1.3 What Is Economics? – Exploring Business

To appreciate how a business functions, we need to know something about the economic environment in which it operates. We begin with a definition of economics and a discussion of the resources used to produce goods and services.

Because a business uses resources to produce things, we also call these resources factors of production . The factors of production used to produce a shirt would include the following:

Resources are combined to produce goods and services. Land and natural resources provide the needed raw materials. Labor transforms raw materials into goods and services. Capital (equipment, buildings, vehicles, cash, and so forth) are needed for the production process. Entrepreneurship provides the skill and creativity needed to bring the other resources together to produce a good or service to be sold to the marketplace.

Economics is the study of the production, distribution, and consumption of goods and services. Resources are the inputs used to produce outputs. Resources may include any or all of the following:

Many of the factors of production (or resources) are provided to businesses by households. For example, households provide businesses with labor (as workers), land and buildings (as landlords), and capital (as investors). In turn, businesses pay households for these resources by providing them with income, such as wages, rent, and interest. The resources obtained from households are then used by businesses to produce goods and services, which are sold to the same households that provide businesses with revenue. The revenue obtained by businesses is then used to buy additional resources, and the cycle continues. This circular flow is described in Figure 1.3 “The Circular Flow of Inputs and Outputs” , which illustrates the dual roles of households and businesses:

Economists study the interactions between households and businesses and look at the ways in which the factors of production are combined to produce the goods and services that people need. Basically, economists try to answer three sets of questions:

Economic Systems

The answers to these questions depend on a country’s economic system—the means by which a society (households, businesses, and government) makes decisions about allocating resources to produce products and about distributing those products. The degree to which individuals and business owners, as opposed to the government, enjoy freedom in making these decisions varies according to the type of economic system. Generally speaking, economic systems can be divided into two systems: planned systems and free market systems.

Planned Systems In a planned system, the government exerts control over the allocation and distribution of all or some goods and services. The system with the highest level of government control is communism. In theory, a communist economy is one in which the government owns all or most enterprises. Central planning by the government dictates which goods or services are produced, how they are produced, and who will receive them. In practice, pure communism is practically nonexistent today, and only a few countries (notably North Korea and Cuba) operate under rigid, centrally planned economic systems. Under socialism, industries that provide essential services, such as utilities, banking, and health care, may be government owned. Other businesses are owned privately. Central planning allocates the goods and services produced by government-run industries and tries to ensure that the resulting wealth is distributed equally. In contrast, privately owned companies are operated for the purpose of making a profit for their owners. In general, workers in socialist economies work fewer hours, have longer vacations, and receive more health care, education, and child-care benefits than do workers in capitalist economies. To offset the high cost of public services, taxes are generally steep. Examples of socialist countries include Sweden and France.

Free Market System The economic system in which most businesses are owned and operated by individuals is the free market system, also known as capitalism. As we will see next, in a free market, competition dictates how goods and services will be allocated. Business is conducted with only limited government involvement. The economies of the United States and other countries, such as Japan, are based on capitalism.

How Economic Systems Compare In comparing economic systems, it’s helpful to think of a continuum with communism at one end and pure capitalism at the other, as in Figure 1.4 “The Spectrum of Economic Systems”. As you move from left to right, the amount of government control over business diminishes. So, too, does the level of social services, such as health care, child-care services, social security, and unemployment benefits.

Mixed Market Economy Though it’s possible to have a pure communist system, or a pure capitalist (free market) system, in reality many economic systems are mixed. A mixed market economy relies on both markets and the government to allocate resources. We’ve already seen that this is what happens in socialist economies in which the government controls selected major industries, such as transportation and health care, while allowing individual ownership of other industries. Even previously communist economies, such as those of Eastern Europe and China, are becoming more mixed as they adopt capitalistic characteristics and convert businesses previously owned by the government to private ownership through a process called privatization.

