Could We Survive by Eating Only Humans?

The premise of the "What If" series has always been to treat stupid theoretical questions seriously, and therefore we may learn something. The dumb theoretical question in this video is "How long can the human race survive on only cannibalism?" Cannibalism is a disgusting idea and has always been taboo, but Randall Munroe and Henry Reich tackle it as serious (while still inserting their opinions). Relying on cannibalism would quickly make us pure carnivores, and there are many reasons that eating carnivores is a bad idea. 

Once you get around that, you get into the law of diminishing returns. If you are trying to "save" humanity, how many people must survive? It won't be enough to keep the freezers full of the unlucky ones going. Otherwise, if we all just eat each other over time, humanity will not last all that long.