Time Zone Differences Induced Trade, Factor Prices and Skill Formation

Abstract

Time Zone difference induced changes in trade and factor prices are relatively new concerns in trade literature as we repeatedly mentioned before. Here in this chapter we formulate yet another trade model capturing the issue of Time Zone difference and communication technology revolution together to show that due to these developments skilled workers benefit. Though wage inequality between skilled and unskilled workers is widened under reasonable and, of course, sensible condition. Return to capital goes down while educational capital gets relatively high return. These changes also attract educational capital from abroad and eventually alter the sectoral composition of the economy in favor of more skill based one.

A different version of this chapter was published as Mandal et al. [41].

Appendices

Appendix 1: Adjustments in ${\varvec{\uptau}}$ and E

Following arguments in the main text we understand that $\tau$ influences E which in turn changes $\mu_{ES}$, productivity of educational capital in upgrading L. An increase in the supply of E owing to higher $\tau$ initially raises average productivity. Such phenomenon is quite sensible as the supply of complementing factor, L, is traditionally huge in supply. Therefore, $\frac{1}{{\mu_{ES} }}$ goes up or $\mu_{ES}$ goes down. But in the long run, productivity of E must fall gradually because of the similar reason iterated before. So, E demonstrates a positive relation with $\tau$, before reaching a certain level. But beyond that level E drags down $\tau$ through changes in the productivity of educational capital. Hence, $\tau$ decreases and gets equalized with international level where inflow or outflow of E comes to a halt. These arguments are described in the following diagrams. Figure 11.3a shows the relationship between $\mu_{ES}$ and τ, whereas Fig. 11.3b defines the desired shape of the curve showing different combinations of E and $\tau$. Both the points G and H denote equilibrium, but H is a stable one.

Fig. 11.3

a Relationship between $\mu_{ES}$ and $\tau$. b Shape of curve for E and $\tau$

Appendix 2: Change in ${\varvec{\uptau}}$

From Eq. (11.9) of the main text we easily derive that $\hat{W}_{s} - \hat{W}\theta_{ls} = \theta_{Es} \left( {\hat{\tau } + \hat{\alpha }} \right)$ as $\mu_{ES}$ and $\alpha \left( E \right)$ both are identical and essentially imply inverse of average productivity of E. However, when there is no endowment change in E, productivity of E will not change. This is what we need to look at as change in $\tau$ would be due to change in $\rho$ only to start with. Substituting the values of $\hat{W}$ and $\hat{W}_{s}$

$$\begin{aligned} \hat{\tau }\theta_{Es} & = - \hat{\rho }\theta_{dx} + \hat{\rho }\theta_{dx} \frac{{\theta_{sy} }}{{\theta_{ky} }}\frac{{\theta_{kz} }}{{\theta_{lz} }}\theta_{ls} \\ \hat{\tau }\theta_{Es} & = - \hat{\rho } \theta_{dx} \left( {1 - \frac{{\theta_{sy} }}{{\theta_{ky} }}\frac{{\theta_{kz} }}{{\theta_{lz} }}\theta_{ls} } \right) \\ \hat{\tau } & = - \hat{\rho }\frac{{ \theta_{dx} }}{{\theta_{Es} }}\left( {\frac{{\theta_{ky} \theta_{lz} - \theta_{sy} \theta_{kz} \theta_{ls} }}{{\theta_{ky} \theta_{lz} }}} \right) \\ \end{aligned}$$

This is the preferred relationship between $\tau$ and $\rho$ when only different input prices change and calls for an international movement of educational capital.

Appendix 3: Output Change Due to ${\varvec{\uprho}}$ and E

For the time being let us abstain from the issue of an inflow of E though it will take place eventually as $\tau$ has already gone up. So, here both $L_{1}$ and $S_{1}$ are zero. Change in output will be due to factor substitution only owing to change in factor prices triggered by change in $\rho$. From the zero-profit condition and Envelope condition

$$\hat{a}_{lz} = \sigma_{z} \left( {\hat{W} - \hat{r}} \right)\theta_{lz} \quad{\text{and}}\quad \hat{a}_{kz} = - \sigma_{z} \left( {\hat{W} - \hat{r}} \right)\theta_{kz}$$

Using full employment condition for L and plugging the values of $\hat{W}$ and $\hat{r}$ one arrives at

$$\hat{Z} = - \hat{\rho }\sigma_{z} \theta_{dx} \frac{{\theta_{sy} }}{{\theta_{ky} }}$$

Again, K constraint gives the value

$$\hat{Y} = \hat{\rho }\sigma_{z} \theta_{dx} \frac{{\theta_{sy} }}{{\theta_{ky} }}\frac{{\lambda_{kz} }}{{\lambda_{ky} }}$$

If one substitutes the value of $\hat{Y}$ in the full employment condition of skilled labor, we have

$$\hat{X} = - \hat{\rho }\sigma_{z} \theta_{dx} \frac{{\theta_{sy} }}{{\theta_{ky} }}\frac{{\lambda_{kz} }}{{\lambda_{ky} }}\frac{{\lambda_{sy} }}{{\lambda_{sx} }}$$

Now let us quickly move to the endowment effect. Equation (11.7) entails $\hat{S}_{1} \left( E \right) = \hat{L}_{1} \left( E \right)$ for non-changing quality parameter of E. Note that Eq. (11.9) can also be written as $W + \tau \frac{E}{{S_{1} \left( E \right)}} = W_{s}$. This argument ensures that $\hat{S}_{1} \left( E \right) = \hat{L}_{1} \left( E \right) = \hat{E}$ for any given $W_{s} ,W$ and $\tau$ (remember that $\tau$ is now higher than the international level). Once E flows in, however, there must be further modifications in $\tau$. It must go down to restore the world-wide balance. But right now we are not interested in that. Consequent upon inflow of E we will have slightly modified full employment conditions where both $L_{1}$ and $S_{1}$ are non-zero and positive. Using the standard Cramer’s rule and substitution of $\hat{S}_{1} \left( E \right) = \hat{L}_{1} \left( E \right) = \hat{E}$ we have

$$\hat{Z} = - \hat{E}\frac{{\lambda_{l1l} }}{{\lambda_{lz} }};\ \hat{Y} = \hat{E}\frac{{\lambda_{l1l} }}{{\lambda_{lz} }}\frac{{\lambda_{kz} }}{{\lambda_{ky} }};\ {\text{ and }}\ \hat{X} = \hat{E}\frac{{\lambda_{S1S} \lambda_{lz} - \lambda_{l1l} \lambda_{kz} \lambda_{sy} }}{{\lambda_{lz} \lambda_{sx} }}.$$