Introduction to Econophysics

Contemporary Approaches with Python Simulations

Carlo Requião da Cunha

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000464238
• Edition: 1
• Topic: Negocios y empresa
• Subtopic: Negocios en general

Econophysics explores the parallels between physics and economics and is an exciting topic that is attracting increasing attention. However there is a lack of literature that explains the topic from a broad perspective. This book introduces advanced undergraduates and graduate students in physics and engineering to the topic from this outlook, and is accompanied by rigorous mathematics which ensures that this will also be a good guide for established researchers in the field as well as researchers from other fields, such as mathematics and statistics, who are interested in the topic.

Key features:

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• Presents a multidisciplinary approach that will be of interest to students and researchers from physics, engineering, mathematics, statistics, and other physical sciences

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• Accompanied by Python code with further learning opportunities, available for readers to download from the CRC Press website.

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• Accessible to both students and researchers

Carlo R. da Cunha is an associate professor of physics and engineering physics at the Universidade Federal do Rio Grande do Sul (Brazil) and has been since 2011. Dr. da Cunha received his M.Sc. Degree from the West Virginia University in 2001 and his Ph.D. degree from Arizona State University in 2005. He was a postdoctoral researcher at McGill University in Canada in 2006 and an assistant professor of engineering at the University Federal de Santa Catarina between 2007 and 2011. He has been a guest professor at the Technische Universität Wien (Austria), Chiba University (Japan) and Arizona State University (US). His research revolves around the physics of complex systems where he has been drawing parallels between physical and economic systems from quantum to social levels.

To access additional resources, such as python code, please take a look here.

1Review of Economics

DOI: 10.1201/9781003127956-1

Economics is a science that deals with complex systems. These systems are not composed of inanimate particles, but of human beings that have their own feelings, desires, that take action. This book analyzes whether these systems have any particular dynamics for which we can use the tools developed for studying physical problems. The theory that emerges from this endeavor is called econophysics and explicitly develops in a per analogiam fashion[2].

The idea of tackling problems of economics from the perspective of physics is as old as Copernicus¹. Copernicus proposed, for instance, the quantity theory of money (QTM) that states that prices are functions of the money supply. Copernicus also proposed the monetae cudendae ratio that states that people tend to hoard good money (undervalued or stable in value) and use bad money (overvalued) instead². Quetelet³ was another scientist that went even further coining the term ‘social physics’ for his work that used statistical methods for social problems.

The same happened in the opposite direction with social scientists trying to use early concepts of physics in their works. For instance, Comte⁴ was a philosopher who wanted to model social sciences as an evolution of the physical sciences. Even Adam Smith⁵ is known to have been inspired by Newton's⁶ works.

It was much more recent that the term econophysics was coined and used by physicists such as Stanley⁷ and Mantegna⁸ when using the tools of statistical mechanics to solve problems related to finances[3, 4].

There are some concepts developed in economics that make a good connection with physics. The first one is the concept of methodological individualism developed by Weber⁹ and further explained by Schumpeter¹⁰. There the focus of analysis of social problems is put on the action-theoretical level, rather than in the whole. It is not to be confused, though with atomism. This is a different term adopted by some economists, including Menger¹¹. Atomism is based on the idea that once we fully understand the individual psychology, it would possible to deduce the behavior of group of individuals. Rather, methodological individualism does not rely on a reduction of the social sciences to psychology. It perceives social phenomena as emerging from the action of individual agents. Moreover, these phenomena can emerge even as unintended consequences of purposeful individual actions¹². This will prove useful, for instance, when we study game theory and agent based models throughout this book.

Dispersed knowledge is another economic concept that we will encounter in our study of econophysics. As the agents individually take action, they produce a knowledge that is dispersed among individuals and no agent has access to all this information at every instant[5]. Although, it may seem obvious, it has huge implications such as the production of genuine uncertainty. On the other hand, this dispersed knowledge can produce regular large-scale consequences constituting spontaneous order. Hayek¹³ provides the example of a virgin forest[6]. The first person walking through this forest creates small modifications that helps other individuals cross this forest. Eventually, as a significant number of individuals cross this forest, a path is naturally formed. The same process happens with prices. Through the interaction of buyers and sellers, prices are created without the need of any central planner. This is known by economists as a price discovery process. Moreover, as Hayek points out, prices carry information that helps agents to coordinate their separate actions towards the increase and decrease of production and consumption. This spontaneous “order brought about by the mutual adjustment of many individual economies in a market” is called catallaxy by Hayek[7].

In order to begin our study of econophysics, let's review three more important concepts in economics that will help us build a solid groundwork: supply and demand, the efficient market hypothesis and the concept of stocks and derivatives.

1.1 Supply and Demand

Imagine that you are starting a business. As an entrepreneur you have to pay employees, you probably have to pay bank loans and also need to make some profit for yourself. Thus, it is likely that you are willing to sell your products at a high price. Just like you, other entrepreneurs want to do the same. The information about the price is not absolute, but dispersed in the society. Therefore, some entrepreneurs may advertise their goods at lower prices and there can even be the cases where the entrepreneurs need to sell a product as soon as possible. Thus, it is expected that many entrepreneurs are willing to sell a product at high prices whereas few entrepreneurs are willing to sell the same product at low prices.

The situation is the opposite for costumers. They have a list of needs and limited money. However, the information is also not certain for them. A product that some consider expensive might be considered not so expensive by others. Also, there can be situations where a product is needed no matter the cost. Therefore, it is expected that many customers are willing to buy a product at low prices whereas not so many customers are willing to buy the same product at high prices.

This competition between agents has captured the attention of many economists from John Lock¹⁴[8] to Adam Smith[9]. It was Cournot¹⁵[10] and Marshall¹⁶[11], however, that formalized supply and demand curves as shown in Fig. 1.1.

Figure 1.1: Supply and demand curves showing an equilibrium point and the situation where there are a) low and high production, and b) low and high prices

Let's see the supply and demand curves in action. Figure 1.1 illustrates a situation where the price is fixed at a high price P_s. In this case, only a few consumers $Q_{ds}$ are willing to pay this price and many entrepreneurs $Q_{os}$ are willing to sell. However, when sales do not materialize, the entrepreneurs are encouraged to lower their prices. On the other hand, not so many entrepreneurs can produce or sell the product at this low price. Therefore, $O_{os}$ tends to move to Q_e and since more consumers are expected to agree with this new price, $Q_{ds}$ is pushed towards Q_e.

Any deviation from this ‘equilibrium point’ tends to produce stimuli that encourages both the consumers and entrepreneurs move back to it. For instance, if there is a movement towards a lower price P_i, fewer entrepreneurs $Q_{oi}$ are encouraged to produce, but there would probably be many consumers $Q_{id}$ willing to buy. This pushes entrepreneurs to try to satisfy these potential consumers. Thus, chances are that the entrepreneurs observe a rise in demand and increase their productions and prices. Once again the tendency is that $Q_{oi}$ and $Q_{di}$ move towards Q_e, and P_i moves towards P_e.

At this point, supply and demand are in equilibrium. We can intuitively notice that this point may not be stable and oscillations can occur due to a set of reasons such as information imperfection as we discussed before. Nonetheless, the incentive is such that a free economic system always tends to move towards the point $Q_e,P_e$. We also notice that the price works as a system of...