It Is Time to Get Some Rest
Posted: 25 Jan 2017 Last revised: 3 Apr 2018
Date Written: January 25, 2017
We introduce the fatigue disutility model. Set in continuous-time, the model captures the notion that fatigue accumulates with effort, decays with rest, and produces an increase in marginal instant disutility. The model is meant to be prescriptive, although it rationalizes several anomalies observed in time preference. It converges to the time separable model when the recovery rate is high. Under very general conditions the temporal profile of effort that economizes fatigue exhibits a high-low-high pattern. We also consider a variant whereby marginal productivity decreases with fatigue. We examine the optimal management of fatigue and productivity under various scenarios. The model also predicts well the patterns observed in athletes under time trial, and we provide a calibration using data from swimming competitions.
Keywords: Disutility, Effort, Fatigue, Time Preferences, Scheduling, Time Trial
JEL Classification: D01, D03, J22
Suggested Citation: Suggested Citation