# Should I keep Working?

Some time ago, I took an Intermediate Microeconomics class. The name “Intermediate Micro” is somewhat deceiving. Turns out it’s less “economics” and more “multivariate calculus with a sprinkling of economics”. Every problem set featured a series of nasty optimization problems requiring 10+ line derivatives.

The week before Thanksgiving, the professor assigned a particularly nasty one. About 12 hours into working on the thing with very little progress, I started to wonder if it was really worth working on anymore.

I thought about it for a bit and realized that this question isn’t all that different from the profit maximization problems I was struggling through! So, I took a break from micro calculus to….. do more micro calculus….

Here’s my model:

We start with the output. Assume a Cobb Douglas production function (because it’s easy).

B is brainpower; t is time; Z is productivity (everything else); a is the brainpower share. a closer to 0 implies mindless tedious tasks, like data entry; a closer to 1 implies work that requires serious thinking, like proofs.

Brainpower (B) is nebulous and annoying. There are two options. 1) The logical option: write B as an increasing function of t. The more time dedicated, the greater the brainpower required. 2) The lazy option: assume B is the same and set B = 1.

I’m lazy:

Doing work isn’t free. Every minute spent working on the econ problem set could have been used to work on Diff Eq, go to the gym or watch Netflix. There’s also disutility from stress and knowing you’re giving up other things. These costs increase with time, and at least for me, increase exponentially

Finally, it’s the little details. Assignments aren’t created equal nor are they equally urgent. I assigned l, between [0,1] for importance (basically giving the task a weight) and k, between [-1 and 1] to represent things like late penalties or probability of getting an extension. The nice thing about applying this to school stuff is that l and k are usually given somewhere on the syllabus:

Now just maximize to optimize:

First order condition (econ speak for derivative- with respect to t in this case)

Rearrange stuff to solve

…. To get….