PTO is a "fringe benefit". Factoring it into productivity levels is orthogonal, as its goal is to increase desirability of the employer, not to ensure "maximum output per employee".
That's what I'm saying - productivity per employee doesn't change. They still make the same widgets/hour on the line on hour 1, hour 35 and hour 40 of their week. The company just employs 1.1 people to run that line full time (well, 40 hours a week, leaving aside 24/7 ops for the sake of simplicity) rather than the mathematical minimum 1 person.
> Paying someone to stay home, and then paying someone else to cover them, reduces productivity of the factory because it requires more total labor to produce the same number of parts.
Maybe it's the pedant in me as I approach an MBA program, but while there are multiple definitions of productivity, in industry it's usually an expression of the output as a factor of input. And generally it's the equipment that's the limitation. A factory whose equipment can produce 200,000 widgets/year can still only produce 200,000 widgets/year, even if you have twice as many employees working 20 hour weeks, i.e. productivity is the same.
"I work just as hard, I just don't work as much."
There is no financial difference between paying someone to not work one day every two weeks, and having them show up that day but not do anything (which we can agree would be unproductive).
Paying someone to stay home, and then paying someone else to cover them, reduces productivity of the factory because it requires more total labor to produce the same number of parts.
You can argue that the person will be more refreshed or whatever, which I think is probably a good argument for many types of jobs that are not manufacturing line work.
People who have engineering or creative jobs constantly think that you can get the same work out of four days as five. And for their jobs, because they have significantly decreasing marginal productivity per hour worked, they might be right. But that's very different than line work. The 40th hour worked does not have appreciably different productivity than the 35th hour worked in a week on a line.