College Math Teaching

January 17, 2012

Applications of calculus in the New York Times: Comparative Statics (economics)

Paul Krugman has an article that talks about the economics concept of comparative statics which involves a bit of calculus. The rough idea is this: suppose we have something that is a function of two economics variables f(x,y) and we are on some level curve: f(x,y) = C_1 at some point (x_0, y_0, f(x_0, y_0) = C) . Now if we, say, hold y constant and vary x by \Delta x what happens to the level curve C_1 ? The answer is, of course, C = C_1 + (\Delta x) \frac{\partial f}{\partial x} (x_0,y_0) + \epsilon where \epsilon is a small error that vanishes as \Delta x goes to zero; this is just multi-variable calculus and the idea of differentials, tangent planes and partial derivatives. The upshot is that the change in C , denoted by \Delta C is approximately (\Delta x) \frac{\partial f}{\partial x} (x_0,y_0)  .

It isn’t every day that someone in the mainstream media brings up calculus.

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