I honestly believe that when Sony is going to stop supporting the playstation 4 in 10 years it would have made a significantly more profit than the Playstation 2. 
Remember, I am talking about the profit not userbase. 

One of the main reasons will be, because of the monthly Playstation Plus subscription and digital games. 

it has a good chance of doing so. Sony's first party is much stronger than it was during the PS2 era, PS+ will make them shit loads of money and Digital downloads make them more money then retail sales.

edit: im assuming we are not considering inflation? 

Nah man.

Edit: Wait, PS+

Yes, I think that the Playstation+ will make a huge difference. It's an easy way of making cash and it's something the Playstation 2 didn't had.

dont forget DLC and microtransactions as well which will increase over PS3 as well because of all the 'free to play' games.

Well, it sells at cost price, while PS2 started selling at a loss. Adding more first party games and PS Plus, you got it. And we still have the fact that the more common architecture will allow them to cut costs quicker (and I'm not even considering PS Now yet).

Yes, PS4 will be by far more profitable than PS2.

PS4 VS PS2

1) PS4 the most powerful Console of its gen / PS2 not.

2) PS4 had a very competitive price at launch and Sony already making profit / PS2 not.

3) PS4 selling a lot more than PS2 in the first months.

4) Playstation plus.

5) PS4 easier to develop for, easy to port from PC / PS2 not

6) PS4 has better development tools and friendly architecture=less money and resources to develop most game / PS2 a nightmare to develop for.

7) DLC and microtransactions.

8) PS4 is the best Sony Console ever.  Sony will dominate this gen.

Easy.

Easily, Ps4 is Sony's first home console not designed as a way to introduce a new media standard or new Sony technology, but pretty much to make profit. They don't have to push the userbase numbers and adoption rate so much (which ironically is the fastest ever lol) so they don't have to rely on the "razor blade" philosophy they used in the past, so are not bleeding money, selling hardware on big loss.

Not to mention they have a way bigger 1st party output which gives them way more revenue and probably profit as well.
And there is also PS+ which I can't believe they profit on considering how good the games there are and how quick after their release, but I hope they do.

Greatness awaits!!! I still need cash and a steady supply to finally get a PS4 :/

You havent seen first party support of sony in ps2 era. Sony still have most amazing first party support at the moment. But compared to ps2 era its nothing.