Abstract
Sleep is a form of rejuvenation, which can be treated as a source of energy. This energy is available in limited quantities and individuals must decide when it should be renewed and when it should be consumed. Sleeping involves investing in energy and alertness but also a sacrifice of time. We derive and solve the inter-temporal utility-maximization problem on the length of sleep to obtain optimality conditions for the length of sleep. Several applications emerge from the analysis. These include the effects of labor-market opportunities on sleep patterns; the effect of having children; the consequences of decreased division of labor within the household; and the relationship between sleep deprivation and obesity. When data allows, those outcomes are tested using panel data from Iceland. The empirical results are consistent with the predictions of the theoretical model.
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Notes
Surprisingly, the effects on health are not clear as several studies have shown sleep duration of more than 7–8 h per day to be associated with increased mortality. Causal links are currently speculative: the available data may reflect such things as depression, socioeconomic status, or even alcohol use, as these studies can only be used to determine correlation, but not causation (Patel et al. 2004, 2006a; Ferrie et al. 2007; Born et al. 2006).
The second-order condition is satisfied: −2a s = −2α1 < 0 since a ss = 0 given our functional form.
The second-order condition for a maximum is satisfied since the Hessian matrix is negative definite.
The second-order condition for a profit maximum is satisfied: \( - 2\beta_{1} < 0. \)
The second derivative is negative:
\( U_{1}^{''} \left( \cdot \right)\left[ {\left( {T - s_{t} } \right)\beta_{1} - \left( {\beta_{0} + \beta_{1} r_{t} } \right)} \right]^{2} - 2\beta_{1} U_{1}^{'} \left( \cdot \right) + RU_{2}^{''} \left( \cdot \right)\left( {T - s_{t + 1} } \right)^{2} \left( {1 - f} \right)^{2} \bar{\beta }_{1}^{2} \, < \, 0 \).
In that raising one's own children is usually not remunerated, having children may be viewed as a form of leisure. In that children may support their parents at later stages of the life cycle, having children may be viewed as work (investment). For analytical purposes, time spent on children is however separated from time spent working and enjoying leisure in this analysis.
The reader is directed to Waldfogel (1997) for a review of studies on how changes in family structure affect the labor market.
John Harlow, “Study finds we get 31 h into a day: Multitasking make the modern man,” The Sunday Times, April 13, 2008.
Public Health Institute of Iceland: Heilsa og líðan.
As the empirical presentations here are meant to show relationships between the variables of interest implied by the theoretical model, rather than to precisely map the sleep behavior of the Icelandic population, results are presented without sample weights.
It should, however, be noted that this overall association between wages and sleep duration, ambiguously predicted by theory, was the only relationship reported in this paper that was not fully consistent across different empirical robustness checks.
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Acknowledgments
We are indebted to Michael Grossman, Dhaval Dave, Ching-to Albert Ma and an anonymous referee for insightful comments and suggestions. Financial support from The Icelandic Research Fund (RANNIS) is acknowledged.
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Asgeirsdottir, T.L., Zoega, G. On the economics of sleeping. Mind Soc 10, 149–164 (2011). https://doi.org/10.1007/s11299-011-0086-5
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DOI: https://doi.org/10.1007/s11299-011-0086-5