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FDI and Gender Wage Inequality

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Foreign Direct Investment in Developing Countries

Abstract

In most countries, particularly the developing ones, gender differentials in labour markets are manifested in terms of a gap in relative wages among men and women workers. There are a few empirical studies that have examined the impact of FDI on the gender-based wage inequality, findings of which are mixed in nature. There may be two contrary effects of FDI on the gender wage differentials: on one hand, the gap may widen due to weakened bargaining power of women crowded in the MNCs, while on the other hand, the MNCs may reward the higher education levels of female workers, lowering the gender wage gap. While it is widely argued that foreign capital propels an economy towards the trajectory of growth, the objectives of an egalitarian welfare-maximizing state are fulfilled only if economic growth and welfare are accompanied by reduction in gender wage inequality. The analysis of this chapter shows that although FDI in countries with female labour-intensive export-oriented sectors may accentuate gender wage inequality, it may also raise the welfare of the economy. These results point towards a trade-off between gender wage inequality and welfare of the economy.

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Notes

  1. 1.

    Nonetheless, there exists a vast literature on the correlation between trade liberalization and gender wage gap.

  2. 2.

    The model in this chapter is based on Mukhopadhyay and Chaudhuri (2013).

  3. 3.

    Some examples of industries intensive in female labour are garments, tea, tobacco and food processing.

  4. 4.

    Here K 1 requires less skill than K 2 and, therefore, can fairly be assumed to be used simultaneously in the agricultural and export manufacturing sectors.

  5. 5.

    In reality, a developing economy is plagued by the existence of involuntary unemployment of both male and female labour due to the presence of factor market distortions. Since our focus is on gender wage inequality and not on unemployment, we have ignored factor market distortions and unemployment of labour. The production structure of our economy is a three-sector analogue (or a 3 × 4 specific factor extension) of the classic 2 × 3 specific factor full-employment general equilibrium model as developed by Jones (1971). As the return to each mobile factor is the same in the two sectors in which it is employed, there occurs full employment of all the mobile factors in the different sectors of the economy.

  6. 6.

    The male female wage gap exists in agriculture as well. For example, in India, the wage rates paid to women workers in the agricultural sector are at least 20–30 % lower than those paid to men for the same activity. In non-agricultural activities, the difference is even more pronounced, with women being paid less than half the wages given to their male counterparts (Ramachandran 2006).

  7. 7.

    Although this is a simplifying assumption, it is not completely without any basis. Agriculture requires inputs like fertilizers, pesticides and weedicides, which are to be used in recommended doses. Now if capital of type 1 is used to purchase those inputs, the capital (of type 1)–output ratio, a K1, becomes constant technologically. However, male labour and female labour are substitutes and the production function displays the property of constant returns to scale in these two inputs. However, even if the capital (of type 1)–output ratio is not given technologically, the results still hold under alternative sufficient conditions incorporating the partial elasticities of substitution between capital of type 1 and the two types of labour used in sector 1.

  8. 8.

    It may be noted that in accordance with the ‘consumption efficiency hypothesis’ as outlined earlier, nutritional efficiencies of the workers actually depend on quantities of commodities consumed by them, which is represented by their wages. However, quantities of consumption must depend on commodity prices, which in turn suggest that commodity prices should figure in the efficiency functions. But since we consider a small open economy where the prices of all traded commodities are internationally given, the inclusion or exclusion of commodity prices into the efficiency functions does not, in fact, make any difference.

  9. 9.

    The model implicitly considers both the cases of male/female households and extended households, which are quite common in developing countries. In case of the latter, empirical results show that household consumption is strongly correlated with their own income, even after extended households’ pooled income is controlled for (Altonji et al. 1992; Park 2001). However, we do not consider the single-parent household case.

  10. 10.

    It is empirically observed that men also contribute to the family although their contribution is far less than that of the women. There can be two extreme cases: (1) men do not contribute at all to family income, and (2) they contribute their whole income to family income. For the sake of analytical simplicity, we have considered the first extreme case. The algebra of the model becomes extremely complicated if we consider the intermediate case. It may, however, be checked intuitively that even if we assume that men do contribute to family income but at a significantly lower rate than women, the qualitative results of the model are retained.

  11. 11.

    Here, P *3  = P 3(1 + t) is the tariff-inclusive domestic price of X 3.

  12. 12.

    The comparative static results have been derived in Appendix 6.1.

