International Trade-Theory
By Alfonso Llanes
November 10, 2016
Abstract
International trade is the inseparable companion of
transportation and this paper will investigate in separate parts theory,
technology, infrastructure, logistics, markets, methodology, commodities,
economics, finance, and the public organizations and NGO’s that encompass international commerce.
How cargo is classified not only for valuation of duties and
taxation but for the efficient packaging, handling and movement from a point
origin to destination as a single cargo units. In addition, this paper will
examine international trade data regarding producer- consumer- countries across
international such as energy, agriculture, base metals, ores and the exchanges for
bulk, semi-manufactured, and manufactured merchandise and commodities were
bidding takes place.
Thousands of books and papers have been written over a long
span of years about transportation, trade, markets and so on, nonetheless, the
intention of this paper is to revisit these same issues with a different lens and
apply recent and the innovative approaches by making use of applied fractals for
the analysis. The reason for taking this
method is that markets behave in chaotic ways with unpredictable economic
swings that go beyond the business cycle, so, new tools are needed to explore
our challenging times.
Introduction
Description
of Fractals
Fractals are used in the study of chaos and chaotic
systems such as the weather and other systems in disarray where mathematical
geometry has proven to be very useful examining the sets that emerge from repeating
patterns of disorder at every scale of reduction or amplification.
Fractal surfaces are set apart from Euclidian surfaces in
unique ways as not being differentiable, usually exceeding its topological
dimension. The term "fractal" was first used by mathematician Benoît
Mandelbrot in 1975 when he came across fractals while studying the weather and
coined the word fractal as in “fractured geometry”.
Some mathematical concepts that had been studied in the
past are now an intrinsic part of a fractal set as is for example the Fibonacci
sequence in a recursive process when a thing are defined in terms of itself or
of its type as in “circular reasoning”.
Computer scientist programmers deal extensively with the
use of self-referencing which is counter intuitive but follows a set of logical
steps in a sequence that a computer can read and execute within the program’s
logic. This is of course the opposite logic for mathematical teaching in
Euclidian space.
There is some disagreement amongst authors on how the
concept of a fractal should be formally defined but the general consensus is
that theoretical fractals are infinitely self-similar, iterated, and detailed
mathematical constructs having fractal dimensions. However, these dimensions
are not limited to geometric patterns, but can also describe processes in time
and patterns with various degrees of self-similarity in images, structures and
sounds.
Since this paper is not about the study of fractals but
rather the application of fractal patterns to the various disciplines that
comprise international trade. This process of removing middle thirds is a
simple example of a finite subdivision rule.
Cantor ternary set finite subdivision rule.
Source: Wikipedia
Trade Theory
A division of
labor in trade theory means that countries produce just a small range
of goods or services, and may contribute only a small part to finished products
sold in global markets. The assembly line and the assembly circles are methods
of production still in use today but more becoming a robotic function as an
economy modernizes from labor intensive to technology oriented and services.
Specialization
is the second fundamental principle associated with trade, and results from the
division of labor. Given each producer a given a specialist role, as efficient
contributors to the overall process of production, and to the finished product.
Specialization can be applied to individuals, firms, machinery and technology,
and to whole countries.
Comparative
advantage is a term associated with 19th Century English economist
David Ricardo (1817) which means that trade, encourages a country to specialize
in producing only those goods and services which it can produce more
effectively and efficiently, and at the lowest opportunity cost. Trade
increases competition and lowers world prices, which provides benefits to
consumers by raising the purchasing power of their own income, and leads a rise
in consumer surplus. The quality of goods and services is likely to increases
as competition encourages innovation, design and the application of new technologies.
Trade will also encourage the transfer of technology between countries. In order to set up comparative advantage to
be studied by the use of fractals we can divide exports by imports of national
economy to obtain and index for a given period of time. 
in logarithmic form 
This relationship can be
displayed in a time series graph and projected over a future period that can be analized with fractals. An iterative equation can convert a time series into a fractal and
use this equation to predict future behavior of the interaction.
Dow Jones industrial
index 1988-97
Source Global Finance Data The DJ chart can be approximated with the
Weierstrass fractal function.
Below is a graph
generated with random using Excel by the author showing a two country analysis
of current accounts for a single year slotted in a regular 52 week interval applying
the moving average method:
The challenge then becomes
writing an equation for this time series that does not converge nor diverge but
it is periodic either with real numbers or in the complex plane of the type x2
+ 1 = 0, a + bi =z in order to project a trend line beyond 52 weeks. The
advantage of using fractals for the
analysis is that a model can be easily simulated by a computer or a worksheet.
