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Simone Alfarano, University of Kiel
A statistical equilibrium model of competitive firms
In the this paper, we introduce a statistical equilibrium model to describe the properties of a large collection of competitive interacting firms. The interaction mechanism is essentially based on the notion of classical competition, i.e. the tendency of equalization of the profit rates irrespectively of the economic activity or sector the firms belong to.
The classical competition framework essentially describes a negative feedback mechanism: the sectors or industries which generate above average profits attract relative more capital than the other sectors. The concentration of capital rises output and lowers prices, ultimately giving an incentive to leave the sector and therefore to increase the profit for the remanning firms. The continuing shocks in terms of technological innovations and changing tastes, for instance, render a complete elimination of differences in profits among the sectors a very improbable event, even in the long run.
The detailed specification of the interaction mechanism among the competitive firm is a demanding task. We take the position that this complex environment might be described in the context of a statistical equilibrium model. Within the concept of classical competition, the incessant movement of capital to equalize profit rates might be decomposed into two aspects: a measure of central tendency to uniform profit rates and a measure of dispersion around the average, which accounts for the complex movements of the capital and the interactions among firms. Essentially, the system of competitive firms is described using two macroscopic constrains: the existence of a profit rate m to which the economy as a whole tends to converge, and a general measure of dispersion, given by the -moment around m, E[|(x−m)/s|^a] = 1, which accounts for the non-elimination of the differences in profit rates among firms, due to the complexity of the competitive environment.
Following Foley (1994), we introduce the maximum entropy principle to derive the statistical equilibrium of profits rates in the economy, given the aforemention constrains. The model predicts, then, a Subbotion or exponential power distribution of profit rates, which is in line with empirical identified distribution, see Alfarano and Milakovic (2007). The equilibrium distribution can be then derived out of a properly constructed diffusion process, which might be used to describe the dynamics of the profit rates and not just their equilibrium properties. In the paper we developed such theory, which leads to a simple stochastic process of competitive firm dynamics.
Masanao Aoki, UCLA
Some non-xponential macroeconomic growth models: non-self averaging behavior and potential policy implications
Dr Metin Arslan, State Planning Organisation, Turkey
Against Newtonian equilibrium
Studies in nonlinear dynamics have made it clear that the conventional notion of stability is at best problematic in such a way that, contrary to common belief, there is an unavoidable trade off between stability and indeterminism in the case of both deterministic and chaotic models. When analyzed in the theoretical, modeling and observational frameworks, the pervasive Newtonian concept of equilibrium, reminiscent of its deterministic modernist Weltanschauung, stands out in need of a reappraisal in terms of its ramifications for the physical and social sciences.
This work aims at assessing the case for its philosophical and methodological import on economics in the context of the recent discussions in the philosophy of science literature.
Luke Bergmann, University of Minnesota
Structured by the pursuit of profit: a coevolutionary, intersectoral model with stochastic technical change
Although “technology” and its dynamics remain of perennial interest in mainstream intellectual life, they are often theorized within a relatively autonomous sphere in our reductionist division of intellectual labor. An adequate conception of production, as a site where the tensions of use-value and exchange-value are mediated, provides a basis for exploring the evolution of technical relations in a manner as broadly systemic as the circuits of capital in which technical relations have come to be enmeshed.
In this paper, I develop a coevolutionary, intersectoral model of stochastic technical change in a society structured by the relentless pursuit of profit. Each sector has a changing population of production techniques, in which more profitable techniques become more prevalent. The set of socially-average techniques is calculated for each sector in the economy, with input requirements specified in material units, and is then used to determine present prices of production (assuming a rate of profit that has become uniform across the socially-average techniques calculated for each sector, but varies within these sectors).
Knowledge of relative expenditures on various inputs within each production technique is then used to implement stochastic technical change. Novel variations on existing techniques pursue superprofits through substituting inputs that are less expensive for those that occupy a larger share of the technique’s costs. However, as neither comprehensive social coordination among capitals nor perfect foresight are allowed, the profitability of a technique is never guaranteed nor unchanging. Over time, the model thus allows for coevolution on the level of the economy’s sectoral structure, as the emergent input-output configuration coevolves with the price vector; and on the level of use- and exchange- value, as the tensions between individual strategies in the pursuit of profit engender a complicated dance between the distinct yet interrelated patterns of physical and monetary flows.
In simulations beginning from uniform technical requirements, richly structured landscapes of sectoral interrelations emerge. Initial attempts at characterizing the resulting systems and comparing them to stylized facts about the structure of capitalist economies will be made. Yet beyond presenting a disequilibrium model that theorizes technical change in societies structured by the pursuit of profit, this approach potentially allows for theorization of the extent of and manner in which broad features of the observed material and technical patterns of production are not only shaped by supposedly autonomous actions of engineers confronting biophysical laws common to all societies but are negotiated through--and circumscribed by--the relentless pursuit of profit itself. We need to reject an ideological basis for economic quantification which centers on simplistic understandings of the money-form. If we instead simultaneously theorize the interrelations of the monetary and physical/technical moments in the circuits of capital, our appreciation for the broader material possibilities open to a society not organized around the pursuit of profit can only grow.
Paul Cockshott and Allin Cottrell, University of Glasgow; Wake Forest University
Probabalistic political economy and endogenous money
Since the foundational work of Farjoun and Machover important contributions to the field of probabalistic economy have been made in Yakovenko and in Wright Both of the later works assume an economy with exogenous money. In this context one naturally has conservation of money as a postulate.
