Brain drain and technological relationship between skilled and unskilled labor: brain gain or brain loss?

Abstract

This study analyzes the effect of an increase in the foreign skilled wage rate on the emigration and education decisions of individuals in the home economy. An increase in the foreign skilled wage rate encourages emigration of skilled workers out of the home country, while possible increase in the supply of skilled labor in the home depends on the technological relationship between skilled and unskilled labor in production. Although the average education level will rise when they are complements, the average education level may not necessarily be raised when they are substitutes.

Appendix: Production sector

As the interest rate is fixed at the world level, we have from Eq. 2a

$$ \label{Equ20} {d}K=\left( {-F_{L^{u}K} /F_{KK} } \right){d}L^{u}+\left( {-F_{L^{s}K} /F_{KK} } \right){d}L^{s} $$

(20)

Substituting Eq. 20 into the following equations

$$ \label{Equ21} {d}w^{s}=F_{KL^{s}} {d}K+F_{L^{s}L^{s}} {d}L^{s}+F_{L^{u}L^{s}} {d}L^{u} $$

(21)

$$ \label{Equ22} {d}w^{u}=F_{KL^{u}} {d}K+F_{L^{s}L^{u}} {d}L^{s}+F_{L^{u}L^{u}} {d}L^{u} $$

(22)

which are obtained from Eqs. 2b and 2c, we have

$$ \label{Equ23} {d}w^{s}=SS{d}L^{s}+SU{d}L^{u} $$

(23)

$$ \label{Equ24} {d}w^{u}=US{d}L^{s}+UU{d}L^{u} $$

(24)

where

$$ \label{Equ25} SS=F_{L^{s}L^{s}} -F_{KL^{s}} \left( {{F_{L^{s}K} } \mathord{\left/ {\vphantom {{F_{L^{s}K} } {F_{KK} }}} \right. \kern-\nulldelimiterspace} {F_{KK} }} \right)\\ $$

(25)

$$ \label{Equ26} SU=F_{L^{u}L^{s}} -F_{KL^{s}} (F_{L^{u}K} /F_{KK} ) $$

(26)

$$ \label{Equ27} US=F_{L^{s}L^{u}} -F_{KL^{u}} \left( {F_{L^{s}K} /F_{KK} } \right) $$

(27)

$$ \label{Equ28} UU=F_{L^{u}L^{u}} -F_{KL^{u}} (F_{L^{u}K} /F_{KK} ) $$

(28)

From Eqs. 23 and 24 we obtain

$$ \label{Equ29} {d}L^{u}=\left( {UU-SU\frac{US}{SS}} \right)^{-1}\left( {{d}w^{u}-\frac{US}{SS}{d}w^{s}} \right) $$

(29)

$$ \label{Equ30} {d}L^{s}=\left( {UU-SU\frac{US}{SS}} \right)^{-1}\left( {\frac{UU}{SS}{d}w^{s}-\frac{SU}{SS}{d}w^{u}} \right). $$

(30)

Assuming monotonicity of the labor demand functions with respect to the wage rates, we obtain the labor demand functions of a small open economy Eqs. 2b and 2c in the text. From Eqs. 29 and 30, we have $L_{s}^{u} [ {\equiv \partial L^{u}/\partial w^{s}} ]=\big( {UU-SU\frac{US}{SS}} \big)^{-1}\big( {-\frac{US}{SS}} \big)$, where $UU-SU\frac{US}{SS}<0$ from the assumption. When ∣ F _jj  ∣ is sufficiently great and $F_{L^{s}L^{u}}$ is positive (negative) and sufficiently great (small), we may have $L_{s}^{u} <0$ ($L_{s}^{u} >0$, respectively).¹⁷