When Yale is ready to break ground on its delayed construction projects, local construction companies will breathe one collective sigh of relief, they said.

But until then, the companies are jockeying for Yale’s remaining construction projects and hoping for an economic rebound. Over the last decade, the University’s ambitious schedule of renovations and new construction has created a thriving local economy of architecture firms, construction companies and subcontractors all eager for a piece of Yale’s physical overhaul. But with most capital projects frozen indefinitely, the bidding for projects on campus has become much more competitive.

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“If there’s less work to bid on, there’s just less work out there for everybody,” said Arthur Kelly, the president of New Haven-based contractor Joseph F. Kelly Co., which has worked with Yale for over 40 years on projects such as the renovation of the Pierson College Master’s House.

The drying up of business from one of Connecticut’s biggest builders has been especially hard, said four Connecticut-based firms interviewed that have worked with Yale.

“Yale has been one of our biggest clients historically,” said Sara Ruggiero, a spokeswoman for Fusco Corp., the construction company headquartered in New Haven that built Swing Space and renovated Saybrook and Silliman colleges. “And currently it’s a zero when it comes to construction work with the University, and that’s a big blow.”

Reggiero said Fusco is still vying for the contract to construct the two new residential colleges, among other projects.

Since many subcontractors are now competing for Yale’s remaining construction projects, the University has been able to get better pricing overall, said Associate Vice President for Facilities John Bollier. The University tries to award contracts to local businesses whenever possible, he said, but major projects often require the expertise of larger firms. For example, international contracting firm Turner Construction is renovating Morse.

“What is key to us is to create as many jobs within the New Haven community as possible,” Bollier said.

In the 16 years of University President Richard Levin’s tenure, Yale has spent over $4 billion on construction and renovation projects. But Levin announced in January that most planned construction projects would be delayed indefinitely to save $2 billion. Harvard, Princeton and the University of California system are among the many other American universities that have frozen campus construction.

Levin said that he does not think the local economy has fully absorbed the effect of Yale’s construction slowdown. Still, he added, there is a “huge link between the University and local economy,” and even at its current levels, Yale’s construction projects make a significant contribution to the city.

Local firms anticipated Yale would reduce its construction expenditures because of the economic slowdown, but they expect the volume of work to rebound in the next couple of years, said Anthony Rescigno, president of the Greater New Haven Chamber of Commerce.

“They all hope this is going to be short-lived, that Yale will get back on track as soon as humanly possible,” he said, adding that the Yale projects still in progress, such as the renovations of Morse and Ezra Stiles colleges, still give contractors “significant” business.

Any projects the University can fund entirely from gifts, such as the renovation of the Yale University Art Gallery, will also move forward, Vice President for Development Inge Reichenbach said last week.

For those local firms that rely on Yale for a good portion of their business, the recession has made it even more important to submit competitive bids for the remaining projects.

New England-based Dimeo Construction has been able to submit lower bids than it has in the past for University projects, partly by working with with subcontractors who are offering lower prices this year because of the recession, said Dimeo spokesman John Hennessy. As general construction management firms such as Dimeo struggle to find work, he said, the subcontractors firms hire to complete different parts of a project — from plumbing to roofing — also suffer.

As a result, just as Yale finds itself in a buyers’ market, so too do the general contractors.

“Obviously the subcontractors are all pretty hungry for work these days, so it’s a pretty competitive marketplace right now,” Hennessy said. “For a number of subcontractors, their bread and butter is working at Yale.”

Dimeo has worked with Yale since 1995, when it built the Joseph Slifka Center for Jewish Life. It has also overseen the renovations of Calhoun and Trumbull colleges and of Linsly-Chittenden Hall, Hennessy said. Currently, Dimeo is managing the renovation of the Yale University Art Gallery.

Other companies, such as the Kelly Co., plan to reduce costs by lowering the number of hours their workers spend on the job, Kelly said.

“You don’t like to do that — you like to keep guys working,” he said. “But you’ve got to cut costs.”

But cost-cutting can only go so far, he sad.

“There’s a value to the whole project, and when you go below that value the risks increase tremendously,” he said. “If a company cannot make some sort of profit on the project, it’s usually not worth it.”

Still, local contractors know they cannot rely solely on Yale for business, Rescigno said.

Indeed, Yale is not the only game in town, he said — there are plenty of other local projects, including the high-rise at 360 State St., Gateway Community College’s new $190 million campus and roughly $500 million of prospective construction work at Quinnipiac University.

“We certainly encourage Yale to do all it can, but we rely on the whole area,” he said.