The Met cannot continue on its present course. The opera’s annual budget was $327 million last year, about $200 million of which goes for payments and benefits to union employees. Those employees, who often work long hours, include some of the most talented people in their professions. Their pay reflects that expertise, with average earnings for the chorus and orchestra running about $200,000 a year. Mr. Gelb estimates that full-time chorus members earn $200,000 in salary and $100,000 in benefits, including nine weeks off with full pay. For the average full-time orchestra member, it’s $200,000 in pay and $85,000 in benefits, including 16 weeks off with pay.

Mr. Gelb has said that “even if I was the worst manager in the world, if two-thirds of the cost structure is going to the unions, clearly that’s an area that has to be cut.” He is asking the unions for an average of 16 percent in cuts to benefits and changes in outdated work rules that rack up exorbitant costs in overtime, especially for rehearsals.

Union officials have balked at Mr. Gelb’s opening bid and challenged his numbers. They also have their own list of cuts, starting with Mr. Gelb’s new productions, which they say are uncommonly lavish. Some cite the $169,000 spent for a poppy-field scene in the spectacular production this year of Borodin’s “Prince Igor.” Mr. Gelb, who argues that the expense was not out of line for one of the most memorable scenes in the entire season, has promised that he and his managers will cut costs, including reducing their own pay and expenses at the same rate as for union members.

Mr. Gelb’s own base pay was lowered to $1.395 million after he took a 10 percent pay cut in April. And he has promised that if costs are cut, he and the Met’s board will find donors to replenish and expand the Met’s insufficient endowment.

Unlike European opera houses, the Met gets very little government financing. For example, the Paris Opera, with a total budget of $263 million, gets $133 million in government help. The Met gets a paltry $490,000 in government funds to cover such expenses as youth programs, television productions and open-air concerts.