ffmpeg MPEG-4 Encoding Guide

ffmpeg -i input.avi -c:v libxvid output.avi
ffmpeg -i input.avi -c:v mpeg4 -vtag xvid output.avi

Variable Bit Rate with qscale
ffmpeg -i input.avi -c:v mpeg4 -vtag xvid -qscale:v 3 -c:a libmp3lame -qscale:a 4 output.avi

Constant Bit Rate
You can target a bitrate with -b:v.
This is best used with two-pass encoding.
Adapting an example from the x264 encoding guide: your video is 10 minutes (600 seconds) long and an output of 50 MB is desired. Since bitrate = file size / duration:(50 MB * 8192 [converts MB to kilobits]) / 600 seconds = ~683 kilobits/s total bitrate 683k - 128k (desired audio bitrate) = 555k video bitrate

Two-pass example
ffmpeg -y -i input.avi -c:v mpeg4 -vtag xvid -b:v 555k -pass 1 -an -f avi /dev/null
ffmpeg -i input.avi -c:v mpeg4 -vtag xvid -b:v 555k -pass 2 -c:a libmp3lame -b:a 128k output.avi

Note: Windows users should use NUL instead of /dev/null.

https://trac.ffmpeg.org/wiki/Encode/MPEG-4