Yes, you need a page file. Windows always needs to have at least a little bit of HDD space (or in your case SSD space) to function properly. Since you are using a SSD, I would lower the size of the page file down to around 0.5GB or so. Normally Windows likes to have 1.5 times the amount of physical RAM as a page file (seems ridiculous to me) as mentioned by this link. I don' know the specifics comfortably enough to explain why you need it (other than reasons you would need RAM and when your computer wakes from sleeping), but I know that your OS should have some allocated for a page file.
An alternative to using your SSD would be to get a 4GB (or whatever you choose) flash drive, and set your page file on that. Then you wouldn't need to worry about your SSD having a page file. :)
-Hope this helps
After answering this question and attempting to do some research on other reasons Windows needs a page file, I noticed the conversation in the comments of the question...