The C-D production function is a pretty uninteresting claim: GDP depends on how much labor and how much capital a country has. However, if we combine it with the Solow growth model we can use it to prove the existence of convergence (poor countries grow faster than rich countries). In the real world,

*absolute*convergence (all countries converge) is a myth however

*conditional*convergence (countries with similar institutions converge) is quite real.

We do not need C-D or Solow to learn this--we can simply look at the data--but it does help explain why this happens in a clean but still useful way. Similarly, we could use pure math to explain or demonstrate conditional convergence but that would be of little use; words are much more appropriate for that. In my defense of math in economics, I ask that Austrians recognize something they've always asserted: people are heterogenous. One person may instantly grasp the intitution of convergence while another may be assisted in the calculus. To dismiss all of mathematics in economics is to deny a potential tool economists can use to demonstrate how the world works. To embrace it completely is also a mistake for it nullifies the most important questions. Mathematics misses the point in some ways, but is appropriate in others.

Math in economics is a siren song. It is beautiful and pure, but also dangerous if we focus too much on it. Yet if we completely avoid the music we will deny ourselves valuable knowledge and drastically limit where we can go (Odysseus

*had*to travel past the sirens' island in order to continue his journey). Economists must learn to straddle this siren song: to hear it but not to succumb to it. If we can force ourselves to stay grounded, like the hero

*The Odyssey*who tied himself to the mast of his ship, we won't miss what can be learned from mathematics nor will we drown in a barren attempt to worship this dirge.

## 6 comments:

David, I enjoy reading your blog but I often don't understand a word of it.

Ah, then he is not all that far from being an Austrian after all ...

David,

It sounds like your response to Jason is that math is a good device to teach economics to people who don't understand abstract concepts. You claim that people being heterogeneous supports this point. Yet heterogeneity is probably the key aspect of economcis that math fails to convey. In using math, you're not teaching people economics at all, you're teaching them math. As you laid out the conversation, I don't think you've succeeded in offering a response to Jason's question.

Dan

I think math has helped some in finance and experimental economics. Consider Vernon Smith's empirical work verifying some equilibrium predictions in a controlled setting.

But the usefulness of math is extremely sensitive to context. Introducing math when you are unsure about any element of the context is like giving the proverbial car keys and whiskey to teenage boys. Mathematical symbols look like the hand of God to some people. If you're bringing down God's hand, you'd better be danged sure about what it is to be smote.

Of course it's extremely sensitive to context; I never said we should teach exclusively mathematics. My core example illustrated that we need

bothin order to convey to as wide an audience as possible what's going on and why. Some people are more convinced with words and others with numbers but to some degree, they need each other for purposes of completeness and clarity.Since Austrians generally glorify "logic," and logic is a branch of mathematics, I think that their argument is flawed. Imposing the assumptions of deductive reasoning on economic theory can be as futile as imposing the assumptions of differential calculus.

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