It builds a standard model of optimising the work-rate in completing a fixed task (e.g. writing a paper by a deadline), where the real question is about procrastination. The punchline is that if agents discount the future, then it is optimal to trade future utility for utility now, i.e. procrastinate.
Specifically the optimal work path will start at or near zero, and continuously rise at the discount rate. The endpoint condition is that agents are working flat out towards the end and complete the last sentence just at the deadline. This is the same kind of result as Hotelling (JPE, 1931) albeit in a different setting.
Theoretically this is all fine but does it match reality: what sort of discount rate is applicable over the three weeks you have to write an essay? Some may argue that the levels of time discounting needed to match this theory to data are too extreme to be plausible. Essentially, this is true. In this model, even minor tradeoffs in marginal utility (1% per day) would require an annualised discount rate of 3,783%. This is somewhat larger than the 5% discount rate that is standard in the literature.
I do not think people behave optimally, but I do think it is a benchmark we should aim for. Teachers may wish to mention to students that the only way to justify procrastination as optimal is with a discount rate in excess of 3,500%. Increasing the salience of the costs of procrastination may just spur them into action.
(Aside: teachers should probably consider this when it comes to grading those papers, too.)
