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Labor Transfer in Emerging Economies pp 161–180Cite as

A Study on Urban Private Capital and the Transfer of Labor in the Modern Agricultural Sector

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Part of the book series: New Frontiers in Regional Science: Asian Perspectives ((NFRSASIPER,volume 12))

Abstract

As urban private capital enters the modern agriculture industry, it divides the agricultural sector into the modern sector and the traditional sector. This chapter establishes a general equilibrium model to study the economic impact of governmental policies aimed at promoting modern agriculture. The main conclusions of this chapter are that interest subsidies implemented by the government to promote modern agriculture can reduce the transfer of labor from the rural areas to the cities, but encourage the movement of rural labor to the modern agricultural sector. Conversely, wage rate subsidies for the modern agricultural sector will lead to rises in the urban unemployment rate and a decrease in the quantity of labor in the traditional agricultural sector.

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Notes

  1. 1.

    There are precedents in China; see Zheng et al. (2009) and Wang (2011).

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Authors and Affiliations

  1. Business School, Nanjing University, Nanjing, China

    Xiaochun Li

  2. School of Economics, Nanjing University, 22 Hankou Road, Nanjing, Jiangsu, 210093, China

    Qin Shen

Authors
  1. Xiaochun Li
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  2. Qin Shen
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Correspondence to Xiaochun Li .

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Editors and Affiliations

  1. Business School, Nanjing University, Nanjing, China

    Xiaochun Li

Appendices

Appendix A

By total differentiation of the capital system Eqs. (10.5), (10.6), (10.7), (10.10), and (10.11′) and making s 1 =0 at the initiation of the subsidy policy, we get the following linear equation system (total differentiation):

$$ \left[\begin{array}{cccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill {F}_{L L}^1\hfill & \hfill {F}_{L K}^1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill {p}_1{F}_{KL}^1\hfill & \hfill {p}_1{F}_{KK}^1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill -{p}_2\left({g}^{{\prime\prime} }{F}^2+{g}^{\prime }{F}_L^2{f}^{\prime}\right)\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{c}\hfill {dL}_1\hfill \\ {}\hfill {dK}_1\hfill \\ {}\hfill {dK}_2\hfill \\ {}\hfill dr\hfill \end{array}\right]=\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill {rds}_1\hfill \end{array}\right] $$
(10.A1)

Let Δ be the determinant of the coefficient matrix, and we have

$$ \Delta ={p}_1\left({F}_{L L}^1{F}_{KK}^1-{F}_{KL}^1{F}_{L K}^1\right)+{p}_2{F}_{L L}^1\left({g}^{{\prime\prime} }{F}^2+{g}^{\prime }{f}^{\prime }{F}_L^2\right). $$

The total differentiation of Eqs. (10.4), (10.8), (10.9), and (10.12) in the labor system can be reorganized as

$$ \left[\begin{array}{ccc}\hfill {L}_1\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ {}\hfill {L}_1{w}_3\hfill & \hfill \left[\left(1+\lambda \right){L}_1+{L}_2\right]{F}_{L L}^3\hfill & \hfill -{L}_2\hfill \end{array}\right]\left[\begin{array}{c}\hfill d\lambda \hfill \\ {}\hfill {dL}_3\hfill \\ {}\hfill {dw}_2\hfill \end{array}\right]=\left[\begin{array}{c}\hfill -\left(1+\lambda \right){dL}_1-{f}^{\prime }{dK}_2\hfill \\ {}\hfill {p}_2\left({g}^{{\prime\prime} }{F}^2+{g}^{\prime }{f}^{\prime }{F}_L^2\right){dK}_2\hfill \\ {}\hfill \left[{\overline{w}}_1-\left(1+\lambda \right){w}_3\right]{dL}_1+\left({w}_2-{w}_3\right){dL}_2\hfill \end{array}\right] $$
(10.A2)

