My son has never been much of a bitter until recently. He attends daycare part-time and when he gets excited or overtired he somtimes nips at me. I do not ever recommend biting your child back. Not even as a last resort. That, in my opinion, only reinforces the behaviour and badly. There are many ways to correct this ethically.
From what I have read, I understand that children often resort to biting out of frustation or irritability due to lack of sleep, over excitment and so forth. The child may not be able to therefore properly express him or herself and thus uses other measures to make themselves 'heard'.
I would firstly suggest, taking out a book from the library on the subject and reading up on it. It is very common. Secondly, you may notice a trend as to when it occcurs (over-excitment, before naps/bed etc) and you can deal with it accordingly using the techniques described in the book. I love the book entitled "mother of all baby books" or " what to expect the toddler years".
As for my son, he is a bit older than yours so I used verbal methods to express how I felt. "That hurts mommy" When my toddler bit another friend I did not go to my toddler and punish or express my distaste, instead, I went to his little friend and soothed them as much as I could.
Hope this helps you!