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"But did they work 10 times as hard as a teacher on £30,000 a year or, in the case of some lawyers and bankers, 100 times as hard?"> It's not about how hard you work, it's about how much free time you have left AFTER work.
Your suggestion-- that income should be justified based on how much of someone's life is eaten by their job-- smacks of the same kind of moralistic posturing for which you criticize the author of the original piece.
Rather than try to morally justify or attack these inequalities (which I regard as silly as trying to morally justify or attack a rainstorm), I'd like to explore ways that the aforementioned teacher might slice himself a bigger piece of the pie.
Imagine that teachers were all free agents. Self-employed contractors free to negotiate their own rates for their services, and free to choose their students from the applicants they consider most promising.
The better teachers would probably make more money than they do under the current system, but still probably nowhere near as much as the successful banker or lawyer.
The exception might be the exceptional teacher who already has a track record of producing Nobel laureates, world leaders, curers of disease, self-made billionaire inventors, etc.
By the time this teacher could command the truly huge rates, he would be pretty old, and might well consider this new windfall to be merely the capstone of an already satisfying and distinguished life.
But the banker and the lawyer sink or swim based on goals that are directly measurable in the short term, so the same cycle that I've postulated for the old teacher (perhaps several lifetimes old!) can happen on a scale of months or years.
So, to achieve parity with the world-class banker or lawyer, the world-class teacher needs not just free-agency, but fine-grained, objective, fast turnaround metrics of performance that directly correlate with economic return.