Analyzing the Effect of Advanced Agriculture Development Policy

Abstract

This chapter broadens the scope of current theoretical studies, divides rural agriculture into two sectors—advanced and traditional—and takes into consideration the land factor and the urban informal sector. Under the assumption that wages in the advanced agricultural sector are higher than in the traditional agricultural sector, this chapter analyzes the effect of policies to promote advanced agricultural development with the comparative static method. The main conclusions of this chapter are wage subsidization of the advanced agricultural sector, in addition to having the same economic impact as interest subsidies on the advanced agricultural sector, could also increase the land employment in the advanced agricultural sector, and reduce that in the traditional agricultural sector. Therefore, the effect of wage subsidizing policies is stronger than that of interest subsidies, while land rent subsidies for the advanced agricultural sector have the same economic effect as wage subsidies.

Appendices

Appendices

1.1 Appendix A

The dynamic adjustment procedure:

$$ \overset{\bullet }{L_1}={d}_1\left({p}_1{F}_L^1-\overline{w_1}\right) $$

(11.A1)

$$ \overset{\bullet }{L_2}={d}_2\left({p}_2{F}_L^2-{w}_2\right) $$

(11.A2)

$$ \overset{\bullet }{L_3}={d}_3\left({p}_3{gF}_L^2-{w}_3\right) $$

(11.A3)

$$ \overset{\bullet }{L_4}={d}_4\left({F}_L^4-{w}_4\right) $$

(11.A4)

$$ \overset{\bullet }{K_1}={d}_5\left({p}_1{F}_K^1- r\right) $$

(11.A5)

$$ \overset{\bullet }{K_3}={d}_6\left({p}_3{g}^{\prime }{F}^3- r\right) $$

(11.A6)

$$ \overset{\bullet }{T_3}={d}_7\left({p}_3{gF}_T^3-\tau \right) $$

(11.A7)

$$ \overset{\bullet }{T_4}={d}_8\left({F}_T^4-\tau \right) $$

(11.A8)

$$ \overset{\bullet }{w_2}={d}_9\left({L}_1+{L}_2+{L}_3+{L}_4- L\right) $$

(11.A9)

$$ \overset{\bullet }{w_3}={d}_{10}\left({L}_3- f\left({K}_3\right)\right) $$

(11.A10)

$$ \overset{\bullet }{w_4}={d}_{11}\left({L}_1\overline{w_1}+{L}_2{w}_2+{L}_3{w}_3-\left( L-{L}_4\right){w}_4\right) $$

(11.A11)

$$ \overset{\bullet }{r}={d}_{12}\left({K}_1+{K}_3- K\right) $$

(11.A12)

$$ \overset{\bullet }{\tau}={d}_{13}\left({T}_3+{T}_4- T\right) $$

(11.A13)

The total differential of (11.A1), (11.A2), (11.A3), (11.A4), (11.A5), (11.A6), (11.A7), (11.A8), (11.A9), (11.A10), (11.A11), (11.A12), and (11.A13) can be written as the following Jacobian matrix:

$$ \begin{array}{ll}\hfill & \left|J\right|\\ {}& =\left[\begin{array}{lllllllllllll}{d}_1{p}_1{F}_{LL}^1\hfill & 0\hfill & 0\hfill & 0\hfill & {d}_1{p}_1{F}_{LK}^1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & {d}_2{p}_2{F}_{LL}^2\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & -{d}_2\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & {d}_3{p}_3{gF}_{LL}^3\hfill & 0\hfill & 0\hfill & {d}_3{p}_3{g^{\prime }F}_L^3\hfill & {d}_3{p}_3{gF}_{LT}^3\hfill & 0\hfill & 0\hfill & -{d}_3\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & 0\hfill & {d}_4{F}_{LL}^4\hfill & 0\hfill & 0\hfill & 0\hfill & {d}_4{F}_{LT}^4\hfill & 0\hfill & 0\hfill & -{d}_4\hfill & 0\hfill & 0\hfill \\ {}{d}_5{p}_1{F}_{KL}^1\hfill & 0\hfill & 0\hfill & 0\hfill & {d}_5{p}_1{F}_{KK}^1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & -{d}_5\hfill & 0\hfill \\ {}0\hfill & 0\hfill & {d}_6{p}_3{g^{\prime }F}_L^3\hfill & 0\hfill & 0\hfill & {d}_6{p}_3{g^{{\prime\prime} }F}^3\hfill & {d}_6{p}_3{g^{\prime }F}_T^3\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & -{d}_6\hfill & 0\hfill \\ {}0\hfill & 0\hfill & {d}_7{p}_3{gF}_{TL}^3\hfill & 0\hfill & 0\hfill & {d}_7{p}_3{g^{\prime }F}_T^3\hfill & {d}_7{p}_3{gF}_{TT}^3\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & -{d}_7\hfill \\ {}0\hfill & 0\hfill & 0\hfill & {d}_8{F}_{TL}^4\hfill & 0\hfill & 0\hfill & 0\hfill & {d}_8{F}_{TT}^4\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & -{d}_8\hfill \\ {}{d}_9\hfill & {d}_9\hfill & {d}_9\hfill & {d}_9\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & {d}_{10}\hfill & 0\hfill & 0\hfill & -{d}_{10}{f}^{\prime}\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}{d}_{11}\overline{w_1}\hfill & {d}_{11}{w}_2\hfill & {d}_{11}{w}_3\hfill & {d}_{11}{w}_4\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & {d}_{11}{L}_2\hfill & {d}_{11}{L}_3\hfill & -{d}_{11}\left(L-{L}_4\right)\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & 0\hfill & 0\hfill & {d}_{12}\hfill & {d}_{12}\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & {d}_{13}\hfill & {d}_{13}\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \end{array}\right]\hfill \\ {}& =-{d}_1{d}_2{d}_3{d}_4{d}_5{d}_6{d}_7{d}_8{d}_9{d}_{10}{d}_{11}{d}_{12}{d}_{13}{p}_1{\Delta}_1\hfill \end{array} $$

