Economic Entropy: A Mathematical Model of Value Flow in Economics


A law of economic entropy: capital flows across a perceived value difference towards higher perceived value and eventual price equilibrium.

The laws of physics have often provided frameworks for understanding systems far removed from particles and energy. One such principle that has been discussed across disciplines is the law of entropy in thermodynamics. In essence, entropy is a measure of disorder or randomness in a system, and systems naturally evolve towards states of maximum entropy. The economy, a complex network of transactions and interactions, appears to follow similar principles. However, instead of energy, what flows in economic systems is value, specifically, perceived value, since value which contributes to things like status often sets prices but has no objective and independent utility.

The Core Idea: Economic Entropy

To understand how value moves within an economy, we introduce a concept called ‘economic entropy.’ This represents the level of disorder or randomness in the distribution of perceived value within an economy. Economic entropy reaches a maximum when both buyers and sellers perceive an equal value, creating a sort of economic equilibrium. This is quite similar to how a closed system aims for thermal equilibrium, a state where energy is evenly distributed.

Entropy was notably introduced, as a concept, into economics by Nicholas Georgescu-Roegen who claimed that the second law implied an inevitable depletion of the Earth’s finite resources and accumulation of waste. This pessimistic view shares much with Malthus and limits to population growth and food production, leading to an argument for degrowth, based on physics. When you consider the Earth as an open system, the flaws in Georgescu-Roegen are obvious just as they are for Malthus.

Malthus, did not account for technological advancements that could increase agricultural yield, thereby effectively “expanding” the resource base. Similarly, Georgescu-Roegen’s entropy argument often overlooks the inflow of low-entropy energy from the Sun.

The Earth as an Open System

The Earth is not a closed system; it continually receives a massive inflow of low-entropy solar energy. This input can be harnessed to reduce localized entropy and create new resources. For instance, solar energy drives the water cycle, facilitates photosynthesis, and can be directly harnessed for electricity, thereby providing a continuous source of low-entropy energy that can counterbalance the localized increase in entropy due to economic activities.

High-Entropy Waste

Georgescu-Roegen’s concern about the accumulation of high-entropy waste also disappears when considering the earth as an open system. The Earth radiates heat back into space, effectively exporting high-entropy waste. In the grand thermodynamic picture, while entropy in a closed system would indeed increase, Earth is continually shipping entropy back out into space as a larger number of lower energy photons than are recived from the sun.

Technological Advancements

Technology plays a crucial role in resource management and waste reduction, an aspect often underemphasized in Georgescu-Roegen’s and Malthus’ frameworks. Recycling, for example, allows high-entropy waste to be converted back into lower-entropy, useful forms. Innovative methods for sustainable agriculture, water use, and energy production are continually being developed, effectively pushing back the ‘entropy wall’ that Georgescu-Roegen warns about.

The Role of Perception in Value Flow

What makes economic entropy interesting is that it is not just a measure of value, but of perceived value. What might be valuable to one person may not be so for another. This subjective nature of value creates a gradient in the economy, driving the flow of capital. For instance, a buyer might perceive the value of an antique as $500, while the seller might perceive its value as $400. Here, capital flows from the buyer to the seller because the perceived value to the buyer ($500) is greater than the perceived value to the seller ($400). Discrepancies in value perception increase liquidity — a gold bar for sale for $1, will sell quickly. Just as energy flows across a temperature gradient towards higher entropy equilibrium, capital flows across a value perception gradient towards price equilibrium.

Trade flows and specialization through separation. The analogies between genetic drift in islands and trade between geographies.

The concept of “economic entropy,” can be applied to the economic and cultural development of ancient civilizations such as Greece or modern economic arbitrage through globalization and trade with lower costs centers of production, such as China over the last few decades. If we take ancient Greece and examine the role of islands and isolation in economic specialization, we can understand how it became one of the cradles of civilization.

Islands as Crucibles for Economic Entropy

Islands, whether they are land masses surrounded by water or isolated ecosystems like lakes for fish, act as isolated environments where unique economic and cultural systems can develop. Genetic drift in isolated biological populations leads to biodiversity, and in a similar fashion, economic drift in isolated economic systems can lead to specialized trades and skills. The Greek islands, teeming with varying resources and isolated from each other by the sea, became hotbeds for specialized crafts, art forms, and trading goods.

Ancient Greek Civilization as an Example of Economic Entropic Forces at Work

Ancient Greece was a conglomerate of city-states, many of which were located on islands. These islands produced specific tradable goods like olive oil, wine, or marble, fostering specialized skills in their populations. The inherent limitations of the islands — such as limited arable land or lack of specific resources — forced the inhabitants to trade for what they lacked, pushing money and goods across value gradients and, in effect, increasing economic entropy. Over time, this isolation and subsequent economic specialization led to a rich tapestry of culture, philosophy, and scientific thought in the wider Greek world. The phenomenon of economic entropy and specialized trade was not limited to Greece; it extended to the wider Mediterranean region. Civilizations like Phoenicia and Carthage had their unique trading goods and economic identities, separated by the Mediterranean Sea, yet connected through trade routes.

The Mathematics of Perceived Value

Real-world Applications: Trade and Policy

In terms of trade between two countries. One country may produce an abundant amount of a particular good, say, oranges. The perceived value of these oranges is low within that country because they are so abundant. However, another country might find them rare and therefore place a higher perceived value on them. Trade naturally occurs, with oranges flowing to where they are most valued until a balance in perceived value is reached — this is when economic entropy is maximized. Policymakers and investors can use this concept to understand how efficient a market is or how dynamically trade occurs.

The notion of economic entropy provides an analytical framework for dissecting the intricacies of economic behavior. It’s a way to understand why and how value — or, more specifically, perceived value — flows within a system. By employing this trivial mathematical model, economists, policymakers, and even everyday investors can gain deeper, more quantitative insights into how markets operate and make more informed decisions as a result.

This model is, of course, a simplification. The actual flow of value in economies is influenced by a myriad of factors, including but not limited to supply and demand, regulatory environments, and socio-political issues. But simplification is the first step towards understanding, and economic entropy could be a useful tool in economics, akin to how the concept of entropy is employed in thermodynamics.

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