Kenneth’s three arrows

Kenneth J. Arrow has died at the age of 95.  He was an important mainstream economist.  He won a Nobel Prize as a mathematical theorist.  Indeed, Arrow was the epitome of the neoclassical general equilibrium theorists who came to dominate mainstream economics, with the avowed aim of using mathematics to deliver economic analysis and answers, in a mimic of mathematical physics.

Arrow was a close associate of that other great neoclassical and anti-Keynesian theorist, John Hicks.  They both aimed to use general equilibrium theory and math to show that markets and economic growth under capitalism could achieve equilibrium through supply and demand in ‘competitive markets’.

Interestingly, Arrow was uncle to a current Keynesian guru of ‘managed capitalism’, Larry Summers and also brother-in-law to that other icon of 1960s mainstream ‘Keynesian’ economics and the then textbook writer to university students, Paul Samuelson.  It’s a small world in the mainstream – although not as small as the Marxist economics world!

What did this ‘giant’ of mainstream economics theory contribute to our understanding of modern economies or the workings of firms and people in a ‘market economy’?  Math was Arrow’s forte.  “I think my biggest hopes were methodological — to apply new developments in mathematics to economics,” he told Challenge: The Magazine of Economic Affairs, in 2000.

There are three areas (arrows) that spring to mind.  The first was Arrow’s ‘proof’ that each individual’s desires or needs cannot be combined into a collective result where everybody gains or their needs are satisfied.  His conclusion as outlined in his famous monograph Social Choice and Individual Values , was that “If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial.”  In other words, it was impossible to deliver what ‘society’ needed from individual preferences as expressed through markets free of ‘unwanted alternatives’, at any time, and for all, unless the market is replaced by ‘dictatorship’.

You can already see the irony of this result.  The leading mathematical theorist of capitalist markets proves that markets cannot meet each individual’s needs without worsening the needs or desires of others, or abolishing itself! As one economist put it, Arrow “proved it was logically impossible for there to be a system of voting which is free of anomalies, no matter what kind of system it is…You can say, ‘There’s no really good way to run an election,’ but it is something else to prove it. . . . It’s like proving a bicycle cannot be stable.”

As developers of this ‘impossibility’ theorem, like Amartya Sen, went on to show, this also meant that there was no way that markets, perfectly competitive or not, could deliver equality of outcomes for each individual – no Pareto optimality.  Another way of putting this is to say that it is impossible to get ‘society’ to make a choice that leads to satisfaction for everyone.  As Sen said, “It is important to recognize that Arrow was not only establishing a theorem, he was opening up a whole subject to social choice.”

Democracy means making choices or plans that the majority want or need even if the minority loses out.  You may find this result self-evident and trite but apparently Arrow gives you a mathematical proof!  But it does not answer the social question: who is the majority and who is the minority?  And in the current world is it not the minority of the 1% and super-rich that get their needs met at the expense of the 99%?  Arrow’s theorem suggests that such inequality is the way of the world of markets.

Arrow’s second contribution was to the notorious foundation of neoclassical theory of capitalist market harmony, general equilibrium theory.  The principle of GE theory is that supply and demand in markets can be equalised and stabilised at a certain price, thus proving that capitalism is not inherently unstable as Marx had argued with his critique of Say’s law.  In a paper to the American Economic Association, Arrow states, “From the time of Adam Smith’s Wealth of Nations in 1776, one recurrent theme of economic analysis has been the remarkable degree of coherence among the vast numbers of individual and seemingly separate decisions about the buying and selling of commodities. In everyday, normal experience, there is something of a balance between the amounts of goods and services that some individuals want to supply and the amounts that other, different individuals want to sell. Would-be buyers ordinarily count correctly on being able to carry out their intentions, and would-be sellers do not ordinarily find themselves producing great amounts of goods that they cannot sell. This experience of balance indeed so widespread that it raises no intellectual disquiet among laymen; they take it so much for granted that they are not supposed to understand the mechanism by which it occurs.”

