# Unrelated Micro Math (again)

Since we didn’t have a class yesterday due to the snow (rain) day, I figured I’d blog about the math I’m doing in other classes.

I know I already mentioned how my Micro class is talking about the production function, but the production function is also related to math in other ways!

Every class in the past two weeks has included my micro professor something along the lines of: “If you’ve taken (linear)(vector)(topology) before…this would be easier”. To someone who’s only in FOM so far, it’s a little intimidating, but interesting at the same time.

The reason he brings it up is because we’re talking about the long run production function right now. This entails the equation Q = F(K,L), where (in the long run), Quantity, Capital, and Labor are all variables. This means that all three deserve an axis to show change (since econ is ALL about those graphs). If vector had been a pre-req, we could use the 3D graph to show the area of a long-run production function with all three as variables, but alas, most of us in the class probably haven’t even taken Calc 1.

Therefore, we keep Quantity constant, and graph all of the possible combinations of Labor and Capital that will produce that Quantity.

BOOM! Learn something new every day. And by something, I mean copious amounts of things usually associated with econ or math.

1. Nice! First, sorry I missed your e-mail and the chance to chat about fom stuff today. Second, these concepts are FOM-related — or, rather, they are made somewhat more palatable after/during FOM. Your function $Q = F(K,L)$ is a function $F:\mathbb{R}\times\mathbb{R}\rightarrow\mathbb{R}$, and, given that the domain is 2-dimensional $\mathbb{R}^2$ while the co-domain is 1-dimension, $\mathbb{R}$, unless your function $F$ is extraordinarily funky, it will be impossible for it to be one-to-one (I’m not certain what injectiveness would sound like in econ-terms: for every particular quantity, there is precisely one combination of labor and capital that can be used to achieve it).