I recently came across an interesting piece by Ian Wright of the Open University, UK. Written in November 2016, Wright considers the cause of rising economic inequality, so evident over the last 30 years or more in most major and smaller economies. Wright dismisses the mainstream causes of rising inequality: namely, unequal distribution of profits and wages or lower taxes on the rich; or automation driving down wages relatively for those not working in ‘knowledge-based’ industries. Instead, the causes of rising inequality must be found in the very nature of the capitalist mode of production. As Wright puts it, “capitalism is a system in which one economic class systematically exploits another. And its economic exploitation — not housing, tax policies or low wages — that is the root cause of the economic inequality we see all around us.”
The original mathematical analysis developed by Wright describes capitalism as an anarchic system that generates what physics calls entropy: “the activity of market exchange is acting just like the cocktail shaker: its mixing everything up, randomising things, and maximising the entropy of the system.” As a result, “we might think that differences in wealth must arise from accidents of birth or personal virtue. But the principle of entropy maximisation tells us there’s a much more important causal factor at work. We quickly get extreme income inequality even in an economy with identical individuals with identical initial endowments of money.”
Wright develops a model of capitalism that is based on this principle of entropy in a market economy, but more than that. “Maximising entropy under the single constraint of conservation of money yields an exponential distribution of wealth. That’s quite unequal. So the first cause of inequality is what Adam Smith called the higgling and haggling of the market. Since people are free to trade then entropy increases and the distribution of money becomes unequal.” But Wright argues that “we don’t find an exponential distribution in actual capitalist economies. We find something more complex. That’s because capitalist economies obey additional constraints on how money moves between individuals. Markets are not the only cause of the inequality we see in capitalism.”
The other aspect is exploitation of labour for a profit. Capitalists accumulate profits as capital. “Firms follow a power law distribution in size. And capital concentrates in the same way. A large number of small capitals exploit a small group of workers, and a small number of big capitals exploit a large group of workers. Profits are roughly proportional to the number of workers employed. So, capitalist income also follows a power law. The more workers you exploit the more profit you make. The more profit you make the more workers you can exploit.” This is the reason for rising inequality when there are no checks on capital accumulation. As Wright sums it: “the fundamental social architecture of capitalism is the main cause of economic inequality. We can’t have capitalism without inequality: it’s an inescapable and necessary consequence of the economic rules of the game.”
This mathematical analysis accords nicely with the empirical evidence. For example, Simon Mohun, Emeritus Professor of Economics, ClassStructure1918to2011wmf has published a paper that showed that Marx’s class analysis, which rests on the ownership of the means of production (between the owner of the means of production and who exploits those who own nothing but their labour power), remains broadly correct, even in modern capitalist economies like the US. He found that the working class – those who depend on wages alone for their living – still constitute 84% of the working population. Managers constitute the rest, but only 2% (Qc in graph) can actually live off rent, interest, capital gains and dividends alone. They are the real capitalist class. And that ratio has little changed in 100 years.
Moreover, this is the group that has gained most during the last 30 years of rising inequality. The income of this capitalist class (Qc) has risen from about 9 times the average income of the working class to 22 times while managers incomes (Lpd) have risen from 2.5 times to 3.5 times workers income. So rising inequality is primarily the result of increased exploitation, a rising rate of surplus value, in Marxist terms.
I commented back in 2013 on the work by the father of inequality research, Sir Anthony Atkinson, now sadly deceased, who showed that it was not new technology and globalisation led to a rise in the demand for skilled workers over unskilled and so drove up their earnings relatively as mainstream economics likes to argue. Atkinson dismissed this neoclassical apologia. The biggest rises in inequality took place before globalisation and the dot.com revolution got underway in the 1990s.
What is decisive for capitalism is surplus value (profit, interest and rent), not differences in wage income or spending. The main feature of the last 100 years of capitalism has not been growing inequality of income – indeed, as Atkinson shows, inequality has not always risen. The main feature has been a growing concentration and centralisation of wealth, not income. And it has been in the wealth held in means of production and not just household wealth. That has generated a power law in inequality at the top.
One study shows how far that has gone in the recent period. Three systems theorists at the Swiss Federal Institute of Technology in Zurich developed a database listing 37 million companies and investors worldwide and analysed all 43,060 transnational corporations and share ownerships linking them (147 control). They built a model of who owns what and what their revenues are, mapping out the whole edifice of economic power. They discovered that a dominant core of 147 firms through interlocking stakes in others together control 40% of the wealth in the network. A total of 737 companies control 80% of it all. This is the inequality that matters for the functioning of capitalism – the concentrated power of capital.
