"The" gross monthly income, as if there is one blob of income that we could turn a knob and increase, by say, 10%? Are we doing this across the board, from migrant farmworkers to the Fortune 500 C-levels? Does this dovetail with UBI so that people who earned $0 + entitlements, lose their entitlements and begin receiving cash instead?
If rental housing is the #1 monthly expense for the working class, or say, the socio-economic class who needs Affordable Housing, and you "fix" their income (which I think you mean raise it, rather than the financial term of art) if you raise their income by a given amount, and housing costs stay constant, then more people get housed?
I mean, the 50s/60s promoted the Nuclear Family for some reason, and it was probably intended to blow up extended family ties, which can make a populace harder to track and control, and because Nuclear Families tend to drive up demand for discrete housings, and also any and all household goods and resources that can no longer be shared. Hmm.
You can "solve" the equation by reducing housing costs, but it is also possible that the "problem" isn't housing costs per se but wage depression, and that the "real" solution is to fix the gross monthly income.