Abstract: which is determined by inherent biological needs. The

Abstract:

This paper is going to show the effects of sleep deprivation on labor market outcomes, specifically in terms of productivity and wages as well as introducing the models used to analyze the sleeping behavior in the economic perspective. It is also going to analyze how economic incentives and leisure compliments, especially in this age of social media and technology, affect the individual choice of his sleeping duration. The concept to be used includes Gary Becker’s model of time allocation, the economics of natural resources and the Hotelling’s rule, and the idea of human capital.

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I. The relationship between sleep and economics

Sleep is an important part of our lives and most of us spend one-third of our lives sleeping (2009, Wheeler). However, sadly, as the society progresses, we’ve been spending fewer hours on sleep and the effects of sleep-deprivation on the body and the brain are detrimental, with some examples such as a higher risk of cardiovascular diseases and obesity and a lower mental clarify and concentration ability(Pietrangelo, Watson, 2017).

Although these negative effects on the brain makes it sensible to draw a relationship between the amount of sleep and productivity and possibly even wages, which in turn allows the choice of sleeping duration to be analyzed in an economic perspective, there’s only a few existing literature on this topic it because it’s hard to obtain reliable data on sleep (Gibson, Shrader,2014).

As a result, in many economic models, the amount of sleep for each individual is not regarded as a choice but rather a constant which is determined by inherent biological needs. The assumption is partially correct as different people have different circadian rhythms that dictate the different sleeping durations they need and whether a person is a “lark” or an “owl” (Turk,2016). Moreover, genetics also plays a role in deciding whether a person is a light sleeper is a heavy sleep (Massachusetts General Hospital, 2010) and hence, the differences in the quality of sleep among different individuals are not voluntary. However, it can also be observed that sleeping duration varies across different countries and cultures, with residents in busy and fast-paced countries such as Singapore, Japan, and Korean having only five to six hours of sleep each night as compared to residents in slower-paced countries such as Australia, to have almost seven hours of sleep each night. This suggests that the individual’s choice of sleep duration may actually respond to economic incentives.

To further draw the connection between sleep and economics, we shall look at the negative effects of sleep-deprivation on one’s wage and productivity. With data collected in the US, it has been shown that for individuals who are sleep-deprived, their wage can experience an increase of 16% if their sleep duration is extended by one hour in the long-term (Gibson, Shrader, 2014). Many health studies have also shown that deprivation leads to a decrease in the ability to innovate as well as negative effects on one’s mental capacity and working memory (Chan, 2014).  It also causes one to become moodier and to make more mistakes at work (Noguchi, 2016). All of these result in a reduced productivity. According to research by RAND,  the US incurs a cost of 1.2 million working days every year due to lack of sleep while Japan comes in second with a cost of 600,000 working days a year (Hafner, Stepanek, Taylor, Troxel, Stolk, n.d). These two points thus show that sleep duration has a definite effect on the economy and therefore, it’s necessary to look at sleep in an economic perspective.

II.  The Application of Gary Becker’s Model of Time Allocation ( Becker, 1965) into the consumer’s choice of sleep duration.

This paper is going to examine how the consumer chooses their sleep duration under an application of Gary Becker’s model of time allocation developed by Biddle and Hamermesh and further expands on it. The following equations and interpretation are from “Sleep and the Allocation of Time” by Biddle and Hamermesh, 1989:

Considering that sleep duration affects productivity and utility, as an individual’s goal is to maximize his utility from consuming a composite good Z (which represents all other activities besides working and sleeping) under his time constraint ( the amount of time he has in a day), the following expression was derived:

” “,    (Biddle, Hamermesh,1989)

where U1 is the marginal utility of consumption of good Z

            U2 is the marginal utility of sleep

            P is the price of good Z or the value of other activities besides sleep and work

            Wm  is the worker’s wage

                Ts: the sleep duration

                Tw: the work duration

                a,b,W1,W2: positive constants

This equation shows that in order to maximize his utility, the consumer should choose his number of units of sleep such that the ratio of the additional utility obtained from consuming good Z over the additional utility from sleeping must be equal to the ratio of the price of one unit of good Z over the price of one unit of sleep.

As a result of the formula, changes in the good Z will lead to changes to the amount of sleep, and this will explain how gadgets and electronic devices reduce the sleep duration, shown through the mathematical formula as well as through empirical evidence.

III. The effect of the Internet and Gadgets on sleep duration

The development of technology and gadgets has allowed the modern workforce to be much more productive than they were before. The internet makes it much easier and faster to find information that would otherwise take a much longer time or even physically impossible to be found.  It also enables us to connect with others at a very cheap cost and to do many other activities such as shopping, online banking, and paying taxes much faster at the comfort of our homes. The use of technology significantly shortens the time needed for such tasks.(Asgeirsdottir, Zoega, 2008). In this sense, technology has helped to increase our productivity at work and increase our efficiency at many daily tasks. Hence, we should be left with more time for other activities and sleep.

