In the world of Panem the country is organised into twelve districts which support the capitol
There are in fact 13 but D13 is no longer under Capitol control
We see the Reaping in D12 which contains (by my estimate around 400 children), again by my estimate this would suggest a population of around 4000? We have no indication of how big the other districts are.
The capitol is seen to be very large and very lavish, resources are squandered and the people are very rich. Could such a small population in the districts feasibly support such a large and wasteful capitol?