However it is questionable whether a capitalist economy could ever work with entirely exogenous money, and it is interesting to see to what extent probabilistic arguments are of use in understanding the evolution of the type of endogenous money system that characterises contemporary capitalism.
We will first argue why, on probablistic grounds, a system with a strict conservation law on money was historically unsustainable. We then go on to examine whether phenomena like
-- the formation of a rate of interest
-- periodic commercial crises
-- the formation of a rentier class
can be understood using the sorts of arguments that Farjoun and Machover pioneered.
Raymond Dezzani and Harley Johansen, University of Idaho
FDI as state/space indicator of world-systems hierarchy
Foreign direct investment (FDI) flows have grown faster than trade since the mid-1980s. Prior to the mid 1990s, these movements were dominated by the “triad” core countries that accounted for almost two-thirds of value flows.
These flows are often seen as representing scale-economy based rent-seeking behavior. However, since 1992, it is also hypothesized that political stability has been a dominant flow determinant. Scale-economies and political stability are reinforcing mechanisms that serve to concentrate capital in core states.
In this research, we seek to examine the veracity of these statements for interstate capital flows. Foreign direct investment as spatial information/probability flows are examined within a hierarchical world-systems context. FDI flows are treated as both continuous movements of surplus value as well as state-space indicators of world-system hierarchical transition.
Luca Di Gennaro and Domenico Costantini, Universitat Pompeu Fabra, Spain; National Cancer Research Institute, Italy
Farjoun and Machover and Keynes and a probabilistic political economy
Anders Ekeland, NIFUSTEP, Norway
Labour content and skills: social justice or statistical pragmatism?
The topic of this
paper is the discussion in Annex II of Laws of Chaos on the question
of “skill coefficients” and their role in the determination of
labour content. The main argument of the paper is that this question
cannot be decided by “statistical pragmatism”, i.e. to which
degree the other main results from a probabilistic approach would be
altered by introducing skill coefficients or going for an egalitarian
solution. The question has to be decided by what we think is true
– since the answer has direct
implications for what we regard as fair wages, a fundamental question
of social justice.
The fundamental question
is whether different skills create different amounts of labour
content (value). Or as the authors of LoC formulate it, if “one
hour’s work done by an air pilot is taken to create the same amount
of labour content as an hour’s work done by an air steward or by a
porter who loads luggage onto the plane”. (footnote 5, p. 259).
If one is dealing
with dead nature then such “complicating” coefficients are more a
question of a trade off between explanatory power and mathematical
simplicity. The authors draw the following conclusion “that our
probabilistically theoretical framework is rather insensitiveto the presence or absence of skill coefficients” (p. 219, my
emphasis).
The
paper will argue that in a social setting this is not the case. For
the air pilot, but probably even more for the air steward and the
porter the question of what a fair – or correct – wage for their
work is a very important one, influencing all aspects of their lives.
As a consequence it becomes a key question for the labour movement.
Like Marx, the LoC adopts a pragmatic egalitarianism, but what the
labour movement need is a value theory,
not a “simplifying assumption”. The fact that LoC by rejecting
“ideal prices” cannot depend on them to determine skill means
that this determination must be done by procedure independent of
prices. The authors ask: “Does such a procedure exist? Perhaps, but
we do not know” – and then opts for the pragmatic egalitarianism.
The probabilistic egalitarian solution has very interesting implications for the questions relating to wage differentials and exploitation. In Annex II they reach the conclusion that – if one uses the egalitarian solution – “a worker whose wages are considerably higher than twice or two and a half times the average wages almost certainly consumes more labour than he or she creates”. Or in my words: exploits other workers. This result is of course very important for class analysis on a national scale, but even more so, on an international one.
The paper goes through both Marx’ various solutions in different versions of Capital. The paper also analyses subsequent “solutions”, in particular those using “embodied education costs” as a proxy for the skill coefficients. This solution is not discussed in LoC - despite being probably the one adhered to by a majority of Marxist economists.
The paper ends up by arguing for an egalitarian conclusion, on the basis of an analysis of the concepts of simple and abstract labour. The core argument is that when creating the abstract concept “simple labour” one disregards a lot of specificities – but what characteristics are we not allowed to disregard? If one has no answer to that question simple labour becomes abstract labour, which by its nature disregards all special characteristics of labour and is the egalitarian solution. This is actually the “instinct” of the radical and progressive parts of the labour movement world wide.
The paper also argues that LoC underestimates to which degree main-stream economic theory is an ideology, especially regarding the concepts of competition. The reason why main-stream, Sraffian and Marxist economists have an ideal (and erroneous) of competition and use ideal prices is because they are primarily interested in creating a theory of “value”, of distributional/social justice - not a theory describing the real dynamics of capitalism.
An alternative paradigm must – if it wants to be useful – also address the question of distribution. It must address these questions directly, i.e. not be egalitarian mainly for technical reasons, but for fundamental scientific ones.
Jurgen Essletzbichler, Department of Geography, University College London
Population perspective, evolutionary economics and probablistic approaches to economic evolution
Evolutionary approaches to economics are increasingly popular among heterodox economists. One of the hallmarks of evolutionary economics is the population perspective recognizing the actually existing diversity of economic agents as real and rejecting the ideal-typical, representative agent as fiction.
