I am asking this question on behalf of a friend...
"When I create an eps file on a mac, it only gives access to the person who created it and it gives the everyone group no access. Is there a way to default this so that everyone has read rights to it?
I have other machines that do not have to change the rights and automatically give read rights to the everyone group by default but I am unsure where or what to change to make this happen for this one user."
Are you logging into a user with Administrative Privileges?
If it is a user account that does not have adminstrative or standard privileges then this might be a problem.
For instance a guest with sharing only.
You set the privileges in the new accounts
You may also have to repair the permissions using the disk utility app in the Applications>Utilities
Or you might have to manually set the sharing to read write for a particular directory which is done with the Get Info dialog.
Logging in with Admin privileges isn't really the best solution.
What the OP needs to do is change the default umask on the machine they are working from 022 (thus applying POSIX perms of 755) to 002 or <BAD IDEA>000</BAD IDEA>. However whilst this can be done in OS X, the system defaults back to 022 on every reboot.
A much better solution would be to apply some ACLs allowing the group all the users are a member of to read/write the file. I'm sorry, but ACLs are a bit too big a subject to go into here, but this should give a starting point.