Happy fat cat day! Around lunchtime the average CEO will have earned as much you do in a year if you’re an employee on the average British wage. After that it’s all gravy for them.

Unless you happen to have a female CEO, that is.

The Equality Trust gave us a twist on what’s become an annual event by highlighting the gender pay gap at the top.

It released figures showing that the FTSE 100's six female bosses collected an average of £3.2m a year last year, compared to £5.9m on average for the men.

So female fat cat day will presumably fall sometime next week.

High executive pay is deeply problematic, and that applies to female CEOs as well as male CEOs. It has spread like a virus through society, infecting the public sector so that the bosses of universities, health trusts, school academy chains, local authorities, expect and get six and seven figure sums benchmarked against the absurd salaries handed to the FTSE’s fatcats.

That there is a golden circle of top people, who rake it in while much of the rest of the country is just about managing, has played a role in fostering many of the political problems from which Britain suffers. The Trust’s research has found countries plagued by inequality suffer from higher levels of drug addiction, mental health problems and other maladies.

However, the gap between female and male CEOs is also problematic. Shortlists for executive positions considered by appointments committees are put together by headhunters and headhunters are paid on commission.

You only have to look at the figures to see why their motivation for including women on those shortlists might not be terribly strong (there are just six female CEOs in the FTSE at present). Because women bosses get paid less, they get paid less.

Throw in the antediluvian attitudes of appointments committee members who are overwhelmingly white, middle aged, male, and from the upper echelons of society, and, well, you see the problem. Anyone with an interest in social justice and the creation of a fair society should be concerned.

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But how to address the issue? There are two very simple ways. You could bring down the level of male CEO pay to that of their female peers. As the GMB’s CEO Tim Roche noted, ultra high CEO pay "makes no sense”. There is simply no evidence that it results in better corporate or economic performance. The reverse may actually be true because it could serve to demotivate those on the shop floor. So bringing the pay of male CEOs down would be a sensible way to proceed.

Bosses pay would still be too high – the average female CEO received £3.2m last year according to the trust’s analysis. But the pay ratio between Britain’s top executives and the people that do the work to make their businesses succeed would at least come down a little. Companies would save money too, and investors are supposed to approve of that. Sensible City institutional fund managers that acted in the interests of their clients really ought to be pushing for such a step because it would benefit everyone but a small number of top CEOs.