Your math seems right but not sure the causality is correct. Is it that the boss gets paid more because he knows less, or is the causality the other way around?
Money = Work/Knowledge
can also be interpreted as meaning "it costs more to do the job when the work is done by someone who knows less." If this is the case, then it implies that the one who makes the more money is one who knows more. The knowledgeable person gets the work done for lower cost. That makes that person more valuable, hence you can increase their salary and still end up costing less than employing an unknowledgeable person. So you end up saving money by paying the knowledgeable person more, a good business practice.
However, your explanation is more emotionally satisfying.
In my opinion, the "Boss" makes more in terms of the total sum , but if you calculate his hourly rate, it will be much less than that of his subordinates
That is because the "boss" has to carry the burden of the project or department almost 24x7. He can be hauled for a meeting on weekends, in the middle of the night and such odd hours by the top executives just to satisfy their queries , has to constant keep on updating on the progress of each of his subordinates and hide all inefficiencies of his team while making presentations to the top bosses.
For what burden he carries , he gets only a pittance in my opinion.
"There could be many reasons. For one thing the manager suddenly is responsible for budgets and schedules and is therefor under more scrutiny."
In some hypothetical case, I suppose. In our specific case, we are responsible for our own schedules. We deal directly with the customers' management, so we are well aware of the schedules we have to meet and our budget. Our immediate manager, within the corporate structure, is not really the one that figures out how the work has to be done, nor do any of us expect that of him. Which is why I chuckle when the corporate execs ask whether our manager "shows us the way." What a bizarre view of engineering reality. That job belongs either to the senior or lead engineer in a group, or to ourselves as the senior or lead engineers.
You're probably right about "is under more scutiny," but I think this has more to do with his superiors' expectations about "what a manager should do," than to actually help engineers get the job done more effectively. That's why I called it "playing manager."
When I worked on the factory floor in a PCB shop, anyone who wore a tie (1970s) was considered a "boss" by the people in the floor. that applied to engineers who might not have anyone reporting to them. Bosses were to be avoided.