Similarly the Weierstrass
fractal function can be iterated using a computer or a worksheet. Here is the
equation as a sum of a series which is entered into an Excel worksheet below.
Original equation
The time series generated indicates a
negative trend; however, running the model for a longer period might bring a
surprising result. Since this is just a sampling of the process this paper
would not explore the issue any further for now as fractals will be taken on
again at later writings on trade issues.
Harmonics
Regular
circular harmonics in nature are often encountered in
physics and engineering. Consider a point moving with constant speed in a
circle of radius r.
The movement of the projection back and
forth along the horizontal axis is described as simple harmonic motion. The
parameters of the function are as follows:
r is amplitude
ω is the angular velocity or frequency
θ is the phase displacement
In order to induce fractal behavior for
this model, only a very small variation is needed on any of the parameters
which will induce unpredictable transformations over a number of iterations.
Irregular
circular harmonics that become fractals can be reasonably model
as seasonal fluctuation in terms of trigonometrical functions; but it is
difficult to model cycles such as trade or economic activity of irregular
cycles without applying better mathematical tools. It seems that something
other than a perfectly regular sinusoidal component is required to model the secular
fluctuations of economic activity which are described as business cycles.
To obtain a model for a cyclic fluctuation,
it should be enough to modify the harmonic cycle by superimposing a disturbance
term which affects the amplitude. However, in order to generate a cycle that is
more affected by randomness the model should include both phase and amplitude
disturbance.
A good example of irregular circular
motion is the differential angular velocity on the wheels of turning car or the
erratic rotation of water wheel with different sizes water buckets which
generates the” chaotic wheel” known as the fractal “Lorenz attractor”.
 | |||
Endowments among
countries are the basis for the Heckscher-Ohlin( 1949)model that relies
on differences in factors of production endowments as the fundament for trade. It
has been argued that world output would increase when the principle of
comparative advantage is applied by countries to determine what goods and
services they should specialize in producing. Trade among core and peripheral countries can
be visualized with this graph generated with Pajek 4G
Modern gravity
theory and gravity models since
its original formulation by Jan Tinbergen ( 1962), gravity has long been one of
the most successful empirical models in economics. (Princeton University Press)
explains it as trade patterns and trade flows that have the tendency of the positive attractiveness between two
national economies based on economic size-- (in a similar fashion as planets
attracting each other based on their mass)-- and the 'economic distance' between
two economies. The stability of the gravity equation and its ability to explain
bilateral trade flows led to the development of theories that could incorporate
the model. The gravity model is now seen
at the workhorse of trade theory, and especially in terms of forecasting the
impact of changes in trade policy on trade costs.
Gravity models begin with Newton’s law for the
gravitational force between two objects i and j. In equation form,
this is expressed as: 
Where the gravitational force is
directly proportional to the masses of the objects (Mi and Mj)
and indirectly proportional to the distance between them
(Dij).
Monopolistic competition
among economies. According to influential US economist Paul Krugman, (1979)
“New Trade Theory” states that the current continual application of new
technology by global manufacturers to produce in large scale and very cheaply can
compete in similar markets and export surpluses. Essentially, the model
predicts that once a national economy achieves manufacturing in an economy of scale
of some particular product, this economy will tend to trade with countries of
similar development in what Paul Krugman describes with his linear model C = F
+ cX, which he calls “Monopolistically Competitive Models” in globalized
economies of scale.
.
Recent research shows that when trade opens up, it is
followed by adjustment not only between industries, but within them as well.
Module
manufacturing leverages and Integrates
managing global supply chains, transferring production flexibly to emerging
markets, refocusing on higher-value-added activities, and forming new pockets
of low-cost expertise. These actions will permit to refocus t resources and
capabilities on higher-value activities, thereby contributing to the further
specialization of the industry’s value chain. Meanwhile, these two companies
have been actively transferring some of their manufacturing activities to
emerging markets for cheaper labor and also as consumers of the products,
i.e. Boeing-Aviation.
Historical
Development of Sea Commerce
According to historian Glenn Markoe, the Phoenicians
established a maritime tradition, and the technology to build ships with a
keeled hull which allowed them to sail the open seas resulting in a tradition
that established sea trade.
The navigation of the Phoenicians was limited to coastal
waters as a cautious and timid approach to the early years of commerce. It
follows that the Phoenicians for a long time confined their navigation within
the limits of the Mediterranean, the Propontis, and the Euxine, seas, which are
far less rough than the open ocean. As they gain navigational experience with
their vessels, no bigger than a fishing smack, the Phoenicians proceeded
southwards along the West African coast, as far as Gambia and Senegal, while on
the northern sided they braved the heavy seas of the Bay of Biscay, on the
coast of Spain moreover, passing Cape Finisterre, these adventurer sailors went
across the mouth of the English Channel to the Cassiterides.
