Communication Cost, Skilled-Unskilled Wage, and Informality

Abstract

This paper establishes an interesting link between informality and time zone differences in a general equilibrium trade model for small open economy. Trading countries are located in different time zones of the world with non-overlapping working hours. Such differences in timing can be utilized in the production of services, and communication technology is an important factor that helps this trading process. In such a setup due to a reduction in communication cost, both skilled and unskilled workers are benefitted, skilled labour using service sector and formal unskilled sector expand. Interestingly, wage inequality between skilled and unskilled workers is widened under reasonable conditions. Another phenomenon that must draw our attention is the contraction of informality due to such changes. Then we extend the basic model to include capital mobility across all sectors and unionized wage in the formal sector. We find that the reduction in communication cost leads to finite change in the structure of production and one of the four sectors of the system vanishes. Subsequently, informal sector contracts while wage disparity is widened.

Appendices

Appendix 1

Equation (1) yields

$$ \hat{W}_{S} = - \theta_{dX} \hat{\rho } > 0\;{\text{as}}\;\hat{\rho } < 0 $$

(19)

where $\theta_{dX} = \frac{{W_{S} \rho }}{{P_{X} }}$ indicates communication cost share in X.

Differentiating Eq. (2) and using Envelope condition and substituting the value of Eq. (19), we get

$$ \hat{r} = \frac{{\theta_{SY} \theta_{dX} }}{{\theta_{KY} }}\hat{\rho } < 0\;{\text{as}}\;\hat{\rho } < 0 $$

(20)

Differentiating Eq. (3) and substituting $\hat{r}$ we get

$$ \hat{W} = - \frac{{\theta_{dX} \theta_{SY} \theta_{KM} }}{{\theta_{KY} \theta_{LM} }}\hat{\rho } > 0\;{\text{as}}\;\hat{\rho } < 0 $$

(21)

The wage gap between skilled and unskilled wages is derived from (19) and (21)

$$ \left( {\hat{W}_{S} - \hat{W}} \right) = - \theta_{dX} \left[ {\frac{{\theta_{KY} \theta_{LM} - \theta_{KM} \theta_{SY} }}{{\theta_{LM} \theta_{KY} }}} \right]\hat{\rho } > 0\;{\text{as}}\;\hat{\rho } < 0 $$

(22)

If, $\left( {\frac{{\theta_{KY} }}{{\theta_{SY} }} > \frac{{\theta_{KM} }}{{\theta_{LM} }}} \right)$⁶

Again, differentiating Eq. (4) and substituting $\hat{W}$ we obtain

$$ \hat{R} = \theta_{dX} \frac{{\theta_{LI} \theta_{KM} \theta_{SY} }}{{\theta_{KY} \theta_{LM} \theta_{TI} }}\hat{\rho } < 0\;\;{\text{as}}\;\hat{\rho } < 0 $$

(23)

Change in output depends on factor substitution owing to changes in factor prices due to change in $\rho$.

Equation (8) yields

$$ \hat{I} = - \hat{a}_{TI} $$

(24)

By definition, the elasticity of substitution between L and T in sector I is given by

$$ \sigma_{I} = \frac{{\hat{a}_{LI} - \hat{a}_{TI} }}{{\hat{R} - \hat{W}}} $$

Using expression for elasticity of substitution and Envelope theorem between L and T in I we have

$$ \hat{a}_{TI} = - \sigma_{I} (\hat{R} - \hat{W})\theta_{LI} $$

Using the full employment condition for T and plugging the values of $\hat{W}$ and $\hat{R}$ we arrive at $\hat{a}_{TI} = - \sigma_{I} \theta_{dX} \left( {\frac{{\theta_{LI} \theta_{KM} \theta_{SY} }}{{\theta_{KY} \theta_{LM} \theta_{TI} }}} \right)\hat{\rho }$

Substituting the values in Eq. (24), it becomes

$$ \hat{I} = \sigma_{I} \theta_{dX} \left( {\frac{{\theta_{LI} \theta_{KM} \theta_{SY} }}{{\theta_{KY} \theta_{LM} \theta_{TI} }}} \right)\hat{\rho } < 0\;{\text{as}}\;\hat{\rho } < 0 $$

(25)

Full employment condition of L gives the value

$$ \hat{M} = - \sigma_{I} \theta_{dX} \left( {\frac{{\theta_{LI} \theta_{KM} \theta_{SY} \lambda_{LI} }}{{\theta_{KY} \theta_{LM} \theta_{TI} \lambda_{LM} }}} \right)\hat{\rho } > 0\;{\text{as}}\;\hat{\rho } < 0 $$

(26)

Again, differentiating Eq. (6) and substituting the value of $\hat{M}$ we obtain

$$ \hat{Y} = \sigma_{I} \theta_{dX} \left( {\frac{{\theta_{LI} \theta_{KM} \theta_{SY} \lambda_{LI} \lambda_{KM} }}{{\theta_{KY} \theta_{LM} \theta_{TI} \lambda_{LM} \lambda_{KY} }}} \right)\hat{\rho } < 0\;{\text{as}}\;\hat{\rho } < 0 $$

(27)

Similarly, Eq. (5) yields

$$ \hat{X} = - \sigma_{I} \theta_{dX} \left( {\frac{{\theta_{LI} \theta_{KM} \theta_{SY} \lambda_{LI} \lambda_{KM} \lambda_{SY} }}{{\theta_{KY} \theta_{LM} \theta_{TI} \lambda_{LM} \lambda_{KY} \lambda_{SX} }}} \right)\hat{\rho } > 0\;{\text{as}}\;\hat{\rho } < 0 $$

(28)

Appendix 2

Equation (14) and (15) yield

$$ \hat{r} = \hat{W} = 0 $$

Differentiating Eq. (12) and using Envelope condition

$$ \hat{W}_{S} = - \frac{{\theta_{dX} }}{{\theta_{SX} + \theta_{dX}^{S} }}\hat{\rho } > 0\;{\text{as}}\;\hat{\rho } < 0 $$

(29)

Where, $\theta_{dX} = \frac{{(W_{S} + r)\rho }}{{P_{X} }}$ indicates communication cost share in X.