If you only gave $100k to the people who are currently homeless that year, then (ignoring that people would start keeping themselves homeless for several years on purpose) you'd still end up better than the present situation.
Thus, cutting all budget for cash transfers could increase homelessness by 80%! (Are those 14,498 now-homeless people eligible for this year's $100k? They can't be, since you already spent it on the 7,973 currently-homeless people).
Model the situation as "X(t) people become homeless at year t, Y(t) people become housed at time t," and you'll see the most important metric is "how much can we decrease X and increase Y per dollar spent"?
"Number of dollars per current homeless" is not really meaningful at all.
If those are the actual numbers, you're proving GP's point. You can give each of those 14.5k people ~$55-60k instead of giving 8k people $100k and homelessness is still solved.
They had homes, cardboard box homes. Then the government said a home couldn't be a cardboard box, and confiscated the cardboard boxes and now they sleep on benches.
Thus, cutting all budget for cash transfers could increase homelessness by 80%! (Are those 14,498 now-homeless people eligible for this year's $100k? They can't be, since you already spent it on the 7,973 currently-homeless people).
Model the situation as "X(t) people become homeless at year t, Y(t) people become housed at time t," and you'll see the most important metric is "how much can we decrease X and increase Y per dollar spent"?
"Number of dollars per current homeless" is not really meaningful at all.