Without representative agent the simple relationship between micro- and macro-behavior breaks down and many of the welfare implications of market based policies do no longer hold in practice. In evolutionary economics, diversity is the fuel that powers evolutionary change. According to Price and Fisher, the extent of variation in economic performance is linked to the average rate of change of traits of selective value such as productivity, unit cost or other measures.
The replacement of representative with heterogeneous agents moves evolutionary economics in the domain of statistical and probability theory and away from deterministic models. Obvious overlaps between evolutionary economic theory and probabilistic political economy thus exist.
This paper puts evolutionary economic theory in conversation with probabilistic political economy and examines common grounds and important differences between the two frameworks.
Piero Ferri and Anna Maria Variato, University of Bergamo
Macro dynamics in a model with uncertainty
A macro model with an investment function based upon both real and financial aspects and a labor market ruled by imperfect competition can generate endogenous fluctuations, when one uses values of the parameters derived from econometric studies. In the paper the model is enriched by a Taylor monetary policy rule and by several different hypotheses about expectations. Simulations show the persistence of oscillations when agents forecast according to a time series strategy based upon a Markov process and monetary authorities learns about the NAIRU.
The following are the main results of the paper:
1. We have already shown that this type of model can create oscillations in the rate of growth of output and inflation that are persistent for a long period of time (see Fazzari et al, 2005). In this framework, the two main sources of endogeneity in the dynamics are analyzed: i) cash flows and debts are endogenously determined and have a powerful influence on investment, a primary factor in the creation of business cycles; ii) the process of learning induce further dynamics.
2. In the present paper, we show that these results are robust to different specifications of the Taylor rule and different expectational hypotheses. Because the model utilizes a Taylor rule, our results may shed light on the policy debate centered on that idea (e.g. Woodford, 2003, Clarida et al., 1999, Taylor, 1999, and Svensson, 2003). The Taylor principle in the "new neo-classical synthesis models" is based on an understanding of the monetary transmission mechanism that relies on price stickiness and substitution effects caused by changes in the real interest rate. The structure of our model is different because policy-induced changes in interest rates can also alter the values of such variables as cash flows and debts. In particular, the manipulation of the coefficient that relates to inflation in the Taylor rule can create stability only for a limited "corridor of stability". In contrast, manipulation of the coefficient relating to unemployment seems to be more stabi lizing, a rather neglected result by the advocates of a more active policy. In fact, they usually support a stronger reaction to inflation than to unemployment.
3. A strategic element in shaping the dynamics of the system is how expectations are formulated. If one abandons the world of perfect foresight and introduces uncertainty and learning, the possibility of checking the cycle becomes even more difficult. Fluctuations persist despite changes in the parameters of the Taylor equations. These results are robust to changes in the specification of the Taylor rule and to the information structure of the model.
Peter Flaschel, Bielefeld University
Labor productivity, a Marxian critique of its value-added decomposition
Peter Karl Fleissner, Institution TU Vienna (retired)
On the production of labour value and use value in capitalist and pre-capitalist worlds
The paper deals with the presentation of several building blocks of an agent based simulation model of idealized pre-capitalist and capitalist economies perceived as value producing and value consuming stochastic machinery.
(A) Inspired by the work of K.K. Valtukh (Marx’s Theory of Commodity and Surplus-Value – Formalised Exposition, Progress Publishers Moscow 1987) it contains
(a) the dynamics of intra-branch competition of producers associations/small commodity producers, their individual and social values, and the possible effects of competition on expansion, contraction and productivity of individual production units and the overall performance of the industry.
(b) Individual branches of production are integrated into a hypothetical input-output structure where the production units are able to move into branches of higher surplus values. (c) The resulting structures of (a) and (b) are aggregated into two different idealized systems of national accounting,
(c1) applying the Material Production System (MPS) used by the late socialist countries, and
(c2) the SNA (Richard Stone’s System of National Accounts) used by United Nations. The difference of the accounting systems from a labour value and a price perspective is discussed.
(B) To reflect contemporary capitalist economies in a better way the producers associations are (partly) replaced by capitalist firms striving for higher rates of profit by exploitation of workers. For this reason not only firms but also workers have to be introduced into the simulation model as agents.
(C) In a next step from rather abstract to more concrete levels of description of a capitalist economy the set of reproducible use values is divided into two groups: goods and services.
It is shown that capitalistic production of services creates use values and allows capitalists to make profit in the same way as if they would produce goods, but from a systemic perspective (and under ceteris-paribus condition) service capitalists do not add anything to the social surplus product of the economy and thus – in a closed economy – reduce the potential for growth via net capital investment.
This is consistent with the assumption that services do not add anything to surplus value and thus do not produce labour value at all. As before under (c) value accounting is applied revealing the opposed logics of SNA and MPS.
Alan Freeman, University of Greenwich
The poverty of equilibrium: law, contingency and motion in economic thought
This paper discusses the relation between law and contingency in the formation of value. It begins from a much-ignored assertion of Marx, repeated throughout his works, that the equality of supply and demand is contingent and their non-equality constitutes their law. This highly complex and original idea leads us to the idea of capitalism, and a market, as an entity which perpetuates itself by failing to perpetuate itself: it is the fact that supply diverges from demand which causes the system to continue, not the fact that supply equals demand, which is only the case as a statistical average and never exactly holds.
This fundamental and unrecognised difference between Marx’s approach and that of the classicals also distinguishes Marx from most modern economics, which has focussed on equilibrium as the de facto defining principle from which value may be deduced. The problem is exactly the opposite: it is to define a conception of value which does not require equilibrium and makes no presupposition that supply equals demand, that goods are sold, that profits equalise, or that any of the ‘lawlike’ properties of an ideal market actually hold.
