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XP-39C²
I dont think that Sony priced the Vita after the 3DS actually. The japanese price (which was the first price announced) for the 3DS was announced in late September 2010. The Vita was first announced, and showed off playable, about 4 months later.Edit:
As for Vita, I think a big mistake was the jump they made to get the price down to $250 at launch to match 3DS, instead of going for a higher initial price. That initial $250 announcement made a lot of people hyped up on the Vita prospects, but if left no wiggle room if sales started off poorly, and early adopters are the least price conscious. Compare a $250 announced Vita, followed by a price dropped 3DS making Vita seem more overpriced to a $350 Vita with room to drop the price a few months in to help spark. It'd be hard to imagine a $350 Vita doing significantly worse than the current system.
Just a thought.
Unless Sony has some inside information within Nintendo knowing the 3DS price long in advance, i think that the developement of the Vita started long before Nintendo announced the 3DS price. And i think that a ballpark price was set before they started developing the Vita.
The only thing that could happen the way i see it is that Sony first planned to sell the Vita with a big overhead, but then decided to drop this after seeing the 3DS price. From the Vita components teardown, and estimating the cost of assembly and shipping etc., it is estimated that the Vita's developement costs is around $250. I'm not sure that Sony would have tried to sell the Vita with such big overhead.
I wonder what would have happened if the Vita was $350/$400 (3G model) at launch though. I think that Nintendo would have gone into panic mode regardless, so then the difference in price would be even bigger. I also think that the launch week would have had lowered sales at $350. The PS3 only opened with ~81k in it's launch week. I think this was mainly due to its high price.