Thermal Macroeconomics: An axiomatic theory of aggregate economic phenomena

Abstract: An axiomatic approach to macroeconomics based on the mathematical structure of thermodynamics is presented. It deduces relations between aggregate properties of an economy, concerning quantities and flows of goods and money, prices and the value of money, without any recourse to microeconomic foundations about the preferences and actions of individual economic agents. The approach has three important payoffs. 1) it provides a new and solid foundation for aspects of standard macroeconomic theory such as the existence of market prices, the value of money, the meaning of inflation, the symmetry and negative-definiteness of the macro-Slutsky matrix, and the Le Chatelier-Samuelson principle, without relying on implausibly strong rationality assumptions over individual microeconomic agents. 2) the approach generates new results, including implications for money flow and trade when two or more economies are put in contact, in terms of new concepts such as economic entropy, economic temperature, goods' values and money capacity. Some of these are related to standard economic concepts (eg marginal utility of money, market prices). Yet our approach derives them at a purely macroeconomic level and gives them a meaning independent of usual restrictions. Others of the concepts, such as economic entropy and temperature, have no direct counterparts in standard economics, but they have important economic interpretations and implications, as aggregate utility and the inverse marginal aggregate utility of money, respectively. 3) this analysis promises to open up new frontiers in macroeconomics by building a bridge to ideas from non-equilibrium thermodynamics. More broadly, we hope that the economic analogue of entropy (governing the possible transitions between states of economic systems) may prove to be as fruitful for the social sciences as entropy has been in the natural sciences.

• The paper introduces Thermal Macroeconomics, demonstrating how axioms modeled on thermodynamics can underpin aggregate economic phenomena.
• It outlines novel metrics such as economic entropy and temperature, providing measurable analogues for inflation and trade dynamics.
• The framework leverages a Carnot cycle analogy to illustrate non-decreasing aggregate utility from trade and improved monetary flow efficiency.

Thermal Macroeconomics: An Axiomatic Theory of Aggregate Economic Phenomena

Thermal Macroeconomics proposes an innovative framework that parallels classical thermodynamics to offer insights into macroeconomic theory. The approach deduces fundamental relations among aggregate properties—such as money flow, trade, and the value of money—without relying on conventional microeconomic foundations.

Axiomatic Framework

The theory introduces the concept of Thermal Macroeconomics (TM) by adopting axioms akin to those in thermodynamics. These axioms underpin an approach that provides a more robust foundation for understanding macroeconomic phenomena, such as market prices and inflation, than models that assume rational behavior of individual agents. The axioms focus on scalability and extensivity assumptions, drawing parallels with thermodynamic concepts like energy and entropy.

Economic Entropy and Temperature

TM introduces novel concepts of economic entropy and economic temperature. Economic entropy is depicted as an aggregate utility that systems strive to maximize, mirroring the second law of thermodynamics whereby entropy in a closed system tends not to decrease. Entropy is grounded in economic realities as an aggregate measure of states, independent of individual agent preferences. Economic temperature is similarly defined, pinpointing the inverse marginal utility of money.

Figure 1: An economic Carnot cycle in the plane of amount $G$ of goods and temperature $T$ for an island economy with $\alpha=2$, $\eta=\frac{5}{2}$, operating between two mainland economies at temperatures $T_H=0.47$ and $T_C=0.24.

Trade and Market Dynamics

The model presents innovative ways to analyze trade dynamics without detailed micro-level interactions. Trade, when allowed between economies, always results in non-decreasing aggregate utility, introducing a measure for the potential gains from trade. This framework notably incorporates the analogy of a Carnot cycle, enabling the extraction of monetary gains from differences in economic temperatures akin to extracting work from temperature differences in physics.

Practical Implications and Measurement Techniques

The concept of economic temperature provides a fresh understanding of inflation, characterized as the rate of increase in economic temperature. TM proposes using ship thermometers for practical measurement of this temperature, thereby facilitating comparative economic analysis without reliance on fixed baskets of goods.

Figure 2: An Edgeworth box plot for the two Cobb-Douglas economies, illustrating mutual benefits from trade increasing the entropy of each economy.

Cross-Disciplinary Extensions

Insights from thermodynamics are extended to explore and quantify phenomena such as production, consumption, and labor, transcending the limits of exchange economies. TM anticipates addressing the intricacies of currency systems, labor markets, and real-world complexities of economic systems by leveraging fundamental thermodynamic principles.

Figure 3: Relationship between volume (quantity of goods) and price, with changes at a constant temperature (light lines) and entropy (heavy lines). The equal area rule clarifies the trading implications within the PV and TS coordinates.

Conclusion

The thermal macroeconomic model stands to revolutionize macroeconomic analysis by offering an axiomatic foundation to describe aggregate economic behavior. By integrating principles from thermodynamics, TM holds potential for wide-ranging applications in economic policy, trade negotiations, and inflation control, promising a shift towards more empirically grounded economic science. The framework invites further exploration of extensions to non-equilibrium systems, opening discussions for incorporating dynamic socio-economic factors.

Incorporating the deep insights of thermodynamics into economics may yield a profound understanding of economic systems as holistic entities, with laws governing aggregate behaviors offering predictive power and insight into economic dynamics.