The ‘lawlike’ properties of a market must then be deduced as an outcome of the dynamic, that is temporal, behaviour of the market, expressed in terms of the interaction between value so defined and use value. In order that such a concept of value may have universal applicability, price has to be reformulated as a form of value, and money theorised on this foundation. This article, presented to the EEA mini-conference on value in 1999, sets out the general principles involved.
Nils Froehlich, Department of Economics, Chemnitz University of Technology
Labour values and market prices in the German economy
In non-mainstream economic theory there are usually two ways of explaining market prices: Firstly, Labor Theory of Value which states that prices are driven by vertically integrated labor time (labor values). This approach, originally used by Karl Marx in “Capital, Volume 1”, evoked the famous “transformation problem” because an equilibrium profit rate seems to exist only in case of uniform capital intensity. Secondly, the discussion about labor values led to the development of Neoricardian Prices of Production based on the work of Pierro Sraffa and his followers. These authors believe their work brought the transformation debate to its well deserved end because their model provides prices generating an equilibrium profit rate. Hence, it’s typically viewed as state of the art. Nevertheless, there are several reasons to be in doubt with this opinion and to prefer the first alternative.
According to the work of Shaikh (1984) and Cockshott and Cottrell (1997, 1998, 2003) the two approaches are tested with OLS-Regression Models using German Input-Output Matrices. In this connection Farjoun’s and Machover’s methodical suggestions are applied as well (Farjoun and Machover 1983). Furthermore, to offer proper results both the distinction between productive and unproductive labor and the profit rate on a stock basis are taken into account.
It turns out that the Labor Theory of Value is most suitable for explaining market prices. Neoricardian Theory comes a close second. Moreover, the performance of the common empirical model used in the “marxian” literature sometimes can be improved by including the vertically integrated wage-profit rate into the regression model.
References
Cockshott WP, Cottrell A. 1997. Labour time versus alternative value bases: a research note. Cambridge Journal of Economics 21(4): 545–549.
Cockshott WP, Cottrell A. 1998. Does Marx Need to Transform? In Bellofiore R (ed.), Marxian Economics: A Reappraisal: Essays on Volume III of Capital, London: Macmillan Press LTD, 2: Profits, Prices and Dynamics, pp. 70–85.
Cockshott WP, Cottrell A. 2003. A note on the organic composition of capital and profit rates. Cambridge Journal of Economics 27(5): 749–754.
Farjoun E, Machover M. 1983. Laws of Chaos: A Probabilistic Approach to Political Economy. London: Verso.
Shaikh A. 1984. The Transformation from Marx to Sraffa. In Mandel E, Freeman A (eds.), Ricardo, Marx, Sraffa: The Langston Memorial Volume, London: Verso, pp. 43–84.
Alberto Russo, Domenico Delli Gatti, Mauro Gallegati, Bruce Greenwald, Joseph E Stiglitz
Business fluctuations in an evolving network economy
Hardy Hanappi, University of Technology of Vienna
Some ideas on a radically new Leitbild for political economy
It is evident that Newtonian physics still provides the formal blueprint for mainstream economic theory. This basic feature is responsible for the two most disastrous – and interdependent – trends of economics:
(1) The retreat of economists into academic ivory towers, where they explicitly proclaim not to be interested in real world political economy issues.
(2) The misuse of the inadequate theoretical products of the ivory towers by politicians, who can trust in the inability of the general public to discover the trick.
Classical political economy – and in particular its most profiled last representative Karl Marx – had started an ambitious research program designed to develop a complement to the approach of the natural sciences, the unified science of social evolution of human society. Since the mid ninetieth century this research program has suffered from continuous political and academic hostility from the ruling classes. As a consequence it remained poorly developed. The new mainstream of 1874 (Walras, Jevons, Menger) was supported by the bourgeoisie to distract and to divert reform-oriented intellectuals from communist ideas. In this ideological endeavour the new mainstream had no need to stay up to date with the dramatic discoveries in contemporary theories of physics – and Marxian theory did not have enough personal and resources to do so. The sclerosis of economic theory was unavoidable.
This contribution sets out to propose lines of argument, which could help to take up some of the many loose ends of political economy that have been left by several outstanding scholars in the last 150 years (Marx, Darwin, Schumpeter, von Neumann, Simon, Goodwin, to name just a few). Fortunately enough our contemporary toolbox for theory building has been substantially extended – the emergence of econophysics has to be interpreted as a symptom of the incapacity of mainstream economics to realize this fact. But where we really are absolute beginners is the production of radically new, adequate metaphors of the processes we want to theorize about - the visions, as Schumpeter would have called them.
To give an example: Human societies develop in an environment, which is governed by two periodic physical cycles: years and days. Re-occurrence, i.e. repetition is the basis for the emergence of sign systems in societies, sign systems which combine two dialectically opposed features: A constant name and an ever changing content. It was René Descartes who famously concentrated this idea in his concept of a variable. But as human individuals use a society’s language they are always finite neg-entropic outliers of the second law of thermodynamics, i.e. they are born and they die. The small finite set of experiences available during their lifetime supports only an extremely restricted scope of personal model-building. With the background of the much more elaborated framing support of the society’s model-building fixed in its knowledge stock this is the basis for a feeling of social randomness. Of course, the social stock of knowledge is still finite too; it is subject to forgetting and inadequacy. The (social) probability to entertain an adequate model thus appears as a natural property of knowledge acquisition – and is radically different from the probability concept used in atom physics. With this starting point (social) probabilistic approaches in agent based modeling of evolutionary economics certainly look different.
