Saturday, June 29, 2013

The Landsburg Multiplier

Steven Landsburg argues that if the Keynesian story of the mulitplier is true, then there’s also a (huge) multiplier on his own personal spending. Your’s too. Here’s the Keynesian story. We start with:

Y = C + I + G

Next, we notice that people tend to spend, oh, say about 80 percent of their incomes. What they spend is equal to the value of what ends up in their households, which we’ve already called C. So we have

C = .8Y

Now we use a little algebra to combine our two equations and quickly derive a new equation:

Y = 5(I+G)

That 5 is the famous Keynesian multiplier.

To see how what story perverts the math, try this:

Let’s start with this one:

Y = L + E

Here Y is economy-wide income, L is Landsburg’s income, and E is everyone else’s income. No disputing that one.

Next we observe that everyone else’s share of the income tends to be about 99.999999% of the total. In symbols, we have:

E = .99999999 Y

Combine these two equations, do your algebra, and voila:

Y = 100,000,000 L

That 100,000,000 there is the soon-to-be-famous “Landsburg multiplier”. Our equation proves that if you send Landsburg a dollar, you’ll generate $100,000,000 worth of income for everyone else.

The argument was originally made by Murray Rothbard.

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