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The Quest of Economic Temperature

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The Quest of Economic Temperature Journal of Business and Economics, 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 economy. The concept of economic temperature has been around in history since the time money 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 econophysics are appealing because of the well-established mathematic formulation, particularly, thermodynamics. 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 economic system 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, entropy 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 Adam Smith (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 energy 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/interests: 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 value 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-interest Cash flow, information 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 investment 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. 917 The Quest of Economic Temperature 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
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