Even as it struggles to balance its own budget, Yale has agreed to raise its voluntary payments to the city by 50 percent, adding $2.5 million to its annual contribution beginning in October 2010.

The increase, which University President Richard Levin announced Thursday, came at the request of Mayor John DeStefano Jr. In a meeting with Levin two months ago, DeStefano pleaded for help from the University in making ends meet with the city’s fiscal year 2010 budget, which is projected to carry a $29 million deficit.

“I said, ‘Rick, we need you to do something,’ ” DeStefano recalled in an interview Thursday.

And Levin did just that.

The increase in voluntary payments — which Yale officials cast as a reaffirmation of Yale’s commitment to New Haven — serves as the high point for the University this week, for the announcement came on the heels of news of layoffs and a halt on capital expenditures, both of which will negatively impact the city’s economy.

Nonetheless, as they struggle to create a fiscal year 2010 city budget, several city officials said they are surprised by — and welcome — Yale’s increased contribution. And University officials are heralding the payment, emphasizing that it represents their continual support for New Haven.

“The University wants to continue to be a good citizen in New Haven by helping to keep New Haven strong,” Vice President for New Haven and State Affairs and Campus Development Bruce Alexander said in an interview Thursday.

The University contributes voluntary payments to City Hall in part because Yale does not pay property taxes for much of its land. The voluntary payments and the state-funded Payment in Lieu of Taxes program help reimburse the city for potential tax revenue lost from the Yale-owned property used in a nonprofit capacity.

Two months ago, shortly after he started to approach city unions about budget cuts and after the University disclosed the 25 percent drop in its endowment since June, DeStefano said he approached Levin to explain his general worries over the city’s budget. (DeStefano said he did not approach any other city organization that contributes voluntary payments.)

As a result of that meeting, and further discussions that followed, the University agreed to tweak the formula used to calculate voluntary payments. The metric is based on an algorithm set by two agreements between the University and the city: the 1990 fire services agreement and the 2005 voluntary payment agreement.

Through the 1990 agreement, Yale provides a contribution to the city based on the number of calls to fire services made by the University, DeStefano said. The 2005 voluntary agreement added a new component based on the total number of beds and employees on campus, multiplied by a factor based on the difference between total PILOT funds for Yale and fire services PILOT funds for Yale.

As part of the new agreement, the University will use a multiplier based solely on the total PILOT value.

The new bottom line: a $2.5-million bonus beginning in fiscal year 2011. (Yale’s voluntary payment in fiscal year 2010 will remain constant at $5.1 million.)

Several city officials interviewed Thursday, including Aldermanic President and Ward 29 Alderman Carl Goldfield, said they were shocked that the University decided to go through with increasing the payment.

Until learning of the agreement over a month ago, Goldfield said he did not believe that the University would consider upping its payments.

“I thought they would think short-sighted, and I think it’s great they hadn’t,” he said. “If New Haven goes down, Yale goes down.”