So the invisible hand of the market (Smith) can lead to harmonious equilibrium in markets where supply and demand are ‘cleared’.  Working with Gerard Debreu, the Arrow-Debreu theorem in 1954 supposedly provided a rigorous mathematical proof of a ‘market-clearing’ equilibrium — or the price at which the supply of an item is equal to its demand.   It became just what mainstream economics needed to ‘prove’, namely that a theory of value and price formation could be based on individual consumer choices and not on the labour theory of value as put forward by the classical economists and Marx.  “Their (neoclassical) theory of value and price formation was really a fundamental element of economics…It’s the ABCs of economics and economic theory.”, said one follower of Arrow.

But again, what is ironic about the Arrow-Debreu proof is that it shows markets have to be completely ‘perfect’ in the sense that no one participant can have extra knowledge or economic power over another and that there must be no restriction or distortion of price from outside.  The theorem has been applied in financial markets on the grounds that these are ‘perfect markets’ where everybody has the same power and knowledge.  Such an assumption, we now know after the global financial crash (in part the result of dysfunctional derivatives markets), is unrealistic to the point of disaster.

That the theorem of general equilibrium in capitalist markets is based on totally unrealistic assumptions is not a decisive critique, because Arrow recognised this.  Indeed, he drew the conclusion that the aim of policy should be to try to ‘correct’ and ‘manage’ any anomalies in markets to achieve something closer to ‘equilibrium’.  As he said, “You cannot get a full understanding of the behavior of any part of the economy without understanding its reaction on other parts.”

He applied this approach to health economics.  In his 1963 paper “Uncertainty and the Welfare Economics of Medical Care”, he found that the delivery of health care deviated in fundamental ways from the traditional competitive market and, for this reason, was a ‘nonmarket’ relationship.  For example, in a ‘perfect market’, the buyer and seller in theory have access to the same information about market price and value. However, in the health-care market, the supplier (doctor) commonly has a superior knowledge of the quality, provision and distribution of health-care services — all of which puts the consumer (patient) at a relative disadvantage.  This creates a problem of ‘information asymmetry’.

Consumers also do not always know when they will need health care until the moment they require it (as with a stroke or heart attack). So when consumers purchase insurance, the cost can be prohibitive.  And insurance companies worry that offering coverage to protect consumers against losses could create ‘moral hazards’, such as risk-taking and irresponsible behaviour (indeed!).

Again it may not surprise you to find that the world’s leading equilibrium economist found that markets are not fair in delivering basic needs like health to people because they are rigged or corrupt!  Of course, unfortunately, that has not led to the conclusion that healthcare should be publicly owned (single supplier) and delivered free at the point of use (public good) to be maximise people’s needs.  Indeed, Arrow never followed his own theoretical conclusion when asked to consider whether money damages could be measured and so awarded to people suffering environmentally from the activities of ‘more informed’ multi-nationals.

What is the decisive critique of the Arrow-Debreu theorem’s relevance to modern economies is that economies are not static systems but dynamic.  Yes, Marx said, supply does equal demand but really only by accident.   In theory, under ludicrous assumptions, markets clear all supply and meet all demand, but in reality, they hardly ever do. Markets keep moving away from equilibrium all the time.  Nothing stands still and there are ‘laws of motion’ that continually change ‘equilibrium assumptions’, making market economies inherently uncertain. These laws of motion (as developed by classical and Marxist economics) rather than the ‘principle of equilibrium’ are much more relevant to understanding the capitalist economy of production and investment for profit.

Arrow did venture into the realm of classical economics of a dynamic economy and proposed an endogenous growth theory, which seeks to explain the source of technical change as part of the process of accumulation and not ‘external’ to the movement of supply or being set by consumer demand.  Yes, I know, it is difficult to believe, but mainstream neoclassical theory argued that aggregate supply and demand in an economy were driven by separate forces (the preference of firms on the one hand and by consumers on the other).

