The company is grappling with the same challenge facing other American opera houses, ballet companies and orchestras: the steady decline of the old subscription model, in which many audience members could be counted on to buy tickets to multiple events each year. But the Met is the nation’s largest performing arts organization, with an annual budget of close to $300 million, so its fortunes are watched particularly closely as a barometer for cultural institutions nationwide.

Mr. Gelb has been trying to maintain interest in the Met by mounting more new productions, engaging prominent theater and film directors and simulcasting performances to cinemas around the world. He said that Yannick Nézet-Séguin, who will be the Met’s new music director, was already exciting audiences, and that he was pleased that James Levine, who became music director emeritus last season after having some health problems, was back in shape.

But the Met has been grappling with budget woes in recent seasons, wresting concessions from its unions, cutting fees to singers and generally trying to reduce its costs as it relies more and more on philanthropy. (The 50th-anniversary concert and dinner raised an impressive $8 million, but even that is a small percentage of the annual budget.) The Met took the unusual step this year of canceling a new production of Verdi’s “La Forza del Destino,” planned for next season by the daring director Calixto Bieito, describing the move as a cost-cutting measure.

Mr. Gelb said in the interview that the 2019-20 season would feature a new production of the Gershwins’s “Porgy and Bess,” directed by Bartlett Sher and starring Eric Owens. And Mr. Gelb added that this past Saturday’s matinee performance of Strauss’s “Der Rosenkavalier,” in which Renée Fleming sang one of her signature roles for the last time, was one of the strongest box-office showings in Met history. It took in about 107 percent of its box-office capacity, he said, thanks to a dynamic pricing model that raised ticket prices as demand grew.

“At the end of the day, it is the work we present on the stage that’s most important,” Mr. Gelb said. “All good marketing must begin with good artistic results.”