Foundations of Economic Development

Foundations of Economic Development

CONCENTRATION/ELECTIVE COURSE | SISG-768 | 3 CREDITS

This course has three aims. It introduces different ways to define and to measure economic development. It examines the nature and causes of the economic challenges in developing countries (growth, employment, poverty, income inequality, gender inequality, financial stability, maintaining balance of payments, etc.). The course also explores debates about the most effective economic policies for promoting the advancement of low and middle-income countries.

Required for the following concentrations at MAIR:

Econophysics and the Entropic Foundations of Economics

While the emerging econophysicists identified themselves as being physicists, an important impetus to their activities came from the intense discussions between economists and physicists at the Santa Fe Institute starting in the late 1980s [ 30 31 ]. While some of the economists defended existing economic theory, these discussions often emphasized dissatisfaction with its ability to explain empirical phenomena exhibiting non-Gaussian distributions with skewness and “fat tails” leptokurtosis [ 32 34 ]. While indeed most of the economists in these discussions disavowed some of the models developed by the econophysicists, the irony is that some of these models introduced by the physicists that could generate such higher moments as well as scaling properties were originally developed by economists, with the most important example of this being the Pareto distribution [ 35 ].

This freshly defined approach involving physicists in particular, sometimes in conjunction with economists, quickly became a self-conscious cottage industry, even though arguably similar efforts had been going on for a long time, if not specifically by self-identified physicists, although some econophysicists have argued that an early inspiration for their work was Ettore Majorana in 1942 [ 6 ], whose untimely death gave him dramatic attention as he argued for the profound identity of statistical methods used in social sciences and physics. Important influences on the self-identified econophysicists included statistical mechanics [ 7 8 ] and also self-organized criticality models derived from models of avalanches [ 9 ] and earthquakes [ 10 ]. These approaches led to studies of many subjects in the early days, generally finding distributions that did not follow Gaussian patterns characterizable solely by mean and variance. These subjects included financial market returns [ 11 18 ], economic shocks and growth rate variations [ 19 20 ], city size distributions [ 21 22 ], firms size and growth rate patterns [ 4 24 ], scientific discovery patterns [ 25 26 ], and the distribution of income and wealth [ 27 29 ].

It has long been argued as for example by Mirowski [ 1 ] that economic theorists have drawn on ideas from physics, with an especially dramatic and influential example being Paul Samuelson’s Foundations of Economic Analysis [ 2 ] from 1947. However, while the influence of physics concepts in Samuelson, as well as many economists much earlier, was enormous and openly acknowledged, it was only much later that the term econophysics would be coined, reportedly at a conference in 1995 Kolkata, India [ 3 ] by H. Eugene Stanley, who as a longtime editor of Physica A has played a crucial role in publishing many papers that have been identified as representing and advancing this approach, with the term first appearing in print in 1996 [ 4 ]. Curiously when it came to define this multidisciplinary neologism, the emphasis given by Mantegna and Stanley [ 5 ] was not upon the ideas or specific theoretical methods involved, but rather on the people doing it: “the activities of physicists who are working on economics problems to test a variety of new conceptual approaches deriving from the physical sciences”.

Nevertheless, parallel developments inspired by Pareto went on through the twentieth century, with some using the stable Lévy distribution developed in 1925 [ 45 ] as a generalization of Pareto’s distribution. Applications included looking at scientific discovery patterns [ 46 ] and city sizes [ 47 ]. A singular figure later in the century would be the father of fractal geometry, Benoit Mandelbrot [ 48 49 ], who directly posed the rival Pareto distribution as being able to model price dynamics [ 50 ] in 1963, in contrast to Osborne’s argument. In 1977, Iriji and Simon [ 51 ] applied this to firm size distributions, a finding generally ignored until verified by Rob Axtell in 2001 [ 52 ].

