In order to understand what impact this action has on gross domestic product (GDP), we must first determine what the multiplier is in this situation. The formula for the multiplier is
Tax multiplier = 1- spending multiplier.
To calculate the value of the tax multiplier, then, we must first calculate the spending multiplier. We use the formula:
Spending multiplier = 1/(1-MPC).
Since you have given us the MPC (marginal propensity to consume), we can calculate the multiplier. Using the figure given for MPC, we have the equation
Spending multiplier = 1/(1-.9) = 1/.1 = 10
Using that number, we can find the tax multiplier. Using the formula above:
Tax multiplier = 1 – spending multiplier = 1-10 = -9
The tax multiplier, then, is -9. This means that every dollar of change in the net tax will result in a $9 change in GDP. Please note that the change in GDP will be in the opposite direction of the change in tax. When taxes go up, GDP goes down. When taxes go down, GDP goes up.
To find the exact change in GDP, we use the formula
Change in taxes x tax multiplier = change in GDP
Using the information we have:
-$3 billion x -9 = change in GDP
Change in GDP = $27 billion.
This tax cut, then, will increase GDP by $27 billion.