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Jeremy Corbyn, the U.K. Labour Party's most left-wing leader for decades, has brought on board a raft of world-famous economists in an effort to boost his credentials.

Corbyn has been in the job for two weeks and has already attracted particularly fierce flak for his economic policies – although his ideas on nuclear weapons, welfare payments and foreign policy have also proved controversial.

The new economic advisers include well-known figures like Thomas Piketty, the French economist, and Nobel Prizewinner Joseph Stiglitz. Their presence will help Corbyn and his team counter suggestions that they are not to be trusted with the economy.

Thomas Piketty
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"I am very happy to take part in this Economic Advisory Committee and assist the Labour Party in constructing an economic policy that helps tackle some of the biggest issues facing people in the UK," Piketty, whose book "Capital in the 21st Century" caused a stir last year, said in a statement.

"There is now a brilliant opportunity for the Labour party to construct a fresh and new political economy which will expose austerity for the failure it has been in the UK and Europe."

Here, CNBC takes a look at Corbyn's potentially controversial economic policies:

Tax take tussle

One key tenet of what John McDonnell, Corbyn's shadow Chancellor of the Exchequer, calls a "radical but pragmatic and deliverable economic policy" is raising taxes on personal wealth, via increasing the 40 percent top income tax bracket back up to 50 percent and the removal of a dramatic rise in the threshold of inheritance tax under the Conservative Party.

Corporation tax is also going to be targeted, with plans for a financial transaction tax that could impact the U.K.'s important financial services sector. If the tax is not implemented internationally, this could make the U.K. a less attractive place for investment.

Bank of England independence

McDonnell, who wants a "new economic discourse" for the country and a move away from the pro-austerity policies of the current government, has clarified earlier suggestions that the Bank of England might lose its independence from the government – a move introduced by a Labour government back in 1997 -- under his plans for "people's QE".

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He told the BBC his plan was to review the Bank's mandate where it may be getting it wrong, specifically on inflation, and focus on growth and investment.

"This would require a change in the Bank of England's mandate, but not a big one," Richard Murphy, author of The Joy of Tax, whose ideas form part of the cornerstone of Corbyn's policies, told CNBC.

Running smoothly

Renationalizing the U.K.'s railways has not been a model of free market success since their privatization during the 1990s, thanks to unreliable operators and inadequate infrastructure. This is one policy where Corbyn may find himself in agreement with many throughout the country, including floating voters.

"The public thinks the railways have let them down, they think the gas and electricity companies have let them down. A lot of people, according to our polling, like the idea of these industries coming back into state ownership," Peter Kellner, president of polling company YouGov, told CNBC.

- By CNBC's Catherine Boyle.