As it was, the Gaussian random walk would come to dominate a great deal of the modeling of price dynamics and financial market dynamics, including the widely used Black–Scholes formula [ 43 ]. Ironically, this triumph of what became the standard economic approach was engineered by the physicist M.F.M. Osborne in 1959 [ 44 ]. His model of dynamic prices, withas the price,the price increase return,as the debt, andas the Gaussian standard deviation, is given by:

Much like the more recent econophysicists, Pareto’s original focus was on income distribution, and he believed (inaccurately) that he had found the universally true value of 1.5 for. In 1931, Gibrat [ 36 ] countered Pareto’s argument with the idea that instead income distribution followed the lognormal form of the Gaussian distribution that can arise from a random walk, first studied by Bachelier in 1900 [ 37 ], with Einstein adopting it to model Brownian motion [ 38 ]. However, further studies suggest that combining these two provides a better description of income distribution, with the upper end of the distribution showing a Pareto pattern and lower portions showing lognormal Gaussian forms [ 39 42 ].

Scaling can be seen as:with it possible to stochastically generalize this by replacingwith the probability an observation exceeds. The log–log form of this is conveniently linear.

This important distribution that shows so many characteristics interesting to econophysicists was initially developed by the socio-economist Vilfredo Pareto in 1897 [ 35 ]. Ifis the number of observations of a variable exceeding, andandare positive constants, then

To a substantial degree, most econophysicists were not aware of either the more recent work along these lines, much less the deeper work further in the past, with this leading to some of them making unfortunately exaggerated claims about the originality and transformative nature of what they were doing. These problems were discussed in a critical essay called “Worrying trends in econophysics” by Gallegati et al. in 2006 in 63 ]. They identified the following as problematic trends: missing knowledge of the existing economics literature, a readiness to believe there may be universal empirical regularities in economics not really there unlike in physics, much use of unrigorous statistical methods sometimes just looking at figures, and relying on inappropriate theoretical foundations such as invalid conservation principles. McCauley responded [ 64 ], taking a hard line, that economic theory is so worthless that it should be totally replaced by ideas coming from physics. Reviewing these arguments, Rosser [ 65 66 ] agreed that economists often make vacuous assumptions, despite excessively unreal assumptions damaging usefulness of models. One way to deal with this is to have more joint research between economists and physicists.

More recently, there have been a variety of economists using statistical mechanics to develop stochastic models of various economic dynamics, including work by Hans Föllmer in 1974 [ 55 ], and then in the 1990s, just as the econophysicists were getting going by Blume [ 56 ], Durlauf [ 31 ] (pp. 83–104) and [ 57 ], Brock [ 58 ], Foley [ 59 ], and Stutzer [ 60 ]. Stutzer applied the maximum entropy formulation of Gibbs with the conventional Black–Scholes model [ 43 ], drawing on Arrow–Debreu contingent claims theory [ 61 ]. Brock and Durlauf [ 62 ] would formalize the general approach within the context of socially interacting heterogeneous agents maximizing utility in a discrete choice setting.

Arguably, the earliest influence of physics on economics was due to Canard in 1801 [ 53 ], who posed supply and demand as being “forces” opposing each other in a physics sense. However, a more specific influence on conventional economics would be statistical mechanics, developed by J. Willard Gibbs in 1902 [ 7 ]. As noted earlier, Samuelson in 1947 [ 2 ], who drew the influence from Irving Fisher [ 54 ], drew on Gibbs’s approach for his reformulation of standard economic theory, a development much criticized by Mirowski [ 1 ], who derided all as economists exhibiting “physics envy”.