In the paper a handful of other lines of argument and their consequences will be highlighted. Though they are not combined into an overarching new theory, they are hoped to be thought provoking.
Edgardo Jovero, University of Kent
A chaotic-dynamic view of investment risk in emerging economies
An open-economy neo-Keynesian model is developed which highlights market power and price-setting behavior as a source of the indeterminacy and structural instability characterizing the risk environment in emerging markets. This should explain why countries, which constitute the whole of the emerging economies as a group, provide different country investment risks individually.
This structural instability in the behavior of emerging countries can take the form of a Hopf bifurcation, the likelihood of which increases as the mark-up power increases. Evidence is presented as to the likelihood of a Hopf bifurcation occurring, using the qualitative geometric theory of nonlinear complex dynamical systems. The Keynesian view that structural instability globally exists in an emerging market economy is put forward, and therefore the need arises for policy to alleviate this instability in the form of dampened fluctuations is presented as an alternative view analyzing the nature of risk and its role in investment management.
Frederico Jayme Katz, Núcleo de Estudos para América Latina, Universidade Católica de Pernambuco
Methodological contributions from chaos theory
Chaos theory has been attracting a lot of attention in the lasts decades. It represented a breath of inspiration for many sciences. Regarding economics, we had an increasing utilization of elements of this theory by those that work with quantitative methods in general, either as a tool or as a branch of investigation in itself. Nevertheless, its impact on non quantitative economics was much smaller.
The main aim of this text is to try to contribute to increase the presence of chaos theory on this area, concentrating on methodological aspects. It is made an effort to show that this theory, like other chapters of mathematics, transcends the limits of a simple calculation tool. It synthesizes also certain ways of thinking and, because they are of a new kind, or at least not of the usual type, it is believed that they can throw light into many areas, even in the non quantitative ones.
Steve Keen, University of Western Sydney
A Marx for the 21st Century
Steve Keen, University of Western Sydney
The non-conservation of money
Stephen Kinsella, University of Limerick and New School for Social Research
Characterising the complexity of an e-commerce market
The emergence and explosive growth of online markets and in particular online retailing has generated a large amount of academic research on online price dispersion. Online price dispersion is defined here as the distribution of prices of a product being sold over the internet (such as range and standard deviation) with the same measurable characteristics across sellers at a given point in time.
This paper presents three interesting and interlocking facets of the problem of modeling disequilibrium dynamics in ecommerce markets.
First, a description of the forces at work on the consumers, producers and institutional structures in the online retail ‘space’.
Second, an empirical analysis of two subsets of these—the markets for DVDs, CDs, and video games searched and compared by internet-driven shopping robots (shopbots)
Finally two models that begin to explain the findings of this analysis in terms of the informational constraints imposed on the consumer by themselves is developed in order to understand the modeling issues a researcher must face if they are to build a convincing model of online buyer behaviour. Using these models we can calibrate an information-theoretic measure of complexity for this market.
Andrew Kliman, Pace University
The tendency of the non-uniform physicalist rate of profit
Laws of Chaos repudiated the axiom of a uniform rate of profit. It also argued that, in the non-uniform case, the general “value” rate of profit closely approximates the actual average rate. It is thus tempting to infer that abandonment of the uniformity axiom rescues Marx’s law of the tendential fall in the rate of profit (LTFRP) from the physicalist (Sraffian, etc.) critique that suposedly disproved it.
However, Laws of Chaos, which rejected the LTFRP, rightly refrained from drawing this inference. The inference is incorrect, because the general “value” rate of profit to which Laws of Chaos refers is not *Marx’s* general rate. It is based on simultaneous determination of labor contents (or values), and is thus physically determined, just like the uniform rate of profit. Therefore, as this paper shows, its movements differ markedly from those of Marx’s rate of profit.
The paper then shows that this conclusion applies to the non-uniform physicalist rate of profit in the general case. Although the *levels* of the uniform and non-uniform physicalist rates may differ substantially, the “laws” governing their *movements* are the same. The most important result is that, in both cases, the expected value of the change in costs per dollar of sales revenue is exactly the same. Thus, the effects of technical change on the physicalist rate will also be the same, apart from non-systematic variations. (Empirical data reported in the paper suggest that these variations can be expected to be very small.) But non-systematic variations tend to cancel out over time, so the uniform and non-uniform physicalist rates of profit have the same long-run tendency.
Thus, the Okishio theorem’s implication that “viable” technical changes raise the uniform physicalist rate of profit applies equally to the non-uniform physicalist rate in the long-run (even if prices equal values!). There is only one way to escape this conclusion: repudiate simultaneous valuation and the physical determination of profitability that follows inescapably from it.
Lin Lin, Kiel University
Some extensions to Wright's ‘social architecture’ model
Ian Wright introduces a dynamic model of social relations between workers and capitalists in his paper "The Social Architecture of Capitalism" (Physica A 346 (2005) 589-620, later named "SA" model).
This agent-based model self-organizes into a dynamic equilibrium with statistical properties that are in agreement with many empirical distributions of developed capitalistic countries, including the power-law firm size distribution, the Laplace GDP growth distribution, the lognormal firm demise distribution, etc. The most important contribution of this paper is the unification of all these empirical distributions into a single causal framework, while conventionally they are studied in an isolated manner.
