Math Homework of the Day 1

Fifteen to twenty-one year old me hated math. It was a function of me liking things that came easily, like English and French and politics and primate diversity (fuck yeah monkeys!), and I'm sorry to say that it took two or three years working for a living for me to understand the value of hard work. It's pretty embarrassing, but now I've changed. I swear. It's sort of the reason I started this bloggy thing: to keep tabs on myself and my productivity.

It's sort of like the three years in college where I tried to convince myself I was too punk rock to follow any sport other than European futball. Thank FSM the Broncos sucked then, but I missed out on some great sports moments (save for me playing NFL ambassador to a packed pub of British students for Super Bowl XXXIX) in the name of commiserating with my one futbol friend about the (once) awesome blackness of Thierry Henry.

The main difference is that I took a three-year hiatus from following sports (something I loved) because I wanted to be cool, but an eight year break from math (minus a required undergrad algebra module) because I hated it and convinced myself that it was worthless for my future career as a writer. It's the reason that architecture appealed to me when I was younger: I could make cool stuff and not bother with hard math, right? But somewhere along the way I decided that I wanted to go into development studies, and some time after that I decided that an economics PhD was the best route. After some quick research, I realized that I have almost no credentials to get into an econ PhD program, but am pretty well qualified for an MA or MS program in development studies, and can cross-study in econ while there.

Thus, one of my new projects is learning Mathematics for Economists by Carl P. Simon and Lawrence Blume, all nine-hundred or so pages of it. I never made it past trig in high school, so this should be a fun adventure, and I'll be posting any successes and [probably more of my] failures. It's like learning a new language, only with more mental blocks and fewer applications in my (current) daily life.

So, with that lengthy introduction, here's what I'm currently stuck on:

In economic models, it is natural to assume that total cost functions are increasing functions of output since more output requires more input, which must be paid for. Name two more types of functions which arise in economics models and are naturally increasing functions. Name two types of such functions that are naturally decreasing functions. Name one type that would probably change from increasing to decreasing.

(Simon & Blume 15-16)

Hmmm....can't cheat with Google. This isn't economic, but according to my future doctor friend Paul, lifting weights longer than forty minutes to an hour per session can cause your muscles to start breaking down and cannibalizing themselves. So maximum output would increase until forty minutes where it would start to level off and start decreasing after an hour of lifting. I imagine the graph wouldn't be a perfect x^2 asymptote, but something like that. I just tried to write it down and only managed to confuse myself. I'll give this another college try tomorrow, armed with more tea.