  13. 13.

    Labour productivity improvements (via increased social spending) result only in declines in wages since the country is a price taker.

  14. 14.

    A Stolper–Samuelson effect is followed by a Rybczynski-type effect if the production functions are of variable-coefficient type.

  15. 15.

    See Appendix 6.2 for mathematical derivations of welfare changes.

  16. 16.

    The liberalized investment policy in the form of an FDI into the export sector(s) may be an instrument that can lead to export-led growth and raise the output of the export sector. On the other hand, contrary to the famous Brecher and Alejandro (1977) proposition that suggests an inflow of foreign capital into the import-competing sector under certain conditions might lead to import substitution and lower the country’s welfare, there are works like Marjit and Beladi (1996), Marjit et al. (1997), Chaudhuri (2005, 2007) and Chaudhuri et al. (2006) which have shown that welfare may improve also in this case. In the present model, both export-promotion and import-substitution policies through FDI may improve social welfare.

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Appendices

Appendices

6.1.1 Appendix 6.1: Effects of Different Policies on Gender Wage Inequality

Total differentiation of (6.1), (6.2) and (6.3) and use of envelope conditions yields

$$ {\theta}_{M1}{\widehat{W}}_{\mathrm{M}}+{\theta}_{F1}{\widehat{W}}_{\mathrm{F}}+{\theta}_{K1}\widehat{R}=0 $$
(6.A.1)
$$ {\theta}_{F2}{\widehat{W}}_{\mathrm{F}}+{\theta}_{K2}\widehat{R}=0 $$
(6.A.2)
$$ {\theta}_{M3}{\widehat{W}}_{\mathrm{M}}+{\theta}_{K3}\widehat{r}=0 $$
(6.A.3)

It may be noted that producers in each industry choose techniques of production so as to minimize unit costs. This leads to the condition that the distributive-share weighted average of changes in input–output coefficients along the unit isoquant in each industry must vanish near the cost-minimization point. This states that an isocost line is tangent to the unit isoquant. In mathematical terms, cost-minimization conditions for the two industries may be written as \( {\theta}_{L1}{\widehat{a}}_{L1}+{\theta}_{K1}{\widehat{a}}_{K1}=0 \) and \( {\theta}_{L2}{\widehat{a}}_{L2}+{\theta}_{K2}{\widehat{a}}_{K2}=0 \). These are called the envelope conditions. See Caves et al. (1990) and/or Chaudhuri and Mukhopadhyay (2009).

Solving (6.A.1), (6.A.2) and (6.A.3) by Cramer’s rule, we get

$$ {\widehat{W}}_{\mathrm{M}}=-\left(\frac{1}{\left|\theta \right|}\right)\widehat{r}{\theta}_{K3}\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right) $$
(6.A.4)
$$ {\widehat{W}}_{\mathrm{F}}=\left(\frac{1}{\left|\theta \right|}\right)\widehat{r}{\theta}_{M1}{\theta}_{K2}{\theta}_{K3} $$
(6.A.5)
$$ \widehat{R}=-\left(\frac{1}{\left|\theta \right|}\right)\widehat{r}{\theta}_{M1}{\theta}_{F2}{\theta}_{K3} $$
(6.A.6)

where |θ| = θ M3(θ F1 θ K2 − θ K1 θ F2) < 0 since it is assumed that sector 2 is more female labour-intensive than sector 1.

Total differentiation of (6.5), use of (6.A.4) and rearrangement give

$$ {\widehat{X}}_3={\widehat{K}}_2+\left(\frac{1}{\left|\theta \right|}\right)\widehat{r}\left\{{S}_{K\mathrm{M}}^3\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\right\} $$
(6.A.7)

Here, S i jk is the degree of substitution between factors in the ith sector, i = 1, 2, 3, for example, in sector 1, S 1 FF  = (∂a F1/∂W F)(W F/a F1), \( {S}_{{}_{F M}}^1=\left(\partial {a}_{F1}/\partial {W}_{\mathrm{M}}\right) \left({W}_{\mathrm{M}}/{a}_{F1}\right) \). S i jk  > 0 for j ≠ k and S i jj  < 0. It should be noted that as the production functions are homogeneous of degree one, the factor coefficients, a ji s, are homogeneous of degree zero in the factor prices. Hence, the sum of elasticities for any factor of production in any sector with respect to factor prices must be zero. For example, in sector 1, with respect to female labour–output coefficient, we have (S 1 FF  + S 1 FM  + S 1 FK ) = 0 and so on. For analytical simplicity, it is assumed that a K1 is constant, ruling out any substitution of capital with male and female labour in sector 1. Therefore, S 1 KM  = S 1 KF  = 0.

