216,558 research outputs found
Allometric Scaling of Countries
As huge complex systems consisting of geographic regions, natural resources,
people and economic entities, countries follow the allometric scaling law which
is ubiquitous in ecological, urban systems. We systematically investigated the
allometric scaling relationships between a large number of macroscopic
properties and geographic (area), demographic (population) and economic (GDP,
gross domestic production) sizes of countries respectively. We found that most
of the economic, trade, energy consumption, communication related properties
have significant super-linear (the exponent is larger than 1) or nearly linear
allometric scaling relations with GDP. Meanwhile, the geographic (arable area,
natural resources, etc.), demographic(labor force, military age population,
etc.) and transportation-related properties (road length, airports) have
significant and sub-linear (the exponent is smaller than 1) allometric scaling
relations with area. Several differences of power law relations with respect to
population between countries and cities were pointed out. Firstly, population
increases sub-linearly with area in countries. Secondly, GDP increases linearly
in countries but not super-linearly as in cities. Finally, electricity or oil
consumptions per capita increases with population faster than cities.Comment: 23 pages, 3 figure
Capabilities' Substitutability and the "S" Curve of Export Diversity
Product diversity, which is highly important in economic systems, has been
highlighted by recent studies on international trade. We found an empirical
pattern, designated as the "S-shaped curve", that models the relationship
between economic size (logarithmic GDP) and export diversity (the number of
varieties of export products) on the detailed international trade data. As the
economic size of a country begins to increase, its export diversity initially
increases in an exponential manner, but overtime, this diversity growth slows
and eventually reaches an upper limit. The interdependence between size and
diversity takes the shape of an S-shaped curve that an be fitted by a logistic
equation. To explain this phenomenon, we introduce a new parameter called
"substitutability" into the list of capabilities or factors of products in the
tri-partite network model (i.e., the country-capability-product model) of
Hidalgo et al. As we observe, when the substitutability is zero, the model
returns to Hidalgo's original model but failed to reproduce the S-shaped curve.
However, in a plot of data, the data increasingly resembles an the S-shaped
curve as the substitutability expands. Therefore, the diversity ceiling effect
can be explained by the substitutability of different capabilities
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