Holyrood will be as much as £950m better off after Treasury ministers caved in to intense pressure from the Scottish government, a finance thinktank has found.

Analysis by the Institute for Fiscal Studies has concluded that the Scottish parliament’s total income from its own taxes and the Treasury’s block grant will reach £31.47bn by 2021, compared to the £30.52bn it would have had under the Treasury’s first proposals.

It said last month’s deal means UK taxpayers will continue subsidising the Scottish parliament’s higher levels of spending for the next five years as if its new tax and welfare powers, which are worth up to £18bn, had never been transferred.

Despite the Scottish National party’s campaign for greater fiscal independence from Westminster, that cushion will protect Holyrood from the effects of Scotland’s lower income tax take and the slower growth in more rapidly ageing population.

The IFS’s calculations, which support strong suspicions that the Treasury surrendered for political and tactical reasons, were released just as Nicola Sturgeon prepared to disclose her government’s plans for the new income tax powers on Tuesday.

The first minister is expected to confirm that she will not pass on the full tax cut for taxpayers in the 40% band announced by the chancellor, George Osborne. Instead, she is expected to announce it will grow by inflation if the SNP wins May’s Scottish elections.

Osborne said last week that the starting salary for that band will jump to £45,000 from April 2017, the date when Holyrood will have full control over all work-related income tax bands and rates above the basic rate.

Sturgeon is expected to unveil a suite of tax changes, which are likely to increase tax for the better off, as she seeks to fend off attacks from Labour and the Lib Dems that she is failing to protect Scotland from Conservative spending cuts in Westminster.

The Treasury deal, struck after months of brinksmanship between the two governments which initially saw the gap between the two sides narrow to £300m, is widely seen as a victory for John Swinney, the Scottish finance secretary.

He said it honours a key principle of the cross-party Smith commission agreement made after the 2014 Scottish independence referendum that Holyrood should suffer “no detriment” as a result of its new powers.

Treasury ministers are thought to have caved in to avoid handing the Scottish government a major propaganda victory so close to May’s Holyrood elections and to settle the dispute before campaigning started in earnest on the EU referendum in June.

But it won important concessions from Swinney who agreed to lower borrowing limits and more tightly controlled borrowing powers, and greater authority for an independent Scottish fiscal commission to assess his financial plans.

Describing the fiscal framework as “convoluted”, the IFS said it meant that Holyrood has the luxury of earning more if things go well while enjoying Treasury “insulation” from any economic shocks.

IFS analysis said that outcome was ironic. By so heavily defending its case that the fiscal deal could have no detriment on Holyrood’s spending, “it has been the Scottish government which has argued most strongly for an approach which ensures the ongoing pooling and redistribution of some proportion of ‘devolved’ revenues across the UK.”

On the other hand, the UK government had fought hard to ensure Scotland “should not be subject to pooling and sharing around the UK” by initially fighting for the other Smith commission principle that UK taxpayers should not be left out of pocket.

The IFS concluded: “That is the same Scottish government that wishes Scotland to move towards ‘full fiscal autonomy’ – which involves the ending of all such pooling – and the same UK government which has emphasised the importance of the union as an institution of risk-sharing and solidarity.”