At a press conference in Edinburgh only 300 metres from where Alexander was giving his own, the first minister claimed that voting yes would leave every person in Scotland £1,000 better off in 15 years' time, as the country profited from a booming economy and rising employment that would outstrip the UK. Alexander sought to outbid Salmond by claiming that a no vote would earn every person in Scotland a "UK dividend" worth £1,400 a year for the next two decades, underpinned by the security and greater wealth promised by the UK.
Salmond, speaking at the Scottish government's headquarters, opened the debate by insisting the "independence bonus" would eventually be worth £5bn a year to the Scottish economy. He maintained that the gains would be secured without tax rises or spending cuts.
Describing the two presentations as "a defining day in the independence debate", Salmond said: "People across Scotland will now be looking at the competing visions of our nation's future outlined today. Our vision, based on the extraordinary wealth of Scotland and the ability of the people who live here to run their own country, or that of a Tory-led Westminster government intent on running Scotland down and whose bogus figures have been brutally exposed."
Less than 30 minutes later at a hotel nearby, Alexander, the chief secretary to the Treasury, dismissed Salmond's figure as a "bogus bonus". He said independence was an immensely costly and risky gamble as he unveiled a detailed Treasury analysis on the costs of Scotland going it alone.
Describing the Treasury analysis as its most forensic document since the last Labour government ruled out joining the euro, the cabinet minister said a yes vote would see Scotland paying up to £1.5bn to build a new state, interest rates up to 1% higher, and new policy pledges that would cost £1.6bn a year.
"By staying together, Scotland's future will be safer, with stronger finances and a more progressive society," Alexander said. "Because as a united kingdom, we can pool resources and share risks."
The rival claims put the economy at the centre of the debate only three days before the formal official campaign period starts on 30 May, 16 weeks before the referendum on 18 September.
The Scottish government made a series of concessions in their latest analysis. They revised earlier, more optimistic oil forecasts downwards by up to £12bn for the next three years after their last analysis overestimated North Sea revenues by £1bn for 2012-13.
After coming under criticism for failing to address these issues in the SNP's independence white paper, Salmond also published his goverment's first broad projections about the impact of possible spending decisions on Scotland's finances for two years after independence.
He said a future Scottish government's public finances would be boosted by its £110bn share of the UK's £1.3tn in state assets, such as buildings, land and military equipment – and its gold reserves in the Treasury. Some of that, he claimed, would help offset Scotland's share of the UK's debts. Salmond's opponents have said that the impact of any cash benefits from that deal would have a trivial impact on Scotland's overall finances.
Independent economists said the rival governments' competing figures were equally speculative. Professor David Bell, an expert in the economics of independence at the University of Stirling, said both relied on "unknowable" facts about oil prices, economic growth and government policy.
The UK government was assuming year-on-year growth of 2.2%, he said, while the Scottish government needs 2.5% annual growth for its sums to work. "There are a lot of projections and these projections are fraught with difficulty," he said. "I wonder if they're just fighting themselves to a standstill on this issue."
Professor John McLaren, of the Centre for Public Policy and the Regions, said: "The degree of certainty [in the rival figures] is unknown." The Scottish government's new estimates relied heavily, he added, on Scotland having to pay a low share of the UK's debts, not on extra income from North Sea oil.
The bitterest conflict came over the Scottish government's refusal to publish a detailed figure for the startup costs of an independent state after the Treasury gave a figure of around £1.5bn, based on a Canadian study into setting up an independent state.
Salmond focused on a part of the Treasury's analysis claiming that a report by Professor Patrick Dunleavy at the London School of Economics put Scotland's startup costs as high as £2.5bn. Dunleavy told the Financial Times that figure was "bizarrely inaccurate" and misrepresented his work, leading Salmond to insist that raised profound questions about the credibility of the entire Treasury paper.
"It exemplifies the politics of 'Project Fear'," Salmond said, referring to the nickname given to the pro-UK campaign by independence supporters. "This is the most devastating hole blown in the Treasury assumptions, not just about the administrative costs, the set-up costs of an independent Scotland, but also typifies their entire approach to this debate."
Salmond was unable to offer a firm Scottish government startup figure, but said he believed Dunleavy's estimate of £150m to £200m was "credible". But Alexander was scathing about that figure. He said John Swinney, the Scottish finance secretary, had been asked 11 times on BBC Radio Scotland to put a firm figure on the startup costs, but had failed to do so each time.
In a leaked Scottish cabinet memo, Swinney himself had estimated the costs of a new Scottish tax authority alone at £650m, Alexander said. The Institute of Chartered Accounts Scotland had put those costs at £750m, while other experts suggested a new welfare system would cost £560m.
Insisting that the Treasury's £1.5bn figure was based on the best independent estimates, Alexander questioned why Salmond had failed to produce that figure: "It's about time that the Scottish government came clean about those costs."
What's the cost of independence?
• According to the Scottish government, an independent Scotland could be £5bn per year better off within 15 years – £1,000 per person by 2029-30.
• This figure is reached by adding together a 0.3% increase in productivity (tax revenues up by £2.4bn a year), a 3.3% increase in employment (revenues up by £1.3bn) and a rise in Scotland's population, still by less than the projected growth for the UK as a whole (revenues up by £1.5bn).
• According to a new analysis also published today by the Scottish government, fluctuations in price, production and investment mean North Sea oil tax receipts by 2018-19 could be anywhere from £3.2bn to £8bn a year.
• According to the Treasury, the Scottish population will benefit from lower tax and higher spending by remaining part of the UK, worth £1,400 per person each year from 2016-17 onwards.
• The report estimates startup costs for an independent state could be £1.5bn, including £400m in IT costs to create a new benefits system and £562m to create a new tax regime.
• To maintain similar levels of public services over the next two decades, the Treasury projects an independent Scotland would need to increase tax revenues by 13%: equivalent to setting a basic rate of income tax at 28%, VAT at 26% and increasing the main duties (on alcohol, tobacco, fuel by almost 40%.
• To maintain similar levels of taxation over the next 20 years, the Treasury argues that an independent Scotland would have to reduce public spending by 11%: equivalent to almost two thirds of Scotland's current health spending.
• The Treasury estimates that policies proposed by in the Scottish government's in its recent White Paper will cost at least £1.6bn every year.
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