Multicolor, multi-quantum well light emitting diodes have been fabricated by molecular beam epitaxy by inserting quantum wells of various widths in the active region. The In content of the wells is 15%-20% and the color is governed by carrier confinement and the Stark effect. Combining a proper number of blue and yellow quantum wells allows to obtain monolithic white LEDs. The electroluminescence spectra of the diodes have been studied. At low injection, the luminescence intensity varies quadratically with the injection current, showing that the electroluminescence originates from the depleted region of the diode, and that non-radiative recombination paths exist. However, for higher injection currents, the luminescence efficiency of the wells situated near the n-side of the junction starts to vary linearly with the current, and this is accompanied by the appearance of GaN electroluminescence. We show that this is due to the entering of these wells into the neutral region of the diode, explaining the injection dependence of the color of these multicolor LEDs.