Unless you have a specific reason to keep it somewhere else, as an attachment to the Zotero item (I presume by "downloading a paper" you mean you used the address bar icon to create a Zotero item for that paper). See http://www.zotero.org/support/attaching_files
If SSRN provides a link to the PDF the easiest way to get it into Zotero is just to drag the link onto the relevant Zotero item. For some databases (I don't know whether this is the case for SSRN as I am not a subscriber) you can automatically store the PDF if you check "automatically attach associated PDFs..." in the general pane of the Zotero preferences.
Upgrade Storage
If SSRN provides a link to the PDF the easiest way to get it into Zotero is just to drag the link onto the relevant Zotero item. For some databases (I don't know whether this is the case for SSRN as I am not a subscriber) you can automatically store the PDF if you check "automatically attach associated PDFs..." in the general pane of the Zotero preferences.