Lots of people have written about how childcare is too expensive in the sense that cheaper care would be beneficial, but it also looks like it's too expensive just from the economics.

The average wage for childcare workers in MA is $10.33/hr or $465/week. [1] If one adult watches three infants the labor cost of childcare is $155/week. And yet I'm sitting here looking at the rate list for a daycare center charging $555/week. Part of this is that a center has lots of costs aside from labor. The big one's rent, but there's also utilities, furniture, toys, snacks, etc. Normally an instutution would be able to make up for these larger costs with some kind of economy of scale, but the law is strict on how many children one person can watch. Which means it's much cheaper for someone to take care of kids in their home, where these extra costs mostly don't apply. Even then, home daycares here average $290/week. [2]

This is puzzling, but what confuses me more is why more parents who stay home with one kid don't take in additional ones, working as a nanny while also watching their own kid. If daycare is expensive enough that you can't afford to work, then by taking in one of someone else's you should be able to bring in almost as much money as when you were working. We should get an equilibrium, where the more expensive daycare gets the more people instead to stay home with a kid and take in a couple more, which increases supply and brings costs back down again, stablizing at something like 1/3 of wages. What am I missing? Is it just that people who would want to watch another kid aren't able to pair up with people who would want their kid watched? Would better matchmaking help or is there a different problem?

[1] Five days a week, nine hours a day.

[2] Calculated from costs listed on Family Day Care Home Providers: Somerville MA (pdf).