Taking advantage of rapidly falling memory prices — and offering customers the lowest entry point in the iPod’s six year history — Apple AAPL today slashed the price of the 1GB iPod Shuffle from $79 to $49.

The 37.9% price cut is even steeper than the $200 (33%) cut in iPhone prices that Apple announced last September.

The company also announced today that a new, 2GB Shuffle will be available later this month for $69.

“At just $49, the iPod shuffle is the most affordable iPod ever,” said Apple VP Greg Joswiak in a press release issued this morning. “The new 2GB model lets music lovers bring even more songs everywhere they go in the impossibly small iPod shuffle.”

AppleInsider notes that the price cut comes amid analysts’ reports that blamed the lack of a refresh in the Shuffle line before the holidays for recent softness in iPod demand. It quotes Citigroup analyst Rich Gardner:

While virtually 100 percent of the unit shortfall was in the low-end iPod Shuffle, allowing Apple to beat consensus iPod revenue despite the unit shortfall. We believe the unit shortfall reflected the lack of a compelling update to the Shuffle product last Fall; the Shuffle simply was not the compelling ‘stocking stuffer’ this year that it was last year. (link)

For more on this, see Analysts: Effect of iPod shuffle price cut is a wash