The Treasury has published an analysis (pdf) of the implications of Britain leaving the EU and concluded that the economy would be 6% smaller by 2030, costing each household £4,300. But how did the chancellor, George Osborne, come to this conclusion and do the numbers stack up?

Will the economy by 6% smaller by 2030?

The short answer is that it is impossible to say. The Treasury numbers are not wildly out of line with other forecasts and are more cautious than some. Osborne’s officials draw the analogy that eating a pizza a day for 15 years will make someone fatter, although it is hard to say exactly how much weight they will put on.

Put in this light, the £4,300 per household figure looks too precise and leaves the Treasury open to the claim that its forecasting record in the past has not been too special. Paul Johnson, the director of the Institute for Fiscal Studies, said the Treasury would have been better off saying that the available evidence points to a price being paid for leaving the EU without putting a figure on it. But doing so would have deprived the chancellor of his big headline grabbing number, which was the whole point of the exercise.

Would every household lose £4,300?

No. The Treasury has arrived at the number by taking the annual gross domestic product of the economy, about £1.7tn. It has then assumed that the some of the benefits of EU membership – stronger trade growth, higher inward investment and improved productivity – would be lost.

Some inward investment has certainly come to the UK as a result of its membership of the single European market and it is likely that prospective Japanese, Chinese and Indian investors would seek alternative sites if Britain left. But it is hard to quantify these effects. The Treasury has assumed the economy would be 6.2% smaller. It has then divided a lower GDP figure by the number of households to come up with the £4,300 figure.

Would households actually be poorer even if the Treasury’s forecasts are right?

Not really. The Treasury is estimating what the economy will look like once it has settled down after the shock of Brexit, something that might take a decade or more. During this time, the economy is likely to keep growing but at a slower pace than it otherwise would have done, if the Treasury is right about the costs of leaving the EU. Assuming that the economy grows at 2.5% a year on average for the next 15 years inside the EU – broadly in line with its pre-2008 trend – average household incomes would rise from just over £60,000 to about £90,000 a year by 2030.

Is a Canadian-style bilateral trade deal the most likely post-Brexit outcome?

The Treasury has three possible scenarios: Britain becomes a member of the European Economic Area, like Norway; it negotiates a bilateral deal; or it has no specific agreement with the EU and relies on securing the same access as any other member of the World Trade Organisation (WTO). All three involve costs, according to the Treasury, with the Norwegian option the least expensive. Given that, it seems probable that the government would pursue the Norwegian rather than the Canadian option in the event of a Brexit vote. The main figures Osborne used are based on a Canada-style arrangement.

Will taxes go up by 8p in £1 or spending on the NHS be cut by a third if Britain leaves?

Again, this depends on whether the Treasury’s assumptions about the economy are right. If the economy really is 6% smaller by 2030, tax receipts will also be lower. That would force the government either to raise taxes or reduce spending. Osborne is assuming that contributions to the EU would fall by £7bn after Brexit. Without this, the loss to the exchequer would be £43bn in 2030, rather than £36bn. The leave campaign says the economy would do better outside the EU, which will continue to struggle as a result of the problems with the euro.

What impact does migration have on the Treasury projections?

The Treasury is assuming that net migration will fall from 329,000 in 2014 to 185,000 a year from 2021 onwards, in line with what the Office for National Statistics expects. The chancellor is right to say that if Britain wanted a Norway-style arrangement after voting to leave the EU, it would have to agree to the continued free movement of people from within the bloc. The only way in which the UK could have total control on migration would be to opt for the WTO approach. Campaigners for Brexit say lower migration would put less of a strain on public services, but it would also have an impact on skills and productivity.