Endogenous theory recognised what any fool could see: that supply was affected by demand but also demand was affected by supply.  Innovation did not come out of the sky but from the drive of companies to grow (or in the case of Marxist theory, to make more profit and reduce labour costs). Of course, the neoclassical version of growth theory did not consider profitability relevant to innovation but instead looked at aggregate output.  This theory became popular with many reformist economists and politicians – apparently, former adviser and minister in the British Gordon Brown Labour government, Ed Balls, was a keen promoter.

So Kenneth Arrow leaves us with three arrows to enrich our understanding of the economic world: 1) markets collectively can never properly deliver every individual’s needs; 2) markets cannot equate supply and demand except under the most unrealistic assumptions and 3) economic growth is not achieved by just meeting the demand of consumers but requires decisions of investors to innovate.  Ironically, none of the implications of these economic arrows have been accepted by the owners of capital and their politicians in practical policy.  To do so, would be to admit that capitalism does not work for the majority or even much of the time for the capitalists.



I omitted to mention that, despite being an apparent standard bearer of neoclassical general equilibrium theory, Arrow was by no means a supporter of capitalism. Indeed, he wrote an article in fall 1978 in Dissent magazine making a ‘cautious case for socialism’.…/a-cautious-case-for-socia…

It’s not a Marxist view (“It was in this area of political-economic interactions that Marxist doctrine was most appealing. I was never a Marxist in any literal sense”) but Arrow still exposed many faultlines in capitalism: “as I observed, read, and reflected, the capitalist drive for profits seemed to become a major source of evil”.

“The absorption of the economy by a small elite implied that the formal democracy and freedom was increasingly a sham; the major decisions on which human welfare depended were being made by a few, in their own interests.”

“To sum up, the basic values that motivated my preference for socialism over capitalism were (1) efficiency in making sure that all resources were used, (2) the avoidance of war and other political corruptions of the pursuit of profits, (3) the achievement of freedom from control by a small elite, (4) equality of income and power, and (5) encouragement of cooperative as opposed to competitive motives in the operation of society.”

“There can be no complete conviction on this score until we can observe a viable democratic socialist society. But we certainly need not fear that gradual moves toward increasing government intervention or other forms of social experimentation will lead to an irreversible slide to “serfdom.”
It would be a pleasure to end this lecture with a rousing affirmation one way or the other. But as T. S. Eliot told us, that is not “how the world will end.” Experiment is perilous, but it is not given to us to refrain from the attempt.”


8 Responses to “Kenneth’s three arrows”

  1. AN Says:

    I follow your blog avidly and rely on your analysis on a number of issues. This post is therefore very disconcerting to me. You have fundamentally misunderstood or misrepresented the Impossibility Theorem, and your interpretation of the “logical implication” of Arrow-Debreu goes far beyond what can actually be inferred from their result.

    It seems to me that the ability to accurately characterize the arguments of your opponents should be a minimum requirement when engaging with these opponents about their ideas. You either misunderstand Arrow, or you are purposefully misrepresenting these results. Both options are troubling to me, as someone who frequently relies on your analysis in areas I don’t know much about.

    • michael roberts Says:

      Thanks for your comments Andrew, but I am not sure where you think I have misrepresented or misunderstood Arrow-Debreu. Have a look at this paper, I quote:

      “Additionally it was claimed that it failed to describe the functions of actual markets. It was shown that such equilibrium was mathematically not impossible, as it heavily depends on full use of available resources according to the concept of Pareto efficiency. However, whether such equilibria could exist, even in mathematical models characterised by stability, is not yet known. Arrow’s co-author Frank Hahn wrote that “the complete market hypothesis completely falsified” and Arrow added that “such a system could not exist”. Hahn went even further by arguing that the conditions for general equilibrium turned out to be so demanding, that the Arrow-Debreu model was mostly useful as a refutation of the market’s ‘invisible hand’.

