Philip Hammond has warned the two Conservative leadership candidates their tax and spending plans would be impossible under a no-deal Brexit.

Here is an analysis of what Boris Johnson and Jeremy Hunt have promised and the constraints on their proposals.

How much will Hunt and Johnson’s promises cost?

The Institute for Fiscal Studies said before this week that Hunt and Johnson’s plans were expensive. Their proposals would require higher national borrowing, raising taxes or the extension of austerity.

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Johnson’s pledge to raise the higher-rate income tax threshold to £80,000 from the current level of £50,000 would cost £9bn and most benefit the richest 10% of households in Britain.

About 4 million income tax payers at the top of the earnings distribution would gain about £2,500 a year on average, the IFS said.

Hunt’s promise to cut corporation tax to 12.5%, matching Ireland’s – one of the lowest corporate tax rates of any wealthy country – would cost £13bn a year in foregone tax revenues. The IFS said it would not “pay for itself”, as argued by some low-tax advocates.

His plan to raise defence spending to 2.5% of GDP over the next five years would cost £15bn a year more in 2023−24 than today. Reaching 4% of GDP by the end of the 2020s would cost more than £40bn a year.

The pledges made this week will be costlier still. Hunt has said his no-deal “bailout” support for fishing, farming and small businesses would cost £6bn. Johnson has made a fresh pledge to unfreeze public sector pay rises, saying it would come from a £25bn increase in spending for all his plans.

How much “fiscal headroom” does the UK have?

Both candidates argue there is “fiscal headroom” to fund their spending plans in the public finances. However, the term describes the difference between the current UK budget deficit – the gap between government income and spending – of 1.2% of GDP and a level of 2% of GDP, which is worth £26.6bn.

Moving back towards the 2% level would therefore mean higher public borrowing.

Hammond had set a target for borrowing to be below 2% of GDP by 2021-22. However, that target has been reached early, which could allow his successor to raise borrowing back up to the 2% limit. In a further complication, the Conservatives also made a manifesto promise to eliminate the deficit entirely by the mid-2020s. Many economists already believe this to be unachievable, particularly when matched with Theresa May’s promise to “end austerity”. A move back towards a 2% level of borrowing would trash it entirely.

Facebook Twitter Pinterest Theresa May pledged last year to end austerity. Photograph: Yves Herman/Reuters

To further complicate the picture, the way student loans appear in government accounts will change this autumn, adding about £10bn a year to the deficit. The switch at the stroke of a pen almost halves the fiscal headroom.

Will it be needed in the event of a no-deal Brexit?

Economists debate the impact on the public finances of leaving the EU without a deal, although most agree it would be negative. The scale of the impact would depend on how the economy performs and the measures taken to address the move to trading with the EU on World Trade Organization terms.

Johnson and Hunt argue the UK would have £39bn that would otherwise be given to Brussels for a deal. However, economic growth would likely slow, reducing tax income for the Treasury. Both could stimulate growth through higher spending. However, it may not be enough.

According to the government’s long-term economic analysis, a no-deal Brexit would mean a rise in public borrowing to 2.4% of GDP by 2035-36 or £95.1bn of borrowing. The analysis estimates an agreed deal with the EU would enable borrowing to fall to 0.03% of GDP over the same time period, or £1.3bn.

Once the dust settles on the Tory leadership race, Hunt or Johnson could take forward any tax and spending plans, even under a no-deal Brexit. The only question would be: by how much would they allow public borrowing to rise?