Abstract: The Economic System as a Scale-Free Network Governed by the Principles of Quantum Physics
It is a well-established empirical fact that the distribution of wealth and income in every society studied, presently or in the past, follows a similar pattern in that a small share of the people control a large share of wealth and income. This observation was enunciated more than 100 years ago and is known as the Pareto law. Economists have debated the causes of this inequality at length over the years. The standard analytical model of economic theory, known as the Arrow-Debreu model, provides a mathematical framework defining the conditions for a competitive general market equilibrium where supply equals demand across all markets, and where the decisions of the members of the economy lead to an efficient, consistent, and stable market equilibrium, assuming perfect competition and rational behavior among its members, but is silent as far as wealth and income inequality are concerned, thereby necessitating the development of an alternative model. Such an alternative model of the economy has been developed based on the science of scale-free networks that are implicitly governed by the principles of quantum physics and specifically statistical thermodynamics. The economy is modeled as a scale free network comprised of nodes representing actors/people that are linked by multiple units of wealth or income. Scale-free networks, which appear in a lot of systems such as, for example, the wide-web, display a quite distinct behavior from that of random or Gaussian networks that have been employed traditionally to describe various aspects of the economy and more specifically finance. Scale-free network are characterized by power laws and display a one-to-one correspondence with Bose-Einstein statistics of integral spin particles, and more specifically with photons (zero mass particles) described by Planck's black body radiation law. Thus, in the model of the economy as a scale-free network, the nodes or actors represent the energy levels allowed to be occupied given a total available energy, which corresponds to the total amount of wealth/income available, while the number of links represent the wealth/income per actor. The economic system reaches a state of equilibrium when its entropy is maximized and a consistent with the empirical Pareto law distribution of wealth/income is obtained. A fundamental tenet of the economy as a scale-free network consistent with its physical description as a system of occupied energy states (nodes or actors) with varying energy levels (number of links of wealth/income per actor) is that all actors have equal access to the system. Moreover, there is a finite, i.e., non-zero, amount of wealth or income (link size) that is designated as the quantum of wealth or income. Under these conditions the resulting distribution of wealth and of income is optimal in the sense of the most efficient (maximum entropy) distribution of a given amount of wealth/income among the actors comprising the economy and corresponds to a Pareto index is two. However, optimal does not mean equal and a certain degree of inequality is unavoidable and necessary to ensure that the economic system displays a hierarchical structure and stability. The "invisible hand" of Adam Smith that is also invoked in the Arrow-Debreu model is none other than the manifestation of the state of maximum entropy in the scale-free network model of the economy. An analytical model of the Pareto index is derived based on the quantum of wealth/ income along with the introduction of the "temperature" of the economy, which is a concept related to the average number of links per node in the system of the economy, and the equipartition of wealth/income in direct analogy to that of energy in statistical thermodynamics. The introduced parameters of the quantum of wealth/income and temperature are easily understood indicators of the state of the economy compared to the rather esoteric Pareto index and Gini coefficient indicators. A comparison of the actual wealth and income distributions for the four largest economies in the world shows that in most instances, particularly regarding wealth, significant deviations from the optimal values, i.e., excessive inequality, exist. This suggests that equal opportunity or access is lacking, specifically regarding education, health, housing, institutions, and regulations, and is a manifestation of the "human hand" at work, whether well-intentioned but misguided or else deliberate. Thus, societies, rather than trying to fix the symptoms of excessive inequality by forcing inefficiently the allocation of scarce resources, should strive instead to ensure equal access and opportunity of all its members to the economy.