IMHO, PS2 with a MSRP below $200 won't happen until Sony brings out its next generation of game device(s). What I might guess on, can be based on past Sony's practices.
1. Sony has dropped the PS1 prices twice. I believe it came out at about $200, later went to $150, and now MSRP at right under $100. When people wants your products or services due to it value, then you can sell at a premium. But, when the N64 came out, Sony decided to keep market share by lowering the PS1 price. For those who remember Marketing 101, the second phase of the marketing cycle. As some posters as mentioned, the PS1 is now a cash cow for Sony. Maybe by lowering the PS2 price, Sony could get those who are like me, saying it ain't worth three hundreds. Either is an X-Box.
2. Add-on products, e.g. memory cards, for the PS2 came on the market quickly, even after Sony's BS that anything not sanctioned by it could destroy your machine. I bought the PS1 at $149.95 with a unofficial memory card that save me about ten dollars. Since I want to use the S-video input on my TV, at that time, my only choice was to pay $35 from the local Sony's part distributor. One now can buy, a cheap and not as good cable for twenty less by mail. Maybe by lowering the PS2 price, Sony could bring a broader market, young kids with their parents, into the stores or on-line and convince them to buy a PS2 with lots of accessories and games.
3. Also Sony's has to keep an eye on what are the plans of companies that develop games for various platforms. A shrinking PS2 market could cause these companies to shift resources into developing for or porting Japanese versions onto the X-Box or the Gamecube platform. Sony may see another set of problems, if lack of demand for the PS2 causes retailers and even rental businesses to change their favorable view of Sony. Maybe by lowering the PS2 price, Sony could keep from becoming the Sega of the 21th Century, a dinosaur that time past by.
I'm hoping that Sony does lower the price on the PS2. My guess is that the price will drop no more then 25% ($224.95) and could only be 20% (239.95). I also see the reduction coming at the same time as FF10 comes out. All of the above is just my 2 cents worth.