Distance, Production, and Virtual Trade

Abstract

In this chapter our endeavor is to briefly argue that distance is not necessarily harmful for trade which is the main preoccupation of gravity model of trade. Interestingly it has been shown that there may be an increase in the production and volume of trade if time zones of the trading nations are non-overlapping, and revolution in information and communication technology helps reducing the cost of virtual transaction of services. This implies a positive effect of distance on the volume of trade. It is also shown that exploitation of time zone differences raises welfare and ensures capital accumulation. Hence this chapter builds on the emerging literature on time zones and pure theory of international trade to examine why distance may be conducive to trade and growth.

This chapter is an extended version of Mandal [20].

Appendix

Now let us define four countries in such a way that we can analyze trade of USA (U) with Mexico (M), India (I) and Australia (A) separately. These representative countries are chosen intentionally to capture the issue of overlapping and non-overlapping time zones. U has a distinct non-overlapping time zone only with I, but the case with M and A with U represent overlapping time zones.

In virtual autarky all U, M, I and A are producing identical amount of S. We further assume that domestic demands are met by domestic supply of service, S.

Geographically, U’s distance from I is exactly that much which is required for non-overlapping time zones. For M and A it becomes slightly overlapping with U. We further assume that in order to exploit the benefit of time zone difference it has to be exactly non-overlapping. One can easily check it from Fig. 6.1 that distance between U and I is maximum. The distance is the minimum requirement for appropriating the benefit of distance. Thus the volume of production of S will increase in both U and I if both of them engage in virtual trade.

Fig. 6.1

Distance and location of countries

Note that $\delta$ takes any value greater than unity for virtual trade between U and any country except I. $\delta$ takes the value $\bar{\delta }$ > 1 for all countries except I. The underlying idea is that U has a distinct non-overlapping time zone with I, i.e. for certain physical distance. For any distance, greater or less than this implies overlapping time-zones (it could be on same day or next day). When $\delta = \bar{\delta },$ no virtual trade takes place. The idea can be portrayed as in Fig. 6.2.

Fig. 6.2

Distance, time-zone, and discount factor

One can easily understand that not only the final good production increases, along with it a double amount of m compared to S is also traded. Because first time a part of S (after the first stage) is exported at the end of U’s working day. I works on it and exports it back/or exports the final S when U starts the second day. This implies a surge or abrupt increase in trade volume between U and I. Hence the relationship between volume of trade and distance can be depicted in the following diagram (Fig. 6.3).

Fig. 6.3

Distance and volume of trade

d_i = physical distance of U with ith country (i = M, I and A); Tp = physical trade (red line); VOT = Volume of trade, Violet line = total VOT

Note that at point C the VOT jumps up to F. This is because when d reaches the required amount, $\delta$ becomes unity and otherwise $\delta = \bar{\delta }.$ This way we modify Eq. (6.7) and make it a continuous function as expressed in Eq. (6.8) as $\delta = \delta \left( d \right).$ Nota that $\delta^{\prime}\left( d \right) < 0$ up to a certain distance, then reaches a minimum and afterwards $\delta^{\prime}\left( d \right) > 0$. Diagrammatically (Fig. 6.4).

Fig. 6.4

Discount and distance as continuous function

It is evident from Fig. 6.3: d_M < d_I < d_A

Therefore, $\delta \left( {{\text{d}}_{\text{M}} } \right) > \delta \left( {{\text{d}}_{\text{I}} } \right) < \delta \left( {{\text{d}}_{\text{A}} } \right)$.

And in what follows

$$\begin{aligned} S_{t}^{M} &= K\left( {P_{S} } \right)^{{\frac{1 - \alpha }{\alpha }}} \left( {\frac{1 - \alpha }{2}} \right)^{{\frac{1 - \alpha }{\alpha }}} \left( {\delta \left( {d_{M} } \right)} \right)^{{\frac{\alpha - 1}{\alpha }}} ;\\ S_{t}^{A} &= K\left( {P_{S} } \right)^{{\frac{1 - \alpha }{\alpha }}} \left( {\frac{1 - \alpha }{2}} \right)^{{\frac{1 - \alpha }{\alpha }}} \left( {\delta \left( {d_{A} } \right)} \right)^{{\frac{\alpha - 1}{\alpha }}} ; \\ S_{t}^{I} &= K\left( {P_{S} } \right)^{{\frac{1 - \alpha }{\alpha }}} \left( {\frac{1 - \alpha }{2}} \right)^{{\frac{1 - \alpha }{\alpha }}} \left( {\delta \left( {d_{I} } \right)} \right)^{{\frac{\alpha - 1}{\alpha }}}. \\ \end{aligned}$$

Therefore, for same level of capital $S_{t}^{M}< {S_{t}^{A} },\ {S_{t}^{A} } > S_{t}^{I}$. We can plot the above ideas in Fig. 6.5.

Fig. 6.5

Distance and trade with discount as continuous function

Tp, Tv and Tt = physical trade, virtual trade and total trade respectively.