Does the Marginal Propensity to Import = negative Marginal Propensity to Tax?

Question

the multiplier $= \frac{1}{(1-MPC)}$

and

the multiplier $= \frac{1}{MPW} = \frac{1}{MPS+MPM+MPT}$.

Now since $MPC + MPS = 1$ it follow that $1-MPC = MPS$,

therefore the multiplier = $\frac{1}{(MPS+MPM+MPT)} = \frac{1}{MPS}$

and so $MPS = MPS + MPM + MPT$

from this, we can see that $MPM = -MPT$

Therefore, Marginal Propensity to Import = negative Marginal Propensity to Tax

I am unable to see what the flaw in the logic is or if there is something I am missing. Any explanation or help would be great.

Answer 1

Hint. Is it always the case that MPC + MPS = 1? Or does this hold only in a certain type of model with assumptions that simplify from reality?

Answer 2

multiplier =1/(1−MPC) holds for a simple closed economy without taxation.

multiplier =1/(MPS+MPM+MPT) holds in an economy that is open and with taxation as a function of income/output.

Both are different economies and therefore the formulas cannot be equated to arrive at your conclusion.