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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