Journal of Business and , ISSN 2155-7950, USA November 2018, Volume 9, No. 11, pp. 915-926 DOI: 10.15341/jbe(2155-7950)/11.09.2018/001  Academic Star Publishing Company, 2018 http://www.academicstar.us

The Quest of Economic Temperature

Matthew Yen, Daming Zhang  (Department of Industrial Technology, California State University, USA)

Abstract: Temperature is the vital sign of life. So is the “economic temperature” a vital sign of . The concept of economic temperature has been around in history since the time used for trading. Nonetheless, economists and scholars struggled with the basic definition of economic temperature. Mathematic modeling and quantitative analysis are essential tools for modern economic analysis. Without clear definition of economic temperature, theoretical discussions are severely handicapped. Recent development of are appealing because of the well-established mathematic formulation, particularly, . However, the lack of clear definition of economic temperature greatly hindered econophysics discussions and application. The Law of Supply-and-Demand and the Law of Ideal-Gas have shared hyperbolic form. Money system and ideal gas are “working-media” or “agents” in and mechanical system respectively. Therefore, the shared forms are not only mathematically intriguing but also bearing theoretical significances. A definition of “Economic Temperature” based on these two well-established laws opens the door for broad-spectrum economic applications. Key words: economic temperature; law of supply-and-demand; econophysics; ideal gas law, JEL codes: B400

1. Introduction

A casual walk around the stores after Christmas, Christmas cards, Christmas decoration items are all at deeply discounted prices. The season is over and the market is “cold”. “Economic temperature” is a qualitative term indicating the level of trading activities in a market. Temperature is the vital sign of life. So is the “economic temperature” a vital sign of economy. This is a good example of the Law of Supply-and-Demand manifests in everyday lives that was postulated by (1776). When a commodity or a stock trades a large volume with increased price, then the market is “hot”. In physics, temperature is a measure of the kinetic of molecules, which is the “frequency of movements” in terms of mass and speed. Therefore, “temperature” may denote the frequency of trading in a market. There is long history of thermometry to quantify temperature in physics. Nonetheless, there is no clear definition to quantify the “economic temperature”. Georgescu-Roegen (1971) pioneered to apply thermodynamics framework to study economics. Mimkes (2006) applied the laws of calculus to formulate the econophysics. Mimkes defined “economic temperature” as an

Daming Zhang, Ph.D., Professor of Transportation Systems Management, Department of Industrial Technology, California State University; research areas/: Transportation Systems Management. E-mail: [email protected].

915 The Quest of Economic Temperature integrating factor. Bryant (2011) presented an application of the ideal gas law as the basic of thermoeconomics. Bryant used the concept of kinetic theory assigned trading as the “economic temperature”.

2. States and Processes

Though scholars and economists have made significant progress to employ tools used in thermodynamics to harness the dynamics of economics, it is essential to examine the common attributes and fundamental differences between these two disciplines. Economics and thermodynamics share the following attributes: 1) Systems of large number constituents (~1023 and beyond) 2) Complex non-equilibrium system behaviors 3) Seeking synergistic explanations of macroscopic behaviors in relation to microscopic kinetics Table 1 summarizes the differences between economics and thermodynamics in terms of equilibrium state and none-equilibrium processes.

Table 1 Summary of State Descriptions and Processes Behaviors of Economics and Thermodynamics Economics Thermodynamics Notes Price, volume, value, temperature Pressure, volume, temperature, Equilibrium state, *Economic State & entropy*, etc. entropy temperature and entropy as state variables variables not well defined Law of Supply and demand, Law Equation of State, phase diagrams There is no counter-parts as three Governing of competitions, Law of phases of matters in economics expressions self- Cash flow, flow, good Heat flow, mass flow, electricity, etc. Non-equilibrium systems Processes flows, people migration, etc. behaviors mathematic modeling, statistical Mathematical modeling Phenomenological relations, e.g.: Governing simulation, etc. (Phenomenological relations), Fourier’s Law, Fick’s Law, etc. are descriptions statistical simulation empirical

A key difference between economics and thermodynamics is the “state of equilibrium”. In thermodynamics, we can maintain the state of equilibrium in labs, while there is no such luxury in economics. System equilibrium is the underpinning assumption of economic analogy to thermodynamics. Table 2 summarizes the analogies of state variables for economic and thermodynamic systems. Saslow has provided detailed comparisons of these state variables in Eq. (2).

