Trade Theory and the Role of Time Zones
Sugata Marjit
City University of Hong Kong
This Draft , June2005
ABSTRACT
International time difference, due to the location of countries in different
time zones, determines pattern of trade in a vertically integrated Ricardian
model. The idea is related to service trade in the information technology
sector. Technological progress helps in generating trade through “nature”
driven comparative advantage. Time-difference emerges as an independent
driving force of international trade besides taste, technology and
endowment. Our model also predicts that free transfer of technology will
improve global welfare.
Key Words: Comparative Advantage, Time Zone
JEL.CL.NO. : F11
Address for Correspondence:
SUGATA MARJIT
Department of Economics and Finance
City University of Hong Kong
Tat Chee Avenue
Kowloon
Hong Kong
Fax 852-2788-8806
E-mail: [email protected]
I am indebted to the seminar participants at the Indian Statistical Institute and University
of Birmingham for comments and Siddhartha Chattopadhayay for research assistance.
Thanks are also due to Murray Kemp for detailed and insightful comments. The usual
disclaimer applies.
I.
Introduction
A fundamental preoccupation in the theory of international trade is to explore and
analyse factors which determine pattern of trade between nations. It is well known that
three major contenders in this area are the Ricardian theory of comparative advantage, the
Heckscher-Ohlin-Samuelson (HOS) model of relative factor abundance and increasing
returns to scale (IRS) models pioneered by Paul Krugman. One may refer to Caves,
Frenkel and Jones (2003), Helpman and Krugman (1987), Feenstra (2003), etc. for
detailed analyses of these theories. Limited amount of work also appeared in terms of
models which explicitly use the “rate of time preference” as a determining factor behind
the pattern of trade in dynamic contexts. Notable among them are Sarkar (1985) which
draws from earlier works of Ronald Findlay, summarized nicely in Findlay (1995) and
Hicks (1973). It is a tradition in trade theory to look for primitives which can explain the
pattern of trade. Such primitives evolve around the trinity – technology, endowment and
taste. In this paper I propose another alternative which does explain a part of trade in the
contemporary world. Let us take the case of a generalized HOS model as elaborated in
Jones, Beladi and Marjit (1999). Countries are endowed with relatively different amount
of various factors of production. They produce different bundles of similar or dissimilar
goods.
As the countries engage in international trade, such goods are physically
transported from one place to another. It is now well recognized that there are many
kinds of trade, particularly in the service sector such as in the information technology (IT)
sector, which do not require physical shipment of goods. For example programming
problems are e-mailed from the USA to India at the end of the day (in USA). Indian
software specialists start working on them in their regular office hours while in USA the
2
office remains closed due to the time difference. By the time the offices reopen in the
USA, the solutions have already arrived mainly as e-mail attachments. This essentially
means that the business operations can continue almost for twenty four hours, with very
little interruptions. This type of trade requires two basic preconditions to be satisfied.
First, the difference in the time zone has to be such that the proper division of labor is
feasible and the time difference can be properly utilized. Second, the technology should
be such that the “services” can be “transported” quickly with little costs. Revolution in
the IT sector has taken care of the second condition, so that the delivery costs are truly
negligible. Therefore, the first factor i.e. the location in significantly separated time
zones becomes the primary driving face behind trade in the IT sector.
Suppose we take the Ricardian case and assume two countries can produce X and Y with
Ricardian technology with the following caveat. One unit of X has to be produced in two
vertically related stages , each requiring one working day where as one unit of Y can be
produced in one working day. There are two countries, USA and India which have the
same technology for producing the goods and they are located in different time zones.
Since they have the same technology, by Ricardian hypothesis they should not engage in
trade with each other. But there is another avenue for trade. Suppose production of one
unit of X starts in Monday morning in USA. The first stage is finished by Monday and
the second stage on Tuesday. Therefore, one unit of X is ready for sale by Tuesday
evening. For Y there is no such problem. It is ready for sale by Monday evening. Now,
with trade, by Monday evening the first stage of X is finished and transported to India
which starts off its Monday at that time and completes production when USA wakes up
3
in Tuesday morning. So one unit of X is ready for sale as Tuesday starts off. Such a
trade saves a day for X to be marketed. It is as if it requires half the time to market the
same quantity of X. Note that X does require close to twenty four hours to produce. But
the time-difference between India and USA allow each of them to avail the product
“earlier” than without trade. With trade the maximum available X in one day is doubled
across the world with the level of Y remaining the same even if the physical productivity
of workers in both countries remain the same before and after trade.
