Home > Uncategorized > Pareto-efficiency, Hayek’s marvel, and the invisible executor

Pareto-efficiency, Hayek’s marvel, and the invisible executor

from Egmont Kakarot-Handtke*

you may download this paper here as a pdf
Abstract
This non-technical contribution to the RWER-Blog deals with the interrelations of market clearing, efficient information processing through the price system, and distribution. The point of entry is a transparent example of Pareto-efficiency taken from the popular book How Markets Fail.
JEL B59, D30.  Keywords price system, information processing, distribution

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That’s good for you and the economy as a whole, modern economists say:
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“For example, let A be a situation in which you earn $ 500 a week and I earn $ 1,000 a week and let B be a situation in which you earn $ 750 a week and I earn 1,000. Then, according to Pareto, B is superior to A, because your pay is higher and mine is the same. . . . Modern economists refer to a shift from A to B . . . as a “Pareto improvement,” and they define an economic outcome in which all such moves have been exhausted as “Pareto-efficient.” “(Cassidy, 2010, p. 54)
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This, of course, is only the first half of the story. What we look at is alone the income situation. To come full circle, expenditures must also be taken into account. So let us assume that our elementary economy consists of one firm, and you and me as workers. Together we produce 1,000 units of the consumption good. We spend our income fully, hence consumption expenditure is always equal to income. Our budgets are balanced.

Thus, in case A total consumption expenditures are $ 1,500. With an output of 1,000 units this gives a market clearing price of $ 1.50. You buy 333.3 units and I buy 666.7. We consume all these units in the period under consideration. Hence my real consumption is initially the double of yours. Note in passing that the profit of the firm we work for is exactly zero. The firm invariably gets back from the consumption good market what it pays in wages. The whole configuration is reproducible for an indefinite time.

Now your income situation improves and mine remains unaltered. In case B the consumption expenditures are $ 1,750. Accordingly, the market clearing price is $ 1.75. You buy now 428.6 units (compared to 333.3) and I buy 571.4 (compared to 666.7). In real terms the situation is no longer Pareto-efficient. Clearly, you are better off and I am worse off. The situation would still be Pareto-efficient if the price had not changed. Under the condition of budget balancing and market clearing, though, the price must rise. Note in passing that the firm’s profit is still zero. The firm is therefore indifferent between A and B.

To define Pareto-efficiency as in the introductory quote is a specimen of superficial economic analysis. The methodological point is that Cassidy’s example is a partial model and what is needed is a total model. From a partial model no general conclusions can be drawn. Ultimately, partial analysis is a shell game.

In the total model the price must increase in order to clear the market. This is the first of the diverse functions of the price mechanism. According to Hayek, the price system is a kind of telecommunications system which makes that the decentralized markets function properly. Not only this, it directs workers and other resources to their most productive uses. In other words: it realizes overall Pareto-efficiency.

“I have deliberately used the word “marvel” to shock the reader out of the complacency with which we often take the working of this mechanism for granted. I am convinced that if it were the result of deliberate human design, and if the people guided by the price changes understood that their decisions have significance far beyond their immediate aim, this mechanism would have been acclaimed as one of the greatest triumphs of the human mind.” (Hayek, 1945, p. 527)

With this, Hayek established the metaphor of the market as ‘superior information processor’ (Mirowski, 2013, p. 78 et seq.) that ultimately guarantees the efficiency of the whole economy and the optimal allocation of resources. This sounds good, nay, irresistibly good in the age of computers, but as Keynes remarked back then with an eye to intolerable unemployment:

“We get on very well in private life. But what rubbish his theory is.” (Keynes, quoted in Cassidy, 2010, p. 40)

Hayek, to be sure, tells at best part of the story. The major function of the price mechanism is not information processing but redistribution. The higher market clearing price in our example does not only signal that a higher nominal demand interacts with an unchanged real supply but it actually redistributes the output. When all is said and done I have 95 units lost and you have them won. This 28 percent reduction of my real income is what shocks me out of complacency about the working of the price system. The real marvel is that it is not you personally who takes something away from me. It is the anonymous market price. You, too, pay the higher price and, in a twisted logic, suffer with me.

