Singapore Brain drain in math terms

Well, I think this math question for my 1506 module will tell us a reason why there is a brain drain in Singapore:

Both Elves and Dwarves live in Rivendell, but there is a certain irrational resentment
between the two groups [placed in their hearts, no doubt, by Sauron]. The amount of
racial prejudice is not the same on both sides, Elves tending to be more intolerant than
Dwarves, but both groups are inclined to move out of Rivendell at a rate controlled by
the number of the other group. Apart from this, both groups reproduce as usual, but
Elves can only be killed by violence –they never grow old– so their overall death rate
per capita is lower than that of the Dwarves; also, the Elvish birth rate per capita is
higher since Dwarf women are scarce [ever seen one?]. Both groups have more births
than deaths. We can set up a model of this situation using a pair of simultaneous ODEs
with a matrix [where the first row describes the rate of change of the Elf population]
5 -4
-1 2

Explain why this matrix does represent the situation we described. At a
certain time, the number of Dwarves is slightly larger than the number of Elves. Predict
what will happen to the population of Elves. This pattern has in fact often been observed
in racially discriminatory societies.

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