Labor says the Morrison government should consider increasing the bank levy in response to the failure by the big players to cut interest rates in line with the central bank, and look at broader measures to boost competition in the sector.

The shadow treasurer, Jim Chalmers, told Sky News on Sunday the government needed to sign off on a new inquiry into competition in the banking sector by the Australian Competition and Consumer Commission, and consider all options, including hiking the bank levy, after the major banks declined to pass through the full rate reduction following the Reserve Bank’s latest cut to the official cash rate.

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The RBA last week cut the official cash rate by 0.25% and it now stands at a new record low of 0.75%. The latest cut was the third reduction in the cash rate in five months. Late last week, Scott Morrison accused the retail banks of “basically profiteering” and declared: “Banks, they never learn.”

Chalmers said there was a problem. “We need to have a broad conversation about how we make the banking system more competitive,” he said on Sunday.

“We do want our financial system to be as competitive as possible. We do want to see those rate cuts passed through so that they can do good, not just in household budgets but in the shops and businesses and in the broader economy as well. We should be up for that conversation.”

While he nominated a new ACCC probe and a potential hike in the bank levy as options, he said Labor would not support legislation requiring the banks to pass through the full value of the RBA’s reduction. “That’s not a proposal that we’ve picked up and run with,” Chalmers said.

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The shadow treasurer said the government also needed to consider making the deeming rate “more responsive to the official cash rate” to help seniors during a period of sustained low interest rates. The government uses the deeming rate for pension income assessments.

“I don’t necessarily think that there should be some sort of automatic mechanism, but I think the government should be more responsive to the legitimate concerns raised by Australian seniors that [the prime minister] is not passing on the benefit of these interest rate cuts at the same time as he’s getting all hairy-chested about the banks not passing it on.”

Chalmers’ comments came as the former Labor leader Bill Shorten on Sunday said he took “collective responsibility for [Labor] falling short” at the May election contest.

In comments ahead of the finalisation of Labor’s official campaign review, Shorten said he misread some of the mood in Queensland and Western Australia. He also singled out Labor’s election policy on franking credits as a particular issue.

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“We misread the mood in terms of the franking credits,” Shorten said. “What everyone thinks about the system in hindsight, and of course hindsight is never wrong is it, what we saw is that there were a lot of older people who felt vulnerable and it also laid the seed bed for the fake campaign on the death tax.”

Shorten used an interview with News Corp to say he wasn’t interested in returning to the party leadership, but also to signal he wasn’t going anywhere. He said he wanted to remain in public life for another 20 years.

Chalmers welcomed Shorten’s comments. He said the former leader had been “classy”.

“We do need to listen to the message that was sent to us on election night,” the shadow treasurer said. “We should have won the election and we didn’t. We’ve got things to learn from that and I think Bill’s contributions are a really important part of that reflection.

“All of us, Bill, myself, [Anthony Albanese], everybody has a job to do. We can’t afford to, you know, drag our bums around and mope around about the last election.

“We need to look to the future.”