Optimal indolence: a normative microscopic approach to work and leisure

Dividing limited time between work and leisure when both have their attractions is a common everyday decision. We provide a normative control-theoretic treatment of this decision that bridges economic and psychological accounts. We show how our framework applies to free-operant behavioural experiments in which subjects are required to work (depressing a lever) for sufficient total time (called the price) to receive a reward. When the microscopic benefit-of-leisure increases nonlinearly with duration, the model generates behaviour that qualitatively matches various microfeatures of subjects' choices, including the distribution of leisure bout durations as a function of the pay-off. We relate our model to traditional accounts by deriving macroscopic, molar, quantities from microscopic choices.