The policy implication of this analysis follows. Yes, increasing taxes on the richest 2%, particularly on capital gains and ‘earnings’ from capital, would make some difference. Atkinson showed this in a study. But the extreme levels of inequality that most capitalist economies have now reached would only be dented a little. What is required is to end exploitation (of labour) for surplus value. That’s where the power law operates. And that means ending the capitalist mode of production.
Michael Roberts Blog 
Prof. Roberts, All of your posts are great – informative, accessible to laypersons (like me). Thank you. – Ramki, India.
Really thought provoking. Just the kind of development of Marx’s theories we need.
I should just like to point out that for Marx class is a relationship of dominance and subjection wherein surplus labour is extracted from the subjected class. This might be expressed legally as ownership or not of the means of production, but not necessarily so. Those who have command over the means of production can use such power to exploit workers even where their juridical status does not formally convey ownership, as with for example the senior cadres of the Chinese ”Communist” Party.
For another and analogous contribution cf. (2012) Biel, ”The Entropy of Capitalism.”
Link for paper “Written in November 2016” is actually to “The Social Architecture of Capitalism” v2 (2004).
Quotes are not from that paper but from Ian Wright’s blog post about it:
https://ianwrightsite.wordpress.com/2017/11/16/the-social-architecture-of-capitalism/
Engels should get credit for first introducing statistical mechanics entropy concepts with his chemical analogy:
“And to expect any other division of the products from the capitalist mode of production is the same as expecting the electrodes of a battery not to decompose acidulated water, not to liberate oxygen at the positive, hydrogen at the negative pole, so long as they are connected with the battery.
We have seen that the ever-increasing perfectibility of modern machinery is, by the anarchy of social production, turned into a compulsory law that forces the individual industrial capitalist always to improve his machinery, always to increase its productive force. The bare possibility of extending the field of production is transformed for him into a similarly compulsory law.”
https://www.marxists.org/archive/marx/works/1880/soc-utop/ch03.htm
That “compulsory law” also translates into Marx’s:
“Accumulate, accumulate! That is Moses and the prophets! “Industry furnishes the material which saving accumulates.” [23] Therefore, save, save, i.e., reconvert the greatest possible portion of surplus-value, or surplus-product into capital! Accumulation for accumulation’s sake, production for production’s sake: by this formula classical economy expressed the historical mission of the bourgeoisie, and did not for a single instant deceive itself over the birth-throes of wealth. [24] But what avails lamentation in the face of historical necessity? If to classical economy, the proletarian is but a machine for the production of surplus-value; on the other hand, the capitalist is in its eyes only a machine for the conversion of this surplus-value into additional capital.”
https://www.marxists.org/archive/marx/works/1867-c1/ch24.htm
Marx pointed to more than growing inequality. Concentration and centralization of capital results in ruin of most capitalists leaving only a tiny handful for workers to expropriate.
In 1928 socialist Frank Ramsey wrote first calculus of variations paper in economics, which described mechanics of concentration where rich can afford to save larger proportion of income while poorest savers find themselves consuming their capital until eventually split into two classes, which he sarcastically concludes by describing an “equilibrium” as follows:
…equilibrium would be obtained by a division of society into two classes, the thrifty enjoying Bliss and the improvident at subsistence level.
Click to access Ramsey1928.pdf
For Marx this process of concentration was closely linked to regular cyclical crises. During boom some expansion of capitalist class relying on credit. But crashes regularly bankrupt far more.
Marx did not have the mathematics to develop his theory of concentration, or indeed his theory of cycles (though when studying calculus he headed straight for Lagrange where duality prices in constrained resource allocation is found). But he did have in mind something along the lines of drive to accumulate to minimize long run probability of ruin as in Bernoullis “St Petersburg paradox”:
https://en.m.wikipedia.org/wiki/St._Petersburg_paradox
There is now an extensive financial literature on risk of ruin.
https://en.m.wikipedia.org/wiki/Risk_of_ruin
Important source is Myron Gordon who does give some acknowledgement to Marx in last chapter of his 1994 book.
