Under which condition does a country with a small GDP have a large per capita income? if it has a large population if it has a small population if the population doesn't change over time

per capita means per head or per person.

now, if a country has a small GDP hmmm say for the sake of example, $1000, and it has 1000 residents, then the per capita is $1000/1000 or a buck each.

now, $1000 is a really tiny GDP, but, if the population is say hmm 20 folks only, then the per capita amount is $1000/20, or $50 per person, now, that's a large "per capita" figure, more so than $1 per person, even though the GDP never changed, it was all along $1000.

so, if the population is comparitively small, the per capita is large, I think a good example of that is Switzerland.

sidenote:

bear in mind that per capita figures are very misleading, since you could have a tiny portion of the population making huge amounts and others making little, like in the US, and the per capita is very inaccurate to reflect the economy wealth distribution.