By totally differentiating (6.6) and (6.7), we get respectively

$$ H\widehat{H}={H}_1 E\widehat{E}+{H}_2\left({W}_{\mathrm{M}}{\widehat{W}}_{\mathrm{M}}+{W}_{\mathrm{F}}{\widehat{W}}_{\mathrm{F}}\right) $$
(6.A.8)
$$ h\widehat{h}={h}_1 E\widehat{E}+{h}_2{W}_{\mathrm{F}}{\widehat{W}}_{\mathrm{F}} $$
(6.A.9)

After substituting (X 3 = K 2/a K3) from Eq. (6.5) in Eq. (6.8) and totally differentiating Eqs. (6.4), (6.8) and (6.9), one respectively gets

$$ {\lambda}_{K1}{\widehat{X}}_1+{\lambda}_{K2}{\widehat{X}}_2+\left(\frac{1}{\left|\theta \right|}\right) A{\theta}_{K3}\widehat{r}={\widehat{K}}_1 $$
(6.A.10)
$$ {\lambda}_{M1}{\widehat{X}}_1+\left(\frac{1}{\left|\theta \right|}\right) B\widehat{r}={H}_1 E\widehat{E} $$
(6.A.11)
$$ {\lambda}_{F1}{\widehat{X}}_1+{\lambda}_{F2}{\widehat{X}}_2+\left(\frac{1}{\left|\theta \right|}\right){\theta}_{K3} C\widehat{r}={h}_1 E\widehat{E} $$
(6.A.12)

Solving (6.A.10), (6.A.11) and (6.A.12) by Cramer’s rule, we get

$$ \begin{array}{ccc}\widehat{r}=&\left(\dfrac{{\widehat{K}}_1}{\Delta}\right){\lambda}_{M1}{\lambda}_{F2}+\left(\dfrac{{\widehat{K}}_2}{\Delta}\right){\lambda}_{M3}\left({\lambda}_{K1}{\lambda}_{F2}-{\lambda}_{K2}{\lambda}_{F1}\right)\\ & + \left(\dfrac{E\widehat{E}}{\Delta}\right)\left\{{H}_1\left({\lambda}_{F1}{\lambda}_{K2}-{\lambda}_{K1}{\lambda}_{F2}\right) - {h}_1\alpha {\lambda}_{M1}{\lambda}_{K2}\right\}\end{array} $$
(6.A.13)

where

$$ \left.\begin{array}{l} A=-{\theta}_{M1}{\theta}_{F2}{\lambda}_{K2}{S}_{K K}^2>0\\ {}\kern7.4em \left(-\right)\\ {} B=\left[\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\left\{{\lambda}_{M3}\left({S}_{K M}^3+{S}_{M K}^3\right)+{\theta}_{K3}\left({H}_2{W}_{\mathrm{M}}-{\lambda}_{M1}{S}_{M M}^1\right)\right\}\right.\\ {}\kern5.55em \left(-\right)\kern7.7em \left(+\right)\kern10.7em \left(-\right)\\ \kern22pt+{\theta}_{M1}{\theta}_{K2}{\theta}_{K3}\left({\lambda}_{M1}{S}_{M F}^1-{H}_2{W}_{\mathrm{F}}\right)\\ {}\kern9.35em \left(+\right)\kern2em \left(+\right)\\ {} C=\left[{\lambda}_{F1}{S}_{F M}^1\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}+{\theta}_{M1}{\theta}_{K2}\right)+{\theta}_{M1}{\theta}_{K2}{h}_2{W}_{\mathrm{F}}+{\lambda}_{F2}{S}_{F K}^2{\theta}_{M1}\right]\end{array}\right\} $$
(6.A.14)

