If we have a $10.9 trillion contractionary gap and the MPC is .86, how much will net taxes need to decrease in order to close the gap?
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To find this answer, we need to know the formula for the tax multiplier. This is given as
Tax multiplier = 1 – spending multiplier.
Therefore, we need to know the spending multiplier. It is found through the equation
Multiplier = 1/(1- MPC).
We know that the MPC is .86 so the spending multiplier is
1/(1-.86) = 1/.14 = 7.14
Therefore, the tax multiplier is
1-7.14 = -6.14.
This means that every $1 of tax cuts leads to a $6.14 gain in aggregate demand.
Now we need to find out how much of a tax cut will close our $10.9 trillion gap. Letting x be the change in taxes, we have the equation
x*-6.14 = 10.9 trillion
We divide both sides by -6.14 and we get
X = -$1.775 trillion.
This means that a net tax cut of $1.775 trillion would be needed to close this gap.
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