How Long Is Too Long?

I am 40 weeks and two days overdue, I have scheduled to be induced on June 18th, but I really want my son to come on his own. There are many disadvantages to have an induce labor (so I have read on babycenter.com) and then there are several risk I have to consider if I wait for Noah to respond on his own(such as my placenta shutting down and not being able to provide my son the nutrients he needs). So moms how long is too long of a wait? Should I just follow through with the induction?