I have put some more links here:
https://thecapitalistcycle.wordpress.com/2018/04/12/ian-wright/
I would caution against using entropy to describe the movement of capital. In contradistinction to entropy, Marx developed the laws which governed the movement of capital. With entropy there is only one law, the inexorable movement towards decay. Capitalism is chaotic but not disorganised. While prices may deviate from values, Marx set the limits of this deviation in Chapter 9 of Volume 3 showing that these limits were set by the process of averaging out the rate of profit. Secondly, capital tends towards concentration and centralisation because the more productive capitals not only exploit their own workers but the workers of their less productive competitors. There is thus a redistribution of profit from the less to the more productive capitalists which makes the system dynamic but also more concentrated. Its always a contradictory process. Finally, the primary cause of inequality is the balance of class forces. The subduing of the organised working class in the 1980s, the fall of the USSR, and the mobilisation of the reserve army of labour in Eastern Europe and South Asia, has decisively strengthened the hand of the employers.
Hence what we are dealing with is contradictory developments. And contradiction, which is the motor of dialectics, has nothing to do with entropy, because it is capable of bringing into being a new synthesis. Instead of decay, rebirth. This is the message we need to pound out now, as the world is about to rocked by events in the Middle East. Now more than ever we need to put the case that the vast majority of society, the beautiful 84%, have an interest opposed to the warmongers, and a future opposed to the capitalists who are putting the world at risk. When we say, socialism not barbarism, we are taking a stand against entropy, a stand against alienation, a stand for conscious change.
Agree with “caution” in use of concepts like “entropy” but it is at least a step forward from the most rigid body “Newtonian” mechanical materialism towards the more “chemical” mechanical materialism of statistical mechanics. Marx did his PhD thesis on the more dialectical uncertainty principle “atoms swerve” of Quantum Mechanics and his mechanical analogies were more like continuum mechanics with “moments” related to stress, strain, elasticity, viscocity, liquidity, tearing, cracking etc.
As Daniel Dennett mentioned, a striking aspect of Capital was its “biological” flavour, describing emergent phenomena of a social “metabolism”, with “morphogenesis” and evolution. I think systems biology will be a more fruitful source for mathematical exposition Capital than statistical mechanics. But the concept of “entropy” is still relevant as a measure of concentration. For explanation of this measure increasing one has to look at the more biological process of metabolism in which order emerges from chaos (negative entropy added in organism sublating the food it ingests into its own organization and excreting high entropy waste). Lenin gave the beginnings of a spreadsheet description of the polarization of peasantry into proletarians and bourgeois with input output tables in “On the the So-called Market Question”. With the contradictory evolution of life and social life, entropy is still involved in the process of birth of the new which goes together with decay of the old.
”I would caution against using entropy to describe the movement of capital. In contradistinction to entropy, Marx developed the laws which governed the movement of capital. With entropy there is only one law, the inexorable movement towards decay. Capitalism is chaotic but not disorganised.”
I am afraid the physics of this is beyond me, but I hope others will contribute to what looks like a very promising discussion, hopefully in terms that non-physicists can understand!
An 18% drop in income share, between 1980 and today, to the lower-earning 90% of workers is noted by Olivier Giovannoni, at the Levy Economics Institute, http://www.levyinstitute.org/publications/what-do-we-know-about-the-labor-share-and-the-profit-share-part-3-measures-and-structural-factors — The chart above notes a 17% drop of income share 1973 till 2011, close enough. The two estimates are somewhat different though, instead of 63% to 46%, Giovannoni states 55% to 37%. In all about a $2.8 trillion shift in income that now goes to the top 1% when before, 1946 to 1980 went to the lower 90%. Restoring former distribution shares would add about $15,000 to $20,000 a year more income to all 145 million lower-earning workers. I write the blog Economics Without Greed, http://benL8.blogspot.com, and I don’t think entropy is quite accurate, simply exploitation or greed states it better. Just as monopoly corporations destroy competition and capitalism, class warfare also destroys it. Keynes was accurate, aggregate demand is essential to vibrant economic environment. Balance is necessary. If workers wish to throw off the capitalists they must also become managers. I’ve only read Robin Hahnel’s book Economic Justice and Democracy where he proposes workers’ and consumers’ councils to manage production, distribution, wages and benefits, and so on; he calls it libertarian socialism. Yes, it would work if implemented. I don’t think we get there by raising up the word “revolution”, I think we slowly evolve into that condition by first taxing the 1% as we did before, at 91% of income, at perhaps 3% of wealth or net worth, and by mandating corporate governance with worker and community positions on all boards, and then a move to the Hahnel condition. It’s all theory and speculation until the population gets a better picture of EXPLOITATION.
“Alienation of the conditions of labour with the development of capital. (Inversion.) The inversion is the foundation of the capitalist mode of production, not only of its distribution.
