Environment and Labor Movement of Skilled Labor and Unskilled Labor Between Sectors

Abstract

In this chapter, we divide the labor into skilled and unskilled labor to investigate the impact that the heterogeneous labor transfer between sectors has on the environment under the international skilled and unskilled labor movements and the price change of the agricultural products. The main conclusions are: under certain conditions, skilled labor inflow deteriorates the environment, while its outflow improves the environment; unskilled labor inflow improves the environment, while its outflow deteriorates the environment; and the increasing price of the agricultural products improves the environment, while the decreasing price deteriorates the environment.

Appendix

Under the present model, the dynamic adjustment process for the supply side is as follows:

$$ {\dot{X}}_1={d}_1\left({p}_1-{a}_{S1}{w}_{S1}-{a}_{U1}{\overline{w}}_U-{a}_{K1} r\right) $$

(8.A1)

$$ {\dot{X}}_2={d}_2\left({p}_2-{a}_{S2}{w}_{S1}-{a}_{U2}{w}_{U2}-{a}_{N2} R\right) $$

(8.A2)

$$ {\dot{w}}_{S1}={d}_3\left({a}_{S1}{X}_1+{a}_{S2}{X}_2-{L}_S\right) $$

(8.A3)

$$ {\dot{w}}_{U2}={d}_4\left({a}_{U1}{X}_1+{a}_{U2}{X}_2+\frac{\overline{w_U}-{w}_{U2}}{w_{U2}}{a}_{U1}{X}_1-{L}_U\right) $$

(8.A4)

$$ \dot{r}={d}_5\left({a}_{K1}{X}_1- K\right) $$

(8.A5)

$$ \dot{R}={d}_6\left({a}_{N2}{X}_2- N\right) $$

(8.A6)

where “.” represents differentiation with respect to time and d _j (j = 1, 2, 3, 4, 5, 6, 7, 8) is the positive coefficient measuring the speed of adjustment and d _j  > 0.

Marshallian adjustment process is assumed for quantities when the demand price differs from the supply price in the goods markets. A Walrasian adjustment mechanism is assumed for the factor prices with the fixed endowment in the factor markets. The determinant of the Jacobian matrix of equations (8.A1), (8.A2), (8.A3), (8.A4), (8.A5), and (8.A6) is:

$$ \left|J\right|={d}_1{d}_2\dots {d}_6{p}_1{p}_2{KNL}_S{L}_U\left|\begin{array}{cccccc}\hfill 0\hfill & \hfill 0\hfill & \hfill -{\theta}_{S1}\hfill & \hfill 0\hfill & \hfill -{\theta}_{K1}\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill -{\theta}_{S2}\hfill & \hfill -{\theta}_{U2}\hfill & \hfill 0\hfill & \hfill -{\theta}_{N2}\hfill \\ {}\hfill {\lambda}_{S1}\hfill & \hfill {\lambda}_{S2}\hfill & \hfill A\hfill & \hfill {\lambda}_{S2}{S}_{SU}^2\hfill & \hfill {\lambda}_{S1}{S}_{SK}^1\hfill & \hfill {\lambda}_{S2}{S}_{SN}^2\hfill \\ {}\hfill \left(1+\lambda \right){\lambda}_{U1}\hfill & \hfill {\lambda}_{U2}\hfill & \hfill B\hfill & \hfill C\hfill & \hfill D\hfill & \hfill {\lambda}_{U2}{S}_{UN}^2\hfill \\ {}\hfill 1\hfill & \hfill 0\hfill & \hfill {S}_{KS}^1\hfill & \hfill 0\hfill & \hfill {S}_{KK}^1\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 1\hfill & \hfill {S}_{NS}^2\hfill & \hfill {S}_{NU}^2\hfill & \hfill 0\hfill & \hfill {S}_{NN}^2\hfill \end{array}\right| $$

It can also be written as follows:

$$ \left| J\right|={d}_1{d}_2\cdots {d}_6{p}_1{p}_2{KNL}_S{L}_U\Delta $$

Therefore, according to the Routh-Hurwitz theorem, a necessary condition for the local stability of the system is that the determinant of the Jacobian matrix is positive. Hence, it is assumed that the equilibrium in this chapter is stable under the condition that |J| > 0. We could obtain that Δ > 0.