Question

Have a good week, Rabbi,
This Sabbath I happened to come across a lost item, and I wondered whether the prohibition of “you shall not ignore it” applies here from several angles:

1. The lost item (apparently a bracelet belonging to a small girl) was of low value (say, 20 shekels). I thought that a reasonable person would waive any claim against the finder if he did not go to the trouble of returning the lost item, since the effort involved would be great relative to its low value. That is, I want to argue that only from a significant value—say 100 shekels—do people expect the finder to make the effort of hanging up notices and locating the owner in order to return it. Below that, one may assume that a reasonable person would forgo it and would not expect the finder to trouble himself with returning it, and therefore there is no obligation to return it.
2. Even aside from consideration no. 1, if I am stringent not to carry on the Sabbath even in a place with an eruv, does that exempt me from the obligation to return it on the Sabbath?
3. Even aside from considerations 1 and 2, I noticed that nowadays the common practice among religious people (correct me if I’m wrong) is that they prefer to leave the lost item where it is, on the assumption that the owner of the lost item will return to the place and find it, and that דווקא taking the lost item into your home is what would harm the chances of its being returned. Is that a valid consideration? 

Best regards,