Let Ω be the determinant of the coefficient matrix of Eq. (10.A2), and we have

$$ \Omega =-{L}_1\left\{\left[\left(1+\lambda \right){L}_1+{L}_2\right]{F}_{L L}^3-{w}_3\right\}>0 $$

Solving Eq. (10.A1) by Cramer’s Rule, we get

$$ {dK}_1/{ds}_1={rF}_{LL}^1/\Delta <0,\kern0.36em {dL}_1/{ds}_1=-{rF}_{LK}^1/\Delta <0,\kern0.36em d{K}_2/{ds}_1=-{rF}_{LL}^1/\Delta >0 $$
$$ {dL}_2/{ds}_1={f}^{\prime }{dK}_2/{ds}_1>0,\kern0.6em dr/{ds}_1={rp}_1\left({F}_{LL}^1{F}_{KK}^1-{F}_{KL}^1{F}_{LK}^1\right)/\Delta =0 $$

Solving Eq. (10.A2) by Crammer’s Rule, we get

$$ {dw}_2/{ds}_1={p}_2\left({g}^{\prime }{F}_L^2+ g{f}^{\prime }{F}_{L L}^2\right){dK}_2/{ds}_1>0 $$
$$ {dL}_3/{ds}_1=\frac{p_2{L}_1{L}_2\left({g}^{\prime }{F}_L^2+ g{f}^{\prime }{F}_{L L}^2\right){dK}_2/{ds}_1+{L}_1\left({\overline{w}}_1{dL}_1/{ds}_1+{w}_2{dL}_2/{ds}_1\right)}{\Omega} $$
$$ {dw}_3/{ds}_1={F}_{LL}^3{dL}_3/{ds}_1>0 $$
$$ d\lambda /{ds}_1=\begin{array}{l}-\left\{\right[\left[{\overline{w}}_1-\left(1+\lambda \right){w}_3\right]{dL}_1/{ds}_1+{F}_{L L}^3\left[\left(1+\lambda \right){L}_1+{L}_2\right]\Big[\left(1+\lambda \right){dL}_1/{ds}_1\\ {}+{dL}_2/{ds}_1\Big]{p}_2\left({g}^{\prime }{F}_L^2+{ g F}_{L L}^2{f}^{\prime}\right){dK}_2/{ds}_1-\left({w}_2-{w}_3\right){dL}_2/{ds}_1\Big\}\end{array}/\Omega $$

Appendix B

Let s 2 = 0 at the initiation of the subsidizing policy, and then the total differentiation of Eqs. (10.4′), (10.5), (10.6), (10.7), (10.8′), (10.9), (10.10), (10.11), and (10.12) could be reorganized into the following linear equation system:

$$ \begin{array}{ll}\hfill & \left[\begin{array}{cccccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill {F}_{LL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {F}_{LK}^1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill -{p}_1{F}_{KL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill -{p}_1{F}_{KK}^1\hfill & \hfill {p}_2\left[{g}^{\prime}\left({K}_2\right){F}_L^2{f}^{\prime }+{g}^{{\prime\prime}}\left({K}_2\right){F}^2\right]\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {p}_2\left[g\left({K}_2\right){F}_{LL}^2{f}^{\prime }+{g}^{\prime}\left({K}_2\right){F}_L^2\right]\hfill & \hfill -1\hfill \\ {}\hfill 1+\lambda \hfill & \hfill 1\hfill & \hfill {L}_1\hfill & \hfill 0\hfill & \hfill {f}^{\prime}\hfill & \hfill 0\hfill \\ {}\hfill {\overline{w}}_1\hfill & \hfill {w}_3-\left(L-{L}_3\right){F}_{LL}^3\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {w}_2{f}^{\prime}\hfill & \hfill {L}_2\hfill \end{array}\right]\\ {}& \times \left[\begin{array}{c}\hfill {dL}_1\hfill \\ {}\hfill {dL}_3\hfill \\ {}\hfill d\lambda \hfill \\ {}\hfill {dK}_1\hfill \\ {}\hfill {dK}_2\hfill \\ {}\hfill {dw}_2\hfill \end{array}\right]\kern1.5em =\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill -{w}_2\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \end{array}\right]{ds}_2\hfill \end{array} $$
(10.B1)

