International factor mobility and environment in a dual agricultural economy

Abstract

The purpose of this study is to investigate the influences that international factor movements have on the environment in developing country under agricultural dualism. By using a general equilibrium model that incorporates a modern agricultural sector in different stages, we analyse the effects of international factor movements on the environment. At the beginning of the modern agricultural sector, international labour movement has no influence on the environment; if the modern agricultural capital share in the economy increases to a certain level, international capital inflow improves the environment in the developing countries whereas international capital outflow harms the environment, otherwise, international capital inflow harms the environment whereas international capital outflow improves the environment. However, after the popularization of modern agriculture, international labour movement and international capital movement affect the environment in the same direction: factor inflow harms the environment, whereas outflow improves the environment. Thus, it is possible for the international factor movement be compatible with the environmental protection in a developing country.

Appendix

In this appendix, we derive various mathematical expressions presented in the main text.

1. Equation (11)

An increase in the output of urban sector equal to $\hat{X}_{1}$ then creates environmental damage [obtained by differentiating Eq. (1)] given by

$$ \hat{e} = - a\hat{X}_{1} . $$

(26)

Notice that by Eq. (2), as wage rate is downwardly rigid, interest rate r will be unaffected to guarantee zero profit. Then, turn to the modern agricultural sector. Substituting the unaffected r into Eq. (3) and then differentiating it, we obtain

$$ \hat{\tau }_{2} { = }b\hat{e}. $$

(27)

Substituting Eqs. (26) and (27) into Eq. (10) yields

$$ \left[ { - \frac{{\lambda_{K1} }}{a} + \lambda_{K2} \left( {S_{KT}^{2} - S_{TT}^{2} } \right)b} \right]\hat{e} = \hat{K}, $$

(28)

Thus, we have Eq. (11) in the text.

2. Equation (13)

Totally differentiating Eqs. (4), (5), (6), and (9), one obtains

$$ \left[ {\begin{array}{*{20}c} {\theta_{L3} } & {\theta_{T3} } & 0 \\ {S_{TL}^{3} } & {S_{TT}^{3} } & 1 \\ A & {\lambda_{L3} S_{LT}^{3} } & {\lambda_{L3} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\hat{w}} \\ {\hat{\tau }_{3} } \\ {\hat{X}_{3} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 0 \\ 0 \\ 1 \\ \end{array} } \right]\hat{L}{ + }\left[ {\begin{array}{*{20}c} {\varepsilon_{3} } \\ {\varepsilon_{3} } \\ B \\ \end{array} } \right]\hat{e}, $$

(29)

where $A = \lambda_{L3} S_{LL}^{3} - \left( {1 + \mu_{1} } \right)\left( {\lambda_{L1} + \lambda_{L2} } \right) < 0$ and $B = \left( {1 + \mu_{1} } \right)\left[ {{{\lambda_{L1} } \mathord{\left/ {\vphantom {{\lambda_{L1} } a}} \right. \kern-0pt} a} - \left( {S_{LT}^{2} - S_{LL}^{2} } \right)\lambda_{L2} b} \right] + \lambda_{L3} \varepsilon_{3}$. Solving Eq. (29), we obtain ${{\hat{w}} \mathord{\left/ {\vphantom {{\hat{w}} {\hat{L}}}} \right. \kern-0pt} {\hat{L}}} < 0{{,\hat{\tau }_{3} } \mathord{\left/ {\vphantom {{,\hat{\tau }_{3} } {\hat{L}}}} \right. \kern-0pt} {\hat{L}}} > 0,{{\hat{X}_{3} } \mathord{\left/ {\vphantom {{\hat{X}_{3} } {\hat{L} > 0}}} \right. \kern-0pt} {\hat{L} > 0}}$, and then ${{\hat{\mu }_{1} } \mathord{\left/ {\vphantom {{\hat{\mu }_{1} } {\hat{L}}}} \right. \kern-0pt} {\hat{L}}} > 0$ by Eq. (5). Thus, we have Eq. (13) in the text.

