Finally... RAINBOW
Once Chazelle's set the stage with his building blocks of color, he's constantly playing with how they interact: The aforementioned purple, or the mix of yellow's change and blue's control to yield the uncertainty of green (see the second rendition of "City of Stars" as Sebastian mulls selling his soul to The Messengers, or Mia's outfits when she's deciding to go on a date with Seb or commit to her dreams).
But he also knows when to withdraw them entirely. Mia's non-entity boyfriend Greg is only seen in monochrome, just as Seb is seen in black and white during the photoshoot that causes him to miss Mia's play. Because Chazelle is using the bright colors of La La Land as an homage to grand Hollywood musicals, black and white isn't used to represent a call back to the past so much as to suggest a blank slate. While towards the beginning of the film it's used as a clear slate of possibilities, by the end it's to represent the faded promise of their relationship. After Mia's botched opening night, when they're at their lowest moments, they're both in black and white, devoid of color.
I love the picture above by the way :)
That expressionistic coloring was present throughout La La Land, as Mia and Sebastian's relationship gradually desaturates the movie as a whole. The full spectrum of colors — part of our introduction to the city of Los Angeles's traffic, dreamers, and the city itself — becomes paler and more pastel, until finally there's nothing left but black, white, and an argument in the street.
It's what makes the "Epilogue" sequence so striking, visually and emotionally. We return to the old scenes of their relationship, Sebastian reconsiders his decisions, and for the first time we see Mia and Sebastian surrounded by a full rainbow.
As it plays, the movie uses the full color range to explore that something was always missing from their relationship; just as you can't have rain without the sunshine or success without the hard work, Mia and Sebastian couldn't live their lives in only one color scheme. By strategically deploying colors throughout the film, Chazelle makes the case that they were, in some sense, doomed to fail because they could never fully find their footing.
A full spectrum means balance and work. From the beginning, the film suggests there was always something they had to sacrifice with their relationship, whether it was their creative drive, the possibility for change, or the promise of living the dream. As the Epilogue's final notes hang in the air, Seb's club is dimly lit by only three colors: red, yellow, and blue. For once La La Land gives Sebastian and Mia a balance. In hindsight, it was just always making it clear that it was something they could never have found with each other.
There couldn't be a more wonderful and colorful movie :)