The Government/Investment multiplier is used when either Government and/or a Business increases or decreases expenditures. It will tell us by how much GDP will increase/decrease given the eventual multiplier effect.
The Government or Investment Multiplier is determined by the simple equation:
1/MPS.MPS is the "Marginal Propensity to Save" each additional dollar.
Example: If the MPS is 25% (.25) then the MPC (Marginal Propensity to Spend) is 75% (.75).
Remember: MPC + MPS = 100% (or +1)
1/25% = 1/.25 = +4.This means each additional dollar spent by either the Government or a Business will create, by the multiplier effect, +$4.00 in GDP in total (this includes the $1.00 originally spent too).
So, if Govt or a Business increases spending by +$100.00 then the eventual impact on GDP will be +$400.00 (+$100 X +4). Easy, right?
The Tax Multiplier formula is a bit different and this is the one that usually confuses students.
The Tax Multiplier equation is:
-MPC/MPS.Using the same Propensity numbers from our first example, we plug them into the equation:
-75%/25% = -.75/25 = -3.
This is where it gets tricky---Notice the negative sign in front of the 3.
If the Government wants to INCREASE GDP through tax policy, then it wants to CUT or DECREASE TAXES. This will be a NEGATIVE amount from the Government's perspective.
If we multiply and Negative by a Negative we get a Positive, right?
So, if Government cut or decreased taxes by $100, then -$100 X -3 = +$300 INCREASE in GDP.
IMPORTANT POINT #1: Notice we use the same Marginal Propensities in both cases, MPC or 75% and MPC of 25%. We also use the same initial amount for "stimulus"---$100.
But we produced 2 different outcomes in terms of increasing GDP.
Government Spending that $100 produced $400 in GDP but the Tax Cut to individuals produced only an increase of $300 in GDP.
If you are a policy-maker and your charge is to get the economy going as quickly as possible and you had to choose only one of the above, which option is optimal, ceteris paribus?
IMPORTANT POINT #2: Why is there a difference between the two multipliers? Notice the Government Multiplier is "4" and the Tax Multiplier "-3". Ignore the "-" sign in front of the 3, it is not important for this part.
The difference between the two numbers is "1". The Government Multiplier is ALWAYS going to be one more than the Tax Multiplier (go ahead, using the formulas above change the MPS to 1%, 10%, 20%, 50% try it. You will get a difference of 1 EVERY TIME).
The difference is derived in the FIRST ROUND OF SPENDING. In the first round of spending it is assumed the Government DOES NOT save any of the $100. The economy benefits by $100 immediately.
In the case of the Tax Cut it is assumed that the individual will SAVE a portion of that $100---25%.
So, in that first round of spending the economy benefits by only $75. Twenty-five dollar less!
All of the above is predicated on the $100 being borrowed, whether it is for the government spending or for the tax cut. Either way, it will create a BUDGET DEFICIT.
The "Third Leg" of the Keynesian Multipliers is something called the "Balanced Budget Multiplier". This is how Keynes suggested a balanced budget could be maintained AND the economy can be stimulated. FUN STUFF!!
I will let you digest the lesson above and get busy writing the lesson for that to come soon.
I hope this helps.