There are close to 400,000 millionaires in the city of New York.

When their fellow citizens chose Bill de Blasio in last November's mayoral election, these occupants of Manhattan's gilded towers reacted as though red revolution had come.

The victor was a Democrat of a type almost forgotten in the United States. He was given to contrasting poverty in the city's outer boroughs with the fact that 39% of all income in New York is earned by 1% of residents. He had a habit of promising to do something about this astounding phenomenon.

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Mr De Blasio's eye-catching plan was, as it remains, to raise an additional $530 million, mostly for nursery and after-school provision, by increasing city taxes on those earning more than $500,000 a year. In cold print, it didn't quite read like a call to the barricades: an increase in local income tax from 3.86% to 4.41% for five years only. This would cost anyone taking home $1m a year a whole $973 (£590).

Michael Bloomberg, De Blasio's predecessor and an individual reputed to be worth $31 billion, nevertheless called the proposal "unfair". The rich, said Mr Bloomberg - this might sound familiar - would flee. What was worse, alleged the business information tycoon, "places like London are going to eat our lunch".

Funnily enough, that statement has just been met somewhere in mid-Atlantic by the cry of British business enraged by Labour's plan to restore the 50% tax band for those earning more than £150,000. Irreplaceable executives denied a reward for their unique talents will flee, we have been told. After last Friday's announcement from Ed Balls, 24 captains of industry wrote to the Daily Telegraph to claim that investment would be put at risk, the recovery threatened, and jobs lost.

This is a proposal for personal income tax, remember, after years of cuts in corporation tax and endemic corporate tax avoidance. The threat, such as it is, is not to "business". Mr Balls offers his plan, moreover, after an average increase of 14% in the pay of FTSE-100 directors in 2012. Mean annual salary for such individuals stood at £2.1m when last assessed. Cuts in bonuses - because the public were wise to those - were more than made up by "long-term incentive" plans.

In other words, those who say a 50% rate is a trivial addition to Treasury revenues forget to add that it is also trivial, in fact irrelevant, when set against the inexorable rise of executive rewards. Even sectors still wedded to bonuses shield elite employees from the nuisance of a bit of income tax. RBS might be facing an £8bn loss thanks to what are winningly described as "mistakes", but it still wants to grant 200% bonuses to investment bankers in defiance of new European rules.

According to the researchers at WealthInsight, there are 281,000 millionaires in London. The city also has more people worth more than $30m than any other metropolis, but that's due to other fascinating quirks in our tax regime. Foreign-born or not, those among the very rich who work in London would not be cast into the gutter by Mr Balls and his temporary measure. Nevertheless, the wealthy and their friends have another argument: a 50% tax band raises no money worth mentioning.

The Shadow Chancellor disputes the assertion, but struggles to come up with a precise figure. Estimates range from £100m (HMRC) to £6bn (Tax Research UK) to £9.5bn (Labour when bold). The explanation for this disparity arises from one of the most splendid euphemisms ever devised by indulgent economists, "taxable income elasticity". You might know it better as tax avoidance.

The simple assertion is that when tax rates exceed a magical (if hard to state) level the resourceful rich go on the dodge. Thanks to legal (supposedly) avoidance, they find ways to ensure that the state gets as little as possible. When George Osborne did these people a favour by cutting the rate from 50% to 45% - but not back to 40% - he toyed with the guess that the highest band was costing more to collect than it was bringing in. He produced no real evidence.

Here, nevertheless, is a statement of fundamental importance in a country given to treating widening inequality as an act of God: if you have the means, you can write your own tax rules.

A friendly government might call it legal avoidance, but in effect you are refusing to meet obligations set down in law. The politicians and the economists simply accept this as reasonable behaviour.

Meanwhile, your corporation does a bit of dodging of its own. Your dividends and your long-term incentives are inflated; your take-home pay rises at a rate that mocks inflation; you might also expect a 200% bonus to tide you over. Then you can affect righteous indignation over a measure you otherwise deem pointless. That piece of theatrical posturing somewhat gives the game away, however.

If the Balls scheme truly brings in no revenue worth the name, why were 24 bosses of major companies quite so upset? If one part of their argument is right, they are making a fuss over what is literally nothing. If, on the other hand, a 50% rate does raise a few billion from people in firms avoiding corporate obligations, granting 14% pay rises, or finding the money for 200% bonuses amid an £8bn loss, Labour could be a little more assertive about that favourite word, fairness.

Thus far, the public have grasped the point, up to a point. A Survation poll says that 60% approve of a restored 50% tax band while they struggle to meet the cost of living. That should count, you might think, as a Labour bounce. But two other poll this week put the party's UK lead over the Tories at between only 1% and 2%.

Crushingly for Mr Balls and Ed Miliband, a ComRes survey contains a brutal judgement. Those who trust the pair with "family finances" account for 28% of voters. Those who would say the same about David Cameron and Mr Osborne return a figure of 39%. Labour's analysis is all well and good, but faith in Labour to achieve change is wanting. If the economy decides electoral outcomes, as number-crunchers always insist, the opposition party is in deep trouble.

If income tax doesn't work with the footloose rich, their property wealth remains vulnerable. Mansions don't flee the country, even if you believe the Laffer curve voodoo equating rising rates with diminishing revenue, and land is not a portable asset. Vince Cable and the Liberal Democrats are once again making noises about such taxes, but they have not yet felt the wrath of the Daily Mail on behalf of the aspirational home-owner. A Mail editor with 13,000 acres in the vicinity of Ullapool might also take a view.

People don't need Labour's lectures on fairness. They know all about injustice within UK plc. But they struggle to believe that the Ed Balls who found no fault with the City before the crash has discovered a new understanding and a new resolve. The rich who howl against the shadow Chancellor sense his weakness too.