Section II illustrates the idea in terms of a simple Ricardian model. Section III concludes.
II.
Time-difference and Comparative Advantage
We have two economies and the Rest-of-the-World (ROW).
These countries can
produce two goods X and Y with Ricardian technology. We assume that the price of X
and Y, Px and Py are determined in the ROW and are beyond control of the countries we
deal with. Given such prices we wish to determine the pattern of specialization. We also
assume that one of the countries, country A and some of the ROW are located in one time
zone and country B and the rest are located in the other. A and B use the same Ricardian
technology to produce X and Y and have same labor endowments1. One unit of labor is
required to produce one unit X and β units are required to produce one unit of Y.
Markets are competitive.
Production of Y is instantaneous in the sense that one unit of Y can be produced within
one working day. But one unit of X requires production in two stages. Each stage
4
requires one working day to complete.
1
is used to produce the first stage and the other
2
1
the second. Committing one unit of labor to X implies that a unit of X is ready for sale
2
after two working days where as the alternative is to employ one unit of labor to produce
Y and get one unit of Y after one working day. If (Px, Py) are the commodity prices, and
WA is the autarkik wage rate for country A then
WA = δ Px
(1)
β WA = Py
(2)
0< δ <1, is a rate of discount because X can be sold after two working days. This captures
the idea that the consumers will like to have the product early. Although we do not
explicitly model the consumption behavior, this seems to be a reasonable assumption.
Countries A and B will produce only Y iff
1
δβ
>
Px
Py
(3)
We also assume that
1
δβ
>
1
Px
>
Py
β
(4)
i.e. if somehow X could be delivered after one working day, as in the case of Y, both
countries will opt out of Y.
Since A and B are located in different time zones, workers in B can work while there in
A take rest and vice-versa. Markets open every twenty four hours. The first half of the
day could be used to produce the first stage of X in A, transfer it to B which completes
5
the second phase and the product is ready for sale after one working day in A, as well as
in B.
Before trade, A and B both have the same wages since they are essentially the same.
Now with vertical trade the resultant wages are (WAT , WBT ). Then for both of them to
specialize in X following must be true.
Px -
1 Py
Py
2 β
>
1
β
2
(for A)
(5)
1 Py
Py
2 β
>
1
β
2
(for B)
(6)
Px -
(5) Suggests that for country A, after paying the country B workers the wage they were
getting before, the new wage is higher than their opportunity cost i.e. wage obtained from
producing Y, similarly for country B.
Both (5) and (6) hold if
1
Px
>
Py
β
(7)
Which is our basic assumption.
Another way of looking at the same problem is to consider the competitive condition for
producing X.
P
1 T 1 T
WA + WB = Px > y
β
2
2
(8)
6
Since initially WA = WB =
Py
β
, for (8) to hold at least one country must get a higher wage
now. This essentially proves the basic proposition.
Proposition I: If shipment cost of goods – in – process is negligible, there are always
gains from trade across different time zones.
Proof. See the discussion above. QED.
One should note that we require a balancing condition such that amount of goodsin-process released by A match exactly the handling capacity of B. If LA and LB are
given labor endowments then,
LA LB
=
1
1
2
2
(9)
(9) Holds since by assumption LA = LB
Models of vertical trade in Ricardian structure are provided by Sanyal (1983), and Marjit
(1987) and in HOS framework by Dixit and Grossman (1982). But all of these models
have to assume a pattern of intra-country comparative advantage in stages of production.
This is not needed here. The driving force behind trade is the time-difference. Even if
both the countries have exactly the same technology for producing various stages of X,
they can still trade because they can take advantage of the time difference. In a way for
either country to complete both stages in one working day is extremely expensive, but
completing one stage is feasible.