3. Equations (22) and (23)

Differentiating Eqs. (15) and (16) by using (18), we obtain

$$ \left[ {\begin{array}{*{20}c} {\theta_{L2} } & {\theta_{T2} } \\ {\theta_{L3} } & {\theta_{T3} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\hat{w}} \\ {\hat{\tau }} \\ \end{array} } \right]{ = }\left[ {\begin{array}{*{20}c} {\varepsilon_{2} } \\ {\varepsilon_{3} } \\ \end{array} } \right]\hat{e}. $$

(30)

Solving the set of equations given by Eq. (30), we have Eqs. (22) and (23) in the text.

4. Equations (24) and (25)

Differentiating Eqs. (19)–(21) by using (17), (22) and (23), we obtain the effects of international factor movements on the environment

$$ \left[ {\begin{array}{*{20}c} {\lambda_{L2} } & {\lambda_{L3} } & {G_{1} } \\ {\lambda_{K2} } & 0 & {G_{2} } \\ {\lambda_{T2} } & {\lambda_{T3} } & {G_{3} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\hat{X}_{2} } \\ {\hat{X}_{3} } \\ {\hat{e}} \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 1 \\ 0 \\ 0 \\ \end{array} } \right]\hat{L} + \left[ {\begin{array}{*{20}c} 0 \\ 1 \\ 0 \\ \end{array} } \right]\hat{K}, $$

(31)

where

$$ \begin{aligned} & G_{1} = - \frac{{\left( {1 + \mu_{2} } \right)\lambda_{L1} }}{a} - \left( {\lambda_{L2} \varepsilon_{2} + \lambda_{L3} \varepsilon_{3} } \right) + \frac{{\left[ {\left( {1 + \mu_{2} } \right)\lambda_{L1} - \lambda_{L2} S_{LL}^{2} - \lambda_{L3} S_{LL}^{3} } \right]\left( {\varepsilon_{3} \theta_{T2} - \varepsilon_{2} \theta_{T3} } \right)}}{{\theta_{L2} \theta_{T3} - \theta_{T2} \theta_{L3} }} + \frac{{\left( {\lambda_{L2} S_{LT}^{2} + \lambda_{L3} S_{LT}^{3} } \right)\left( {\varepsilon_{3} \theta_{L2} - \varepsilon_{2} \theta_{L3} } \right)}}{{\theta_{L2} \theta_{T3} - \theta_{T2} \theta_{L3} }}, \\ & G_{2} = - \frac{{\lambda_{K1} }}{a} - \lambda_{K2} \varepsilon_{2} + \frac{{\lambda_{K2} \left[ {S_{KT}^{2} \left( {\varepsilon_{3} \theta_{L2} - \varepsilon_{2} \theta_{L3} } \right) - S_{KL}^{2} \left( {\varepsilon_{3} \theta_{T2} - \varepsilon_{2} \theta_{T3} } \right)} \right]}}{{\theta_{L2} \theta_{T3} - \theta_{T2} \theta_{L3} }}, \\ & {\text{and}}\quad G_{3} = - \left( {\varepsilon_{2} \lambda_{T2} { + }\varepsilon_{3} \lambda_{T3} } \right) - \frac{{\left( {\lambda_{T2} S_{TL}^{2} { + }\lambda_{T3} S_{TL}^{3} } \right)\left( {\varepsilon_{3} \theta_{T2} - \varepsilon_{2} \theta_{T3} } \right)}}{{\theta_{L2} \theta_{T3} - \theta_{T2} \theta_{L3} }} + \frac{{\left( {\lambda_{T2} S_{TT}^{2} { + }\lambda_{T3} S_{TT}^{3} } \right)\left( {\varepsilon_{3} \theta_{L2} - \varepsilon_{2} \theta_{L3} } \right)}}{{\theta_{L2} \theta_{T3} - \theta_{T2} \theta_{L3} }}. \\ \end{aligned} $$

Solving the set of equations given by Eq. (31), we have Eqs. (24) and (25) in the text.