Malcolm Turnbull will resign from parliament on Friday.

His departure will trigger a byelection in his Sydney seat of Wentworth, with suggestions it may occur in October.

The former prime minister informed his federal electorate conference of his decision on Monday evening, and said he would send a letter to his local constituents this week.

He told them he did not want to dwell on the events of last week, “a pointless week of madness” that disgraced the parliament and appalled the nation, and repeated his belief that the best place for former PMs was out of parliament.

“Your support has enabled me to be a minister and, for the past three years, prime minister,” it is understood he told the conference.

“Everything I have achieved for Australia in public life has been due to you – built on the foundation of this community, which Lucy and I love and where we have always lived.”

“Thank you, from the bottom of my heart.”

A number of potential candidates for Liberal preselection for Turnbull’s seat have already put their hands up.

Tony Abbott’s sister, Christine Forster, confirmed on Monday that she intends to run after being encouraged by several people within the party to replace the ousted prime minister.

“It’s a difficult situation and I don’t want to be seen to be disrespecting Malcolm – who I do respect,” she said on Monday.

Businessman and former Australian ambassador to Israel, Dave Sharma, is said to be the frontrunner to replace Turnbull as the Liberal candidate. Sharma formerly worked for Alexander Downer as a legal adviser and is understood to have the backing of the Liberals’ moderate faction, which controls the majority of Wentworth branches.

Turnbull’s son-in-law, James Brown, a non-resident fellow at the University of Sydney’s US Studies Centre, was touted as a possible Liberal candidate, but ruled it out on Monday.

After Turnbull’s leadership loss last week, his son Alex Turnbull has started speaking publicly about his frustrations with the federal Coalition.

On Monday, Alex said he suspected a powerful group of coal mining companies on Australia’s east coast was having an “undue level of influence” on federal Liberal party policy.

He said the Coalition’s “singular fixation” on the Galilee Basin – a gigantic coal deposit in central Queensland – and on keeping ageing coal-fired power stations alive, had led him to believe “there are other forces at work” to explain the Coalition’s unproductive policymaking.

Turnbull, who runs his own hedge fund from Singapore, said he no longer felt obligated to keep his head down after his father was rolled.

After telling Fairfax Media he was “massively in favour of a federal ICAC” to shine a light on the level of corruption in federal politics, he has told the ABC’s PM program that he’s concerned about the Liberal Party’s relationship with the coal industry.

“That there is an undue level of influence on Liberal Party policy by a very small group of miners who have some assets they probably now regret having purchased which did not make a lot of sense anymore and are trying to engineer an outcome which makes those projects economic,” he told the ABC on Monday.

When asked who the miners were, he laughed. Then he said: “People who own a lot of coal in the Galilee Basin.”

Turnbull used to work as an investment banker for Goldman Sachs where he would speculate on the value of debt held by energy companies. It gave him an appreciation of the economics of the industry, including the long-term future of coal.

“Every time you have a cycle of panic and mania, and these things occur regularly in financial markets with zero government inducement, that creates opportunities for people like me,” he said.

“[But] what’s happened in Australian power is, in a sector which is naturally extremely boring, government policy has created cycles of mania and panic which has created a lot of opportunities.

“I have been quietly very frustrated at how unproductive policymaking has been in this area and how partisan it has been, because generating tonnes of volatility is great for hedge funds and so forth, [but] it is not particularly good for consumers.”

Turnbull said the push by conservatives inside the Coalition to use federal tax dollars to underwrite the construction of new coal-fired power plants makes no economic sense.

“The reason is that coal prices, now, are high enough that it is very hard for coal to be competitive,” he said.

“You cannot buy a tonne of coal at the 2002 price anymore easily than you can send your kids to a private school for 2002 school fees any more.”

“At some point we’ve got to decide whether to invest in things which have a brighter future and a longer term prospect or we can try to turn back the tide and fight forces beyond our control.

“I think there is a mistaken idea that there is a conflict between de-carbonisation and reducing power prices. Renewables are the cheapest incremental source of power. If firmed well with hydro projects, they are unquestionably the lowest-cost way to get more power generation and thus reduce peoples’ power bill,” he said.