I have a link to an article on JSTOR. I can't see the DOI mentioned. Is there a standard way to find the DOI? Do all articles on JSTOR have an assigned DOI?
DOI's are managed by Crossref.org. For each DOI, Crossref's database has a redirect to the current location of that digital object, and the owners can move things around and update the Crossref database as needed. When you follow a link to
https://doi.org/<DOI>, the crossref servers redirect this request to the current location of that paper. As mentioned in another answer you can lookup an article in the crossref.org database to see whether or not it has a DOI.
Recent articles have typically been assigned a DOI by the publisher, and most publishers put the DOI on the title page of the paper so it's easy to find that way.
Older articles were originally published without a DOI, but the publisher may have assigned one after the fact. If the publisher has not already assigned a DOI, then JSTOR may have assigned a DOI to the article that will point to the copy of the article in the JSTOR database. This is a service offered to publishers by JSTOR, but not all publishers use it. Thus not all articles in JSTOR have DOI's.
It appears that the article you linked to has not been assigned a DOI by either its original publisher or JSTOR and thus has no DOI. I can't find the article in the crossref database. The "stable URL" that you linked to is probably the best way to link to the article.
You could try to query Crossref (of it are not to many articles); http://www.crossref.org/
Just enter the title in the search box
you can search for Crossref DOIs at search.crossref.org (disclaimer: I work there) but if not found it doesn't mean there is no DOI. We house the metadata for 87 million DOIs but there are other registries too such as DataCite, KISTI (Korea), etc. Crossref is a good start though!
Try viewing the page source and then search for "DOI". Worked for me.