The Moog Minimoog is an monophonic analogue synthesiser. Prince used one on For You and Prince.
It was the first portable synthesizer available in retail stores. It has a distinctive round, warm tone compared to the rawer Arp and Oberheim synthesizers Prince usually used. It appears on the songs "Just As Long As We’re Together", "Baby" and possibly "When We’re Dancing Close And Slow". The Minimoog was also a popular bass synth, and it is possibly the bass synth that appears on "In Love" and "I Wanna Be Your Lover".
I had brought my Minimoog along. It was my solo instrument at the time, and I could do quite well with it. He didn't have one, so that impressed him quite a bit.
Dr Fink also owned one before joining Prince’s band, something that impressed Prince. He used one live on the Prince tour.