Towards macroeconomic analysis without microfoundations: measuring the entropy of simulated exchange economies

TL;DR

In more complex cases, where microfoundational analysis is infeasible, the method of measuring entropy still applies and is validated by demonstrations that entropy is a state function of an economic system, i.e., exhibits path independence.

Abstract

The theory of thermal macroeconomics (TM) analyses economic phenomena within the mathematical framework of classical thermodynamics, using a set of axioms that apply to the purely macroscopic aspects of an economy [CM]. The theory shows that the possible macro-behaviours are governed by an entropy function. In simple idealised cases, the entropy function can be calculated from the rules governing the interactions of individual agents. But where this is not possible, TM predicts that the entropy can nonetheless be measured empirically through an economic analogue of calorimetry in physics. We show using computer simulations the in-principle feasibility of this approach: an entropy function can successfully be measured for a range of simulated economies that we tested. In cases where entropy can be calculated analytically from microfoundational assumptions, the measured entropy agrees well. In more complex cases, where microfoundational analysis is infeasible, our method of measuring entropy still applies and is validated by demonstrations that entropy is a state function of an economic system, i.e., exhibits path independence. This appears to hold even for some systems to which we don't have a proof that the Axioms of TM apply. Furthermore, in all cases tested, entropy is concave, as predicted by TM. As shown in [CM], once the entropy function is established for a simulated exchange economy, it is possible to derive prices, the value of money and various other quantities, and make predictions about the effects of putting two or more economies in contact.

Figures (12)

• Figure 1: Measured entropy per agent for a homogeneous CD economy with $\eta=3 , \alpha_1=3 , \alpha_2 =3$, as a function of amounts of the two types of good (with $M=1000$). The goodness of fit is $8.34 \times 10^{-6}$. The goodness of agreement is $9.87 \times 10^{-7}$.
• Figure 2: Measured entropy per agent for a heterogeneous CD economy with half of the agents with $\eta=3 , \alpha_1=3 , \alpha_2 =3$ and half of the agents with $\eta=2 , \alpha_1=2 , \alpha_2 =2$, as a function of amounts of the two types of good (with $M=1000$). The goodness of fit is $9.18 \times 10^{-6}$. The goodness of agreement is $9.15 \times 10^{-6}$.
• Figure 3: Measured entropy per agent for an economy of 500 substitutes and 500 complements agents, as a function of amounts of the two types of good. The goodness of fit is $9.5 \times 10^{-6}$. The goodness of agreement with the theoretical free energy function is $4.64 \times 10^{-3}$.
• Figure 4: Measured entropy per agent for an economy of 300 substitutes, 300 complements and 400 CD agents, as a function of amounts of the two types of good. The goodness of fit is $1.081 \times 10^{-5}$. The goodness of agreement is $8.72 \times 10^{-4}$.
• Figure 5: Utility function $U_1$ for satiable agents, with $c=0.3, k=0.6$.