Page 243 - GHES-3-3

Global Health Economics and
Sustainability
Empirical resource allocation in healthcare

similar to our findings, thereby supporting our hypothesis. Such a statistical environment of conscious, non-
For example, Arnold (2014) noted that Pareto distributions random choice transforms the central limit theorem, which
are useful modeling and predicting tools in a wide variety states that the sum of a large number of approximately equal
of socioeconomic contexts. Pareto distributions and the and independent factors assumes a normal distribution.
related generalizations have been historically viewed as But, when the assumptions of independence are violated,
suitable for modeling income and wealth distributions. the Pareto distribution occurs, where an entity’s resources
attract additional resources based on its current “statistical
Power law distributions characterize many natural and weight.” The uneven distribution of competitors is driven
social phenomena. A large number of studies have focused by the non-stationary nature of resource, income, and
on the distribution of the city populations. Zipf’s law, which wealth distribution. This non-stationarity is statistically
describes the rank-size distribution of cities, is a notable characterized by an “unbounded mathematical
example (Bergs, 2021). Zipf concluded that this law applies expectation,” meaning the parameters influencing the
best in large countries. The city-primacy law, introduced process change over both space and time.
by Jefferson (1939), offers a basic generalization of city size
distributions. Such instability means a violation of the law of large
numbers: as the sample size increases, the average does
Seekell & Pace (2011) investigated whether the Pareto not converge to a constant value (the mathematical
distribution applies to lake sizes and found that truncated expectation), evading stabilization. Instead, the expectation
lognormal datasets are statistically indistinguishable from grows indefinitely, leading to continuous reproduction of
the Pareto distribution. the initial non-stationary economic state based on differing
Let’s consider the distribution model of a resource statistical weights.
strategically important for the sustainable economic In the context of conscious, non-random distribution,
development and growth of any national economy – human the methods and assumptions of probability theory are
capital, particularly highly qualified healthcare specialists insufficient for defining the empirical distribution of
(hereinafter referred to as specialists). Strengthening health specialists among institutions. Probability theory relies
financing is one of the objectives of the United Nations on the concept of a random variable, which takes values
Sustainable Development Goal 3 (SDG target 3.c). The determined by unpredictable random factors. However,
need for investment in healthcare is critical to achieving Pareto’s law approximates the distribution of factors that
overall health coverage, which ensures access to quality are not independent. In this case, the choice is largely
health services without financial hardship (SDG 3.8). determined by the status of the specialist and the rank
It is obvious that in some “ideal” initial market states, of the object. To describe this rank-size dependence,
specialists have a high degree of freedom in choosing where we propose applying thermodynamic methodologies
to apply their skills and abilities, making the process appear and the “generalized theory of competition” (Statistical
homogeneous. However, as market dynamics evolve, their Interpretation of Entropy and the Second Law of
Thermodynamics, 2009), which determines the nature of
choices become increasingly non-random. Specialists tend the distribution of rare resources. Both theories implement
to favor the most competitive and prestigious entities – Boltzmann’s principle of maximum entropy (S), interpreted
leading firms or regions with high market ranks – resulting as the logarithm of the number of possible ways to
in a heterogeneous process. distribute objects by states (in this study, by resource m), as
“The approximation of heterogeneous processes expressed in Equation IV.
in which economic actors make choices using their S = k ln Ω (IV)
knowledge and skills differs from the Pareto distribution”
(Arnold, 2008). The non-random choice of a specialist is Where Ω is the statistical weight, and k is the
determined by his formed competitive status, which can proportionality coefficient (Boltzmann constant).
be described by various factors such as level of education, In thermodynamics, elementary particles are analyzed
qualifications, health status, and income level. At the same based on statistical weight. Analogously, we suggest using
time, firms and territorial authorities actively seek to competitive status or rank as statistical weight. Consider
attract high-status specialists in the competition for human an ideal model where K units of a resource (for example,
capital (Kryscynski et al., 2021). This results in a “two-way specialists) are distributed among N objects of the
non-random choice” scenario: Specialists choose the best economic system ranked by their resource holdings. In
institutions to apply their skills, while the management this case, both specialists and the objects themselves can
chooses the best specialists (Sambodo et al., 2023). be considered resources.

Volume 3 Issue 3 (2025) 235 https://doi.org/10.36922/ghes.8283