Also, it very well could be that reducing to 4 from 5 does nothing but simply reduce the number of hours 'the factory is operating'. Surely there'd be a bonus because people might be more relaxed, but it's hard to weight that against the lost day.
For example, my local coffee shop is open 7 days a week, let's say that their staff works 5 days on, 2 off so there's a steady rate of staffers.
If they just switched to 4 on 3 off ... I'm not sure anything would materially change in terms of productivity etc. - and 'all else being equal' (i.e. demand, cost of goods, wages/hour), the staffers would simply make less money and I doubt they'd chose that.
But maybe '3/4 days' would be better in some industries than others.
I recommend reading The Phoenix Project. It does a great job of dispelling the myth that software engineering is unpredictable and artisanal and whatnot. At the abstraction layer of a department or division manager it becomes indistinguishable and the same stochastic modeling principles apply.
But that’s besides the point. A more important point is the idea of effectiveness.
4 days of effective work are often better than 5 days of being busy but ineffective.
Personally I get more done in a 4 day week because I am more cut-throat about saying No to things that don’t matter.
Again, this could only be (dis)proven in a large-numbers experiment (so no, not in a single cafe :)), but I don't think this is limited to any one particular area of work.
The reason for this are statistical perturbations in stochastic events. If a task takes a worker rand(1,4) units of time you can expect them to do day/1 to day/4 tasks in the day.
You look at the worker doing day/1 tasks and you say, "Well shit, that person is slacking most of the time. Most of these tasks take 2 units, 4 is very rare". So you ask them to work harder and impose rules so they must perform day/3 number of tasks per day.
You look at your constantly busy workers and you're happy. No more slack in the system.
But your assembly line grinds to a halt. Nothing ever gets done anymore. Everyone is busy all the time. Everyone's always working. But nothing is finishing.
What gives?
Turns out any task that hits N=4 on the random curve, wreaks havoc and you fall behind. Then you have both yesterday's and today's tasks to do. You can't. The next day ... well the problem ends up growing exponentially.
Efficient systems have slack.