An obvious question arises as to how this widely used and influential metaphorical entropy measure relates to the ontological one of Boltzmann. In fact, they are proportional to each other as the number of possible states,, approaches infinity, because, resulting in [ 74 75 ]:

Gibbs [ 7 ] famously declared that “mathematics is a language”, which indeed he viewed as applying to his analysis of entropy within statistical mechanics. However, while we can view the mathematical formulation of Boltzmann entropy as a linguistic matter, it describes the real physical phenomenon of thermodynamics. Thus, it can be viewed as being ontological entropy [ 70 ], as it can be applied to more abstract phenomena with less linkage to definite physical processes, thus allowing them to be labeled metaphorical entropy. The first application beyond thermodynamics was information patterns in the form of Shannon entropy [ 71 ]. This describes—the probability distribution of informational uncertainty states for message i that reflects the whole set of information concerning the relevant microstate,). Therefore, informational entropy involves adding up the individual log probabilities times their probabilities to give [ 71 73 ]:

Moreover, the transition to the thermodynamics of an ideal classical gas at a temperature of T > 0 requires additional conditions to be taken into account, concerning the consistency of the total number of molecules of the gas, N , and the total energy, E , of all molecules.

In the Gibbsian statistical mechanics, the question of maximizing entropy is a crucial element, which leads us to the question of what entropy is. Its original formulation came from Ludwig Boltzmann [ 67 ], although it was not as many thought the form that appeared on his grave [ 68 ] that has long received a great deal of attention. The statistical mechanics problems involve aggregating out of individual molecular interactions to observe systemic averages, such as temperature out of such a motion in a space. Lettingbe entropy,be the Boltzmann constant, andbe the statistical weight of the system macroscopic state (also known as the “thermodynamic probability”), then the following equation can be written as:where the configurational statistical weight of the macrostate of the system,, defines the number of ways (configurations) of the arrangement ofof the identicalideal classical gas molecules in the microstates of the system (constituting a given macrostate), whereis the number of the identical molecules in the microstate. The author uses this physical interpretation later in the work, givenis the sum of over theavailable microstates of the system each given by. Then according to Chakrabarti and Chakraborty [ 69 ], this implies that one is dealing with factorials multiplying each other as:

Many ecological economists [ 81 82 ] have supported the idea of entropy as an ontological limit to growth. However, while this is clearly true, others have noted that the limit is many orders of magnitude above other limits that are more immediate [ 83 85 ]. Drawing down stored fossil fuel energy sources generates climate-changing pollution by releasing COand thus further limiting growth. Others note the unlimited ingenuity of the human mind, with Julian Simon [ 86 ] (p. 347) arguing that “those who view the relevant universe as unbounded view the second law of thermodynamics as irrelevant to the discussion”.

Ontological entropy lies at the heart of the econophysics foundation of economic growth due to the profound importance of energy both through the role of steam engines in industrial production and electricity and in agriculture through the thermodynamic transmission of solar energy through the larger global biosphere. The origin of understanding thermodynamics came from Sadi Carnot [ 76 ] in 1828 and later more fully Rudolf Clausius [ 77 ]. In 1971, Nicholas Georgescu-Roegen, [ 78 ] argued that the openness of the global biosphere to the sun allows temporarily overcoming the law of entropy [ 79 ]. Even so, there is a limit to solar energy, which implies limits for economic activity. However in an open system, anti-entropic forces can operate to develop order in local areas, drawing on the argument of Schrödinger [ 80 ] that life is ultimately an anti-entropic process involving the drawing of energy and matter from outside the living organism until it dies. Georgescu-Roegen also argued for this to extend to broader material resource inputs, subject to a form of the law of entropy. More broadly for Georgescu-Roegen [ 78 ] (p. 281), “the economic process consists of a continuous transformation of low entropy into high entropy, that is, into, or, with a topical term, into pollution”.

Lotka [ 81 ] (p. 355) himself noted limits to this argument: “The physical process is a typical case of ‘trigger action’ in which the ratio of energy set free to energy applied is subject to no restricting general law whatsoever (e.g., a touch of the finger upon a switch may set off tons of dynamite). In contrast with the case of thermodynamics conversion factors, the proportionality factor is here determined by the particular mechanism employed”. Georgescu-Roegen [ 78 ] saw value as ultimately coming from utility rather than entropy. Thus, most people value the high-entropy beaten egg more highly than the low-entropy raw egg, and nobody valuing low-entropy poisonous mushrooms, due to utility rather than entropy.

