### Discussion Paper

## Abstract

The article attempts of apply econophysics concepts to the Eurozone crisis. It starts by examining the idea of conservation laws as applied to market economies. It formulates a measure of financial entropy and gives numerical simulations indicating that this tends to rise. We discuss an analogue for free energy released during this process. The concepts of real and symbolic appropriation are introduced as a means to analyse debt and taxation.

We then examine the conflict between the conservation laws that apply to commodity exchange with the exponential growth implied by capital accumulation and how these have necessitated a sequence of evolutionary forms for money, and go on to present a simple stochastic model for the formation of rates of interest and a model for the time evolution of the rate of profit.

Finally we apply the conservation law model to examining the Euro Crisis and the European Stability pact, arguing that if the laws we hypothesise actually hold, then the goals of the stability pact are unobtainable.

## Comments and Questions

See attached file

The bibliography is coherent and suitable, even though I was surprised for not seeing a reference to the work of Nicholas Georegescu-Roegen, mainly to Roegen (1960).

We thank the reviewer for pointing out Roegen (1960), which was unknown to us. That said, the referenced paper is mainly concerned ...[more]

... with the inadequacies of a deterministic model that is not considered in our manuscript.

All in all, I would have appreciated reading an 'introduction with motivations', to figure out the field, and a final section of 'conclusive remarks', to summarise the main findings.

We think this is a fair point and have added an introduction and conclusion to the manuscript.

(a) on page 5 the authors set an analogy between the mass of a particle and the financial position of a firm on a phase-space, so implicitly assuming the mass is one of the degrees-of-freedom;

If one draws the analogy that far, then ‘mass’ would be one degree of freedom.

(b) formulae (1) and (2) on page 5 and 6 are used to explain conservation laws for system's observables totals but they seem more like constraints on their expected values;

Formulae (1) and (2) are effectively summing the total net debts and their rates of change, upto normalization constants given by density functions Px and Py. To illustrate the point in an extreme case, suppose there are only two agents in the system. Then Px = (1/2)*delta(x - x0) + (-1/2)*delta(x+x0), where delta(x) is a Dirac delta function, x0>=0 and the division by 2 is due to normalization. Inserting Px into (1) we get the debt x0 from one agent canceled by the –x0 debt of the other. They are thus stronger than constraints on expected totals. They are constraints that the system must obey, and in this sense analogous to a conservation law.

(c) on page 7 they introduce the notion of financial-entropy: it is not so clear why it should be always growing, except in the provided example;

Since we are unable to derive a formal proof we argue why this conjecture follows from the conservation laws and agent dynamics. At the most basic level, any system micro configuration with a dispersion along the y-axis (i.e. growth of debt/credit) will increase the dispersion along the x-axis (i.e. debt/credit). Now, at any instance in which voluntary borrowing falls short of lending, involuntary borrowing must rise. This will increases the dispersion because the latter agents belong to the extreme end along the debt axis already; and their rising borrowing only extends this position further.

We have now tried to clarify this polarizing dynamic in section 2.2 of the manuscript.

(d) on page 13 they draw an analogy between the 'work' done by credit and the free energy by means of the (financial) entropy increase. All these analogies are foundational of the model but they are not so easy to be understood beyond the level of the intuition.

At the most basic level the argument is that while the dispersion of the credit/debt PDF Px,y increases, not only does ‘financial entropy’ rise by definition, but barrier of money-constrained private production and consumption units are overcome as they now increasingly operate on credit. This enables more work to be extracted from the economic system than would otherwise have been possible. We now tried to highlight this conclusion in the manuscript.

See attached file

For the approach followed in this paper I would rather suggest the authors to consider Sraffa and his “Production of commodities by means of commodities”, which seems to me more suitable for the theory presented here.

We deliberately do not follow the approach of Sraffa because we consider that ...[more]

... since the pioneering econophysics work of Farjoun and Machover, the methodology of Sraffa has been theoretically discredited. In particular the assumption in Sraffa of unique economy wide profit rate rather than having the sectoral profit rate as a random variable is incompatible with the inherently chaotic character of a market economy. It amounts to assuming that the entropy of the profit rate is zero without providing any plausible thermostat to cool it. It has also been empirically discredited by a number of studies which have confirmed that prices are equally well predicted by a simple classical Ricardian labour theory of value as they are by Sraffa’s model. Occam’s razor suggests that we should adopt the simpler theory. We will add a footnote to this effect.

Anyway, I have the impression that the authors refer to an industrial economy but I wonder how much of their reasoning is applicable to a post-industrial system, when the financial sector accounts for a large percentage of the economic activity.

