New Haven aldermen approved residential college – and Science Hill expansion – related legislation last Thursday because they learned that Yale will give the city $250,000 every year.

But why would Yale give away this money?

The University is suffering through a year of lower endowment gains due to the world’s economic rut. Yet in 2007 Yale gave a voluntary payment of $4.3 million to the city because most of the land the University uses receives a city property tax exemption from the state. And Yale already swapped $10 million for development rights to three streets around where the residential colleges will lie.

In fact, the mechanics of how Yale gives the voluntary payments makes it simple for the University to give New Haven the extra quarter million.

“When they [Yale] have new employees and new resident students, there’s a certain multiplier that Yale pays to the city of New Haven for each increase,” Ward 14 Alderwoman Erin Sturgis-Pascale said at last week’s Board of Aldermen meeting, “so this is something that is happening every year.”

Although Yale officials have refused to disclose the precise formula used to determine its yearly contribution to the city, the future addition of about 850 students from the two residential colleges and dozens of new employees needed for the colleges and new science buildings must increase the amount paid.

Yale will not pay the nominal $250,000-per-year addition until students and employees enter the college in 2013. But the money will come, and that fact alone works for city officials who disliked the legislation.

“It’s all about money,” Sturgis-Pascale said.

“That’s what my colleagues are making sure,” she said. “They want to know it’s a fair deal.”

Indeed, city officials will certainly not complain about receiving the extra money, considering New Haven’s recent budget crisis.