Another argument has seen ontological entropy as the fundamental source of economic value in a parallel to the labor theory of value. The earliest version of this dates to the turn of the twentieth century in arguments by “energeticist” physicists [ 87 89 ]. Julius Davidson [ 90 ] saw the economics law of diminishing returns based on the law of entropy, with the law of diminishing marginal returns, probably the only “economic law” that has no exception to it. Davis [ 91 ] claimed “economic entropy” underlies the utility of money, but Lisman [ 92 ] argued this is not how thermodynamics operates in physics. Samuelson [ 93 ] ridiculed such arguments as a “crackpot”, even as he drew on entropic ideas of Gibbs [ 7 ] and Lotka [ 81 ].

The dependence versus autonomy of systems on their environment, derived from dissipative structures of open systems considered by Prigogine [ 100 ], was formulated by Morin [ 106 ] and then used by Marchinetti et al. [ 97 ]. This finds urban systems development between autarchy and globalization, either extreme unsustainable, advocating a balanced path they see urban–regional systems as ecosystems operating on energy flows [ 107 ] based on a complex wholes emerging out of interacting micro-level components [ 108 ].

Zhang et al. [ 96 ] use entropy concepts to study sustainable development in Ningbo, China, a city near Shanghai, relying on ideas in [ 95 105 ]. They examine both ontological and metaphoric information entropy measures, as they consider four distinct aspects. The first two are sustaining input entropy and imposed output energy, arising from production. The second two constitute the urban system’s metabolic functions, regenerative metabolism and destructive metabolism, which linked to pollution and its cleanup, a measure of environmental harmony. These contrast developmental degree and harmony degree, with the finding during the 1996–2003 period that these two went in opposite directions, with the developmental degree rising (associated with declining entropy) and the harmony degree falling (associated with rising entropy). Thus, we see Chinese urban development sustainability issues clearly.

Balocco et al. [ 95 ] consider exergy in construction and building depreciation in Castelnuovo Beardenga near Siena, Italy, relying on an adaptation by Moran and Sciubba [ 103 ] of Rant’s model. Studying particularly the input–output of the construction industry, it is seen that those built in 1946–1960 provide higher sustainability than newer ones.

The right-hand side of Equation (11) simply holds for an isolated system, from which we see the anti-entropic nature of exergy, determining the irreversible spontaneous time evolution (or “time arrow”).

The maximum amount of the useful work possible to reach a maximum entropy condition of zero has been calledby Rant [ 101 ] initially for chemical engineering. This term is essentially identical to the term “chemical potential” and also “Gibbs-free energy”. Rant’s original formulation holds, whenis the exergy,is the internal energy,is the pressure,is the volume,is the temperature,is the entropy,is the chemical potential of component, andis the moles of component, implying:

Given that d/dcan be either sign, when negative with an absolute value greater than that of, then total entropy may fall as the system absorbs energy and materials creating order, with entropy increasing outside as waste and disorder leave the system. Wackernagel and Rees [ 102 ] state, “Cities are entropic black holes” implying, as they produce large ecological footprints, their sustainability becomes impaired.

Three concepts to distinguish areas total entropy,as inside entropy, andas outside entropy. Assuming the statistical independence between both the internal states and the external states, then their dynamic relationship can be written as:

Considering urban–regional systems as open and dissipative systems, experiences allows the analysis of sustainability, depending on their energy and material flows [ 81 100 ]. In open systems, entropy can rise or fall, as energy and materials flow into them, in contrast to closed systems where entropy can only rise. This is the key to Schrödinger’s [ 80 ] that life is an anti-entropic process with organisms drawing in energy-generating structure and order while life lasts. Anti-entropy is also known 101 ] and also negentropy or “negative entropy”.