After detailed investigation, we have found several possibilities to enhance and extend this SA model. In this paper, we will address the following issues:
1. The "Actor Selection Rule" selects an actor according to a uniform distribution. Within a limited selection times, it is highly possible that some actors are selected many times while the others are not selected at all. We found that, by a simple modification to this rule, considerable improvements can be achieved in the resulting distributions.
2. The SA model is designed to reveal the stylized fact of "wage differential" through the "Wage Payment Rule", which allows capitalists to uniformly choose certain payment amounts between the highest and lowest wages. Consequently, the wage expenditure of a capitalist will not be changed as long as the median of the boundaries remains unchanged. We propose a Gaussian-like selection rule which makes the wage distribution more reasonable and better reveal the fact of wage differential.
3. The SA model in fact simulates a society without development, i.e., the sum of market value and actors’ money holding is always the same. Besides, the wealth distribution shows that the majority of people are extremely poor, while few of them are extremely rich, which violates the empirical findings. In this paper, possibilities of extending this model are pointed out, such as including a role of central bank.
Thomas Lux, Kiel University
Parameter estimation for stochastic models of interacting agents: an approximate ml approach
A large body of literature has proposed models inspired by particle physics as formalizations of collective processes in the economic and social spheres of human societies. However, attempts at empirical validation of such models have been very sparse so far.
This paper develops a broadly applicable methodology for estimating the parameters of microscopic models of social interactions. Its application to a popular business climate survey indicates that the collective behaviour of the survey respondents is well explained by a simple `particle' model of social interactions. This result also lends support to the view that the large fluctuations of investors' and consumers' confidence are mostly due to `animal spirits' rather than new information.
Mishael Milakovic, Kiel University
The empirical distribution of firms’ profit rates
The classical notion of competition rests on the idea that entrepreneurs will allocate their capital into the most profitable sector or business activity, utilizing the average rate of profit as a benchmark in their investment decision.
We propose a statistical equilibrium model in the spirit of Foley (1994) that interprets the tendency for competition to equalize profit rates as a dispersion measure around an average profit rate.
The model predicts an exponential power (a.k.a. Subbotin) distribution of firms’ profit rates. We investigate the profit rate distribution among more than a dozen diverse US business sectors, and find that profit rates have a clearly non-Gaussian distribution, mostly speaking in favor of the so-called Laplace distribution. The Laplace distribution is a particular case of the more general Subbotin distribution, having previously been observed in firm growth rates as well.
Paul Plummer and Eric Sheppard, University of Calgary and University of Minnesota
Rationality, stability and endogenous price formation in spatially interdependent markets
In Plummer & Sheppard (2006) we argued in favor of an understanding of the capitalist space economy that is grounded in a socio-spatial dialectic and a complexity-based modeling methodology based upon the Goodwin Code. The socio-spatial dialectic represents an ontology which takes both space and time seriously. At any given time, agents are constrained by the uneven socio-spatial structures within which they are embedded, over time structures and agency are mutually constitutive, giving rise to persistent non-equilibrium space-time trajectories. The Goodwin Code proposes a methodology in which models are formulated using the mathematics of non-linear interdependent systems and analyzed in terms of their global behavior, and socio-structures are characterized by the interdependence between economic agents who engage in out-of-equilibrium problem solving.
In this paper we extend the Goodwin Code to encompass a situation in which the geography of uneven development makes a significant difference to theoretical propositions that are widely accepted by both mainstream and heterodox economists: oligopolistic competition in spatially interdependent markets. To demonstrate the difference that space makes, we explore the extent to which decisions about whether to treat space as uneven has substantive implications for the set of spatio-temporal trajectories that are possible when oligopolistically competitive firms follow a ‘local’ or partial out-of-equilibrium adjustment strategy and are assumed to possess limited computational abilities and only limited information about the pricing strategies of their competitors.
In our model, we assume that these firms occupy fixed locations, setting prices under conditions of uncertainty, and sell a homogeneous product to spatially dispersed consumers who choose retailers probabilistically, based upon relative prices in their choice set. In previous research, we have established that both locational advantage and the nature and degree of market interdependencies imply that excess profits accrue to some retailers even at equilibrium, and that it is rational for firms to charge rate of profit (markup) rather than conventional total profit maximizing retail prices. Such an equilibrium is only weakly stable, however, raising questions about whether equilibrium is an emergent outcome of out-of-equilibrium profit seeking actions by retailers, responding to competitors’ price setting strategies.
Adopting the hierarchical classification scheme of Chomsky-Wolfram we employ a computationally intensive research design to explore the qualitative dynamic properties of this spatially interdependent system. We focus on three questions about the possible set of spatio-temporal trajectories that are generated by our model: (a) under what conditions does the partial adjustment model tend to drive the market towards an equilibrium configuration of prices, outputs, and profits, (b) under what conditions is it rational for retailers to experiment by charging prices other than those prevailing in a spatial price equilibrium, and (c) to what extent does the nature and degree of spatial interdependencies endogenously generate irregular price structures that can be substantively disrupted by external shocks and display significant dependence on parameter values and initial conditions?
David Rigby, UCLA
Probabilistic political economy and the evolution of regional economies
For much of the last one hundred years, the models that have dominated our understanding of the economy have been based on the concept of the representative agent. This is the homo-economicus of Mill, a “species” most starkly characterized by its homogeneity, a trait resulting from the genetic endowment of perfect information and an ability to optimize instantaneously and at zero cost.
