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.

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Notes

  1. 1.

    Related studies include Copeland and Taylor (1999), Rapanos (2007), Tawada and Sun (2010) and Kondoh and Yabuuchi (2012).

  2. 2.

    Beladi and Rapp (1993), Beladi and Frasca (1999), Daitoh (2008), Tsakiris et al. (2008) and Tawada and Sun (2010) have focused on the environmental problem under general equilibrium analysis. In addition, Kar and Guha-Khasnobis (2006), Yabuuchi (2007), Beladi et al. (2008), Chaudhuri and Banerjee (2010), and Chaudhuri and Gupta (2014) have paid attention to the influences of international factor movements on the economy.

  3. 3.

    At the beginning of development, modern agricultural sector is mainly concentrated in the districts near urban areas and important transport corridors. The scale of land factor for the modern agricultural sector is small, and land mobility is not a major feature. Moreover, if mobility of land between traditional and modern agricultures is allowed, the calculation is too complicated, which will dilute the research theme.

  4. 4.

    At the beginning of the development, because of the limited supply of land and the small scale of production, the products of modern agriculture are in short supply, and they can still rely on imports.

  5. 5.

    The form of Eq. (1) that describes the relation between the production of the urban sector and the environment could be also found in Copeland and Taylor (1999), Tawada and Sun (2010) and Li et al. (2014).

  6. 6.

    Because it is convenient for workers in the modern agricultural sector to transfer into the urban sector, the wage rate in the modern agricultural sector should not be lower than urban wage rate, otherwise, it will be difficult for the sector to attract labourers.

  7. 7.

    See Footnote 3.

  8. 8.

    When L* and K* are positive, they represent inflows of labour and capital, respectively; while when L* and K* are negative, they represent outflows of labour and capital, respectively.

  9. 9.

    See the Appendix for detailed derivations.

  10. 10.

    We assume that \( \left( {S_{KT}^{2} - S_{TT}^{2} } \right)\lambda_{K2} b \ne {{\lambda_{K1} } \mathord{\left/ {\vphantom {{\lambda_{K1} } a}} \right. \kern-0pt} a} \) to ensure stability of equilibrium in capital market.

  11. 11.

    See Jorgenson (2006), Jorgenson et al. (2007), Tawada and Sun (2010), Cole et al. (2011), and Shahbaz et al. (2015).

  12. 12.

    See the Appendix for detailed derivations.

  13. 13.

    Farmers will compare the wage rate obtained by the traditional production with the wage rate as workers in the modern agricultural sector. As long as the latter is higher than the former, farmers will transfer to the modern agricultural sector, and only when the wages of the two sectors are equal, the transfer will stop.

  14. 14.

    See the Appendix for detailed derivations.

  15. 15.

    See the Appendix for detailed derivations.

  16. 16.

    Kondoh and Yabuuchi (2012) believed that international immigration improves the environment if pollution abatement equipment is sufficiently effective; Li et al. (2014) found that the skilled labour inflow deteriorates the environment while the unskilled labour inflow improves the environment.

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Acknowledgements

We acknowledge that this work has been supported by Key Research Base of Humanities and Social Sciences of the Ministry of Education of China (17JJD630002) and Yuxiu Postdoctoral School of Nanjing University.

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Appendix

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.

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Wu, Y., Li, X. International factor mobility and environment in a dual agricultural economy. Ann Reg Sci 66, 75–89 (2021). https://doi.org/10.1007/s00168-020-01010-5

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