If we educated people about family planning or to be responsible then this would not be an issue, but because humans propagate like Rabbits, they will have same problems when food is scarce!, it's a simple concept!, not Rocket Science!
There is enough food on the globe, sadly there are many limitations on infrastructure, government trade policies and money to give everyone the food they need. There are glaring differences in reproduction rates between the western world and the rest (which accounts for nearly all of the human population growth). Google demographic transition for some more depth on the subject. I'm not going into details as I don't have the resources available now, but your 'simple concept' just isn't feasible in the real world.