Arguably, the greatest year for the MGM musical was 1951, with the studio winning the Best Picture award at the Oscars for An American in Paris and having several ultra-profitable box office successes. Yet, within four years, the MGM musical went into freefall at the box office.
Through the magic of Wikipedia, I was able to access, year-by-year, the actual profits for these musicals as recorded by Eddie Mannix, the long-time vice-president (and fixer) at MGM. Apparently, he kept a real time ledger (now titled 'The Eddie Mannix Ledger') with profit information on every single MGM release. So, as time allows, I'm going to provide a year-by-year analysis of what (and who) was making money for the studio before the collapse in 1955.
Note: This isn't a commentary on the aesthetic merits of these musicals. Nor does it track how certain movies (like Singin' in the Rain) have kept right on earning for someone over the intervening decades.
1951: 6 musicals released/42 total films released
The Great Caruso (w/ Mario Lanza/Ann Blyth) profit: $3,977,000
Show Boat (w/ Kathryn Grayson/Ava Gardner/Howard Keel/Marge&Gower Champion) profit: $2,337,000
An American in Paris (w/ Gene Kelly/Leslie Caron) profit: $1,346,000
Texas Carnival (w/ Esther Williams/Red Skelton/Howard Keel/Ann Miller) profit: $681,000
Royal Wedding (w/Fred Astaire/Jane Powell) profit: $584,000
Rich, Young and Pretty (w/ Jane Powell/Fernando Lamas/Vic Damone) profit: $54,000
Basically, everything the studio released in 1951 found favor with audiences and three of the releases -- The Great Caruso, Show Boat and An American in Paris -- were box office smashes. The Esther Williams "aquacals", then in their eighth year, continued to make money. Even the one laggard -- the Jane Powell musical Rich, Young and Pretty - broke even.
Based on this year, the studio would have been justified in thinking that the Golden Age would continue on forever!
Last note: The studio weathered the firing of Judy Garland in 1950 very well considering she had been associated with two of the releases -- Show Boat and Royal Wedding (which was the film she was "working on" when MGM fired her.) It is tempting to speculate how Show Boat (w/ Garland as Julie) and Royal Wedding would have fared with her in them. My own feeling is that her box office impact on Show Boat would have been negligible (given its walloping box office total without her) and Royal Wedding would have seen only a mild boost.