http://www.endhomelessness.org/pages/cost_of_homelessness http://usich.gov/usich_resources/research_and_evaluation/cos... http://www.politifact.com/truth-o-meter/statements/2012/mar/...
The biggest costs are pretty concrete. They are 'after the fact' emergency services like emergency room hospital care (vs cheaper preventative care) and jail (instead of housing). It's clear that these costs are higher for the homeless than average, but that leaves the question of housing changing that for this specific group of people (e.g. maybe they are just inherently more likely to end up in an emergency room) which is a valid question.
The evidence is that people with housing are more able to get the help they need earlier (such as preventative care), and are less likely to commit crimes out of desperation, because they have housing. This leads to a much lower rate of using these expensive services, leading to a clearly lower cost to provide housing vs concrete cost of emergency services.
That's why I believe this approach is both humane and effective. This is why I believe housing first is better for everyone.