Under the condition of a stable system, there must be |J| < 0, and thus Δ₁ > 0.

1.2 Appendix B

If the government subsidizes loan interest, wage and land rent for the advanced agricultural sector with the rates of s ₁, s ₂, and s ₃, respectively, Eq. (11.14) becomes:

$$ {p}_2{g}^{\prime}\left({K}_2\right){F}^2= r\left(1-{s}_1\right) $$

(11.14′)

Equation (11.11) becomes:

$$ {p}_3{gF}_L^3={w}_3\left(1-{s}_2\right) $$

(11.11′)

Equation (11.15) becomes:

$$ {p}_3{gF}_T^3=\tau \left(1-{s}_3\right) $$

(11.15′)

Then, the total differential of (11.5), (11.6), (11.7), (11.8), (11.9), (11.10), (11.11′), (11.12), (11.13), (11.14′), (11.15′), (11.16), and (11.17′) can be organized as follows:

$$ \begin{array}{ll}\hfill & \left[\begin{array}{lllllll}{F}_{LL}^1\hfill & 0\hfill & 0\hfill & -{F}_{LK}^1\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & 0\hfill & {p}_3\left({g^{\prime }F}_L^3+{gF}_{LL}^3{f}^{\prime}\right)\hfill & {p}_3{gF}_{LT}^3\hfill & -1\hfill & 0\hfill \\ {}0\hfill & 0\hfill & {F}_{LL}^4\hfill & 0\hfill & -{F}_{LT}^4\hfill & 0\hfill & -1\hfill \\ {}{p}_1{F}_{KL}^1\hfill & 0\hfill & 0\hfill & -\left[{p}_1{F}_{KK}^1+{p}_3\left({g^{{\prime\prime} }F}^3+{g^{\prime }F}_L^3{f}^{\prime}\right)\right]\hfill & -{p}_3{g^{\prime }F}_T^3\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & -{F}_{TL}^4\hfill & {p}_3\left({g^{\prime }F}_T^3+{gF}_{TL}^3{f}^{\prime}\right)\hfill & {p}_3{gF}_{TT}^3+{F}_{TT}^4\hfill & 0\hfill & 0\hfill \\ {}1\hfill & 1\hfill & 1\hfill & {f}^{\prime}\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}\overline{w_1}\hfill & {w}_2+{L}_2{p}_2{F}_{LL}^2\hfill & {w}_4\hfill & {w}_3{f}^{\prime}\hfill & 0\hfill & {L}_3\hfill & -\left(L-{L}_4\right)\hfill \end{array}\right]\\ {}& \times \left[\begin{array}{l}{dL}_1\hfill \\ {}{dL}_2\hfill \\ {}{dL}_4\hfill \\ {}{dK}_3\hfill \\ {}{dT}_3\hfill \\ {}{dw}_3\hfill \\ {}{dw}_4\hfill \end{array}\right]=\left[\begin{array}{l}0\hfill \\ {}-{w}_3{ds}_2\hfill \\ {}0\hfill \\ {}{rds}_1\hfill \\ {}-\tau {ds}_3\hfill \\ {}0\hfill \\ {}0\hfill \end{array}\right]\hfill \end{array} $$

(11.B1)

By dynamic adjustment, we get that the value of the coefficient matrix (11.B1) Δ₁ > 0.

