First 20 hours: read a bunch of math papers about some obscure part of stochastic programming.
Second 20 hours: figure out how to apply it to problems useful for the company.
The first 20 hours are worth $0, not $100k. If I spend an additional 10 hours/week improving my skills, that effect is multiplicative rather than additive.
Claudia Goldin has a great paper on this effect, focused on using this phenomenon to explain gender gaps in pay. (Specifically, the fields with the lowest gender gaps are the most linear fields, e.g. Pharmacists.)
Week 1: First 20 hours: read a bunch of math papers about some arcane aspect of stochastic programming. Second 20 hours: figure out how to apply it to problems useful to the company.
Week 2: First 20 hours: read a bunch of math papers about some arcane aspect of partial differential equations. Second 20 hours: figure out how to apply it to problems useful to the company.
If you are only working 40 hours rather than 80 in those two weeks and you choose to do the first half of each week then, sure, your net value to the company will be $0. So don't do that. Pick one of those two 40-hour chunks and do it in two weeks instead of one.
And, boom, your value to the company has scaled linearly.
Now, no doubt your work on stochastic programming and PDEs has prepared you for some other future work of still greater value. So there's nonlinearity on longer timescales. But we can get an estimate of just how much nonlinearity there is there by looking at how your salary increases over time. Maybe you're worth 20% more each year than the year before. (That would be bigger pay rises than most people get after the first few years of working.) In that case, the first half of a given year is worth about 47.7% of what the whole year would be worth instead of 50%.
So, if your work's value is nonlinear enough to justify giving you a 20% pay increase every year, then it's nonlinear enough to justify paying you about 5% less pro rata. (Plus, of course, giving you only about half as much pay increase per year.)
That assumes that the growth in your value to your employer comes only from this nonlinearity in your work. If some of it is because of other things that you're learning in other ways, then the reductions should be less.
Sure, but that assumes I can break everything down as granularly as a pharmacist breaks down their work. But in reality I can't. First of all, if I do it like you describe, the company's velocity is halved. Timeliness matters.
Second, by working more slowly and parallelizing across many more low productivity people, you lose the ability to make connections and reuse relevant expertise.
For instance, consider two lawyers each of whom are running half of a major case. When the opposing attorney presents claim A, the two lawyers may not realize that evidence X (in lawyer A's half) and evidence Y( in lawyer B's half) put together refute A.
Like it or not, there is value to having a single person who can keep the whole thing in his head.
> if I do it like you describe, the company's velocity is halved.
Well, sure, half as much work means getting half as much done. That's why the pay is also half as much.
I don't disagree with any of the things you say here; there are some ways in which working part-time is less efficient than working full-time. I just think you overstated the case before.
First 20 hours: read a bunch of math papers about some obscure part of stochastic programming.
Second 20 hours: figure out how to apply it to problems useful for the company.
The first 20 hours are worth $0, not $100k. If I spend an additional 10 hours/week improving my skills, that effect is multiplicative rather than additive.
Claudia Goldin has a great paper on this effect, focused on using this phenomenon to explain gender gaps in pay. (Specifically, the fields with the lowest gender gaps are the most linear fields, e.g. Pharmacists.)
http://www.aeaweb.org/aea/2014conference/program/retrieve.ph...