Leaving the European Union could mean £36 billion less to spend on public services, according to a Treasury analysis launched by George Osborne.
The Chancellor warned that British families would pay a "heavy economic price" if the country votes to break from Brussels on June 23, with the UK left permanently poorer.
The 200-page analysis produced by officials in Mr Osborne's department was mocked by Brexit campaigners and branded "dodgy", but the Chancellor insisted it was a "serious and sober analysis".
However, the Chancellor tried to make light of criticism of the equation used by the Treasury to calculate the figures by joking: "That's a gravity model - a regression gravity model with a general equilibrium NiGEM model for the economy. Obvs."
Speaking on ITV's The Agenda, Mr Osborne said: "One of the things we've proved, if you don't have as much money coming into the country either you have a big hole in your public finances, or you put income tax up by eight pence.
"Let's be clear, Britain would be poorer. Don't pretend that the economy won't suffer," Mr Osborne said.
The Chancellor also faced questions over the assumption used in the document that net migration would fall to 185,000 a year from 2021 onwards - far in excess of the Government's goal of reducing it to the "tens of thousands" - with Leave supporters arguing that the Treasury had failed to take into account the costs of coping with an ever-growing population.
The Treasury analysis examined three potential options for the UK if it left the EU - the status currently enjoyed by Norway, which makes payments to the EU and accepts free movement in return for access to the single market, a bilateral free trade deal of the kind obtained by Canada, or a relationship under the rules of the World Trade Organisation.
The Chancellor focused his assessment on the Canada-style model, which has previously been championed by Boris Johnson.
Under the terms of a Canadian-style bilateral trade deal with Brussels, the economy would be 6.2% smaller by 2030, the equivalent of £4,300 per household, the analysis suggested.
Mr Osborne rejected the claims of Leave campaigners that the country would benefit from the savings made by not contributing to Brussels' coffers.
"We'd lose tens of billions of pounds in money for our public services, because our economy would be smaller and our families poorer.
"The most likely bill our public services would pay for leaving the EU is £36 billion," Mr Osborne said.
The Treasury document suggests that the Norway-style approach would see GDP fall by a central estimate of 3.8% in 2015 terms, the equivalent of £2,600 per household.
If there was no deal with the EU, and the UK fell back on WTO rules, the economy would suffer by between 5.4% and 9.5%, with a central estimate of a 7.5% fall - hitting each household by £5,200.
The analysis suggests that Norwegian-style European Economic Area membership would result in £20 billion lower public sector net receipts, the Canadian approach would leave the public sector £36 billion worse off and the WTO route could mean £45 billion less for services.
Brexit-backing former chancellor Lord Lamont of Lerwick dismissed the report's projections.
"They say economists put a decimal point in their forecasts to show that they have a sense of humour," he said. "The Chancellor has endorsed a forecast which looks 14 years ahead and predicts a fall in GDP of less than 0.5% a year – well within the margin of error. Few forecasts are right for 14 months, let alone 14 years. Such precision is spurious, and entirely unbelievable."
Pro-Brexit minister Andrea Leadsom, who had served in the Treasury under Mr Osborne, mocked the report's long-term prediction, telling BBC Radio 4's World at One: "It's extraordinary to have such an accurate central figure and it implies a clarity of crystal-ball gazing that even I, as a fully paid up witch, couldn't possibly presume."
In an apparent effort to demonstrate the academic rigour behind its calculations, the Treasury attached an annex peppered with algebraic equations, one of which - a "gravity model" examining the impact of EU membership on inflows of foreign direct investment - sparked humour on social media after it was shown on TV, with one Twitter user saying it looked like "the key to the Philosopher's stone".
Labour leader and Remain backer, Jeremy Corbyn, said he wanted more details on how Mr Osborne made the calculation.
Mr Johnson dismissed the Treasury figures as unreliable.