and

$${\left.\begin{array}{l}\Delta =\left(\frac{1}{\left|\theta \right|}\right)\left[{\lambda}_{M1}{\theta}_{K3}\left\{{\lambda}_{K2}{\theta}_{M1}{\theta}_{K2}{h}_2{W}_{\mathrm{F}}\right.\right.\\ \quad \left(-\right)\\ \qquad\left.+{\lambda}_{K2}{\lambda}_{F2}{\theta}_{M1}\left({S}_{F K}^2+{S}_{K F}^2\right)-\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}+{\theta}_{M1}{\theta}_{K2}\right){\lambda}_{K2}{\lambda}_{F1}{S}_{F F}^1\right\}\\ \qquad\qquad \left(+\right) \left(-\right)\\ \qquad+\left({\lambda}_{K2}{\lambda}_{F1}-{\lambda}_{K1}{\lambda}_{F2}\right)\left[{\lambda}_{M1}{\theta}_{K3}{\theta}_{M1}{S}_{M M}^1{\theta}_{F2}+{\theta}_{M1}{\theta}_{K3}\left({\lambda}_{M1}{S}_{M F}^1-{H}_2{W}_{\mathrm{F}}{\theta}_{K2}\right)\right.\\ \qquad\qquad \left(-\right)\left(-\right)\\ \qquad\left.\left.+\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\left\{{\lambda}_{M3}\left({S}_{K M}^3+{S}_{M K}^3\right)+{\theta}_{K3}\left({H}_2{W}_{\mathrm{M}}-{\lambda}_{M1}{S}_{M M}^1\right)\right\}\right]\right]\\ \qquad\qquad \left(-\right) \left(+\right)\left(-\right)\end{array}\right\}}$$
(6.A.15)

Since it is assumed that the male labour intensity in sector 1 is not at least less than the female labour intensity in sector 2 with respect to capital, i.e. θ M1 θ K2 ≥ θ K1 θ F2, from (6.A.15), it follows that

$$ \Delta <0\kern1em \mathrm{if}\kern0.5em {\lambda}_{M1}{S}_{M F}^1\le {H}_2{W}_{\mathrm{F}}{\theta}_{K2} $$
(6.A.15.1)

Now, if (6.A.15.1) holds, then from (6.A.14) we have A > 0, B < 0 and C > 0.

Substituting (6.A.13) in (6.A.4) and (6.A.5) yields

$$ {{\begin{array}{l}{\widehat{W}}_{\mathrm{M}}=-\left[\left(\dfrac{{\widehat{K}}_1}{\left(\left|\theta \right|\Delta \right)}\right){\theta}_{K3}{\lambda}_{M1}{\lambda}_{F2}\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\right]\\ \qquad{}\kern4em \left(-\right)\kern7.1em \left(-\right)\\ \qquad\qquad-\left[\left(\dfrac{{\widehat{K}}_2}{\left(\left|\theta \right|\Delta \right)}\right){\theta}_{K3}{\lambda}_{M3}\left({\lambda}_{K1}{\lambda}_{F2}-{\lambda}_{K2}{\lambda}_{F1}\right)\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\right]\\ \qquad\qquad{}\kern3em \left(-\right)\kern8.2em \left(+\right)\kern6.35em \left(-\right)\\ \qquad\qquad{}-\left[\left(\dfrac{E\widehat{E}}{\left|\theta \right|\Delta}\right){\theta}_{K3}\left\{{H}_1\left({\lambda}_{F1}{\lambda}_{K2}-{\lambda}_{K1}{\lambda}_{F2}\right)-{h}_1\alpha {\lambda}_{M1}{\lambda}_{K2}\right\}\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\right]\\ \qquad\qquad{}\kern2.7em \left(-\right)\kern8.2em \left(-\right)\kern13em \left(-\right)\end{array}}} $$
(6.A.16)

and

$$ {{\begin{array}{c}{\widehat{W}}_{\mathrm{F}}=\left[\left(\dfrac{{\widehat{K}}_1}{\left(\left|\theta \right|\Delta \right)}\right){\theta}_{K3}{\theta}_{M1}{\theta}_{K2}{\lambda}_{M1}{\lambda}_{F2}\right]+\left[\left(\dfrac{{\widehat{K}}_2}{\left(\left|\theta \right|\Delta \right)}\right){\theta}_{K3}{\theta}_{M1}{\theta}_{K2}{\lambda}_{M3}\left({\lambda}_{K1}{\lambda}_{F2}-{\lambda}_{K2}{\lambda}_{F1}\right)\right]\\ \quad\, \left(-\right)\kern13.5em \left(-\right)\kern11em \left(+\right)\\ {}\kern-4em+\left[\left(\dfrac{E\widehat{E}}{\left(\left|\theta \right|\Delta \right)}\right){\theta}_{K3}{\theta}_{M1}{\theta}_{K2}\left\{{H}_1\left({\lambda}_{F1}{\lambda}_{K2}-{\lambda}_{K1}{\lambda}_{F2}\right)-{h}_1\alpha {\lambda}_{M1}{\lambda}_{K2}\right\}\right]\\ \kern-11em \left(-\right)\kern11.5em \left(-\right) \end{array}}} $$
(6.A.17)

