trust me,

a psp with 20 million units sold wont cost more than 100 $ to make

That settles it then...

Ok, let's say a PSP takes $100 to make. Tack onto that $15 for marketing, $20 to the retailer, $5 distribution, $3 packaging. Yup, PSP sure is making a lot of money.

 It's not just the DS. The PS1 and PS2 also had pretty high attach rates. So the PSP is also lookd down for not living up to its heritage.

Yet to the OP, yes the PSP is sold at a profit. Even though sales have slown down, the fact that it sold so quickly at first dropped the manufacturing cost at probably a record pace for a Sony system.

When the PSP was first released, they were being made for about the same price they were being sold for.  I recall a few reports stating that they were being produced for a small loss initially.  Once they have sold a few million units and new manufacturing costs, the cost to produce would have drastically reduced over the first year.

I wouldn't be surprised if they were making a reall healthy profit at one stage before the pricecuts.

Also here in the UK...for the price to be reduced by £50 since it release under 2 years ago....says to me that they've been making at the very least £50 profit per unit before the price reduction.

I reckon that Sony has made a bigger profit per system sold for the PSP compared to Nintendo for the DS seeing as it has constantly been at the same price...yes they may have sold double the units...but on a per unit basis.

 I'm guessing you probably have no idea what the attach rates were for the PS1 or 2 after two years of being on the market, so there's no way you can make the claim that it's not living up to its heritage. I know that I have no idea. The fact is PSP attach rates are about 3-4 games per system after just 2 years. PS2 attach rates are about 7 after 6.5 years. Generally attach rates increase the longer the system has been out because people have more time to buy more games. Therefore reaching 6 games per system after year 5 wouldn't be crazy. So we can say with some confidence that attach rates for the PSP are doing fine compared to earlier Playstations. 

DS attach rates are just an anomaly. We've never seen anything like it before. Why? Because they're not at all special in America or Europe. They're the same as the PSP! (which is yet another indication that PSP attach rates are solid) It's Japan that's gone totally nuts for the thing. Attach rates are over 8 games per system. 

 As for the original question: If the PSP wasn't profitable after 2 years of selling the system at the same price, the original manufacturing cost would have to have been astronomical. Or somehow the PSP's technology did not drop in price at the same rate as all other pieces of technology. Anyway, no one really knows. They are making money off software and off memory sticks and a tiny bit off UMD movies. Whenever/If a music and video download service comes out, that'll be another source of income (Station Launcher could be that service). 

PSP makes profits. I've read about it somwhere on the PSPFanboy site IIRC.

No I highly doubt the PSP makes more per unit sold than the DS. Iwata said that the DS has a higher profit margin than the Wii, and we know that the Wii is sold for a decent profit so I bet they make a killing off the DS.

The question is not which system makes more profit but IF psp makes any profit. I wonder how costs both DS and PSP to make. Two smaller displays are always more expensive than one big. Probably display isn't the most expensive part of both systems but it's always a factor. Hardware in PSP is more expensive than DS's for sure.

Before the price of the PSP was reduced from £180 in the UK to £150....I would be pretty sure at one stage in the process...Sony were making more money per unit sold than Nintendo were with the DS.

Although, now, Nintendo are maybe making a killing as they haven't reduced the cost at all in 2.5 years.

Keep in mind that the PSP did not drop in price at all until just recently. $250-$200 wasn't a real price drop as Sony just removed the bundled accessories.

It's been around for over two years and was initially being sold at a small loss(I believe around thirty dollars), so manufacturing costs have probably dropped by atleast $100 if not more, so even with the recent price drop, Sony would be making a profit on each system sold.