Some Work and Some Play: Microscopic and Macroscopic Approaches to Labor and Leisure

Given the option, humans and other animals elect to distribute their time between work and leisure, rather than choosing all of one and none of the other. Traditional accounts of partial allocation have characterised behavior on a macroscopic timescale, reporting and studying the mean times spent in work or leisure. However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved. We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity. We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.Author Summary: Dividing limited time between work and leisure when both are attractive is a common everyday decision. Rather than doing one exclusively, humans and other animals distribute their time between both. Traditional explanations of this phenomenon have studied the macroscopic average times spent in both. By contrast, we develop a microscopic framework in which we can model the real-time decisions that underpin these averages. In the framework, subjects' choices are approximately optimal, according to a natural, microscopic, utility function. We show that the assumptions of previous theories are not necessary for partial allocation to be optimal, and show possibilities and limits to the integration of macroscopic and microscopic views. Our approach opens new vistas onto the real-time processes underlying cost-benefit decision-making.