If (6.A.15.1) holds, the effects of changes in different parameters on male and female wages can be obtained as follows:

$$ \left.\begin{array}{r} \left(\mathrm{i}\right)\;{\widehat{W}}_{\mathrm{M}}>0\;\mathrm{and}\;{\widehat{W}}_{\mathrm{F}}>0\;\mathrm{when}\;{\widehat{K}}_1>0\hfill \\[6pt] \left(\mathrm{i}\mathrm{i}\right)\;{\widehat{W}}_{\mathrm{M}}>0\;\mathrm{and}\;{\widehat{W}}_{\mathrm{F}}>0\;\mathrm{when}\;{\widehat{K}}_2>0\hfill \\[6pt] \left(\mathrm{i}\mathrm{i}\mathrm{i}\right)\;{\widehat{W}}_{\mathrm{M}}<0\;\mathrm{and}\;{\widehat{W}}_{\mathrm{F}}<0\;\mathrm{when}\;\widehat{E}>0\hfill \end{array}\right\} $$
(6.A.18)

Total differentiation of Eq. (6.15) yields

$$ {W}_{\mathrm{I}}{\widehat{W}}_{\mathrm{I}}={W}_{\mathrm{M}} H\left(\widehat{H}+{\widehat{W}}_{\mathrm{M}}\right)-{W}_{\mathrm{F}} h\left(\widehat{h}+{\widehat{W}}_{\mathrm{F}}\right) $$

Use of Eqs. (6.A.8) and (6.A.9) yields

$$ {{\begin{array}{l}{W}_{\mathrm{I}}{\widehat{W}}_{\mathrm{I}}={W}_{\mathrm{M}}\left\{{H}_1 E\widehat{E}+{H}_2\left({W}_{\mathrm{M}}{\widehat{W}}_{\mathrm{M}}+{W}_{\mathrm{F}}{\widehat{W}}_{\mathrm{F}}\right)\right\}+{W}_{\mathrm{M}} H{\widehat{W}}_{\mathrm{M}}\\ \phantom{{W}_{\mathrm{I}}{\widehat{W}}_{\mathrm{I}}=} -{W}_{\mathrm{F}}\left({h}_1 E\widehat{E}+{h}_2{W}_{\mathrm{F}}{\widehat{W}}_{\mathrm{F}}\right)-{W}_{\mathrm{F}} h{\widehat{W}}_{\mathrm{F}}\\ \phantom{{W}_{\mathrm{I}}{\widehat{W}}_{\mathrm{I}}}= E\widehat{E}\left({W}_{\mathrm{M}}{H}_1-{W}_{\mathrm{F}}{h}_1\right)+{W}_{\mathrm{M}}{\widehat{W}}_{\mathrm{M}}\left({H}_2{W}_{\mathrm{M}}+ H\right)+{W}_{\mathrm{F}}{\widehat{W}}_{\mathrm{F}}\left({H}_2{W}_{\mathrm{M}}-{h}_2{W}_{\mathrm{F}}- h\right)\end{array}}} $$
(6.A.19)

Now the effects of \( {\widehat{K}}_1>0 \), \( {\widehat{K}}_2>0 \) and \( \widehat{E}>0 \) on \( {\widehat{W}}_{\mathrm{I}} \) are obtained by substitution of (6.A.4) and (6.A.5) in (6.A.19) and expressed in Eqs. (6.16), (6.18) and (6.19), respectively.