Historians often refer to Henry the Navigator, prince of
Portugal, as the initiator of the first great enterprise of the ‘Age of
Discovery’—the search for a sea route east by south to Cathay. The Spanish galleon
and the- caravels favored by pirates because of its speed and agility on the
water—were the ships used by the explorers in the ‘Age of Discovery’. The
Spanish embarked in long-distance maritime travels in search of alternative
trade routes to "the East Indies” moved by the trade of gold, silver and
spices.
In “The Golden Age of Sail” David Ross, (2013) describes
it as a period in which international
trade and naval warfare were dominated by sailing ships, lasting from the 16th
to the mid-19th century in the European
"Age of Sail" international trade and naval warfare were both
dominated by sailing ships.
In the 20th century, the internal combustion engine and
gas turbine came to replace the steam engine in most ship applications.
As ships evolved and merchants gain trade experience
everyone foresaw the advantage of having trade agreements. The first
international free trade agreement, the Cobden-Chevalier Treaty, was finalized
in 1860 between the United Kingdom and France, prepared by Richard Cobden and
Michel Chevalier; it sparks off successive agreements between other countries
in Europe.
Trade Agreements after
WW II
In 1946 the Bretton Woods system went into effect; it had
been in the works since 1944 as an international economic structure to prevent
further depressions and wars. In 1947, 23 countries agree to the General
Agreement on Tariffs and Trade to rationalize trade among the nations.
For the first time there was a codified form of rules and
principles that imposed some obligations on states in the conduct of their
monetary affairs. Given that money had always been a symbol of political power,
the incursion of Bretton Woods into state sovereignty was considerable as
quoted from John Maynard Keynes the principal doctrinaire economist of the agreement.
List of
International Trade Agreements active in 2016
African,
Caribbean, and Pacific Group of States (ACP Group)
Andean Community
of Nations (CAN)
Arab Cooperation
Council (ACC)
A Black Sea
Economic Cooperation Zone (BSEC)
Asia-Pacific Economic
Cooperation (APEC)
Caribbean
Community and Common Market (Caricom)
European Free
Trade Association (EFTA)
North American
Free Trade Agreement (NAFTA)
Shipping Insurance and
Risk. Historical Perspective
Historians have traced the earliest instances of
insurance to the Babylonian period circa 2250 BC, when they developed a type of
loan insurance for maritime business. Examples can be found in the Code of
Hammurabi 1750 B.C.E. It formalizes the concepts
of “bottomry” and “respondentia” (protection against loss of hull and cargo,
respectively) – the link pins of maritime insurance.
Historian, Mark Cartwright, states that the ancient
Athenian maritime loan advanced money for voyages with repayment being cancelled
if the ship was lost. Ships sank, ran afoul of piracy, suffered delays due to
weather, or arrived to find that prices of the goods they were carrying had
unexpectedly drop in value. The practice and use of the maritime loan persisted
until the thirteenth century in the Italian city - states of Genoa and Venice.
Shipwreck by storm or poor navigation was common while ships
and their cargoes were constantly in danger of being seized by pirates or
corrupt officials, or made to pay exorbitant tolls for safe passage.
In the late 1600s seafarers, merchants and insurers meet at
the Edward Lloyd’s Coffee House for insurance business and coffee. (Lloyd’s of
London, history of insurance).
The term “underwriting” is today synonymous with Lloyd’s contracts
specified the premium with explicit sensitive to distance, route, season, and
type of ship, as well as hostilities or piracy. Premiums were generally arrived
at by bargaining for either ship or cargo coverage. Moral hazard encouraged
captains to deliberate shipwreck to collect the insurance. One method of
transaction that was particularly common was–the advance purchase–that combined
a forward transaction with the extension of credit. (American Association of
Law Libraries)
Trade
Routes Between 1400-1800
Source: Hofstra
University
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Markoe, Glenn Peoples
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Thomas Chaney, Working Paper 19285 NATIONAL BUREAU OF
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Tinbergen J, Shaping the World Economy. Twentieth
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J. Orlin Grabbe, Three Essays in International Finance,
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The Fractal Geometry of Nature (1975)’
Markoe, Glenn Peoples of the Past: Phoenicians (Berkeley:
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John Maynard Keynes Collected Writings, London, vol. 26,
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. 2016
