# 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.