A new analysis of the Morrison government’s planned tax cuts shows they would entrench inequality between what men and women earn.

The Australia Institute’s examination of the three-stage $158 billion tax plan comes as Labor renews its push for the government to provide a detailed breakdown of the cost to the budget.

The progressive public policy think tank says the first part of the tax plan – which is supposed to help taxpayers for the financial year about to end but is yet to be legislated – would almost equally benefit men and women.

But the later stages, which offer the biggest benefits to top earners, would give men $2 worth of tax cuts to every $1 women get.

“As the tax cuts progress through the three stages, women get a smaller and smaller share,” Australia Institute senior economist Matt Grudnoff said on Monday.

“The final stages of these tax cuts will further entrench gender inequality.”

The coalition has repeatedly knocked back the idea of splitting the tax cuts bill that would see changes out to 2022 and 2024, arguing it has ae mandate to implement it in full after being returned to government in the May 18 election.

But it looks increasingly likely this could lead to a political stand-off when the new federal parliament sits for the first time in July.

Shadow treasurer Jim Chalmers says splitting the tax bill, so low- and middle-income earners can get immediate relief, would likely garner unanimous support in the Senate, where the government doesn’t have the numbers.

He has written to Treasurer Josh Frydenberg asking for year-by-year costings of the tax package, and separate costings for the components benefiting people earning more than $180,000.

“We require this additional information to properly consider the latter stages before making final decisions,” he wrote.

Labor’s vote wouldn’t be needed if the coalition can secure the support from four Senate crossbenchers.

But One Nation, which holds two crucial votes, isn’t budging on its opposition to the full tax package.

Party officials met with treasury bureaucrats on Friday but One Nation Leader Pauline Hanson continues to favour increased infrastructure spending to stimulate the economy.

And Finance Minister Mathias Cormann hasn’t called to change her mind.

“I haven’t been approached by Mathias Cormann. There has been no negotiations that have gone on. I haven’t spoken to the prime minister,” she told Nine’s Today program on Monday.

Centre Alliance, which also directs two votes, hasn’t backed the plan yet either.