The ontological entropic analysis of urban and regional systems sees them driven by the second law of thermodynamics based on actual energy transfers as argued by Rees [ 94 ], Balocco et al. [ 95 ], Zhang et al. [ 96 ], Marchinetti et al. [ 97 ], and Purvis et al. [ 98 ]. Alan Wilson [ 99 ] reviews both ontological and metaphorical approaches to the entropic analysis of urban and regional systems.

Papageorgiou and Smith [ 119 ] and Weidlich and Haag [ 120 ] have shown that rising agglomeration economies can overcome congestion costs to manifest urban concentration. However, such models have been partially replaced by “new economic geography” ones emphasizing economies of scale appearing in monopolistic competition studied by Dixit and Stiglitz [ 121 ]. Fujita [ 122 ] first applied this approach to urban–regional systems, although Krugman [ 123 ] received much more attention for his version [ 124 ].

Long viewed as foundational for economic complexity, increasing returns may provide a basis for power-law distributional outcomes [ 115 ]. Three different kinds of these have been identified for urban systems: firm-level internal economies [ 116 ], external agglomeration between firms in a single industry providing localization economies [ 117 ], and external agglomeration economies across industries generating yet larger-scale urbanization economies [ 118 ].

US city size distributions seem to have shown power-law distributions from 1790 to the present, although not precisely following the rank-size rule (the size of Los Angeles is now larger than half the size of New York), according to Batten [ 112 ]. A meta-study of many empirical studies by Nitsch [ 114 ] finds widely varying estimates over these studies, although showing an aggregate mean of α = 1.08, near Zipf’s value. Berry and Okulicz-Kozaryn [ 111 ] say Zipf’s law strongly holds if one uses consistent measures for urban regions across studies, especially the largest ones for megalopolises. Anyway, city size distributions seem to be power-law-distributed, suggesting dominance by anti-entropic econophysics forces in this matter.

This is the rank-size rule of Auerbach [ 110 ] from 1913 and generalized in 1941 as Zipf’s law, claimed to be applied to many distributions [ 47 ]. Since Auerbach [ 110 ] proposed it and Lotka [ 81 ] challenged it, there has been much debate regarding the matter. Many urban geographers [ 111 ] claim it is a universal law. Many economists have doubted this, saying there is no reason for it, even as urban sizes may show power-law distributions [ 112 113 ]. However, Gabaix [ 22 ] says Zipf’s law holds in the limit if Gibrat’s law is true with growth rates, independent of city sizes.

Power-law distributions of econophysics reflect dominant anti-entropic forces [ 70 ], and urban size distributions seem to show these [ 22 ]. For the Pareto power-law distribution of city sizes [ 35 ],is the population,is the rank, withandare constants, implying:

Opposing this entropic version urban and regional systems structure is a power law version. In higher-level distributional systems, entropy ceases to operate and become irrelevant. This reflects a balance of entropic and exergetic forces operating in the relations and distributions within urban–regional systems [ 109 ].

Shannon entropy of this multiplicity involves summing over these proportions similarly to Equation (7) and is written as:

If there arecommodities,agents of typewho make a transactionof which there isproportion of agents typeout of, which make transactionout of an offer set, of which there are, thenof an assignment foragents assigned toactions, each of them, which gives the probabilistic states across these possible transactions as:

Foley [ 59 ] assumes all possible transactions within an economy have equal probability, implying a statistical distribution of behaviors in the economy where a particular transaction is inversely proportional to the exponential of its equilibrium entropy price. This is a shadow price derived from a Boltzmann–Gibbs maximum entropy set. The special case when “temperature” is zero implies Walrasian general equilibrium. The solution is not necessarily Pareto optimal, and it allows for possible negative prices as Herodotus observed in ancient Babylonian bridal auctions, where they sold brides in descending prices that started out positive but then would go negative [ 126 ]. Foley emphasizes the crucial importance of constraints in this approach, as one finds in the Arrow–Debreu model.

