Econophysics is a developing field of physics that seeks to establish mathematical models for understanding price fluctuations. It applies the principles of statistical mechanics to reinterpret the dynamics traditionally described by classical economics.
Since its inception in the late 1990s, much of the work in this area has concentrated on fluctuations in stock prices. However, in many economies, the production of goods—whether for consumption or capital formation—plays a more significant role in shaping overall wealth and societal well-being. This raises the question of whether econophysics could also provide insights into the fluctuations in product prices.
We wish to pioneer a new direction for econophysics which explores how the material world of atoms and electrons works its way into the price system.
Daniel Packwood
Product-commodity price interplay
Product prices tend to fluctuate when they compete with commodities for consumer demand. Commodities, such as crude oil and pure metals, are known for their volatile and unpredictable price movements (Figure 1).
Credit. Author
When a commodity’s price unexpectedly rises, demand often shifts towards substitute products, driving up their prices. Conversely, a sudden drop in the commodity’s price can redirect demand back to the commodity, creating downward pressure on the product’s price.
It is logical to expect a correlation between product prices and the prices of competing commodities in such cases. However, accurately capturing this interplay through mathematical modelling remains a challenging task.
The concept of product-commodity competition extends beyond theoretical discussions and finds practical relevance, particularly in the chemical industry. Ethanol, a commodity chemical, often competes with chlorhexidine, a product chemical, for use in antiseptic solutions. Similarly, polyethylene, a widely used commodity polymer, competes with specialised polymers across various applications.
Gaining a more nuanced understanding of this competition could provide valuable insights for investors in these industries, particularly those seeking stable and predictable returns in markets influenced by such dynamics.
A new econophysics model for product price
A novel econophysics model has been developed to analyse the price movements of products competing with commodities. This framework stems from a mathematical study of the interaction between consumers and suppliers.
By incorporating standard microeconomic principles and probability theory, the research led to the derivation of a differential equation describing the time evolution of product prices. This model offers a fresh perspective on understanding price fluctuations in competitive markets.
Interestingly, the derived differential equation bears a striking resemblance to those used in biophysics to model neuronal firing dynamics. While this similarity does not suggest any direct relationship between product pricing and neuronal behaviour, it opens the door to borrowing terminology from biophysics.
For instance, the equation enables commodity price fluctuations to be described as “transmitting” to product prices through an activation function. This parallels how electrical signals are transmitted to ion pulses in neuronal systems, providing a useful analogy for understanding the interplay between commodity and product prices.
Simulation results and product performance parameters
Computer simulations of the developed differential equation effectively replicated the observed phenomenon: commodity price increases exert upward pressure on product prices, and decreases do the opposite. The simulations also revealed how product performance parameters influence price fluctuations.
These parameters, embedded within the equation, assess a product’s performance relative to a competing commodity for specific applications. For example, in antiseptic solutions, these parameters would quantify the effectiveness of chlorhexidine compared to ethanol.
The findings indicate that higher product performance parameters mitigate the transmission of commodity price fluctuations to product prices. In practical terms, the model predicts that superior-quality products, which outperform their commodity counterparts, are likely to experience more stable prices.
Implications for investors
The model reinforces a well-known principle for investors: higher product performance correlates with more stable returns. However, its significance lies in offering the first mathematical framework to encapsulate this relationship.
This framework provides a tool to quantify the level of performance improvement needed to minimise product price fluctuations to a desired degree, offering valuable insights for strategic decision-making in competitive markets.
Integration of computational chemistry
Computational chemistry seeks to calculate material properties, such as electrical conductivity and colour, by solving quantum mechanical equations. The potential integration of this field with econophysics has not been explored widely. Such a combination could help explain how material properties, along with economic and social factors, influence material pricing.
One approach to this integration involves a hypothetical scenario examining the competition between two materials as oxygen-splitting catalysts for hydrogen fuel cells. The first material, platinum (Pt), is a well-established catalyst and an expensive commodity. The second, monolayer platinum (MPt), consists of a single layer of platinum atoms on a low-cost copper substrate. Though MPt has never been experimentally realised, computational studies suggest that it would be a more efficient catalyst than Pt if mass produced. However, its potential price stability remains uncertain (Figure 2).
Credit. Author
Density functional theory in price modelling
Using density functional theory, a computational method often employed to evaluate material properties, the catalytic rate constants for both materials in oxygen splitting were calculated. The results showed that MPt had a moderately higher catalytic rate than Pt, consistent with earlier theoretical predictions. These rate constants were incorporated into a previously developed price differential equation to simulate MPt’s price dynamics.
The simulations yielded surprising results. The moderate improvement in MPt’s catalytic rate was enough to eliminate price fluctuations entirely. While this behaviour is unlikely to occur exactly in real markets, the findings highlight the impact of material performance improvements on price stability.
More significantly, this example demonstrates a practical method for integrating computational chemistry with econophysics. Expanding research in this direction could allow computational chemistry to include price stability as a critical criterion in material design, creating new opportunities for innovation at the intersection of these fields.
Moving forward
While financial markets remain a focal point for many experts in physics and mathematics, the foundations of a nation’s wealth lie primarily in production and consumption. Historically, the most influential works in economics—ranging from Smith’s insights into wealth to Keynes’s and Friedman’s contributions on monetary theory and consumption—have centered on prices, consumption, and stability. Yet, contemporary studies in econophysics and even mainstream economics have largely neglected these critical areas.
The proposed model represents a step towards addressing product price fluctuations within econophysics. However, it remains incomplete. Future developments must account for factors such as interest rates, exchange rates, production costs, community income, and consumption tendencies. Efforts are already underway to incorporate these elements into the framework.
Perhaps the most innovative aspect of this work is the integration of computational chemistry with econophysics. This connection, while executed using standard computational chemistry techniques, represents a potentially transformative approach.
Keynes, in 1936, once noted that the influence of vested interests pales in comparison to the quiet but persistent encroachment of ideas. This vision of connecting the material and economic worlds offers fertile ground for new ideas and possibilities, leaving much to contemplate about the evolution of econophysics in understanding market dynamics.
Actionable recommendations
- Research and development into new materials for the public good should give consideration to the potential price stability of these materials. This is especially the case when these materials are intended to displace commodity chemicals or metals.
- Rather than investing massive funds into grand materials science projects, it might be more effective to invest smaller funds into research efforts on existing classes of materials. Incremental material property improvements might be enough to eliminate potential price fluctuations, improving the attractiveness of these materials for commercialisation.
- Public funding schemes for materials research could encourage the participation of economists and researchers from other social sciences. This would improve the chances that new materials would achieve their potential social impact.
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Journal reference
Sakakibara, K., & Packwood, D. M. (2024). Desensitization to commodity price fluctuations by product characteristics. Physical Review E, 110(3), 034106. https://doi.org/10.1103/PhysRevE.110.034106