6.1.2 Appendix 6.2: Effects of Different Policies on Welfare

Differentiating (6.10) and (6.12.1), one gets

$$ \begin{array}{ccc}\left(\frac{dU}{U_1}\right)&= d{D}_1+{P}_2 d{D}_2+{P}_3^{*} d{D}_3= d{X}_1+{P}_2 d{X}_2+{P}_3^{*} d{X}_3\\ & \quad - Rd{K}_{\mathrm{F}1} - rd{K}_{\mathrm{F}2}- dE \end{array} $$
(6.A.20)

Differentiation of (6.14) gives

$$ dY= d{X}_1+{P}_2 d{X}_2+{P}_3^{*} d{X}_3+ t{P}_3 dI+{P}_3 Idt- Rd{K}_{\mathrm{F}1}- rd{K}_{\mathrm{F}2}- dE $$
(6.A.21)

Note that the production functions in the two sectors are given by X 1 = Q 1(M 1, F 1,K 11 ), X 2 = Q 2(F 2, K 12 ) and X 3 = Q 3(M 3, K 23 ). The full-employment conditions for the four factors are given by M 1 + M 3 = W M H(.); F 1 + F 2 = W F h(.); K 11  + K 12  = K D1 + K F1 = K 1 and K 23  = K D2 + K F2 = K 2 where K i j is the employment of capital of type i in the jth sector. Now, dM 1 + dM 3 = W M{H 1 dE + H 2(dW M + dW F)}; dK 11  + dK 12  = dK F1; dK 23  = dK F2 and dF 1 + dF 2 = W F(h 1 dE + h 2 dW F).

Also P i Q i j is the value of the marginal product of the jth factor in the ith sector, which is equal to the factor price.

Hence, by differentiating production functions, from Eq. (6.A.21), we get

$$ \begin{array}{ccc} d Y&={Q}_F^1 d{F}_1+{Q}_K^1 d{K}_1^1+{Q}_M^1 d{M}_1+{P}_2\left({Q}_F^2 d{F}_2+{Q}_K^2 d{K}_2^1\right)\\ & \quad+{P}_3^{*}\left({Q}_M^3 d{M}_3+{Q}_K^3 d{K}_3^2\right)+ t{P}_3 d I - Rd{K}_{F1}- rd{K}_{F2}- dE\\ &=\left({W}_{\mathrm{F}} d{F}_1+ Rd{K}_1^1+{W}_{\mathrm{M}} d{M}_1\right)+\left({W}_{\mathrm{F}} d{F}_2+ Rd{K}_2^1\right)\\ & \quad+\left({W}_{\mathrm{M}} d{M}_3+ rd{K}_3^2\right) + t{P}_3 d I- Rd{K}_{F1}- rd{K}_{F2}- dE\\ & ={W}_{\mathrm{F}} F\left({h}_1 d E+{h}_2 d{W}_{\mathrm{F}}\right)+{W}_{\mathrm{M}} M\left\{{H}_1 d E+{H}_2\left( d{W}_{\mathrm{M}}+ d{W}_{\mathrm{F}}\right)\right\}+ rd{K}_{F2}\\ & \quad + Rd{K}_{F1} + t{P}_3 d I- Rd{K}_{F1}- rd{K}_{F2}- dE\\ & = d{W}_{\mathrm{F}}\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)+ d{W}_{\mathrm{M}}{W}_{\mathrm{M}} M{H}_2+ d E\left({W}_{\mathrm{F}} F{h}_1\right. \\ & \quad \left. +{W}_{\mathrm{M}} M{H}_1-1\right)+ t{P}_3 d I \end{array} $$
(6.A.22)

Differentiating (6.13) and using (6.A.22), we get

$$ \begin{array}{l}dI=\left(\dfrac{\partial {D}_3}{\partial {P}_3^{*}}\right) d{P}_3^{*}+\left(\dfrac{\partial {D}_3}{\partial Y}\right)\left[ d{W}_{\mathrm{F}}\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)+ d{W}_{\mathrm{M}}{W}_{\mathrm{M}} M{H}_2\right. \\ \ \ \quad\quad \left.+ d E\left({W}_{\mathrm{F}} F{h}_1+{W}_{\mathrm{M}} M{H}_1-1\right)+ t{P}_3 dI\right]- d{X}_3\end{array} $$

or

$$ \begin{array}{l} dI\left[1- t{P}_3\left(\dfrac{\partial {D}_3}{\partial Y}\right)\right]=\left(\dfrac{\partial {D}_3}{\partial {P}_3^{*}}\right) d{P}_3^{*}+\left(\frac{m}{P_3^{*}}\right)\left[ d{W}_{\mathrm{F}}\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)\right. \\ \ \ \qquad\qquad\qquad\qquad\qquad \left. + d{W}_{\mathrm{M}}{W}_{\mathrm{M}} M{H}_2 + d E\left({W}_{\mathrm{F}} F{h}_1+{W}_{\mathrm{M}} M{H}_1-1\right)\right. \\ \ \ \qquad\qquad\qquad\qquad\qquad \left.+ t{P}_3 dI\right]- d{X}_3\end{array} $$