The phase space analysis and conservation laws in equations 1 and 2 apply equally to industrial and financial companies. The simulation model in the Appendix is undoubtedly simplified as it represents the financial system as one large bank and as such ignores mutual debts between different financial firms. In the construction of agent based simulation models it is often better to start simple. The more complex the model you build, the harder it is to determine which feature of your model is responsible for the results you observe when you run simulations.

As for the supply of money, in many points of the paper the authors seem to ignore the fact that credit supply and money supply are endogenous in contemporary economies. Almost all the central banks target the overnight interbank lending interest rate also because they are aware of

their limit in controlling the supply of money.

Our whole analysis is an attempt to explain what is customarily called the endogenous ‘money supply’ in terms of a different conceptual paradigm based on agent distribution in a phase plane. What is customarily termed the endogenous money supply represents the integral over the left half of the phase plane in Figure 1 of our paper: the sum of all credit balances. But the conservation laws imply that this is exactly equaled by the integral over the right half of the phase plane: sum of all negative balances. The aggregate endogenous money is thus always zero. In a phase plane analysis the concept of endogenous money supply is replaced by a different one, that of the dispersion of agents in the financial phase plane. One can measure this dispersion in various ways, one could use the moments of the PDF in this plane or as we do the entropy of the distribution. Within the conceptual model we present in the paper, what is conventionally called the money supply is an epiphenomenon arising from the dynamical evolution of the positions of a population of agents in the phase plane.

The fact that the Gold Standard was abandoned in the Seventies is a consequence of the problem in the current account balance of the US rather than in the limit to the production of gold.

At that point in the seventies the reviewer is correct, the US deficit arising during the Vietnam war was the precipitating factor, but that was just the last of a series of crises that had affected the gold standard from the late 19th century. The constraint that the gold standard imposed on interest rates had been the central issue of political controversy in the US during the aftermath of the financial panic of 1893 and was behind the policies of Jennings Bryan. The constraints had become more generally evident by the 1920s as is evident in Keynes writings of the period and in the abandonment of the general convertibility of many currencies into gold in the 1930s. These repeated crises and the progressive abandonment of the gold standard need to be explained, not just the final act in the tragedy. Our explanation is that so long as you have a gold standard then the tendency of financial entropy to increase, along with the model we present of the formation of interest rates predicts repeated crises when the ratio of the gold stock to the integral of the right of the phase plane reaches a critical ratio.

As for the interest rate, the authors, in presenting an example, quantify it as a premium on risk. Actually this is only a component of the interest rate, which adds to the market rate (according to the neoclassicals) or to the mark-up on the official interest rate (according to some Post-Keynesians), just to name some examples of more comprehensive explanations.

We are not using the idea of risk premium in the same sense as the reviewer mentions. The reviewer is referring to the risk that a given loan will not be repaid, which induces a premium on loans to more risky borrowers. We are talking about the risk to the bank that the depletion of its reserves incumbent upon making a loan will leave the bank with insufficient reserves to meet the stochastic pattern of withdrawals by its depositors. This model predicts a negative correlation between bank reserve to asset ratios and the interest rate such as was observed by Cagan. We have added a citation to the relevant paper by Cagan.

The reviewer refers to Gallegati et. al. “Worrying trends in Econophysics” which criticises the use of ideas of conservation laws applied to incomes. We are not applying conservation laws to incomes, we are applying them to the analysis of debt. Wagner’s paper on the application of maximum entropy models to market clearing in stock markets addresses a slightly different form of entropy analysis. He is looking at the use of maximum entropy estimates of information about prices by individual agents, ie the Shannon entropy of the information available to the agent. We are looking at something that is somewhat closer to Boltzman entropy as it relates to the distribution of particles (agents) in a phase space. We make no assumptions about the availability of this as information to the agents.

Third, the facts that the Euro crisis has been originated by trade imbalances that could not be corrected by the exchange rate and that the stability pact will have the only effect of worsening the situation are well established not only in non-neoclassical academic literature, but also in the general press (see for example a number of commentaries by Martin Wolf on the Financial Times).

This is a fair point. We thought that it was significant that you could draw these conclusions within a conservation law framework, but we agree that Wolf has made similar points in the Financial times, so we will remove this section from the paper.

The reviewer asks for simulation data. We do include the results of simulation runs in figures 10 to 13. We do not compare these to empirical data. Doing this is certainly scientifically worthwhile but it would be a major study involving very large scale data analysis of large samples of firms and household debts over time in order to estimate the empirical PDF of agents in the phase plane. At present we do not have access to the data required.