For the first time in the 60 years since Disneyland opened, Walt Disney Co. is considering switching to demand-based pricing at its domestic parks, where tickets would cost less or provide added benefits on slower days and cost extra or come with more restrictions on dates when there tend to be too many people.

“We have to look at ways to spread out our attendance throughout the year so we can accommodate demand and avoid bursting at the seams,” said Walt Disney Parks and Resorts Chairman Bob Chapek.

Continuing to raise overall prices, as Disney has done well above the inflation rate for several years, wouldn’t fully solve the problem, said Mr. Chapek, as he is also seeking to raise attendance during slower times of the year. In addition, for Disney’s brand, keeping park vacations within the reach of middle-class families is important.