Let $a={F}_{LL}^1$ ,$b={p}_1{F}_{KL}^1$, $c=\overline{w_1}$, $d={w}_2+{L}_2{p}_2{F}_{L L}^2$, $e={F}_{LL}^4$, $f=-{F}_{TL}^4=-{F}_{LT}^4$, g = w ₄, $h=-{F}_{LK}^1$, $j={p}_3\left({g}^{\prime }{F}_L^3+{ g F}_{L L}^3{f}^{\prime}\right)$, $k=-\left[{p}_1{F}_{KK}^1+{p}_3\left({g}^{{\prime\prime} }{F}^3+{g}^{\prime }{F}_L^3{f}^{\prime}\right)\right]$, $m={p}_3\left({g}^{\prime }{F}_T^3+{ g F}_{T L}^3{f}^{\prime}\right)$, n = f ^′, p = w ₃ f ^′, $q={p}_3{gF}_{LT}^3$, $s=-{p}_3{g^{\prime } F}_T^3$, $t={p}_3{gF}_{TT}^3+{F}_{TT}^4$, u = L ₃, v =  − (L − L ₄).

Using the Cramer rule to solve (11.B1), we get:

$$ \begin{array}{l}{dL}_1/{ds}_1=-{F}_{KL}^1r\Big\{\left({p}_3{gF}_{TT}^3+{F}_{TT}^4\right)\left[{w}_2+{L}_2{p}_2{F}_{LL}^2-{w}_4\right]\\ {}+{p}_3{gF}_{TT}^3{F}_{LL}^4\left(L-{L}_4\right)-{F}_{TL}^4{p}_3{gL}_3{F}_{LT}^3\Big\}/{\Delta}_1<0\end{array} $$

$$ {dL}_2/{ds}_1\left(<,=,>\right)0 $$

$$ {dL}_4/{ds}_1\left(<,=,>\right)0 $$

$$ {dK}_3/{ds}_1=- ar\left( dt- gt+ fqu+{f}^2v- etv\right)/{\Delta}_1>0 $$

$$ {dK}_1/{ds}_1=-{dK}_3/{ds}_1<0 $$

$$ {dL}_3/{ds}_1={f^{\prime } dK}_3/{ds}_1>0 $$

$$ {dT}_3/{ds}_1\left(<,=,>\right)0 $$

$$ {dw}_3/{ds}_1\left(<,=,>\right)0 $$

$$ {dw}_4/{ds}_1\left(<,=,>\right)0 $$

$$ dr/{ds}_1={p}_1{F}_{KL}^1{dL}_1/{ds}_1+{p}_1{F}_{KK}^1{dK}_1/{ds}_1=0 $$

$$ d\tau /{ds}_1={F}_{TL}^4{dL}_4/{ds}_1+{F}_{TT}^4{dT}_4/{ds}_1\left(<,=,>\right)0 $$

$$ {dL}_1/{ds}_2={w}_3 fhsu/{\Delta}_1<0 $$

$$ {dL}_2/{ds}_2={w}_3 u\left( akt- bht- ams- fhs+ afns\right)/{\Delta}_1\left(<,=,>\right)0 $$

$$ {dL}_4/{ds}_2={w}_3 u\left( bht- akt+ ams\right)/{\Delta}_1\left(<,=,>\right)0 $$

$$ {dK}_3/{ds}_2=-{w}_3 afsu/{\Delta}_1>0 $$

$$ {dK}_1/{ds}_2=-{dK}_3/{ds}_2<0 $$

$$ {dL}_3/{ds}_2={f^{\prime } dK}_3/{ds}_2>0 $$

$$ {dT}_3/{ds}_2={w}_3 fu\left( ak- bh\right)/{\Delta}_1>0 $$

$$ {dw}_3/{ds}_2\left(<,=,>\right)0 $$

$$ {dw}_4/{ds}_2=-{w}_3 u\left({bf}^2 h- beht-{af}^2 k+ aekt- aems\right)/{\Delta}_1\left(<,=,>\right)0 $$

$$ dr/{ds}_2={p}_1{F}_{KL}^1{dL}_1/{ds}_2+{p}_1{F}_{KK}^1{dK}_1/{ds}_2=0 $$

$$ d\tau /{ds}_2={F}_{TL}^4{dL}_4/{ds}_2+{F}_{TT}^4{dT}_4/{ds}_2\left(<,=,>\right)0 $$

