Go Forth And Multiply

The simplest of simple Keynesian economics on a napkin:

Let 0<b<1, where b is a constant, the marginal propensity to consume.  Specifically, let b = 0.9

The government spending multiplier is 1/(1-b), therefore = 10

The tax multiplier, -b/(1-b) is therefore = -9

For ease, break the current stimulus policy down to $450 billion in new government spending, and $300 billion in new tax cuts.  Using our multipliers, and other things constant, then the stimulus package would, in the limit, generate an additional

$4.5 trillion + 2.7 trillion = $7.2 trillion dollars.

Stones into bread.  Some $750 billion stimulus package can increase aggregate demand up to $7.2 trillion.

2008 nominal GDP was $14.3 trillion.  The administration's Keynesian economists are acting as if, without the stimulus, 2009 nominal GDP would fall 50%.

But, with the intervention, our economy should be on track by the end of the year.

So, Congressmen and women, go forth and multiply.

 

Comments

[Tom]

Dave,

How about working backwards. The proponent of the stimulus tell us that the multiplier is 1.5. This means that 1/(1-X) = K, where X = MPC and K = the Multiplier. And 1/(1-X) = 1.5, therefore X = .33. That is, the MPC is .33 and the MPS is .67. So for every additional dollar an American receives he "spends" $.33 and he saves $.67. What do you know, according to the logic of the multiplier, America is a nations of savers!!!

[John]

Well, let's get a little more technical and say K=1/(1-X*(1-t)*(1-M)) where t is the tax rate and m is the marginal propensity to import. t is probably at 35% for the whole economy. For values of M = 5%, 10%, or 15%, and a multiplier of 1.5, we would be assuming X = 54%, 57%, 60%.

Even using more advanced assumptions, you're still assuming a very low MPC given a savings rate in the economy of 5%.

[Dave Prychitko]

You boys are demonstrating that it's nonsense in every direction! Thanks!

[highmesa]

"where b is a constant"

As my auto mechanic said yesterday as he looked under the hood of my car, "I think I see a problem."

[amv]

.. the haavelmo-theorem ... the underlying logic: the paradox of trift, perhaps the most devastating nonsense in macroeconomics: the government does not save, so let's tax incomes and spend it that way!

[Bob]

"You can lead sheep to slaughter, so why make them think." Too Baaaad! Now you know why the chimps who so insulted when the NY Post blamed them in a cartoon for the stimulus bill. Chimps would do no harm and that would be better than what congress and Obama did!

[PG]

And what if there is more than one period? And what if the gifts that keep on taking become costly to maintain? And on and on. We're placing a huge bet on a stupid model.

[Bob Murphy]

Dave,

Far be it from me to defend Krugman et al., but what are you saying here? That their empirically-derived multipliers are so far below the standard theory's prediction, that the Keynesians should realize their standard theory is totally wrong?