      Recently, many Nobel laureates expressed serious doubts about the validity of the orthodox neoclassical theory20 and specifically, the ArrowDebreu general equilibrium model. They also provided many suggestions about improving the classic, economic models. Among them, Kornai (2014) has developed a new model in his newest book. His DRSE (Dynamism, Rivalry & Surplus Economy) theory adopts the ex-post model philosophy; it radically rejects the ex- ante set of conditions adopted by the dominant neoclassical school and the stringent limits of equilibrium and defines its own premises for the functioning of capitalist economy. In other words, the DRSE theory represents an extremely novel trend among the various schools of economics. It is still only a verbally described model featuring the following supporting pillars of the capitalist system: dynamism, rivalry and the surplus economy. The model highlights the dominance of the surplus economy, the replacement of oversupply by monopolistic competition, uncertainty over the volume of demand, Schumpeterian innovation, dynamism, technological progress, creative destruction and increasing return to scale with rivalry between producers and service providers for markets.

      I think it makes similar points to me.

  2. michael yates Says:

    Thanks for an interesting piece, Michael. It made me think of the drudgery I endured with this boring stuff in graduate school nearly 50 years ago. Thank god for Samuel Bowles’ great workbook in microeconomics. I did every problem, and somehow I managed to pass my comprehensive PhD exam in micro economics. Here is something I wrote about neoclassical economics:

    “Economics is a peculiar discipline. The dominant economic theory is called the “neoclassical” theory; it is the only one taught in all but a handful of graduate schools. It is the one I was taught, and it is the one the economist we met in Santa Fe learned. It is preached with a zeal and demand for conformity that has led critics to characterize it as a religious cult. Newly-minted PhDs leave school convinced that they have a special knowledge unavailable to the ordinary person, and they devote themselves to giving this knowledge to others.

    The main trick used by professors of economics is to draw their pupils into a make-believe world and then convince them that this is a good approximation to the real one, enough so that the world in which we live can be studied effectively by analyzing the fantasy construct. In fact, the professors also claim that this pretend world is a good approximation not just of where we live today but of that of any time in human existence, so that any society can be studied through its lens. To them the neoclassical theory is as universal and timeless as the theories of Einstein. They see economics as the physics of society.

    The economists take their analysis one step further. The hypothetical world of their theory is in all important respects ideal, the best we could have. Therefore any deviation from it that we observe in the realm of existence should, in the interest of human happiness, be eliminated.

    It is a curious thing to say that something should change in the living world because it does not conform to a creation that does not, and, as we shall see, could never, exist. For example, a minimum wage set by the government interferes with the efficient operation of the ideal world by causing a loss of employment. The neoclassical economists then conclude that we should not have a minimum wage in the actually existing world. Or, the economists conflate the ideal economy of their theory with the real economy, which is capitalism. Since the imaginary economy is good, so too is capitalism. It is no wonder that economics has been compared to religion. To hold such views requires a strong faith.”

  3. Edgar Says:

    “Consumers also do not always know when they will need health care until the moment they require it “

    Yeah but when did they ever matter! At a society level we know approximately how many people will have an heart attack, which groups are most at risk etc. So public goods can be calculated in this way.

    For private goods the need is manufactured, more often than not, and in distribution capitalism can be described as a system that rations goods based on people’s ability to pay. So the coherence of the market between what people want to buy and sell doesn’t factor in that the rich ‘want’ to buy high art, yachts and expensive cars and the poor ‘want’ to buy lottery tickets. What a wondrous coherence!

  4. oakesj Says:

    Hello Robert, long time listener, first time caller.

    I’m having trouble tracking down the accounting methods you use to calculate the rate of profit. I see that according to you (and Andrew Kliman) the rate of profit has been in decline for some time, but I read from economists working in another tradition (e.g. Bruce Greenwald) that profits are elevated since the crisis. Can you help me understand (or point me towards literature or posts that would explain) why Marxists and New Keynesians(?) come to such different profit numbers.

    I apologize for commenting off topic; I just wanted to make sure this got read. Please feel free to delete it afterwards.

    Thanks in advance!

  5. oakesj Says:

    Never mind. Dumb question. Went and found it myself.

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