However, the Internet has also become our main source of entertainment (buzz2fone,2014) in the modern society. Hence, according to the model discussed above, the Internet and Gadgets are classified as commodity Z, which is neither working nor sleeping. The equation for individual’s time constraint was derived as follows:

    (1)

                 (2)                                (Biddle, Hamermesh, 1989)

As people spend more time on these forms of entertainment, Tz increases. From equation (2), assuming that the time spent on working remains the same, Ts has to decrease to maintain the equation balance. Thus, as people choose to spend more time on their devices, their sleep duration decreases.

Assume that these forms of entertainments are more interesting than before, making Pz increases. From equation (1), the left-hand side must increase as well. Assuming that Tz and T* remain unchanged, Ts has to fall to achieve this effect and hence, the sleep duration decreases.

Empirical evidence also supports these results. According to experiments conducted in a paper by SOEP,  the usage of smartphone and laptop aided by the Internet before one goes to sleep contributes to his lack of sleep due to a shorter sleep duration and a worse quality of sleep (Billari, Giuntella, Stella, 2017).

III. The effects of wage rate on sleep duration

We use the backward-bending labor supply curve which to analyze how changes in the market wages affect the number of hours an individual decides to work Tw, and hence the effect on the sleep duration TS.

At the wage rate of $10, the worker begins to supply his labor. As the wage rate increases until $20, the worker increases his working time. This is because, before the wage rate of $20, the substitution effect is in place: the value obtained from the use of non-work hour for either leisure or sleep is less than the value from the wage received as a result of an additional hour of work. Hence, when wage rate is still relatively low, the working

time Tw increases.

However, when the wage goes above $20, meaning it has reached a sufficiently high level, the income effect is in place: value obtained from the use of non-work hour for either leisure or sleep is greater than the value from the wage received as a result of an additional hour of work. Hence, at higher wage rates, the worker begins to reduce his working time.

Since it was shown that when one spends more time at work, he reduces his sleep duration ( Biddle, Hamermesh, 1989),  it seems reasonable to conclude that an individual will have shorter sleep durations when his wage rates are relatively low. However, surprisingly, experimental data (Biddle, Hamermesh, 1989) reveals that individuals with higher wage rates actually work for longer hours and thus, have shorter sleep durations (Biddle, Hamermesh, 1989). This is because the satisfaction that they achieve during their awake non-working time with higher income at disposal outweighs the value of time to be spent asleep. A similar argument was also made in “The economic decision to sleep”: a higher wage will raise the “opportunity cost” of more time-consuming activities such as sleep and thus, the individual will substitute their sleep time for more interesting leisure activities (Marsden, 2009).

IV. Application of the economics of natural resources to analyze the optimal sleep duration.

Sleep evidently helps to restore the brain and the body’s after a long duration of being awake ( Bertrand D.C, 2013). After sleep, we achieve a refreshed body and most important economically, an alert mind. Another way to look at sleep in an economic perspective is to treat sleep as an “investment decision” that affects how “alert” we are during the day: the more “alert” we are, the ” higher utility level” we can derive from both work and leisure. In this model from “The Economics of Sleeping”, the “alertness” that one gets from sleeping is a form of resource and hence, an analogy is drawn between the economic interpretation of sleep and that of resource extraction. As a result, the choice of the optimal sleep amount can similarly be derived from Hotelling’s rule for the maximizing utilization of resources. (Asgeirsdottir, Zoega, 2008) .

The following equations and interpretations are from “The Economics of Seeping”:

where:

·         : a constant that reflects the level of alertness at the end of the day, right before bed.

·         : the rate at which “alertness” is obtained during sleep.

·         t0:  the sleep duration

·         : the rate of how fast we become tired as the day goes on

·          t1: the time budget

From the above equation, the optimal amount of sleep t0*  can be determined as:

The equation above is the integrated form of the Hotelling’s Rule (Hotelling,1931) in the application of sleep duration. The right-hand-side of the equation represents the extra cost for an additional unit of sleep time or equivalently, the extra benefits of one more unit of awake time;  while the right-hand side represents the extra cost for one unit of time awake when one already does not have enough sleep. Under the resource interpretation, the former benefit is the utility obtained from being able to do more thing such as leisure activities when one sleeps less, which is analogous to the value of “extraction” at the moment. Meanwhile, and the later cost is the reduced level of alertness that one experiences during the day, which is analogous to the “alertness” level which could have become higher or more valuable had one decided to sleep more. (Asgeirsdottir, Zoega, 2008).

The following derived equation also assists in explanation of the effects of various factors which influence f ( how fast we get tired during the day),  on the amount of sleep that one needs.

  (Asgeirsdottir, Zoega, 2008)

According to the equation right above, the positive value for the derivative means that if f increases ( as one gets tired fast er), the value of t0 will increase: meaning that one will choose to sleep for longer hours. The value of f can be affected by various factors: it can be reduced by the consumption of caffeinated drink and energy drinks,  the usage of modern technology and comfort furniture and devices; meanwhile, it can be increased by having children and many other activities.

