It seems likely that working more will increase your expected future income. That's obvious for overtime or a paid side project. The effect I'm trying to model here is different: putting more time into work and work-related activities — the job itself, self-development, networking — makes you better at your job, so you get promoted sooner, or generate better-paid options outside your current organisation.
One assumption throughout: these are decent hours. I'm not imagining you working ragged at the end of a fourteen-hour day — I'm imagining you substituting an hour you would otherwise have spent on your groceries or your taxes.
If you expect to earn —/year over the next ten years,
you might be able to boost your income by — per additional hour worked (on expectation).
Let's anchor the analysis to a ten-year period, and suppose you put in 10% more time — about four hours a week on a 2,000-hour year.*
* Finding an extra 10% of time by buying time is quite difficult, unless you really haven't picked up low-hanging fruit like reducing your commute. I'm using 10% because it's a round number which feels large enough that I can imagine a qualitative change in how my career goes.
Hours are fixed at 2,000 a year here. No discounting, no risk, no returns curve — that's what the complex model is for.
The simple model assumes the return to an hour is flat. This one doesn't. It assumes earnings rise with the square of your weekly hours (you can change that), that the money arrives a few years after the effort, that it might not arrive at all, and that the tax office gets a cut.
—
Why increasing returns at all? The mechanisms are mostly long-run. Skill compounds — twice the hours is roughly twice the rate of improvement, so next year's hours are worth more than this year's. A big share of any role's hours are fixed costs (staying current, managing, keeping the machine running), so the marginal hours go disproportionately into the proactive work that actually moves your trajectory. People who are visibly a force of nature get handed bigger, higher-leverage roles — the return isn't doing the same work faster, it's being asked to do different work. Relationships and reputation accumulate with network effects. And many careers have tournament dynamics, where slightly better wins much more. A cross-field sanity check points the same way: the observed gaps between 40-hour GPs and 60-hour surgeons, or family-practice lawyers and Magic Circle partners, are if anything steeper than the square.
And the case against. Within a single week returns genuinely diminish — your task list is fixed, and extra hours pick off increasingly marginal items. The increasing returns show up over years, which is the horizon this model runs on. More awkwardly, the best within-occupation evidence finds close to no wage return to extra hours below roughly 48 a week — the big measured returns come from switching into greedy jobs, not from working harder in the one you have. The curvature dial is the whole model: set it to 1 and the premium disappears, and that is a perfectly respectable opinion. Note that at the defaults, the whole move happens below 48 hours a week — inside the region where that literature finds nothing.
The risk cuts both ways. There are also financial risks to not working more — you could be worse at your job and take a hit. And there are risks to not spending money to save time: you make your life harder, and you're more likely to get overwhelmed, burnt out, or need a break.
Inflation: everything here is in today's money — the incomes are real, so the discount rate should be a real (after-inflation) rate too. Keep both sides real and inflation drops out; the only way to get it wrong is to feed in a nominal discount rate.
Made-up numbers to flesh out a point, not financial advice.