Table 2 Summary of Analogies Between Economic And Thermodynamic Systems According to Saslow (1999) P V, Q T S w q Economics price Volume or quantity trading value entropy Money circulation Thermodynamics pressure volume temperature entropy Work, PV Heat, TS

The advantage of applying the thermodynamic framework is that all state variables can be determined with the aid of state functions, such as: Gibbs free energy and Helmhotz free energy, chemical potential, etc. These frameworks are mathematically elegant. Nonetheless, it is difficult to decipher especial for scholars who do not have background of thermodynamics. Table 3 summarizes the characteristics of state variables. In thermodynamics, volume and entropy are extensive variables. In other words, they are additive. Pressure and temperature are intensive variables. They are not additive. Furthermore, pressure, volume and temperature can be directly measured. Entropy can be determined once the equation of the state is known. While in economics, price, quantity can be measured. However, as for

916 The Quest of Economic Temperature temperature and entropy scholars struggle to provide clear definitions.

Table 3 Characteristics of State Variables State Variables Economics Thermodynamics Measurable Non-Measurable Measurable Non-Measurable Extensive (additive) Volume (Quantity) Entropy Volume Entropy Intensive (non-additive) Price Temperature Temperature, pressure

3. Ideal Gas Law

In thermodynamics, temperature measurement also known as thermometry has a long history in the past. Nonetheless, the development of ideal gas law considered an additional aid of the thermometry because of its simple form. Figure 1 showing that pressure and volume are related in hyperbolic form along the isothermal-constant temperature lines. Thus, if pressure and volume is known, temperature can be readily determined according to the law: PV = nRT. Note that T is the absolute temperature. This is the base form for the equation of state for real gases, such as: oxygen, nitrogen, air, etc.

Figure 1 Equation of State of the Ideal Gas

4. Law of Supply and Demand

Adam Smith stated three laws of economics: (1) Law of Self-Interest, (2) Law of Supply-and-Demand, (3) Law of competitions. The Law of Supply and Demand is widely used in explaining the behavior of economics. Figure 2 is an illustration of the Law of Supply and Demand. The general form of these curves is hyperbolic, which is the same as that of the equation of state of an ideal gas.

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The phenomenological macroscopic pattern of market supply-and-demand and the ideal gas is an evidence of the shared theoretical microscopic kinetics, i.e., the behavior pattern of an “ideal medium” or “ideal agent”. Adopting the analogy of economics and thermodynamics described previously, the “economic temperature” can be readily determined by the equation PV = nRT. This intuitive definition of ‘economic temperature’ enables us to relate the change of “economic entropy” and other economic state variables without invoking abstract state functions. The hyperbolic form of both the law of supply-and-demand and the law of the ideal gas are “hypothetical”. In reality, the Law of the supply-and-demand assumes many forms: linear, non-linear, inelastic, etc. Likewise, for real-gases, such as: oxygen, hydrogen, air, etc., the general hyperbolic form considered as the “template” for theoretical discussions. This paper uses it as a “bridge” to connect two distinct disciplines: economics and thermodynamics.

Figure 2 Law of Supply-and-Demand

4.1 Phenomenological Conjugate In thermodynamics, the product of PV represents work, w, performed by a mechanical system. The product of TS represents heat, q, transferred across the system. According to the first law of thermodynamics, work and heat are interchangeable via certain medium. Change of internal energy, u = Heat, q – work, w (1) Here u represents the change of internal energy. The state diagrams of the conjugate of P-V and T-S often used to illustrate the performance of a mechanical system. In thermodynamics, entropy defined as: Entropy = Unavailable Energy or Heat/Temperature Similarly, economic entropy can be defined as: Economic Entropy = Unavailable Capital (Resources)/Economic Temperature According to thermodynamics, the change of entropy of an ideal gas are:

12= 2-1 = (T2/T1) + R (v2/v1) (2a)

12 = 2-1 = p (T2/T1) - R (p2/p1) (2b)

12 = 2-1 = (p2/p1) + p (v2/v1) (2c) Equation (2) may be viewed as the “production function” of a single product. For large quantities, Mimkes suggested to use the Shannon Entropy following Boltamann’s work:

918 The Quest of Economic Temperature

S ∑ ( ) (3) This is the expression for aggregated supply and demand. Mimkes suggests use Eq. (3) as the “production function” in place of Douglas Cobb’s production function. On the other, Eq. (3) can be viewed as the function in . Table 4 summarizes these in relation to temperature and entropy changes.

Table 4 Summary of Entropy Changes and Temperature Changes Demand Supply Entropy Change Utility Function Production Function Temperature Change Technology, income, population, , complement, expectation, tastes, culture paradigm, etc.