or

$$ \begin{array}{ccc} dI &= V\left[ Z{P}_3 dt+\left(\frac{m}{P_3^{*}}\right)\left\{ d{W}_{\mathrm{F}}\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)+ d{W}_{\mathrm{M}}{W}_{\mathrm{M}} M{H}_2\right.\right.\\ & \quad {}\left.\left.+ d E\left({W}_{\mathrm{F}} F{h}_1+{W}_{\mathrm{M}} M{H}_1-1\right)+ t{P}_3 dI\right\}- d{X}_3\right]\end{array} $$
(6.A.23)

where m = P *3 (∂D 3/∂Y) is the marginal propensity to consume commodity 3; V=[(1+t)/{(1+t(1−m)}]={1+(tmV/(1+t)}>0; and Z = [(∂D 3/∂P 3*)+ D 3(∂D 3/∂Y)] < 0 is the Slutsky’s pure substitution term.

Using (6.A.20) and (6.A.23) and arranging terms, one gets

$$ \begin{array}{ccc} \left(\dfrac{dU}{U_1}\right) &= V\left[ d{W}_{\mathrm{F}}\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)+ d{W}_{\mathrm{M}}{W}_{\mathrm{M}} M{H}_2\right. \\ & \quad \left. + d E\left({W}_{\mathrm{F}} F{h}_1+{W}_{\mathrm{M}} M{H}_1-1\right)\right]- t{P}_3 Vd{X}_3\end{array} $$
(6.A.24)

Now substituting (6.A.13) in (6.A.7), one gets

$$ {{\begin{array}{l}{\widehat{X}}_3={\widehat{K}}_1\left[\left(\dfrac{S_{K M}^3}{\Delta \left|\theta \right|}\right)\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right){\lambda}_{M1}{\lambda}_{F2}\right]\\ \quad\quad{}\kern3.5em \left(-\right)\kern2.5em \left(-\right)\\ \ \ \quad\quad{}+ E\widehat{E}\left[\left(\dfrac{S_{K M}^3}{\Delta \left|\theta \right|}\right)\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\left\{{H}_1\left({\lambda}_{F1}{\lambda}_{K2}-{\lambda}_{K1}{\lambda}_{F2}\right)-{h}_1{\lambda}_{M1}{\lambda}_{K2}\right\}\right]\\ \quad\quad{}\kern5em \left(-\right)\kern4.5em \left(-\right)\kern7.7em \left(-\right)\\ \ \ \quad\quad{}+{\widehat{K}}_2\left(\dfrac{1}{\Delta \left|\theta \right|}\right)\left[{\lambda}_{M1}{\theta}_{K3}\left\{{\lambda}_{K2}{\theta}_{M1}{\theta}_{K2}{h}_2{W}_{\mathrm{F}}+{\lambda}_{K2}{\lambda}_{F2}{\theta}_{M1}\left({S}_{F K}^2+{S}_{K F}^2\right)\right.\right.\\ \quad\quad{}\kern4.1em \left(-\right)\kern20.8em \left(+\right)\\ \ \ \quad\quad{}\left.-\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}+{\theta}_{M1}{\theta}_{K2}\right){\lambda}_{K2}{\lambda}_{F1}{S}_{F F}^1\right\}+\left({\lambda}_{K2}{\lambda}_{F1}-{\lambda}_{K1}{\lambda}_{F2}\right)\left[{\lambda}_{M1}{\theta}_{K3}{\theta}_{M1}{S}_{M M}^1{\theta}_{F2}\right.\\ \quad\quad{}\kern16.8em \left(-\right)\kern5.7em \left(-\right)\kern8em \left(-\right)\kern0.5em \\ \ \ \quad\quad{}+{\theta}_{M1}{\theta}_{K3}\left({\lambda}_{M1}{S}_{M F}^1-{H}_2{W}_{\mathrm{F}}{\theta}_{K2}\right)+\left({\theta}_{F1}{\theta}_{K2}-{\theta}_{K1}{\theta}_{F2}\right)\left\{{\lambda}_{M3}{S}_{K M}^3\right.\\ \quad\quad{}\kern19.2em \left(-\right)\\ \quad\quad{}\left.\left.\left.+{\theta}_{K3}\left({H}_2{W}_{\mathrm{M}}-{\lambda}_{M1}{S}_{M M}^1\right)\right\}\right]\right]\\ \quad\quad{}\kern8.7em \left(-\right)\end{array}}} $$
(6.A.25)

