The Coalition’s plan to flatten tax brackets for middle to high income earners will provide twice as much benefit to men than women, a new analysis has found.

The analysis by the Australia Institute, released on Monday, found that in 2024-25, the first year of the controversial third stage of the government’s tax plan, men will pocket $11bn in income tax cuts while women receive just $6bn.

Income tax cuts are the first order of business when parliament resumes in the first week of July but the Coalition and Labor are locked in a high stakes game of chicken, with both warning cuts for low and middle income earners should not be delayed by political posturing over the final stage.

The Morrison government’s income tax package is divided into three parts: the first stage provides a tax offset to benefit low and middle income earners from 2019 to 2022; the second stage raises the 19% tax bracket threshold from $41,000 to $45,000 from 2022; and the third stage flattens tax brackets from 2024 so everyone earning between $45,000 to $200,000 would pay a marginal rate of 30%.

While Labor has agreed to the first stage and is open to the second, it has thus far balked at stage three, demanding to know how much of the tax cuts will flow to high-income earners in a bid to pressure the government to split the bill.

Crossbench demands for a new coal power station or gas reservation have been rebuffed by the finance minister, Mathias Cormann, who has refused to horse trade or split the bill, pressuring Labor to pass the cuts in full.

The Australia Institute found that, because the tax cuts in the third stage flow mainly to high-income earners, men get most of the benefit because males are more likely than females to earn higher incomes.

The distributional analysis by senior economist Matt Grudnoff found the top 10% of income earners will get 31% of the tax cut in stage three, of which 23% goes to males and 8% goes to females.

The benefits of the first stage of the tax plan are “almost equal”, with 47% going to women and 53% to men, it said.

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“When stage two begins in 2022-23 the female share falls … to 43%. When stage three begins the female share falls to 36%.”

Grudnoff said “the final stages of these tax cuts will further entrench gender inequality”.

“With the slowing economy, the government needs to be clever with its fiscal stimulus,” he said. “The tax cuts to high-income earners in 2024-25 are not well targeted and are too far off to help the economy right now.”

On Friday the shadow treasurer, Jim Chalmers, wrote to the government asking the total cost of tax cuts and how much would flow to people earning $180,000 or more.

Chalmers cited estimates by the Australia Institute that high-income earners would receive $77bn of the benefit, while the Grattan Institute has put the figure at $89bn and the ANU’s Centre for Social Research and Methods had suggested $88bn.

“As you know, Labor stands ready to urgently pass the first tranche of tax cuts to address the weakness in the economy on your watch,” he said. “We require this additional information to properly consider the latter stages before making final decisions.”