Table 5 Proposed Temperature and Entropy Computations for and Macroeconomics Microeconomics Macroeconomics Total capital E distributed T = PQ/k T = E/cN Temperature among N agents, c is

proportional factor Entropy Equation (2) Equation (3) Statistical mechanics & Methodology Equation of State & statistics Calculus

Price and quantity are conjugate state variables for the Law of Supply-and-Demand. Likewise, economic temperature-economic entropy can represent the amount of money circulated in a market. Followings are brief explanations of iso-processes using these conjugate variables. 4.2 Isothermal (Constant-Trading Value) Process Economic temperature represents trading value and volume of products and . It also includes perceived value due to the psychological effect. Regardless, it reflects in terms of dollar amount in the market. Therefore, isothermal can be viewed as the trading value of /services in a market at the equilibrium state. Figure 3 illustrates the isothermals in the TS diagram. Isothermal of value-added products include labor cost, material cost, distribution cost, etc., tend to trade at higher temperatures. At equilibrium state, the supply temperature and the demand temperature are equal. Therefore, the isothermal line in TS diagram represents economic temperature for both the supply curve and the demand curve. Note: Basic material such as air has no trading value in the market. Yet, it is priceless or invaluable. This is a good example that economic temperature is mostly a perceived value rather than the content value.

Figure 3 Isothermal (Constant-Temperature) Process in TS Diagram

919 The Quest of Economic Temperature

4.3 Isobaric (Constant-Price) Process Suppose the living standard of a poor region represented by the economic temperature of TL and the living standard of a rich country is maintained at the economic temperature of TH. Figure 4 illustrates the isobaric process in the PQ diagram. Figure 5 illustrates the isobaric process in the TS diagram. If price remains the same, people of high income region has more purchasing power than people of that of the low-income region. This additional purchasing power represented by the shaded area in TS diagram.

Figure 4 The Isobaric (Constant-Price) Process in PQ Diagram

Figure 5 Isobaric Process in TS Diagram

On the other hand, if goods maintained at a constant price or isobaric level. Figure 6 illustrates that more goods, Q2, can be produced along TL than Q1 produced along TH. Consequently, the low-income region tends to draw manufacturing from the high-income region as shown in Figure 7.

Figure 6 Isobaric Process and Isothermal Process of Supply Curves in PQ Diagram

920 The Quest of Economic Temperature

Figure 7 Isobaric Process of Supply Side in TS Diagram

4.4 Isochoric (Constant Volume) Process

A good example of isochoric process is in an auction. Item quantities fixed at Q0, but the price can rise sharply from PL to PH during the auction. Likewise, speculation can cause a hot stock price rising up quickly without increased production (see Figure 8). Figure 9 illustrates the area under the isochoric line represents the increased amount of money change hands in auction and speculative stock market.

Figure 8 Isochoric (Constant-Volume) Process in PQ Diagram

Figure 9 Isochoric Process in TS Diagram — the Slope Is Steeper Than that of the Isobaric Process

4.5 Isentropic (Constant-Entropy) Process In the cases of security, defense, emergency, rescue, political manipulations, or humanity aids, the goal of mission transcends economic values. Military operation, donations and voluntary servicces will go beyond market

921 The Quest of Economic Temperature constraints regardless the market constraints. Figures 10 and 11 illustrate such activities as isentropic process.

Figure 10 Isentropic (Constant-Entropy) Process of Supply Curve in PQ Diagram

Figure 11 Isentropic (Constant-Entropy) Process in TS Diagram

5. Supply, Demand and Carnot Cycles

Historically Carnot cycles is a theoretical reference to guide the design of all types of engines and refrigeration systems. Therefore, it is worthy to explore the opportunity to adopt this framework for economic development once we can determine the “economic temperature”. Figure 12 illustrates the typical Carnot cycle in the TS diagram in economics. Note: the Carnot cycles may be a “power cycle” or a “cooling cycle” depending the direction of the media, i.e.: money flow.

Figure 12 Carnot Cycle in TS Diagram

922 The Quest of Economic Temperature

In the case of production mode or supply cycle, money flows counter-clockwise as that of the “cooling cycle” of a refrigeration. While in the marketing mode or demand cycle, money flows clockwise as that of the “power cycle” of an engine. Figure 13 shows the Demand cycle (in red) and the Supply cycle (in blue) superimposed at the “equilibrium point” of the supply-and-demand diagram.