Typological approaches, that ignore variety in individual characteristics and behaviors and that employ notions such as the representative agent, are useful insofar as they facilitate solutions to highly abstract, deterministic models of complex phenomena.
However, the costs of such approaches are generally very high. There are alternatives to the typological approach. Population approaches explicitly recognize heterogeneity in the characteristics and behaviors of economic agents and show how change both originates in, and at the same time produces, that heterogeneity. This is real change, system dynamics driven by opportunity and strategy, constrained by resources and played out in historical environments characterized by local accumulations of knowledge amidst global uncertainty.
At this time these debates are well-known. So why resurrect them now? For two reasons. First, because representative agent models have recently resurfaced in attempts to provide micro-economic foundations for macro-economics as well as in the so-called new economic geography.
Second, because the recent development of micro-databases allows us to explore the extent of plant-level heterogeneity and its impacts on the economy in ways that were previously impossible. Although we have known for a long time that establishments differ from one another in terms of their characteristics and their behavior, until the recent development of plant-level micro-data, those differences were typically concealed in industry or regional aggregations, casting some doubt on the significance of variety.
This prompts the question of how much heterogeneity exists within the economy, and in particular, how do technologies vary within the plants of a single industry. This paper explores the variety in techniques of production within a number of manufacturing sectors that differ in terms of age, technological dynamism and growth trajectories. Five specific issues are addressed.
First, how much variety in production technology is present within different industries?
Second, what happens to this variety over time, does it tend to increase or decrease and thus refute or support claims of technological convergence and standardization?
Third, is there a geography to variety? That is, do geographical differences account for a significant portion of the overall variety in techniques of production among the establishments of a particular industry?
Fourth, how do these geographical differences move over time?
Fifth, what are the mechanisms that drive the creation and destruction of technological variety, and do they change across industries and regions?
Ubaldo Garibaldi, Enrico Scalas, and Paolo Viarengo, Universita’ del Piemonte Orientale
Statistical equilibrium in simple exchange games II
We propose a simple stochastic exchange game mimicking taxation and redistribution. There are g agents and n coins; taxation is modeled by randomly extracting some coins; then, these coins are redistributed to agents following Polya's scheme. The individual wealth equilibrium distribution for the resulting Markov chain is the multivariate uniform Polya distribution. In the continuum limit, the wealth distribution converges to a Gamma distribution, whose form factor is just the initial redistribution weight.
The relationship between this taxation-and-redistribution scheme and other simple conservative stochastic exchange games (such as the Bennati-Dragulescu-Yakovenko game) is discussed.
Menno van Benthem, TNO / University of Groningen
The security of natural gas supply: an agent-based model of an out-of-equilibrium phenomenon
Introduction: In 1998, The European Commission issued the first Gas Directive. This directive laid the foundation for an extensive reform process of European natural gas markets. The goal of the reform process was to increase the competitiveness of the industry. The security of natural gas supply, an equally important goal of energy policy, was assumed to be unaffected. Ten years onwards, many doubts have arisen concerning the validity of this assumption.
However, an important obstacle to substantiating these doubts is the equilibrium nature of existing gas market models. In an equilibrium model, demand is by definition equal to supply, and therefore supply is always secure. To analyze the security of supply therefore requires a methodology that avoids equilibrium assumptions and quantifies security of supply as the probability of demand-supply equilibrium at an ‘acceptable’ price level.
Method: An agent based simulation model is employed to study the issue of security of supply. Agent-based simulation uses autonomous decision-making units (‘agents’) as its building blocks. The model incorporates five different types of agent to cover the whole value chain: producers, transporters, storage operators, traders and consumers. Various types of behavior can be programmed into each type of agent, ranging from profit maximization to the performance of public duties. In this way, crucial phenomena such as imperfect information, uncertainty and bounded rationality can all be taken into account.
Agents are connected in one of three ways: they are integrated into a single company, are connected through a bilateral long term contract, or trade on a (spot) market. A combination of agents, contracts and markets is chosen to create an initial market structure. A dynamical simulation is then performed to determine the behavior of the model over time. The security of supply is quantified as the probability of supply-demand equilibrium, which in turn is a function of market structure, agent behavior and data. In addition, a range of external influences can be added to the model, all affecting the probability of equilibrium. These influences include extremely cold winters, the breakdown of crucial infrastructure and different regulatory regimes.
Results: An optimal market structure for maintaining the security of supply ensures that the goals and incentives of individual actors are aligned with the goals of policy makers and will therefore promote rather than endanger security of supply. However, several aspects of the liberalized market structure are found to fail this test.
The abolishment of long term contracts, the functional unbundling of transport, supply and storage and the introduction of competition in supply have together led to a decrease in available information combined with an increase in uncertainty for all companies and also hinder efficient coordination between companies. This has increased the probability of suboptimal investment and has affected the industry’s resilience against external shocks to the supply system. Some market-based remedies are proposed.
Michael Webber, The University of Melbourne
Primitive accumulation: interactions between capitalist and noncapitalist modes of production
Formal models of capitalist development may be classified as ‘classical’, following the mathematical methods laid out by Marx, or 'microfoundational', building a macrodynamics from an analysis of individual behaviour. Both have typically examined the dynamics of a system that is purely capitalist. This is despite the fact that even the earliest qualitative analyses of capitalist dynamics recognised the centrality of competition between capitalism and other modes of production.
