Apple - Can I increase the resolution of a 13-inch MacBook Pro?

Sorry, no. The resolution of the display panel itself is only 1280x800, so there is no way to display more without physically replacing the panel.

There is an app named Retina Display Menu. You can find it like rdm.tar on google and it allows you to switch to whatever resolution you want on your Mac. I have a MBP mid 2012 running 1440x900 as native and it works perfectly.

You can do it virtually using SwitchResX, but it looks really bad. I changed back within a few minutes.