Hi i happen to see this band on youtube .. can anyone tell which model does the singer is using on this live video? cos this is the first time i see moog keytar, or maybe she customized the body so the can slip the moog in? cos i saw another live video with a white body there.
Moog Liberation
The white ones are relatively rare. Many of them were one-off custom jobs, I believe. The Liberation itself was the very first keytar. 
I take it it’s polyphonic?
It had a poly mode, which was rather weak and sounded like a cheesy organ. The Liberation was actually based off the MG-1 Moog built for Radio Shack, and shared many of it’s features.
… Moog built for Radio Shack …
That seems almost like airing Moog’s dirty laundry! I’m surprised you don’t get insta-banned just for mentioning that 
Common knowledge, my friend. That’s all it is. Of course, that was the NEW old Moog…the one after Bob left the company to start this one.