$$ {dL}_1/{ds}_3=-\tau hs\left( g- d+ ev\right)/{\Delta}_1<0 $$

$$ {dL}_2/{ds}_3\left(<,=,>\right)0 $$

$$ {dL}_4/{ds}_3\left(<,=,>\right)0 $$

$$ {dK}_3/{ds}_3= as\tau \left( g- d+ ev\right)/{\Delta}_1>0 $$

$$ {dK}_1/{ds}_3=-{dK}_3/{ds}_3<0 $$

$$ {dL}_3/{ds}_3={f^{\prime } dK}_3/{ds}_3>0 $$

$$ {dT}_3/{ds}_3=\tau \left( bh- ak\right)\left( g- d+ ev\right)/{\Delta}_1>0 $$

$$ {dw}_3/{ds}_3=\tau \left( bhq- akq+ ajs\right)\left( g- d+ ev\right)/{\Delta}_1\left(<,=,>\right)0 $$

$$ {dw}_4/{ds}_3\left(<,=,>\right)0 $$

$$ dr/{ds}_3={p}_1{F}_{KL}^1{dL}_1/{ds}_3+{p}_1{F}_{KK}^1{dK}_1/{ds}_3=0 $$

$$ d\tau /{ds}_3={F}_{TL}^4{dL}_4/{ds}_3+{F}_{TT}^4{dT}_4/{ds}_3\left(<,=,>\right)0 $$

1.3 Appendix C

When the labor endowment increases, the total differential of (11.5), (11.6), (11.7), (11.8), (11.9), (11.10), (11.11), (11.12), (11.13), (11.14), (11.15), (11.16), and (11.17′) can be written as the following (11.21):

$$ \begin{array}{ll}\hfill & \left[\begin{array}{ccccccc}\hfill {F}_{LL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill -{F}_{LK}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {p}_3\left({g^{\prime }F}_L^3+{gF}_{LL}^3{f}^{\prime}\right)\hfill & \hfill {p}_3{gF}_{LT}^3\hfill & \hfill -1\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill {F}_{LL}^4\hfill & \hfill 0\hfill & \hfill -{F}_{LT}^4\hfill & \hfill 0\hfill & \hfill -1\hfill \\ {}\hfill {p}_1{F}_{KL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill -\left[{p}_1{F}_{KK}^1+{p}_3\left({g^{{\prime\prime} }F}^3+{g^{\prime }F}_L^3{f}^{\prime}\right)\right]\hfill & \hfill -{p}_3{g^{\prime }F}_T^3\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill -{F}_{TL}^4\hfill & \hfill {p}_3\left({g^{\prime }F}_T^3+{gF}_{TL}^3{f}^{\prime}\right)\hfill & \hfill {p}_3{gF}_{TT}^3+{F}_{TT}^4\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 1\hfill & \hfill 1\hfill & \hfill 1\hfill & \hfill {f}^{\prime}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill \overline{w_1}\hfill & \hfill {w}_2+{L}_2{p}_2{F}_{LL}^2\hfill & \hfill {w}_4\hfill & \hfill {w}_3{f}^{\prime}\hfill & \hfill 0\hfill & \hfill {L}_3\hfill & \hfill -\left(L-{L}_4\right)\hfill \end{array}\right]\\ {}& \times \left[\begin{array}{c}\hfill {dL}_1\hfill \\ {}\hfill {dL}_2\hfill \\ {}\hfill {dL}_4\hfill \\ {}\hfill {dK}_3\hfill \\ {}\hfill {dT}_3\hfill \\ {}\hfill {dw}_3\hfill \\ {}\hfill {dw}_4\hfill \end{array}\right]=\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill dL\hfill \\ {}\hfill {w}_4 dL\hfill \end{array}\right]\hfill \end{array} $$

(11.C1)

Apparently, the value of the coefficient matrix (11.C1) is Δ₁.

When the capital endowment increases, the total differential of (11.5), (11.6), (11.7), (11.8), (11.9), (11.10), (11.11), (11.12), (11.13), (11.14), (11.15), (11.16), and (11.17′) is (11.22) as follows:

