Have the two protagonists considered that considering that simple population density figures (area divided by population) might be meaningless?
Mauritania has only 3.77 people per sq. km. Wow! The place is virtually empty! The could afford to take many millions more.... except that the country is 100% Sahara desert.

Let's compare two countries whose are is comparable in size:-
At http://data.worldbank.org/indicator/EN.POP.DNST it tells us that the density figures for Japan is 350 whilst for the UK it is 265. That makes Japan 1.32 times more crowded than the UK except that Japan has vastly larger areas of uninhabitable highlands compared with Britain.

Then as well as these two elements you have factor in the state of economic, industrial and agricultural development, climate and a whole range of other considerations before you can arrive at a figure for how many people a country can reasonably sustain.