Tax Multiplier and Govenment Spending Multiplier

2024-05-10 18:28:46

Tax Multiplier and Govenment Spending Multiplier

文章目录

Tax Multiplier and Govenment Spending Multiplier
- Govenment Spending Multiplier
- Tax Multiplier

Govenment Spending Multiplier

spendingmultiplier=1+MPC+MPC2+…spending\ multiplier = 1 +MPC+MPC^2+\dots spending multiplier=1+MPC+MPC2+…
spendingmultiplier=Σi=0inf⁡MPCispending\ multiplier = \Sigma_{i=0}^{\inf}MPC^{i} spending multiplier=Σi=0infMPCi
spendingmultiplier=1⋅1−MPCinf1−MPC=11−MPCspending\ multiplier = 1·\frac{1-MPC^{inf}}{1-MPC} = \frac{1}{1-MPC} spending multiplier=1⋅1−MPC1−MPCinf=1−MPC1
Government spending directly becomes part of GDP so the first term is 111.

Tax Multiplier

taxmultiplier=MPC+MPC2+…tax\ multiplier = MPC+MPC^2+\dots tax multiplier=MPC+MPC2+…
taxmultiplier=Σi=0inf⁡MPCitax\ multiplier = \Sigma_{i=0}^{\inf}MPC^{i} tax multiplier=Σi=0infMPCi
taxmultiplier=MPC⋅1−MPCinf1−MPC=MPC1−MPCtax\ multiplier = MPC·\frac{1-MPC^{inf}}{1-MPC} = \frac{MPC}{1-MPC} tax multiplier=MPC⋅1−MPC1−MPCinf=1−MPCMPC
Decreased tax becomes a part of individuals’ source of income so the first term of the geometric series is MPCMPCMPC.

All in all, tax multiplier is smaller than spending multiplier, ceteris paribus.

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