Does International Outsourcing Really Lower Workers’ Income?

Abstract

We analyze the impact of international outsourcing on income, if the domestic labor market is imperfect, i.e. there is a bilateral bargaining between a firm and a labor union. In our analysis we distinguish between the cases where the parties negotiate over the wage only and where they negotiate over both wage and profit sharing. We find in the first case that outsourcing has an ambiguous effect on the workers’ income, while it increases the workers’ income in the second case. For the optimal amount of international outsourcing, we find that, depending on the wage effect of outsourcing, in a pure wage bargaining system it can be higher or lower than the level where domestic and foreign marginal labor costs are the same. In contrast, in a wage and profit share bargaining system, the amount of outsourcing lies below this level.

Appendices

Appendix A: Derivation of the Wage Effects

As the mark-up we have $A = \frac{{\gamma \cdot \eta \left[ {\eta \left( {1 - \alpha - \beta } \right) - \left( {\alpha + \beta } \right)} \right] + \left( {1 - \gamma } \right)\left( {\alpha + \beta } \right)}}{{\left( {\eta - 1} \right)\gamma \cdot \left[ {\eta \left( {1 - \alpha - \beta } \right) - \left( {\alpha + \beta } \right)} \right] + \left( {1 - \gamma } \right)\left( {\alpha + \beta } \right)}} = \frac{T}{Z}$, which depends on the wage and the amount of outsourcing. The wage impact is shown by ${A_w} = \frac{{{T_w} \cdot Z - T \cdot {Z_w}}}{{{Z^2}}}$, where ${T_w} = \gamma \cdot {\eta_w} \cdot \left( {\left( {1 - \alpha - \beta } \right) + {M \mathord{\left/{\vphantom {M L}} \right.} L}} \right) - \gamma \cdot \eta \frac{M}{{{L^2}}}{L_w}$ and ${Z_w} = {T_w} + \gamma \cdot \frac{M}{{{L^2}}}{L_w}$. Using this, we obtain

$$ {A_w} = \frac{\gamma }{{{Z^2}}}\left[ { - {\eta_w} \cdot \gamma \cdot {{\left( {\left( {1 - \alpha - \beta } \right) + \frac{M}{L}} \right)}^2} - \frac{M}{L}\frac{\eta }{w}\left( {1 - \gamma } \right)\left( {\alpha + \beta } \right)} \right]. $$

(A1)

Since ${\eta_w} = \frac{1}{{1 - \alpha - \beta }}\frac{\eta }{w}\frac{M}{L} > 0$, we have A_w < 0 and thus $1 - \frac{{{A_w}w}}{A} > 0$.

The impact of outsourcing can be analyzed in a similar way. Here we have ${A_M} = \frac{{{T_M} \cdot Z - T \cdot {Z_M}}}{{{Z^2}}}$, where ${T_M} = \gamma \cdot {\eta_M} \cdot \left( {\left( {1 - \alpha - \beta } \right) + \frac{M}{L}} \right) + \gamma \cdot \eta \frac{{L - M \cdot {L_M}}}{{{L^2}}}$ and ${Z_M} = {T_M} - \gamma \cdot \frac{{L - M \cdot {L_M}}}{{{L^2}}}$. Using these expressions we find that

$${A_M} = \frac{\gamma }{{{Z^2}}}\frac{\eta }{L}\left[ { - \gamma {{\left[ {\eta \cdot \left( {1 - \alpha - \beta } \right) - \left( {\alpha + \beta } \right)} \right]}^2} + \left( {1 - \gamma } \right)\left( {\alpha + \beta } \right)\left( {1 - \alpha - \beta } \right)} \right]. $$

(A2)

From (A2) we obtain

$${A_M}\left\{ \begin{gathered} < \hfill \\= \hfill \\> \hfill \\\end{gathered} \right\}0. $$

(A3)

Appendix B: Relationship between Profit Sharing and Outsourcing

Equation (13) can be reformulated to $\tau = \gamma \cdot \frac{{V + bM}}{{V + bM - f(M)}}$, where $V = {b^{ - \frac{{\alpha + \beta }}{{1 - \alpha - \beta }}}} \cdot {\alpha^{\frac{\alpha }{{1 - \alpha - \beta }}}} \cdot {\beta^{\frac{\beta }{{1 - \alpha - \beta }}}} \cdot \left( {1 - \alpha - \beta } \right)$. Thus, the effect of outsourcing on bargained profit sharing is $\frac{{\partial \tau }}{{\partial M}} = \gamma \cdot \frac{{ - f(M) \cdot b + f\prime (M) \cdot V + f\prime (M) \cdot bM}}{{{{\left( {V + bM - f(M)} \right)}^2}}}$. Using $f(M) = \frac{1}{2}c{M^2}$, we can write the effect of outsourcing on the profit share as

$$ \frac{{\partial \tau }}{{\partial M}} = \gamma \cdot \frac{{cM \cdot \left[ {V + \frac{1}{2}bM} \right]}}{{{{\left( {V + bM - f(M)} \right)}^2}}}, $$

(B1)

which equals Eq. (14).