My external monitor doesn't work at full resolution with my MacBook
You can go to System Preferences > Displays, then option-click (press option key while left-clicking) on Scaled to expose additional resolutions that aren't exposed with a normal left-click.

Otherwise, you have a great choice of software for that, like switchResX:


  Why hassling with Apple's inbuilt screen settings, when there is so
  much more to get and much easier, too? 
  
  With SwitchResX you get back control on your screen – or screens even!
  There are plenty of inbuilt options...