From Krugman (Bang for the Buck):
Consider an increase in government spending; assume that the
interest rate is fixed (a good assumption right now, because interest
rates are up against the zero lower bound). Then textbook analysis says
that if the stimulus is dG, the increase in GDP is 1/(1 - c(1-t)) where
c is the marginal propensity to consume out of income and t is the
marginal tax rate. Suppose c is 0.5 and t is 1/3; then the multiplier
is 1.5, which is more or less the conventional wisdom right now.
But if $100 billion in spending raises GDP by $150 billion, and the
marginal tax rate is 1/3, $50 billion of the spending comes back in
additional revenue. So bang for the buck — increase in GDP per dollar
of added debt — is 3, not 1.5. Since the main concern about stimulus is
that it will add to government debt, it’s this bang for the buck
measure, rather than the multiplier, that’s relevant. And 3 sounds a
lot better than 1.5.
Take this a bit further: $150 billion is about 1 percent of GDP, which
Romer and Bernstein
say means a million jobs; so this says $50,000 per job, which is a much
better number than the critics have been throwing around (plus many
more workers with full-time rather than part-time jobs).