$$ \begin{array}{ll}\hfill & \left[\begin{array}{cccccccc}\hfill {F}_{LL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill -{F}_{LK}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {p}_3\left({g^{\prime }F}_L^3+{gF}_{LL}^3{f}^{\prime}\right)\hfill & \hfill {p}_3{gF}_{LT}^3\hfill & \hfill -1\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill {F}_{LL}^4\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill -{F}_{LT}^4\hfill & \hfill 0\hfill & \hfill -1\hfill \\ {}\hfill {p}_1{F}_{KL}^1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {p}_1{F}_{KK}^1\hfill & \hfill -{p}_3\left({g^{{\prime\prime} }F}^3+{g^{\prime }F}_L^3{f}^{\prime}\right)\hfill & \hfill -{p}_3{g^{\prime }F}_T^3\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill -{F}_{TL}^4\hfill & \hfill 0\hfill & \hfill {p}_3\left({g^{\prime }F}_T^3+{gF}_{TL}^3{f}^{\prime}\right)\hfill & \hfill {p}_3{gF}_{TT}^3+{F}_{TT}^4\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 1\hfill & \hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill {f}^{\prime}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill \overline{w_1}\hfill & \hfill {w}_2+{L}_2{p}_2{F}_{LL}^2\hfill & \hfill {w}_4\hfill & \hfill 0\hfill & \hfill {w}_3{f}^{\prime}\hfill & \hfill 0\hfill & \hfill {L}_3\hfill & \hfill -\left(L-{L}_4\right)\hfill \end{array}\right]\\ {}& \times \left[\begin{array}{c}\hfill {dL}_1\hfill \\ {}\hfill {dL}_2\hfill \\ {}\hfill {dL}_4\hfill \\ {}\hfill {dK}_1\hfill \\ {}\hfill {dK}_3\hfill \\ {}\hfill {dT}_3\hfill \\ {}\hfill {dw}_3\hfill \\ {}\hfill {dw}_4\hfill \end{array}\right]=\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill dK\hfill \\ {}\hfill 0\hfill \end{array}\right]\hfill \end{array} $$

(11.C2)

Assume that the value of the matrix (11.C2) is Δ₂, then Δ₂ =  − Δ₁.

Using the Cramer rule to solve (11.C1) and (11.C2), we get:

$$ {dL}_1/ dL= fhs\left( d- g\right)/{\Delta}_1>0 $$

$$ {dL}_2/ dL\left(<,=,>\right)0 $$

$$ {dL}_4/ dL=-\left( d- g\right)\left( akt- bht- ams\right)/{\Delta}_1\left(<,=,>\right)0 $$

$$ {dK}_3/ dL=- afs\left( d- g\right)/{\Delta}_1<0 $$

$$ {dK}_1/ dL=-{dK}_3/ dL>0 $$

$$ {dL}_3/ dL={f^{\prime } dK}_3/ dL<0 $$

$$ {dT}_3/ dL=- f\left( bh- ak\right)\left( d- g\right)/{\Delta}_1<0 $$

$$ {dw}_3/ dL=- f\left( bhq- akq+ ajs\right)\left( d- g\right)/{\Delta}_1\left(<,=,>\right)0 $$

$$ \begin{array}{l}{dw}_4/ dL=- f\left( d- g\right)\\ {}\left({bf}^2 h- beht-{af}^2 k+ aekt- aems\right)/{\Delta}_1\left(<,=,>\right)0\end{array} $$

$$ dr/ dL={p}_1{F}_{KL}^1{dL}_1/ dL+{p}_1{F}_{KK}^1{dK}_1/ dL=0 $$

$$ d\tau / dL={F}_{TL}^4{dL}_4/ dL+{F}_{TT}^4{dT}_4/ dL\left(<,=,>\right)0 $$

$$ {dL}_1/ dK\left(<,=,>\right)0 $$

$$ {dL}_2/ dK\left(<,=,>\right)0 $$

$$ {dL}_4/ dK=- ht\left( d- c\right)\left( z- s\right)/{\Delta}_2<0 $$

$$ {dK}_1/ dK\left(<,=,>\right)0 $$

$$ {dK}_3/ dK=\left( cfhs- dfhs\right)/{\Delta}_2>0 $$

$$ {dL}_3/ dK={f^{\prime } dK}_3/ dK>0 $$

$$ {dT}_3/ dK=\left( dfhz- cfhz\right)/{\Delta}_2>0 $$

$$ {dw}_3/ dK= cfh\left( js- zq\right)/{\Delta}_2>0 $$

$$ {dw}_4/ dK\left(<,=,>\right)0 $$

$$ dr/ dK={p}_1{F}_{KL}^1{dL}_1/ dK+{p}_1{F}_{KK}^1{dK}_1/ dK=0 $$

$$ d\tau / dK={F}_{TL}^4{dL}_4/ dK+{F}_{TT}^4{dT}_4/ dK\left(<,=,>\right)0 $$

In the above, the letters a, b, c, d, e, f, g, h, j, k, m, n, p, q, s, t, u, and v have the same meaning as in Appendix B. Besides, $y={p}_1{F}_{KK}^1$, $z=-{p}_3\left({g}^{{\prime\prime} }{F}^3+{g}^{\prime }{F}_L^3{f}^{\prime}\right)$.