The fact that in the development of the productive powers of labour the objective conditions of labour, objectified labour, must grow relative to living labour – this is actually a tautological statement, for what else does growing productive power of labour mean than that less immediate labour is required to create a greater product, and that therefore social wealth expresses itself more and more in the conditions of labour created by labour itself? – this fact appears from the standpoint of capital not in such a way that one of the moments of social activity – objective labour – becomes the ever more powerful body of the other moment, of subjective, living labour, but rather – and this is important for wage labour – that the objective conditions of labour assume an ever more colossal independence, represented by its very extent, opposite living labour, and that social wealth confronts labour in more powerful portions as an alien and dominant power. The emphasis comes to be placed not on the state of being objectified, but on the state of being alienated, dispossessed, sold [Der Ton wird gelegt nicht auf das Vergegenständlichtsein, sondern das Entfremdet-, Entäussert-, Veräussertsein]; on the condition that the monstrous objective power which social labour itself erected opposite itself as one of its moments belongs not to the worker, but to the personified conditions of production, i.e. to capital. To the extent that, from the standpoint of capital and wage labour, the creation of the objective body of activity happens in antithesis to the immediate labour capacity – that this process of objectification in fact appears as a process of dispossession from the standpoint of labour or as appropriation of alien labour from the standpoint of capital – to that extent, this twisting and inversion [Verdrehung und Verkehrung] is a real [phenomenon], not a merely supposed one existing merely in the imagination of the workers and the capitalists. But obviously this process of inversion is a merely historical necessity, a necessity for the development of the forces of production solely from a specific historic point of departure, or basis, but in no way an absolute necessity of production; rather, a vanishing one, and the result and the inherent purpose of this process is to suspend this basis itself, together with this form of the process. The bourgeois economists are so much cooped up within the notions belonging to a specific historic stage of social development that the necessity of the objectification of the powers of social labour appears to them as inseparable from the necessity of their alienation vis-à-vis living labour. But with the suspension of the immediate character of living labour, as merely individual, or as general merely internally or merely externally, with the positing of the activity of individuals as immediately general or social activity, the objective moments of production are stripped of this form of alienation; they are thereby posited as property, as the organic social body within which the individuals reproduce themselves as individuals, but as social individuals. The conditions which allow them to exist in this way in the reproduction of their life, in their productive life’s process, have been posited only by the historic economic process itself; both the objective and the subjective conditions, which are only the two distinct forms of the same conditions.
The worker’s propertylessness, and the ownership of living labour by objectified labour, or the appropriation of alien labour by capital – both merely expressions of the same relation from opposite poles – are fundamental conditions of the bourgeois mode of production, in no way accidents irrelevant to it. These modes of distribution are the relations of production themselves, but sub specie distributionis. It is therefore highly absurd when e.g. J. St. Mill says (Principles of Political Economy, 2nd ed., London, 1849, Vol. I, p. 240): ‘The laws and conditions of the production of wealth partake of the character of physical truths … It is not so with the distribution of wealth. That is a matter of human institutions solely.’ (p. 239, 240.) The ‘laws and conditions’ of the production of wealth and the laws of the ‘distribution of wealth’ are the same laws under different forms, and both change, undergo the same historic process; are as such only moments of a historic process.
It requires no great penetration to grasp that, where e.g. free labour or wage labour arising out of the dissolution of bondage is the point of departure, there machines can only arise in antithesis to living labour, as property alien to it, and as power hostile to it; i.e. that they must confront it as capital. But it is just as easy to perceive that machines will not cease to be agencies of social production when they become e.g. property of the associated workers. In the first case, however, their distribution, i.e. that they do not belong to the worker, is just as much a condition of the mode of production founded on wage labour. In the second case the changed distribution would start from a changed foundation of production, a new foundation first created by the process of history.”
Grundrisse, pp. 831-833
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Ian Wright’s econophysics methodology is in my view the future of Marxist Economics.
Let me point you though to a possibly divergent opinion of his. He considers the property relations between the workers and the firm as the only reason for the existence of such a power law. Because of this he proposes that we replace wage labor, in which labor is bought but equity remains to the capitalists/shareholders, to worker cooperatives in which all income is given to the workers and workers lend capital.
In short, instead of buying worker power, we would buy capital.
In my opinion, this is wrong and it would contradict even his own work. Capital in the form of money is able to control production and exploit workers even if it does not directly control the worker cooperative.
Change “lend” to “borrow” in my previous comment.