It started over lunch with two economist friends. We were having one of those long conversations about AI and economics — what happens to labor income when machines get good enough, whether capital saves you or dooms you, the usual cheerful lunchtime topics. By dessert, we had talked ourselves into a challenge: write an interactive research paper about it, in the style of the AER, with Yannick's idea as the starting point.
The result is here: How to Die Optimally — A Theory of Consumption When AI Takes Your Job.
It is an interactive paper with sliders and live plots — go play with it.
What it is about
Imagine your labor income is being eaten away by AI — exponentially. You can save, you can invest, but eventually the math catches up: your lifetime earnings cannot fund subsistence forever. The question is not whether you die (economically), but when — and whether you do so with dignity or surprise.
We set up a classical optimal control problem — a consumer maximizing log-utility over an endogenous horizon — and solve it with Hamiltonian methods. The punchline: if you plan ahead, you live significantly longer and better than if you just spend your paycheck as it comes. Above a critical rate of return on capital, you can even live forever. Below it, at least you die optimally.
The paper features what we call an immortality frontier — a boundary in parameter space between finite and infinite life:
The green zone is where capital returns grow fast enough to sustain you indefinitely. The orange zone is everyone else. Reassuringly, which zone you're in is just a function of the parameters.
The paper is short, somewhat irreverent, and comes with interactive visualizations so you can drag sliders and watch the optimal death date move in real time.
How it was made
This was my first serious experimentation using frontier LLMs on a research project. Starting from Yannick's idea and a few days of pen-and-paper scribbling to sharpen intuitions, get a clear formulation of the optimization problem, and understand the shape of the solution, we delegated most of the execution to AI. After a few back-and-forth prompting rounds — mainly with Claude and GPT — to get proper visualization, polish the text, and explore extensions, voila, we got the paper.
The whole process took a few hours of work here and there over a two-week span, on top of our regular full-time jobs. This is truly amazing, but as the paper itself suggests, there may be some big downsides to it.