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Keynesian Multipliers Made Easy. Ok, maybe a little less hard is a better way to put it.

The Keynesian Multipliers, both the Govt/Investment and Tax Multipliers, can be a tricky concept.  I am going to TRY to simplify it as much as possible.

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.

Nice resource for illustrating "Increasing Opportunity Costs" and the concave nature of the PPF

Here is a nice article on the great productivity slowdown in the US, and in the developed world for the most part.

The article is interesting throughout but the excerpt below caught my eye.

It goes to the edge but does not explicitly mention the important concept of "Increasing Opportunity Costs" and the reason the Production Possibility Frontier (or Curve) is "bowed", or concave from the origin.

While Services Sector Booms, Productivity Gains Remain Elusive 

“The changing distribution of workers might be able to explain up to one-half of the slowdown in labor productivity growth from 2.5% to 1.5% per year since the 1960s," said Dietrich Vollrath, a University of Houston economist. Indeed, this effect has accelerated since 2000, when workers, in aggregate, started to move from higher to lower productivity sectors. 

Services productivity, besides its natural disadvantage, may be facing an added headwind: The sector is absorbing millions of workers whose underlying skills may not be well suited to the jobs they take on. 

If people start doing work they are relatively good at, and if manufacturers shed their least efficient workers first, manufacturing productivity will improve as it downsizes but services-sector productivity will suffer as it absorbs workers who are a poor fit. (Sections in bold are mine).

All resources, including labor, are not "perfectly adaptable" to a alternative uses.  If you employ/deploy resources to such alternative uses they tend to be less productive, hence more costly.

Simple example.  The decline of steel manufacturing or coal production coincided with a increased demand for truck drivers.  While some unemployed steel workers/miners may make fine truck drivers, the "marginal" ones or additional ones after a certain critical mass, may not be so good. They may have more accidents or load mishaps and are more expensive (ceteris paribus) to employ.

I think this is an issue in many different industries/professions where there is a surge (short term or longer term) in demand for workers with certain skills.

It is discovering that point of inflection where the diminishing returns of labor start to turn negative and adding those workers becomes counter-productive.