Let Δ2 be the determinant of coefficient matrix, and we have

$$ {\Delta}_2={L}_1\left[{w}_3-\left( L-{L}_3\right){F}_{L L}^3\right]\Delta >0 $$

From Eq. (10.B1), we have

$$ {dK}_1/{ds}_2={dL}_1/{ds}_2={dK}_2/{ds}_2={dL}_2/{ds}_2={f}^{\prime }{dK}_2/{ds}_2= dr/{ds}_2=0 $$
$$ \begin{array}{l}{dw}_2/{ds}_2={w}_2>0,\kern0.36em d\lambda /{ds}_2=\frac{w_2{L}_2}{L_1\left[{w}_3-\left( L-{L}_3\right){F}_{L L}^3\right]}>0,\\ {}{dw}_3/{ds}_2={F}_{L L}^3{dL}_3/{ds}_2>0\end{array} $$

Appendix C

By total differentiation of the capital system Eqs. (10.4′), (10.5), (10.6), (10.7), (10.8), (10.9), (10.10), (10.11), and (10.12), we get the following linear equation set:

$$ \begin{array}{ll}\hfill & \left[\begin{array}{cccccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill {F}_{LL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {F}_{LK}^1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill -{p}_1{F}_{KL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill -{p}_1{F}_{KK}^1\hfill & \hfill {p}_2\left[{g}^{\prime}\left({K}_2\right){F}_L^2{f}^{\prime }+{g}^{{\prime\prime}}\left({K}_2\right){F}^2\right]\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {p}_2\left[g\left({K}_2\right){F}_{LL}^2{f}^{\prime }+{g}^{\prime}\left({K}_2\right){F}_L^2\right]\hfill & \hfill -1\hfill \\ {}\hfill 1+\lambda \hfill & \hfill 1\hfill & \hfill {L}_1\hfill & \hfill 0\hfill & \hfill {f}^{\prime}\hfill & \hfill 0\hfill \\ {}\hfill {\overline{w}}_1\hfill & \hfill {w}_3-\left(L-{L}_3\right){F}_{LL}^3\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {w}_2{f}^{\prime}\hfill & \hfill {L}_2\hfill \end{array}\right]\\ {}& \times \left[\begin{array}{c}\hfill {dL}_1\hfill \\ {}\hfill {dL}_3\hfill \\ {}\hfill d\lambda \hfill \\ {}\hfill {dK}_1\hfill \\ {}\hfill {dK}_2\hfill \\ {}\hfill {dw}_2\hfill \end{array}\right]\kern1.5em =\left[\begin{array}{c}\hfill d K\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \end{array}\right]+\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill d L\hfill \\ {}\hfill {w}_3 dL\hfill \end{array}\right]\hfill \end{array} $$

Let Δ3be the determinant of the coefficient matrix, and we have

$$ {\Delta}_3={\Delta}_2={L}_1\left[{w}_3-\left( L-{L}_3\right){F}_{L L}^3\right]\Delta >0 $$

By calculating, we get

$$ \begin{array}{l}{dK}_1/ dK=1,\kern0.36em {dL}_1/ dK=-\frac{F_{LK}^1}{F_{LL}^1}>0,\kern0.36em {dw}_3/ dK={F}_{LL}^3{dL}_3/ dK>0,\\ {}{dK}_1/ dL=1,\kern0.36em {dw}_3/ dL={F}_{LL}^3{dL}_3/ dL<0\end{array} $$

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Li, X., Shen, Q. (2017). A Study on Urban Private Capital and the Transfer of Labor in the Modern Agricultural Sector. In: Li, X. (eds) Labor Transfer in Emerging Economies. New Frontiers in Regional Science: Asian Perspectives, vol 12. Springer, Singapore. https://doi.org/10.1007/978-981-10-3569-2_10

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