DETROIT, MI - Developers driving the Detroit Red Wings arena and entertainment development project now under construction in the city's core have frequently cited a $650 million total cost.

That cost includes at least a $250 million public contribution.

But an economist who has worked with Olympia Development of Michigan on crunching some of the numbers surrounding the project says the price is likely to go beyond that.

"It's obviously going to be a bit more than a $650 million," said Mark Rosentraub, a professor of sports economics at the University of Michigan, adding that the early building designs released by Olympia appear to go beyond the $200 million set aside for mixed-use development outside the 20,000-seat, $450 million arena. "Now how much more, you have to wait until the dust settles and the buildings start coming out of the ground."

Those buildings are supposed to rise from the ground in a 45-block area at the same time as the arena, located along Woodward Avenue between Midtown and downtown, and construction of the project was given the go-ahead by city officials via a zoning change last week, though a small part of the project still faces Detroit's Historic District Commission.

While the total project cost could inflate further, the state's share of the arena cost remains fixed, at least in terms of what it's paying for the arena.

The public is backing $250 million in Series A bonds, while Olympia, the development arm of Red Wings owners Ilitch Holdings, is backing $200 million in Series B bonds. Ilitch Holdings also owns the Detroit Tigers, the Fox Theatre and MotorCity Casino. It is overseen by Mike and Marian Ilitch, the founders of the Little Caesars Pizza chain.

The public money is coming from a tax increment financing district used by Detroit's Downtown Development Authority for the past 20 years. It captures about $15 million a year from taxpayers in the DDA district, including about $13 million from a school millage capture and $2 million from other city and county levies.

The school capture is reimbursed via the state's school aid foundation grant system, so the $13 million is essentially the state's contribution to the project, according to a document provided by the Michigan Economic Development Corporation.

Olympia has acknowledged the total cost of the project is likely to exceed that cost since at least September, when the MEDC first issued the document with information on the project's finances. A spokesperson for Olympia could not be reached for comment.

However, Olympia will also have up to $74 million in public funds pledged by the DDA for ancillary development, or what's been called an "entertainment district," in that 45-block, now-mostly-vacant area around the arena. According to the state, if Olympia doesn't invest that $200 million in a timely manner, it may lose access to that $74 million.

The $250 million for the arena is set, though, and Rosentraub, who has vocally backed Olympia's project (it was Rosentraub who came up with the estimated $1.8 billion in economic impact for the project), argues the public investment is "extraordinarily small" when considering the potential impact it could have on the city of Detroit.

He notes that if, in the unlikely scenario that nothing ever gets built in the TIF district and there is no tax revenue generated, the state would be on the hook for $250 million. But he argues that would be less than 1/10th of 1 percent of the state's $54 billion budget for 2016.

Still, Rosentraub acknowledged that the development has to have a positive impact on the entire state to justify being backed by state money.

But he said the decentralization of cities in the U.S. over the last several decades has hurt places such as Detroit, which he noted is now among one of the worst racially and financially segregated regions in the country. And in the case of the Red Wings project, the state government agrees that putting money back into the state's urban core is a worthy investment, he said.

"I think what's been misreported is that the governor and the legislature have gone the extra mile in saying, look, this is not going to hurt the schools, we guarantee that, and they're saying it's in the state's best interest," he said.

Olympia currently aims to have construction of both the arena and accompanying entertainment district to be complete by the summer of 2017.

Last week, City Council and the DDA approved a zoning change needed for the project to move forward. It also signed off on Olympia's plans to demolish the former Park Avenue Hotel while redeveloping the Eddystone Hotel. Olympia has also said ti would set aside 20 percent of the Eddystone for affordable housing.

Both the Park Avenue and the Eddystone currently sit empty and in relative disrepair, but the Park Avenue is in an historic district, so its proposed demolition will have to go through the Detroit Historic District Commission, which has its next meeting on May 13.

According to Olympia, the project will have an economic impact of at least $1.8 billion, while creating thousands of jobs, some of which will be permanent. The arena alone will create 8,300 construction and related jobs, in addition to 1,100 permanent jobs, according to the company.

Olympia has promised that 51 percent of the construction work on the site will be done by Detroiters.

David Muller is the automotive and business reporter for MLive Media Group in Detroit. Email him at dmuller@mlive.com or follow him on Twitter