INCOME tax has been paid in Britain for more than two centuries. First introduced by William Pitt the Younger to finance the war against Napoleonic France, it is the Treasury's biggest source of revenue, raising 30% of tax receipts. It arouses strong political emotions, regarded as fair by some because it makes the rich pay a bigger share of their income than the poor, but unfair by others because it penalises enterprise and hard work.

During the past 30 years, income tax has been subject to sweeping changes, notably the cut in the top rate from 98% to 40% under Margaret Thatcher between 1979 and 1988. Now another Conservative politician, George Osborne, is floating a radical reform to match that earlier exploit. The shadow chancellor announced on September 7th that he was setting up a commission to explore the possible introduction of a flat tax in Britain.

Mr Osborne's big new idea stems in part from frustration at the Conservative party's failure to win votes on tax in the past two elections. Their proposal to cut taxes by £4 billion ($7.4 billion) a year did them few favours at the polls in May. Such a paltry reduction in a trillion-pound economy seemed an apology of a policy.

By contrast, the introduction of a flat tax would be a radical step. The reform is already being tried elsewhere. Mr Osborne first expressed interest in the flat tax after a visit in June to Estonia, which introduced it in 1994. Since then eight other countries in eastern and central Europe have followed suit. Poland appears likely to adopt a flat income tax. Even Germany is flirting with the idea (see article).

Introducing a flat income tax into Britain would involve two main changes. At present, there are three marginal tax rates. The first £2,090 of taxable income is taxed at 10%; the next £30,310 is taxed at the basic rate of 22%; and income above that is taxed at the higher rate of 40%. These three rates would be replaced by a single rate, which would be considerably lower than the current top rate. At the same time there would be an increase in the tax-free personal allowance, currently worth £4,895.

Flat-tax proponents say that the reform would yield many economic benefits. If it were combined with an assault on other tax reliefs, then it would simplify a tax system that is groaning with complexity. The latest edition of “Tolley's Yellow Tax Handbook”, which contains all direct-tax legislation for 2005-06, runs to four weighty volumes and has roughly doubled in length since Gordon Brown became chancellor of the exchequer in 1997. Only this week, Mr Brown was upbraided by a parliamentary committee for the complex “nightmare” of his system of tax credits, designed to help poorer families.

Another advantage is that reform could sweep a lot of low-paid people out of income tax altogether. In the past eight years under Labour, the number of income-tax payers has risen from 26.2m to 30.5m. Over the same period, the number of higher-rate taxpayers has risen from 2.1m to 3.6m.

Flat-tax fans also think that it could trigger a new economic dynamism, as people respond to the enhanced incentive to work harder. The more this happens, the more the reform could pay for itself as a bigger economy generates more tax revenues.

So much for the economic case for a flat tax. What of its politics? One obvious objection is that the reform would be unfair, since the richer would pay less tax than they do at present. Advocates of a flat tax make two rejoinders. First, an income-tax system with a single rate remains progressive—the rich pay a higher proportion of their income than the poor—as long as it is combined with a tax-free allowance. Second, the rich can exploit current complexities to avoid taxes in ways that could be curtailed in a flat-tax system.

But could a flat tax be introduced without there being losers? A recent paper from the Adam Smith Institute suggested that this would indeed be possible. Richard Teather, its author, proposed a flat-rate tax of 22%, the present basic rate, with a tax-free personal allowance of £12,000, more than double the current one. “All taxpayers would be better off under the reform,” he argued.

However, the proposal has an obvious flaw. As Mr Teather himself admits, it would result in an initial loss in revenue of £50 billion a year. That is over a third of the total income-tax receipts of £138 billion that the Treasury expects this year; and a tenth of all government revenues.

Unless public spending were slashed, other taxes would have to rise to meet this shortfall. So a more realistic simulation of the impact of a flat tax is to make it revenue-neutral. The Economist asked John Hawksworth, an economist at PricewaterhouseCoopers, an accountancy firm, to calculate what that might involve. He said the current yield of income tax could be preserved with a flat rate of 30% and a personal allowance of £10,000. We also asked Mr Hawksworth to estimate what impact such a reform would have on income-tax payers. Under this revenue-neutral approach, there would be losers as well as winners compared with current tax bills (see chart).

Those who would gain are low-earners as well as high-fliers. For example, someone on £10,000 would gain 8.7% of their income; someone on £100,000 would gain 5% of their income. Those who would lose are in the middle, with losses peaking at 3.5% of income at the current higher-rate threshold of £37,295. In all, more than 10m income-tax payers—a third of the present number—would lose from such a reform.

Clearly, different combinations of allowance and tax rate would generate different results. But the general pattern would remain the same. “If you raise the same revenue but increase the allowance, then it is the people in the middle of the income tax paying population that lose from a flat tax,” says Christopher Heady, head of tax policy at the OECD.

This finding is politically awkward for the Tories. Unless a flat income tax were financed by big increases in other taxes, it is difficult to see how it could realistically be introduced without exacting a lot of pain among middling earners. Yet their votes will be crucial if the Conservatives are to stand any chance at the next election.

The flat tax is an arresting idea—and politically attractive because it gives the Tories a platform to attack Labour's itch to meddle with the tax code—but it does not get the Conservatives off the hook. Mr Osborne wants lower and simpler taxes. However, he will be able to achieve that goal only if he can work out a convincing set of proposals to cut public spending.