In my experience, it seems to be sub-linear. Subsequent ones don't require all new everything.
That depends on gender and age difference with sibilings.
Which just brings us back to linear again
You forgot to include the increased medical costs due to the higher probability of inter-sibling stabbings.
Asides from car seat we've never bought anything new. We couldn't find a used seat that we liked. It's weird some people insist on new when accepting baby presents. All of the best toys we've got were second or third generation!