Use of (6.A.15.1) and (6.A.25) yields the following:

$$ \left.\begin{array}{c}\hfill \left(\mathrm{i}\right)\;{\widehat{X}}_3<0\;\mathrm{when}\;{\widehat{K}}_1>0\hfill \\[6pt] {}\hfill \left(\mathrm{i}\mathrm{i}\right)\;{\widehat{X}}_3>0\;\mathrm{when}\;{\widehat{K}}_2>0\hfill \\[6pt] {}\hfill \left(\mathrm{i}\mathrm{i}\mathrm{i}\right)\;{\widehat{X}}_3>0\;\mathrm{when}\;\widehat{E}>0\hfill \end{array}\right\} $$
(6.A.26)

Substituting (6.A.16), (6.A.17) and (6.A.25) in (6.A.24), one gets

$$ {{\begin{array}{l}\dfrac{1}{U_1}\left(\dfrac{d U}{d{ K}_1}\right)= V\left[\left(\dfrac{d{ W}_{\mathrm{F}}}{d{ K}_1}\right)\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)+\left(\dfrac{d{ W}_{\mathrm{M}}}{d{ K}_1}\right){W}_{\mathrm{M}} M{H}_2\right]- t{P}_3 V\left(\dfrac{d{ X}_3}{d{ K}_1}\right)\\ {}\kern8.8em \left(+\right)\kern4.2em \left(+\right)\kern6.2em \left(+\right)\kern10.1em \left(-\right)\kern1.25em \end{array}}} $$
(6.A.27)

From (6.A.27) it follows that dU/dK 1 > 0, which means that an inflow of foreign capital of type 1 is welfare improving.

From (6.A.24) we have

$$ {{\begin{array}{l}\dfrac{1}{U_1}\left(\dfrac{d U}{d{ K}_2}\right)= V\left[\left(\dfrac{d{ W}_{\mathrm{F}}}{d{ K}_2}\right)\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)+\left(\dfrac{d{ W}_{\mathrm{M}}}{d{ K}_2}\right){W}_{\mathrm{M}} M{H}_2\right]- t{P}_3 V\left(\dfrac{d{ X}_3}{d{ K}_2}\right)\\ {}\kern8.8em \left(+\right)\kern12.2em \left(+\right)\kern9.7em \left(+\right)\end{array}}} $$
(6.A.28)

From (6.A.28) we find that dU/dK 2 > 0 and that welfare improves owing to an inflow of foreign capital of type 2 if the sum of the two positive terms within the square brackets is greater than the negative term within the parentheses. Why this can happen has been explained intuitively in Sect. 6.4.1.

From (6.A.24) we get

$$ \begin{array}{ccc}\dfrac{1}{U_1}\left(\dfrac{d U}{ d E}\right)&= V\left[\left(\dfrac{d{ W}_{\mathrm{F}}}{ d E}\right)\left({W}_{\mathrm{F}} F{h}_2+{W}_{\mathrm{M}} M{H}_2\right)+\left(\dfrac{d{ W}_{\mathrm{M}}}{ d E}\right){W}_{\mathrm{M}} M{H}_2\right.\\ & {}\kern3.8em \left(-\right)\kern4.4em \left(+\right)\kern6.2em \left(-\right)\\ & \quad +\left({W}_{\mathrm{F}} F{h}_1+{W}_{\mathrm{M}} M{H}_1-1\right)- t{P}_3 V\left(\dfrac{d{ X}_3}{ d E}\right)\\ & \ \ \qquad\qquad\qquad\qquad\qquad{}\kern6.7em \left(+\right) \end{array} $$
(6.A.29)

From (6.A.29) it follows that dU/dE < 0 if (W F Fh 1 + W M MH 1) ≤ 1.

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Chaudhuri, S., Mukhopadhyay, U. (2014). FDI and Gender Wage Inequality. In: Foreign Direct Investment in Developing Countries. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1898-2_6

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