V. The sleep market – when sleep is considered as an input to health capital

For most people who have no trouble sleeping and who are not sleep-deprived, sleeping is classified to be of relatively same importance as an entertainment activity (Cameron,2012). However, for individuals who have sleeping disorders or just difficulties sleeping, sleep is treated explicitly as an input into their stock of health capital that later enables them to consume more of health. Thus, devices and equipment that help one to have better sleep are classified as part of the healthcare market which stems from individuals’ demand for health (Pruckner,2010).

Some examples of items in the sleep market are specially-designed mattress and pillows, eye masks, sleep lamp, white-noise machines and sleep medications (BCC Research, 2014). Applying Grossman model (Grossman, 1972), the health investment model taking into account the sleeping time can be represented as:

I=I(SMP, SA, SMA, SME, Ts, Th), where

·         I: the investment in health

·         SMP: sleep mattress and Pillows

·         SA: Sleep accessories such as sleep masks and sleep lamps

·         SMA: sleep aid machines such as white-noise generating machine

·         SME: sleep medications

·         Ts: the amount of sleeping time

·         Th: the amount of time used to improve health

To further elaborate on this idea under the utility-maximizing framework, we have the following equation from the “Handbook on the Economics of Leisure”, (Cameron, 2012).

                                     SET, SIP, SPL, X, ZTu), where

·         ZZHK: sleep “health capital”

·         SHW: sleep “hardware”, the most fundamental physical items needed for sleep and is often fixed in number, such as a bed frame.

·         SSW: sleep “software”. Some examples include pillows and blankets. The number of these items can be easily varied.

·         SET: technology that helps to improve the quality of sleep

·         SIP: sleep-aid medications

·         SPL: practitioners that help one to sleep better by either consulting or physical-therapy.

·         ZTu: amount of time one stays in bed, taking into account possible effects by sleeping disorders or sleeping difficulties

·         X: all other activities that may affect the quality of sleep, ranging from playing with electronic devices to having headaches due to work stress.

In order to maximize the individual’s utility level,  ZZHK has to be maximized, called ZZHK*, according to the optimal levels of the different variables in the function. The level of SHW remains relatively the same due to its expensive costs and the lack of need for more of SHW items since having more of them wouldn’t help one to sleep better and thus, it doesn’t give one any additional utility. However, as the other components, namely SSW, SET, SIP, and SPL can be varied in their numbers and having additional units of these items are more likely to increase the level of improvement on one’s sleep quality, and thus, giving one the additional level of utility.

However, it’s difficult for the individual to determine what’s the optimal SSW*, SET*, SIP*, and SPL* due to the inability to quantify the additional utility that these items bring about. Hence, it’s hard to consume them at the optimal level according to their relative prices. As for the use of SIP,  the problem of imperfect information or asymmetric information further obscures the issue. Many research has shown that the effectiveness of many over-the-counter sleep aids still remains either unknown or very limited ( Adams,2013). In fact, prolonged usage of many sleep-aid medications can lead to harmful side effects such as drug-tolerance issues, behavior changes, and sleepiness even after one wakes up (Daiwik,2017). These sides effect results in a reduction in the healthy capital and thus, the utility level. However, again, due to imperfect information, the consumers are unable to quantify these additional costs so that one can consume the optimal amount of SIP*.

Hence, as analyzed above, the sleep market is not a very efficient one. Due to the market failure of imperfect information, consumers may end up incurring more cost or loss of utility than the additional utility that they gained, which is especially more so for SIP (sleep-aid medications).

 

VI. Conclusion:

This paper has shown that there are many ways one can look at sleep in an economic perspective, namely through Gary Becker’s model of time allocation (Becker, 1965; Biddle, Hamermesh, 1989) and through the economics of natural resources (Asgeirsdottir, Zoega, 2008). Finally, the presence and the analysis of the economics of the sleep market further enhances the point that our choice of sleep duration and our effort to improve our sleep quality are strongly tied to ideas of economics.

Even so, we have definitely been sleeping fewer hours than before: using worldwide statistics, it was common for one to sleep for 8 hours back in 1942; but now one only sleeps 6.8 hours and that’s even a luxury for residents who live in fast-paced and busy financial hub such as Singapore and Japan (Horan, n.d).

As it’s hard, though not impossible, for the corporate to estimate a specific cost that its employees’ sleep deprivation has on its business, companies find it hard to employ a monetary-based sleep incentive program effectively. As a result, they usually end up ignoring this issue (Neuron, 2017). Hence, a better approach towards this issue would be to prevent it now rather than to fix it later with monetary incentives (Neuron, 2017).

For the corporate side, this can be done by adopting a more work-life balance working culture with more break times, fewer overtime hours, and a minimal level of work communication through smartphones after office hours(Hafner, Stepanek, Taylor, Troxel, Stolk, n.d).

At the individual level, since one still has some degree of control over his quality of sleep, he should refrain from spending too much time on electronic devices before sleep. He should also engage in more physical activities in order to enhance his sleep quality (Smith, Robinson, Segal, 2017).