As Jezebel noted earlier this week, major retailers including Wal-Mart and Toys 'R' Us are having trouble meeting demand for the popular merchandise.
A Disney spokesperson told the Orlando Sentinel this week that "Frozen" products have been "extremely popular" and Anna and Elsa dresses are among the most popular items.
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"Every mom in the world is dying for this dress," Aaryn Costello, a Los Angeles marketing consultant with a "Frozen"-obsessed 4-year-old told Bloomberg News. "The lucky moms who have found this dress for their daughters brag about their success and unanimously proclaim how their kid can't stop wearing it."
Internet entrepreneurs have taken advantage of the high demand by selling merchandise on sites like eBay, where some sellers are asking for thousands of dollars for the dresses and hundreds of dollars for limited edition Anna and Elsa dolls.
A 5-foot plush version of Olaf, the lovable snowman sidekick from the film, was sold recently for $1,199.
Retailers didn't order enough of the dresses, according to Dena O'Loughlin, director of marketing for Disney-licensed girls costumes at Jakks Pacific in Malibu, Calif., which sells to mass-market chains like Target and Wal-Mart.
Dresses that have been licensed out to mass-market stores differ from a more costly version sold at Walt Disney World and other Disney Parks.
That dress, retailed at $149.99, is the one fetching bids of $1,000 or more on eBay, but the more affordable Jakks Pacific versions, which originally retailed for $20, are also selling on eBay for between $150 and $350.
According to the Disney merchandise spokesperson, additional "Frozen" products are in the works, including plush items, which are expected to arrive at Disney Parks in May, and ladies T-shirts, which will be available this summer.
From the creators of "Tangled" and "Wreck-It-Ralph," Frozen is based on Hans Christian Andersen's "The Snow Queen," but the story is adapted to feature the sisterly bond between Anna and her older sister Elsa, who was born with the power to create snow and ice.
The film has earned more than $1 billion in box office receipts, making it the highest grossing animated feature of all time. It also had mass critical acclaim and won the Oscar for Best Animated Feature Film and Best Song for the smash hit "Let It Go."
The song, performed by Idina Menzel, who voiced the character Elsa in the film, was the first song from a Disney animated musical to reach the top 10 of the Billboard Hot 100 since 1995, when Vanessa L. Williams' "Colors of the Wind" from "Pocahontas" peaked at No. 4.