The Relationship Between Hours Worked and Productivity
There are two main explanations for the observation that overwork leads to decreased total output. First, we note that in cases where overwork has been observed to lead to a decrease in total output, it must be the case that average productivity decreased enough that the total output produced under such conditions (i.e., the increased number of hours worked per week, say 60, multiplied by the decreased average productivity) was actually less than the total output produced under normal work hours. Thus, if total output was observed to decrease when employees who had been working 40 hour weeks were made to work 60 hours per week, it would be the case that
60 x P60 < 40 x P40,
where P60 is the average productivity of employees working 60 hour weeks, and P40 is the average productivity of employees working 40 hour weeks. This effectively means that productivity during 60 hour weeks would be less than two-thirds that of what it was when 40 hour weeks were worked.
This dramatic decrease in average productivity can be explained in two primary ways. First, it may be the case that employees simply become much less efficient: due to stress, fatigue, and other factors, their maximum efficiency during any given work day may become substantially less than what it was during normal working hours. Thus, overworked employees may simply be substantially less productive at all hours of the work day, enough so that their average productivity decreases to the extent the additional hours they are working provide no benefit (and, in fact, are detrimental). This explanation is certainly very possible. As will be discussed in the next section, overwork very often leads to sleep deprivation, for example, and sustained reduced sleep is known to negatively impact productivity at all hours of the day.
The second explanation for the dramatic decrease in average productivity that has been observed in overworked employees is to some extent an extension of the first. It may be that the reduced productivity of overworked employees manifests itself much less during some periods of work and much more during others. For example, an overworked employee may very well be just as productive (or almost as productive) during his or her first, say, 4 hours of work while working 60 hour weeks as he or she was while working 40 hour weeks. However, it may be the case that productivity drops dramatically after say, 8 hours of work; in fact, productivity may drop so much after some point as to become negative. In other words, an overworked employee might, after a certain number of hours (or, perhaps, on the last day of the week) be so fatigued that any additional work he or she might try to perform would lead to mistakes and oversights that would take longer to fix than the additional hours worked. This sort of occurrence is clear and has been long-recognized in industrial labor: overworked employees using heavy machinery are much more likely to injure themselves and to damage or otherwise ruin the goods they are working on.