7
It should be clear by now that country A may produce the second half of X and country
B the first. It does not matter. But they should not produce both the stages on their own.
We have imposed a lot of structure in the framework discussed so far. This has been
helpful in driving home the basic point we are trying to make. However, we can easily
generalize the model and do away with redundant assumptions.
Let us assume that LA ≠ LB and the stages of production of X are indexed in a continuum
by z ∈[0, 1] with m( z ) denoting the requirement of labor to produce the zth stage for
one unit of X. This characterization is the same for both countries.
Furthermore,
~
z
∫ m(z )dz = M(~z )
(10)
0
M (~z ) is the cumulative function with the obvious property M ′ > 0 and reaching
maximum at M (1) = 1.
Free trade equilibrium conditions then imply,
W AT M ( ~
z1 ) + WBT [1 - M ( ~
z1 )] = Px
(11)
LA
LB
=
= X
z1 ) [1 - M( ~
z1 )]
M(~
(12)
th
Therefore, country A will produce up to ~
z1 stage and the rest is produced by B. Some
observations are in order.
th
z1 stage from one country to the
First, WAT = WBT = Px . If not, then shifting around the ~
other, one could reduce average cost of producing X. Competition will rule that out.
8
Second, ~z1 , derived from (11) is one candidate for the equilibrium cut-off point. The
other candidate will be ~z 2 .
Such that
LA 1 - M(~z2 )
=
LB
M(~z2 )
(13)
There is no guarantee that ~
z1 = ~
z 2 except when LA = LB.
Consistency requirement
suggests that the cumulative labor-intensities embodied in goods in process must be
proportional to the relative labor endowments.
Third, one must keep in mind that the two countries are exactly identical except that they
are located in opposite time zones. It is now well known that similar countries can trade
with each other because of the “love-for-variety” in consumption and this can be proved
in models with increasing returns to scale but here we have two identical countries
trading with each other because they are located in different time zones. One does not
need “love for variety” considerations and increasing returns. Interestingly there is a
similarity because the pattern of trade is indeterminate in both cases., nonetheless gains
from trade exist.
A) Technology Transfer
Transfer of technology in the international context has been quite an interesting and
vibrant research topic. For a general overview one may refer to Singh and Marjit (2003).
In particular transfer of technology in Ricardian trade model have been analyzed by
Beladi, Jones and Marjit (1997) and Ruffin and Jones (2004 ) Again such papers do not
consider ‘time’ as the driving factor behind trade. In the current context we can ensure
the following.
9
Proposition II: If initially country B does not have the technology to produce X,
country A should costlessly transfer such technology to B so that B participates in
production of X.
Proof. Since B does not have the technology to produce X, it will produce Y and earn
Py
β
. Similarly if B can not help A in producing X, A also specializes in Y and gets
By transferring technology to B, each can get Px >
Py
β
.
Py
β
QED.
Proposition II illustrates the case where USA will donate free computers to the Indian
software professionals so that they choose the right kind of specialization not only for
themselves but also for USA. This proves the case that even if USA charges zero price
for these machines, it can still be better off.
B) Shipment Costs
One can invoke “iceberg” type shipment costs between two countries. This implies that
to process 1 unit of X, one has to process
X
units, with 0 < s < 1 , since (1 - s) X will be
s
lost in the process. This in turn means that for each unit of X produced, the effective
price is s Px. The new condition for a profitable X venture is
1 P
Px > . y
s β
(14)
10
With 0 < s < 1, (14) is less likely to hold then without such transportation cost. We also
know that initially Px <
1 Py
. . Therefore, our story will go through if s > δ , i.e. if the
δ β
benefit from exploiting the time difference exceeds that of the shipment cost. One way of
looking at the impact of technological change on pattern of trade and specialization is as
follows.
Introduction of computers may improve the productivity in both X and Y in a way such
that the comparative cost ratio remains unaffected and by itself it does not alter the
pattern of trade.
Both countries continue to specialize in Y.
However, internet
connections installed in the existing hardware can change the situation considerably.
Now, along with the separated time zones, e-mail technology transforms the trade pattern
in both countries. Production of Y is no longer sustainable and both of them shift to X,
producing parts of it. Even if all technological changes take place in USA, it pays for the
USA to train Indian workers free of charge to specialize in X.
