Ask your parents to give you really good reason why should you cut your hair. If oyu have mess of porely done dreadlocks or something then i understand they want it too look different but if it is normal long hair then only you have to do it make your parents understand that it is quite normal thing and that your view of aesthetics can be different than theirs, also try digging their old teenage photos.
Lastly do you really bealive in 'I will give you something if you cut your hair'? It's farie tales, by not giving you money they probably want you to learn earning a bit for your own which is absolutely fair as long as you live under their roof. Getting part time job would cover all those little expenses and make you feel much better about yourself.