Metaphorical Shannon entropy offers a different approach than Arrow–Debreu general equilibrium theory of value. Arrow and Debreu views equilibrium as a fixed point set of steady prices. However, in the reality of a stochastic world, equilibrium may be a probability distribution of prices that are constantly varying everywhere at any point in time for any commodity that can be modeled entropically. The Arrow–Debreu solution is a special case of Lebesgue measure in the space of outcomes. Initially conceived by Föllmer [ 55 ], Foley [ 59 ] developed it, followed by Foley and Smith [ 125 ].

More recent studies have expanded the forms of entropy used in studying financial market dynamics. Thus, transfer entropy has been used by Jizba et al. [ 131 ] to study differences in related financial times series focusing on spike events by Dimpli and Peter [ 132 ] to study cryptocurrency dynamics and by Kim et al. [ 133 ] for directional stock market forecasting. In addition, permutation entropy has been used in a variety of financial market econophysics applications [ 134 ].

Thus, the Black–Scholes option-pricing formula can be derived from a martingale product density arising from relative entropy minimizing conditional risk for an asset subject to IID normally distributed shocks. Stutzer understood this does not generate non-Gaussian distributions such as econophysics power law ones. He poses using Generalized Auto Regressive Conditional Heteroskedastic (GARCH) processes as an alternative.

The order-maximizing solution for the neutral density of relative entropy-minimizing conditional risk given by the integral is written as:which satisfies a martingale restriction withas a quantity:

Using the entropy law with Shannon or Boltzmann–Gibbs distributions can model distributions involving lognormality, both exhibiting normal Gaussian characteristics, Michael J. Stutzer [ 60 129 ] has drawn on both types of entropy to model Black–Scholes [ 43 ] formuli. In [ 129 ], he uses Shannon entropy, like Cozzolino and Zahner [ 130 ], allowing them to derive lognormal stock price distributions at the same time, similar to what Black and Scholes [ 43 ] did in deriving their options formuli without using entropy measures. Stutzer [ 129 ] considered a discrete form version modeling a stock market price dynamic by:withis the price, Δp is the random shock, Δis the time interval, and the second term on the right hand side is the random shock, distributed ~(0,).

“Entropy is a measure of dispersion, uncertainty, disorder and diversification used in dynamic process, in statistics and information theory, and has been increasingly adopted in financial theory”.

Schinkus [ 127 ] points out that econophysicists are more willing than most economists to approach data open to more possible distributions or parameter values, while favoring ideas from physics, including entropy for financial modeling. According to Dionisio et al. [ 128 ] (p. 161):

11. Using Statistical Mechanics to Model Income and Wealth Distributions

Income and wealth dynamical systems can be driven by interactions between power-law distributions and non-power-law ones. Wealth dynamics apparently exhibit power-law distributions, while income distribution dynamics look to consist of entropy-related Boltzmann–Gibbs distributions. The former seem to drive the top 2–3 percent of income distributions, while the latter seem to drive income distributions below that level in the UK and US [ 28 40 ].

Entropy came to be used in generalizations of various income distribution measures as early as 1981, when Cowell and Kuga [ 135 ] presented a generalized axiomatic formulation for additive measures of income distribution. Adding two axioms to the standard model allowed a generalized entropy approach to subsume the well-known Atkinson [ 136 ] and Theil measures [ 137 ]. The former can distinguish the skewness of tails, while latter has more generality, with Bourgignon [ 137 ] showing the Theil to be the only zero-homogeneous decomposable “income-weighted” inequality measure. Adding a sensitivity axiom to others, Cowell and Kuga [ 135 ] argued a generalized entropy concept implies the Theil index, even as some argued that this linking was a challenge, with Montroll and Schlesinger [ 138 ] (p. 209) declaring

“The derivation of distributions with inverse power tails from maximum entropy formalism would be a consequence only of an unconventional auxiliary condition that involves the specification of the average of a complicated logarithmic function”.

