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The optimal emigration rate that can be obtained for the maximization of appears to be
directly related to most of the parameters of the problem. It has to be noted though that
the numerator should be positive in order to meet the conditions imposed on . This
leads to the following restriction: . This condition implies that
is the minimal value for the relative productivity or relative wage below which migration
is not optimal.
The above results are shown in Figure 2 where point A refers to the maximum of
attained at . Point B corresponds to
ii where starts getting lower than
Figure II.1.3: Domestic human capital stock with emigration and risk aversion
HR
HRO
0
A
m *
Proposition 1: A net human capital gain (brain gain) results when the value of human
capital, under different values of emigration rate, is superior to the value of the initial
ii is the solution of the following equation:
iii is the value of attained at with
Net human capital gain
! *++!
B
m **
1
m
(6)
Net human capital loss
iii .