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Here is a link to Sony's earning report as covered by VGChartz:

http://vgchartz.com/news/news.php?id=1155

The PS2 sold 13.73 million units and 154 million software. It's reasonable to guess the software profit at $4/unit or so, because many of them will be sold as budget games (over 600 million). I guess I'd estimate the hardware profit at $40 or so for the PS2, all said and done. (over $500 million)

So well over a billion in profit from the PS2, based on relatively conservative estimates.

The PSP sold 13.89 million units and 55 million software. Assuming no money is made on PSP hardware (very conservative estimate) and $6/unit in royalties on PSP software: 330 million in profit.

About 300 million profit from the PSP, based on (I believe) conservative estimates.

Yet, somehow, Sony lost more than a billion dollars in that division when you add the PS3 to the mix.

Where did their money go?

If we're really looking for profitability information, why don't we just look at their financial reports and deduce software licensing revenue, software profit, and hardware profit from that?  Surely it would be more accurate than this shot in the dark.