It is unsurprising that both wealth and financial market distribution dynamics exhibit power-law distributions taking into account their close link, given Vilfredo Pareto’s [ 35 ] role in discovering them. Initially trained to be an engineer, Pareto came to study the dynamic social classes relations manifested by income distribution. He claimed a universally true pattern that held throughout “the circulation of elites” he studied, but he was wrong, with ironically his method superior for the study of wealth distributions. He claimed incorrectly that because of the constancy of the income distribution pattern, little can be performed to equalize income, because changes in political leadership simply substitutes one power elite by another with no income distribution change. However, large changes occurred, so his approach went “underground”, reappearing for other uses such as for urban metropolitan size distributions [ 111 ].

140, The sociologist, John Angle [ 139 ], revived using Pareto’s power-law distribution for studying income and wealth distribution dynamics starting in 1986. Then, econophysicists followed up with this, with their finding that wealth distributions follow Pareto’s power law view well [ 27 141 ].

The question arises as to whether we are dealing with ontological or “merely” metaphorical models in studying wealth and income distributional dynamics. Some see the stochastic elements in these distributions associated with thermodynamical processes fundamentally driving the distributional dynamics of income and wealth. However, these do not appear to be direct ontological processes as with Carnot’s steam engines. More likely, these reflect dynamics associated with no substantial changes in public distributional policies.

Yakovenko and Rosser [ 40 ] show a model with an entropic Boltzmann–Gibbs dynamics for lower-income distribution and a Paretian power-law distributions for higher-level income dynamics. There is an assumption of the conservation of money or income or wealth, which has not held in recent years as top-level incomes have exploded although it did much more so in earlier decades. This is consistent with lognormal entropic dynamics appropriate for the majority of the population below a certain level where wage dynamics predominate, while a Pareto power law is more appropriate for the top level whose income is more determined by wealth dynamics.

m , the Boltzmann–Gibbs entropic equilibrium distribution has probability, P , with m seen as: P ( m ) = ce − m / Tm , (20) c is a normalizing constant, and T m is the “money temperature” thermodynamically, equaling the money supply per capita. The portion of the income distribution below about 97–98 percent seems to be well modeled by this formulation. Assuming money conservation,, the Boltzmann–Gibbs entropic equilibrium distribution has probability,, withseen as:withis a normalizing constant, andis the “money temperature” thermodynamically, equaling the money supply per capita. The portion of the income distribution below about 97–98 percent seems to be well modeled by this formulation.

γ, then the Gamma distribution rather than the Boltzmann–Gibbs distribution better describes the stationary money distribution with a power-law prefactor, mβ , such that: β = −1 − ln 2/ ln (1 − γ) . (21) If there is a fixed rate of proportional money transfers equalingthen the Gamma distribution rather than the Boltzmann–Gibbs distribution better describes the stationary money distribution with a power-law prefactor,, such that:

P(m) = cmβe−m/T . (22) This Boltzmann–Gibbs version more simply relates to a power law equivalent than that posed by Montrell and Schlesinger [ 138 ]. The connection between the models of wealth and income distributions is described as:

m grow stochastically disconnects this outcome from the maximum entropy solution [ w as the wealth per person and J as the average transfer between agents, with σ being the standard deviation: P(w) = c[(e−J/σσw)/(w2+J/σσ)] . (23) Lettinggrow stochastically disconnects this outcome from the maximum entropy solution [ 142 ], so the stationary distribution becomes Fokker–Planck equation-driven mean field situation, not Boltzmann–Gibbs distribution, although inverse Gamma in [ 27 142 ] is a Lotka–Volterra form showingas the wealth per person andas the average transfer between agents, with σ being the standard deviation:

42, This model provides an empirical explanation of income distribution consistent with Marxist and other classical economic views of socio-economic class dynamics [ 41 143 ].

Figure 1 exhibits this in the log–log form for the 1997 US income distribution, with the Boltzmann–Gibbs section for the lower 97 percent of the distribution being nonlinear on the left-hand side, while the Pareto section is linear in logs on the right-hand side showing the top 3 percent of the income distribution (Figure 4.5 of [ 144 ]).