Figure 13 Demand Cycle (Red) and Supply Cycle (Blue) TS Diagrams Superimposed behind the Equilibrium Point in PQ Diagram

6. Examples

Suppose a store selling polo shirt for Ralph Lauren. Current unit price is $90 and demand is 1000 shirts. Assuming price elasticity is 1.0 and does not change when price changes. The demand curve is PQ = (8.1*106 )T Assuming the business economic temperature changes from 1 to 12 and the demand quantity varies between 200 to 5000. The business Carnot cycle entropy change would be according (2a)

12= 2-1 = ln(T2/T1) + R (Q2/Q1) (2a)

12= 2-1 = 1.5R ln(12/1) + R n(5000/200) 6 8 12 = (2.5)8.1*10 (2.48 + 3.22) = 1.15*10 (Potential Revenue??) 8 9 T12 12 = (11)(1.15*10 ) =1.27*10 ($) Assuming the supply economic temperature changes from .1 to .8 and the inventory quantity varies between 50 to 6000. The supply Carnot cycle entropy change would be according (2a)

12= 2-1 = 1.5R ln(.8/.1) + R ln(6000/50) 6 8 12 = (2.5)8.1*10 (2.08+ 4.79) = 1.39*10 8 8 T12 12 = (.7)(1.39*10 )= .97*10 ($) Profit potential = 1.17*109 ($) So, what does it mean? Birkershire Hathaway Amazon Apple Microsoft

923 The Quest of Economic Temperature

7. Conclusions and Discussions

1943 Maslow proposed the Hierarchy of Needs in his paper: “A Theory of Human Motivation”. It is a visual illustration of the Law of Self-Interest (see Figure 14).

Figure 14 Maslow’s Hierarchy of Needs Is a Visual Illustration of the Law of Self-Interest

This levels of needs and respective intensity of needs may serve as a good reference of Economic Temperature. It is a reference of motivation based on needs, wants, desires, interest, passion, etc. In a

924 The Quest of Economic Temperature economy, T = 0 when an individual has no interest to trade; a contract is breached between two companies; or two countries cut off diplomatic relationship, etc. On the other hand, it can be a comparative measure of worth, the economic potential, or driving force for a particular product/service, such as: the GDP of a country, average income of a region, income or wealth of individuals, etc. Exchange rate of is another example of “economic temperature”. Mathematically: an integrating factor (Jürgen Mimkes) Average amount of a total capital E distributed among N agents: T= E/cN where c is a proportional factor In a market, T is proportional to the mean price In a society of N T is proportional to the mean capital per , or standard of living In countries, T is proportional to the GDP per capita Psychologically: the degree of interest, motivation of a value system (Maslow Hierarchy of Needs) Willard Gibbs formulation: T ≡ / (Note: is a hypothetical variable as an aid for formulation) Temperature is the change of internal energy with respect to the change of the number of microstates . In economics, it expresses the “interest” of people with respect to the changes of products and services. According to Boltzmann*: S =() or S =−∑() Entropy of a system is the logarithmic function of the total number of the microstates, . If there are sub-categories of the microstates, then the = 1 + 2 + …. The probability associated with is *Boltzmann original definition is S =() where k is a physical constant. The constant k is not included for the purpose of clarity and discussion What would be the state of economic equilibrium?  Isolated society  w/o any trading medium  Supply = demand at all time  Instantaneous communication and deliveries  Kung ! society  A self-sustaining farm or society  Water, power, energy, railroad, rural real estate  Industry of less of changes, infrastructures, dam, highway, bridge, The Demand curve defines the economic temperature (Iso-thermal in TS diagram) The similarity of Law of Demand and the Ideal Gas Law serves as visual aids of economic processes Currency system in economics exhibits behavior similar to that of the ideal gas The ability of applying widely established First Law of energy conservation: Internal Energy Change, U = Heat, Q – work, PV in economics in conjunction with the ideal behavior offers a set of tools for economic study. These laws are scalable, i.e., macroscopically and microscopically. Temperature, entropy, price and volume are equilibrium state variables. Potential energy (market potential), Kinetic energy (internal organization) Eigen vectors, Eigen value of the market.

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References Bryant J. (2011). Thermoeconomics — A Thermodynamic Approach to Economics, VOCAT International Ltd. Eftimov T. (2013). “Ideal Gas Laws in thermoeconomics and financial bubble formation”, Fundamental Sciences and Applications, Vol . 19. Georgescu-Roegen N. (1971). The Entropy Law and the Economic Process, Harvard University Press. Maslow A. H. (1943). “A theory of human motivation”, Psychological Review, Vol. 50, No. 4, pp. 370-396. Mimkes J. (2006). “A thermodynamic formulation of economics”, in: B. K. Chakrabarti, A. Chatterjee (Eds.), Econophysics and Sociophysics, Wiley, Hoboken. Saslow W. M. (1999). “An economic analogy to thermodynamics”, Am. J. Phys., Vol. 67, No. 12, pp. 1239-1247. Smith A. (1776). An Inquiry into the Nature and Causes of the Wealth of Nations, W. W. Strahan and T. Cadell, London.

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