What is the MGM logo font?
From the looks of it, it appears to be custom made or drawn font. As you can see in the picture below the ‘y’ in Goldwyn is extended longer than the ‘y’ in Mayer. The r’s are also not the same thickness. This all suggests to me that the letters were custom made at the time of the logos creation. I also looked through this list of Disney fonts http://mickeyavenue.com/fonts/disney-fonts-list/ and didn’t find the one for MGM. If it was a font it would definitely be listed there.