An impatient Alexander the Great sliced through the Gordian Knot with his sword. Rather than puzzling over how to unravel the damn thing, as countless others had done unsuccessfully before him, the Macedonian opted for the brutally direct approach.

Our modern-day debates on corporation tax – with all the technical detail about “profit shifting”, “arm’s-length pricing” and semi-philosophical musings on what constitutes substantive economic activity – are starting to feel somewhat Gordian in their complexity. So do we need an Alexandrian solution?

How about if we simply scrap corporation tax? That has been mooted by a number of commentators and libertarian-leaning think-tanks in recent weeks, in the wake of the latest outbreak of public outrage and confusion over Google’s meagre back-tax settlement with Her Majesty’s Revenue & Customs.

The “just scrap it” proposition sounds suicidal from the point of view of the public finances. Corporation tax is expected to raise £42bn over the current financial year – that’s almost as much as all our excise duties bring in. HMRC would miss that money if it disappeared.

Yet would it simply flow into the state’s coffers by another route? Other things being equal, lifting the burden of corporation tax ought to translate one-for-one into higher surpluses for companies. That cash has to go somewhere. Managements could use it to invest. Or hire more staff. Or they could pay it out in dividends to shareholders.

If businesses increased investment, that would boost the UK’s GDP growth directly, and tax receipts indirectly. And more employment would bolster the Government’s income tax and national insurance take. And if the money were disbursed in dividends, a good deal would be caught by the income tax net. What left one pocket would come into another.

Alas, “other things” are seldom equal. And there are other possible outcomes from such a radical move.

The benefiting company could use the windfall to build up its cash reserves. Rather a lot of that has been going on in recent years. The aggregate cash balance of the UK’s corporate sector stands at around £560bn, according to the Office for National Statistics. That’s around 30 per cent of GDP, up from 25 per cent before the financial crisis.

And those reserves have been building even though George Osborne has slashed the UK’s headline rate of corporation tax from 28 per cent to 20 per cent since 2010, in the hope of sparking a corporate spending boom.

Or the company might use the cash to buy back its own shares in the market in order to push up its share price and trigger bonus payouts for executives. Rather a lot of that has been going on in recent years too.

And if the benefiting firm is a multinational, it may use the windfall cash to invest and hire not here in the UK but abroad. And who are the company’s shareholders? Let’s imagine the entire windfall is paid out in dividends. If the shareholders reside abroad, other governments, not ours, might see a fattening of their income tax take. And that’s assuming, of course, that the recipients pay much income tax on their dividends anywhere.

Still, this is a useful thought experiment because it compels us to consider what corporation tax actually is and who pays it. Many assume it’s just a tax on companies – but companies never shoulder the burden of tax, people do. The right question to ask is: which people? Does the tax mean smaller payouts to shareholders? Or does it mean less employment than would otherwise take place? Does it mean higher prices for the company’s customers?

In other words, what is the tax’s “incidence”? Economists disagree about the incidence of corporation tax. Some insist it merely depresses employment, but other evidence suggests it does primarily fall on shareholders. The answer probably depends to some extent on the country and the sector. The Institute for Fiscal Studies, although it sees corporation tax as flawed for a variety of reasons, notes that the levy is a practical means of taxing the incomes of overseas shareholders in companies operating in the UK.

Simply scrapping corporation tax plainly won’t work. But could it be replaced by something smarter? Some have suggested taxing the dividends paid by all companies operating here. But there is no way for the UK, for instance, to tax dividend distributions by Google made in the US.

A tax on corporate sales, as recommended by the former Tory chancellor Nigel Lawson, sounds on the face of it like a simple solution. But it would, in fact, be wildly disruptive since it would breach the fundamental principle that profits, not turnover, should be taxed. And to make allowances for corporate investment and other business costs would merely recreate corporation tax under another name.

Ultimately, the only viable solution to legitimate public frustration over corporate tax dodging by multinationals is co-operation between governments to tackle it – co-operation that goes far beyond their current efforts under the auspices of the OECD.

When American states faced an analogous problem of corporate tax dodging by new cross-state railroad companies in the 19th century, they sat down and agreed to share corporate taxes between them on the basis of a formula. Companies were required to create a comprehensive report of their activities in all states. And the share of the profit tax due to each jurisdiction would depend on the relative shares of the firm’s sales, employees and assets in each state.

Such an overarching tax framework – a so-called unitary tax – is needed to govern multinationals in today’s global economy. This would treat an individual multinational's profits as a global cake to be divided between all countries where the company does business on an agreed forumula.

Some disruption would be unavoidable from such a reform. Some countries would lose tax revenues from some companies. Yet they would also gain them from other firms. And it would shut down the tax havens, which have no legitimate claim to be the source of a multinational company's profits.

Most valuable of all, such a system could actually be defended as equitable to citizens around the world, unlike today’s increasingly frustrating chaos. Even the multinationals might eventually come to value the stability it created.