C) General Equilibrium
So far we have assumed that countries A and B are small compared to the rest of the
world - and therefore, they can get away by specializing only in fragments of X. If A and
B are the only two countries in the world Y has to be produced by at least one of them.
Zero production of Y will raise its relative price attracting workers to the production of Y.
*
 P 
The equilibrium  x  will be given by
 P 
 y
11
*
 Px 

 =1
 P 
β
 y
(15)
This is exactly what one would expect given the Ricardian structure of the model. Wages
in both countries have to be the same. The pattern of trade will still be similar, both of
them will produce different stages of X and some Y. The general equilibrium for the
global economy will be described as follows.
( )
( )
W A* M ~
z * + WB* [1 - M ~
z * ] = Px*
(16)
WA* β = WB β = Py*
z * X + β YA* = L A
M~
z * X + β . YB* = L B
1- M ~
(17)
*
( )
[ ( )]
P
X
= φ x
*
P
Y + YB
 y
*
A




(18)
(19)
*
(20)
(16) – (19) are usual price and full employment conditions, (20) is the relative demandsupply
equality
with a
WA* = WB* = W * = Px* =
(
1
β
homothetic
demand
function.
(16),
(17)
determine
Py*
)
1
From (20) , X = Y A* + Y B* φ 
β



(21)
(
)
Substituting (21) in (18) and (19), one can solve for YA* , YB* given ~z *. As anticipated ~z *
is indeterminate excluding the cases that ~z * = 0 or ~z * = 1. In both these extreme cases it
will be difficult to produce X over a single day or period of time. But it can take any
value between 0 and 1. Since both A and B have exactly the some technology, it does not
matter how many stages each one produces.
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Concluding Remarks
In this paper we have suggested that countries located in opposite time zones can save
time and costs if they can produce various stages of a commodity, which can be
transported without much of a cost. Two countries, identical in every respect, can gain
from such a trade. We have discussed generalization of our basic model and other
complications which continue to preserve the essence of the result. In the Krugman type
intra-industry increasing returns to scale models, similar countries can gain from trade by
extending the set of varieties of consumables.
But the pattern of trade is really
indeterminate. It does not tell us who exports what since the countries are really the same.
In our model although the countries are really the same, they gain through trade. But the
pattern of intra-industry trade is difficult to determine, since ~z * can take any value
between 0 and 1. One could get a determinate solution to ~z * by incorporating a shipment
cost which is increasing in the number of stages shipped across the world. While this is a
suitable extension, it does not alter the qualitative result. Identical countries across time
zones, will always gain from trade because they are “naturally” different.
13
Appendix
Pattern of Trade in General Equilibrium. Countries of Similar Size, LA = L B = L
W * = Px
(1a)
W * β = Py* ≡ 1
M(~z * ) . X + β . YA = L A
[1 - M(~z * )] X + β Y = L
(2a)
B
(3a)
B
1
X
= φ  
YA + YB
β
(4a)
(5a)
Note that (1a) and (2a) determine the equilibrium relative price as
1
β
, a Ricardian
outcome. Then from (3), (4) and (5) we determine X, Y and YB for a given ~
z * . In fact
one can identify three possible specialization patterns (1) both produce stages of X and Y.
(2) A produces stages of X and Y, B produces only stages of X. (3) B produces stages of
X and Y, A produces only stages of X.
From 3(a) – 5(a)
1
M(~
z * ) φ   (YA + YB ) + β YA
= LA
β 
1
[1 - M ( ~
z * )] φ   (YA + YB ) + β YB = L B
β 
(6a)
(7a)
14
Now follow the standard (2
2) general equilibrium model to argue that,
Both YA and YB will be positive iff.
[M (~
M(~
z x )φ + β ] L A
z x )φ .
>
>
[1 − M ( ~
z * )] φ L B [1 − M ( ~
z * )φ + β ]
Note that this will be one of the specialization patterns for a given ~
z * , LA and LB. But
other patterns are possible if
LA
lies beyond the cone of diversification.
LB
15
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