Theresa May sent a strong message to the corporate world when she criticised the ‘irrational, unhealthy and growing gap’ between the pay of top executives and average workers. Yet what should be a vigorous debate on this topic — about the balance between fairness and the right incentives for optimum performance — never quite takes off. More evidence came to hand this week from the ‘independent non-party’ High Pay Centre: it reports that average pay for a FTSE 100 chief executive last year was £5.5 million, up by 10 per cent on 2014 and a third since 2010, and that the ratio between chiefs’ average total pay and that of their workers stood at 129:1.

Why should anyone earn so much, in absolute or relative terms, just for sitting at a desk? On the other hand, why compare bosses and workers when they operate in completely separate employment markets? A chief executive of a global business that happens to be listed and headquartered in London can only be compared to other chiefs in the same sector, and if we’re not prepared to pay for talent… These arguments are tiresomely familiar, yet still we wonder why top pay continues to grow several times faster than average pay without corresponding advances in profitability, productivity, shareholder value and other measurables of strategic management skill.

The answer is that most big companies are no better run today than they were a generation ago, when the top-to-bottom pay ratio was probably a third of what it is now. It’s just that everyone at the top of the corporate anthill has vested interests in the continuation of the trend, while no board would dare be first to break it — unless and until shareholders force them to do so.

What would be a ‘fair’ top-to-bottom ratio anyway? Is it 75:1, as decreed by the mutually owned John Lewis Partnership, or 65:1, as applied by TSB in its spin-out flotation from Lloyds? Those levels would demand a halving of average chief executive pay, which seems highly unlikely. But someone needs to do something to bend a trend that causes such social offence without delivering significantly better results.

Well, here’s a suggestion: Mrs May’s government is the major shareholder in RBS, which after eight years of losses is so close to a basket case that it might as well serve as a laboratory experiment. Its chief executive, Ross McEwan, saw his pay more than double last year, to £3.8 million, despite the bank’s troubles. Why not halve it again, and decree that no one can earn more than the chief? Who knows: freed from the risky behaviour and internal frictions that come with executive greed, the bank might even start to perform a little better.