The theoretical advances made possible by Farjoun and Machover's Laws of Chaos reflect both increased sophistication over the classical models and a reliance on macroeconomic methods rather than microfoundations. Even so, there has still been little progress within Marxist political economy in formally modelling the interaction between different modes of production. This is a serious lack, even though the reasons for it are readily understandable.
This paper considers some of the issues involved in creating models of the competition between two sectors that have different modes of production – a capitalist mode and an independent commodity producing mode. These issues are drawn from a consideration of capital formation and primitive accumulation in China. That accumulation involves both dispossession by force, not much different from that analysed by Marx, and dispossession through the market. In this paper I shall consider dispossession through the market with the goal of formally analysing the markete-based dynamics of primitive accumulation.
Julian Wells, Kingston University
Marxism, probabilism, and Laws of Chaos
Farjoun and Machover’s Laws of Chaos proposes a probabilistic reconceptualistion of Marx’s political economy. This paper draws on Chapter Five of Wells (2007) to (a) show the fundamentally probabilistic and statistical character of Marx’s thought, and hence (b) assess Farjoun and Machover’s interpretation of Marx.
Reference
Wells, J. (2007) ‘The rate of profit as a random variable’, PhD thesis, The Open University.
Julian Wells, Kingston University
Modelling profit rate distributions: testing profit rate hypotheses
According to Farjoun and Machover (1983) capital-weighted company profit rates should be expected to have a gamma distribution. The only known previous hypothesis about the distribution of company profit rates is the claim in Gibrat (1931) that they should have log-normal distribution.
This paper draws on Chapter Five of Wells (2007) in using a large set of UK company accounts data to show that while different definitions of the rate of profit give rise to substantially different distributions, power law tails are ubiquitous in both capital-weighted and unweighted distributions
In the case of the profit rate definition discussed by Farjoun and Machover these tails render moot discrimination between their hypothesis and Gibrat’s.
References
Farjoun, E. and Machover, M. (1983) ‘Laws of Chaos’, Verso: London.
Gibrat, R. (1931) ‘Les inegalites economiques’, Sirey: Paris
Wells, J. (2007) ‘The rate of profit as a random variable’, PhD thesis, The Open University.
Ian Wright, The Open University
A closed social architecture model
In the probabilistic model described in 'The Social Architecture of Capitalism', Physica-A, 346, pp. 589--622, the average wage rate is an exogenous parameter. In this paper I describe a simpler, closed variant of the model in which the average wage rate is endogenous. One consequence of the closed model is a candidate probabilistic explanation of the observed distribution of income between workers and capitalists.
Reference
Wright, I. (2005) The social architecture of capitalism. Physica A: Statistical Mechanics and its Applications, 346, pp. 589-622.
Victor Yakovenko, Department of Physics, University of Maryland
Statistical mechanics of money, income, and wealth
We proposed an analogy between the thermal Boltzmann-Gibbs distribution of energy in physics and the equilibrium probability distribution of money in a closed economic system [1]. As a result of multiple money transfers between interacting economic agents, the system develops a stationary probability distribution of money. When the transfer rules satisfy a certain symmetry condition, the distribution of money is always exponential, which corresponds to the state of maximal entropy.
This work was followed by many other papers reviewed in my recent review article [2]. The probabilistic approach to money distribution is largely ignored by and unknown to mainstream economics, with some exceptions, such as the recent paper [3] which independently studied similar models. Current effort concentrates on finding empirical data for the distribution of money balances (perhaps from big banks) for comparison with the theoretical results and on development of more realistic mod els reflecting the structure of the economy [4].
In the absence of empirical data on the distribution of money balances, we spent a lot effort on analyzing the data on probability distribution of income data in the USA, which is available from the Internal Revenue Service and the Census Bureau. We found that income distribution in the USA has a well-defined two-class structure [5]. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs ("thermal") distribution. The upper class (1-3% of population) has a Pareto power-law ("superthermal") distribution, whose parameters change in time with the rise and fall of stock market.
We argued that this kind of two-class distribution can be described by a stochastic process with additive and multiplicative components [5]. We derived the probability distribution for this process [2] and are comparing it with the empirical data on income distribution. While the existence of social classes has been known since Karl Marx, on ly recently their spontaneous development was explicitly demonstrated in agent-based models [4]. More work in this direction would be certainly interesting.
For more references and computer animation videos, please see http://www2.physics.umd.edu/~yakovenk/econophysics/ and the review article [2].
References:
[1] A. A. Dragulescu and V. M. Yakovenko, "Statistical mechanics of money", European Physical Journal B 17, 723 (2000).
[2] V. M. Yakovenko, "Econophysics, Statistical Mechanics Approach to", http://arxiv.org/abs/0709.3662, to be published in the "Encyclopedia of Complexity and System Science" by Springer.
[3] M. Molico, "The distribution of money and prices in search equilibrium", International Economic Review 47, 701 (2006).
[4] I. Wright, "The social architecture of capitalism", Physica A 346, 589 (2005).
[5] A. C. Silva and V. M. Yakovenko, "Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983-2001", Europhysics Letters 69, 304 (2005).
Dave Zachariah, Global IP Solutions
Determinants of the average profit rate
The paper investigates the determinants of the average profit rate using the framework outlined by Farjoun and Machover (1983) and developed in Cottrell and Cockshott (2006). Empirical data from several countries are considered.