LONDON — The British government outlined the central argument on Monday it hopes will persuade voters to stay in the European Union, publishing a detailed economic analysis finding that Britons will be poorer if they quit.
The release of the publication by the Treasury, complete with complex algebraic calculations, is an important moment before a referendum, to take place June 23, on whether Britain should end more than four decades of integration and quit the 28-nation bloc.
Those who oppose a British withdrawal from the European Union, known as “Brexit,” say that it would inevitably lead to economic uncertainty and deter investment, and that it could complicate ties with the bloc, the country’s biggest trade partner.
On Monday, the government put a number on that claim, asserting that, under one midrange situation, annual economic output would be 4,300 pounds, around $6,100, lower per household if Britain left than if it stayed in the bloc.
Some critics quickly attacked the government for trumpeting the £4,300 figure as a net annual cost per household, noting that domestic product divided by the number of households is not the same as household income.
In any event, the chancellor of the Exchequer, George Osborne, said at a speech in Bristol, England, that the country “would be permanently poorer if it left the European Union” because “we’d trade less, do less business and receive less investment.”
Mr. Osborne, who with Prime Minister David Cameron is campaigning for Britons to vote to remain, added: “The price would be paid by British families. Wages would be lower, and prices would be higher.”
Those advocating an exit, including dissenters in the governing Conservative Party, quickly dismissed the analysis. Andrea Leadsom, a government minister who used to work in the Treasury, called it “extraordinarily biased.”
The release of the document highlights the quickening tempo of the referendum campaign, which officially began last week.
And it precedes a visit to Britain this week by President Obama, who is expected, if asked, to endorse continued British membership in the bloc but to note that it is a decision for British voters.
Advocates of remaining in the bloc say they believe the economic warnings will prove decisive. The Treasury document outlines the impact on Britain under three main situations, depending on the terms of trade Britain would negotiate after leaving the European common market.
In the first of those, Britain would participate in the European Economic Area, like Norway, which is not a member of the European Union but which pays for access to Europe’s single market and accepts the free movement of labor and capital. Under this situation, average annual output per household would be £2,600 lower after 15 years, the report says.
Under a bilateral trade agreement — like the ones the European Union has with Canada, Switzerland and Turkey — the reduction would be £4,300, the Treasury found.
In the worst case, if Britain relied solely on the trading rules laid down by the World Trade Organization, as Russia or Brazil do, the amount would be £5,200, according to the report.
“It’s a complete fantasy to claim we could negotiate some other deal, where we have access to the E.U.’s single market but don’t have to accept the costs and obligations of E.U. membership,” Mr. Osborne said in his speech. “Other member states have made it very clear in recent weeks that’s not on offer — and how could it be? How could other European countries give us a better deal than they have given themselves?”
Ms. Leadsom told the BBC that the Treasury analysis ignored the benefits of increased trade with non-European nations, which, she argued, would be possible outside the European Union. She also added that it had failed to take into account the economic advantages of being free of burdensome regulations from Brussels.
Paul Johnson, director of the Institute for Fiscal Studies, a nonpartisan research group, said precise figures were difficult to come by, for several reasons. However, he added that, compared with other estimates, the Treasury document was “broadly in that range,” arguing that “it is not out of line with what many independent forecasters are suggesting.”
The publication follows warnings that, were Britain to leave the bloc, its negotiations with continental partners may not be smooth.
Speaking on Sunday, the French economy minister, Emmanuel Macron, said if Britain voted to leave, the European Union would have to take a tough stance in the negotiations that followed, to set an example.
“We have to be very clear that Brexit will have consequences; otherwise, that is the beginning of the dismantling,” he told the BBC. “Everybody who disagrees on one or two points will decide to do the same.”