You are sometimes told that you must create a seamless / frictionless shopping experience across channels, right?
And yet, here's Amazon, the very company that is putting you out of business, offering the same text at a veritable plethora of prices across digital or dead-tree channels. Heck, there are differences among paperbacks. And look at all the profit that the publisher gets when they sell a unit via Kindle, at essentially no physical cost whatsoever.
But, again, the experts tell you that you must offer a seamless / frictionless shopping experience across channels - telling you that the customer "demands" that you offer the same item at the same price in all channels. Why does the customer demand that from you but not demand that from a company (Amazon) that the customer clearly prefers?
Find out how much a customer wants to pay for the merchandise you sell. If you must maintain pricing parity across channels, then why not take comparable items and vary prices across the board on comparable items - for a month or two? What would stop you from learning the truth about customer response?