1 - i 1 + M 1 + C 1 t 1 Investmentmultiplier D @ Y, M 0 D - 1 1 - C 1 - i 1 + M 1 + C 1 t 1 Importsmultiplier Clear @ Y D TosolvefortheactualvalueofNationalincome, wepluginvaluesforthevariables.Bysolving, weget: Solvingfortheequlibriumnationalincome: 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 10392.7 << Solvingfornationalincomewheni 0 increased by30.Weincreasethe initialvalueofi 0 bythespecified increase.Bysimplifying, weget:

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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 10465.9 << Clear @ Y D Solvingfornationalincomewhencomponetsofautonomousconsumption decreased by 20.Wedecreaseautonomousconsumption, C 0 by20togetthenewvalueofY.Weget: 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` << WhenYisequalto10465.9, G = 150andT = 3209.7.
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Compilation - PSET 2 - Problem 1 Find the reduced form of...

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