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?
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.