I was under the impression that having an external power supply actually costs more money than having it internally.
Anyway, a PS4 Slim....the PS4 is actualky a nice size as it is. Of course it can get smaller, but I'm not sure if it's necessary at this moment in time. What we may see is a rebuilt PS4 with cheaper components, slightly different form factor and of course cheaper. With the imminent release of the Neo and PSVR I don't think it's a good time to release a PS4 Slim, surely it would be better to leave it until next year and then release the cheaper smaller version.
On other hand they could do a double-whammy and it could go something like this:
PS4 Slim - Same old PS4 but in a smaller box and cheaper, coming in at $299
PS4 Ultra - PS4 on steroids, more then twice as fast, starting at $399
Prediction (June 12th 2017)
Permanent pricedrop for both PS4 Slim and PS4 Pro in October.
PS4 Slim $249 (October 2017)
PS4 Pro $349 (October 2017)