However, if the productivity increases in the period under consideration then the redistribution can even take place at a constant market clearing price. In this case my real income remains constant but you cash in on the productivity effect. The market price would not signal anything and the whole action would count as a Pareto-improvement. Note again that profit does not change at all, it is still zero.

The distinctive feature of the elementary economy is that, as a matter of principle, there is no hindrance to repeat the shift from A to B as often as anybody likes. In other words, you can push me over the economic cliff with active support from the price system, or I can push you. All this is Pareto-efficient in nominal terms. Needless to emphasize that the elementary economy does not cover profit, interest, investment, etc. because all this would not affect the key point of the analysis.

In sum, our exemplary price system clears the market but does not help to bring about Pareto-efficiency in real terms. Just the contrary, it helps to bring about a redistribution of the real product. The remarkable thing about the price system is not that it is a superhuman information processor but that it is an invisible executor that, in a sense, serves social peace. Imagine for a moment that the tax collector takes 28 percent of your real income away and gives it to me, or vice versa. Such madness would be beyond all bearing. The price system can perform this feat Pareto-efficiently.

References

Cassidy, J. (2010). How Markets Fail. The Logic of Economic Calamities. London, New York, NY, etc.: Penguin.

Hayek, F. A. (1945).  The Use of Knowledge in Society.  American Economic Review, 35(4): 519–530. URL http://www.jstor.org/stable/1809376.

Mirowski, P. (2013). Never Let a Serious Crisis Go to Waste. London, New York, NY: Verso.

*Affiliation: University of Stuttgart, Institute of Economics and Law, Keplerstrasse 17, 70174 Stuttgart, Germany. Correspondence address: AXEC-Project, Egmont Kakarot-Handtke, Hohen- zollernstraße 11, 80801 München, Germany, e-mail: handtke@axec.de

Papers on SSRN: http://ssrn.com/author=1210665; Website: http://www.axec.org, see Terms of use; © 2014 Egmont Kakarot-Handtke

 

  1. January 20, 2014 at 7:40 am

    That in one way is a fine example of how the price system works, as well as of some aspects of Pareto efficiency (which I tend to think of as a somewhat useless normative concept—meaning something one strives for as desirable), and also how the price system itself is not intrinsically any obstacle to ‘social justice’ or alternative ways of distributing income and labor. But, this all follows from the basic theorems of welfare economics (1st and 2nd, if i recall)—any distribution of income can be achieved, and be justified using pareto efficiency as a criteria, and then be used itself as a benchmark to measure pareto efficiency for any future economic configurations (so that if they differ from that benchmark they are seen as inneficient).

    But this begs the question.You say ‘it is not you who takes something away from me, but the price system’.

    I think that is incomplete. The thing is, the price system did not change the incomes in second stage. The price system does not set the minimum or maximum wage. Those are political or social issues. The price system merely acts on prices (wages, costs, etc.) set by owners, workers, society in general etc.

    And that is why many people distrust the price system because even if it operates as an objective maximizing algorithm, the inputs are the products of human choice as well as ignorance. In fact, it is Hayek’s view (and others) that the market is an information processing system which makes people nowadays even more suspect of the price system, given ‘bounded rationality’, behavioral economics, paradox of choice, stochasticity and noise, noncomputability etc.

    Even if you trust the market mechanism or algorithm, noone knows if the price is right. Part of current ideology is to promote the market system while keeping people away from thinking about what the value of their labor is, and the product. (This is why its always posed as $9.99, not 10; or ‘we’re the 99%’, without mentioning there are differences in the 99%).

    In addition, as the SMD theorem for example shows, the above result doesn’t hold in general when you get past the 2 people, 1 good case. (The same is true in ecology—its easy to solve ecosystem dynamics when there is one predator and one prey. Throw in one more, and you start to get chaos.)

  2. January 20, 2014 at 5:31 pm

    “Imagine for a moment that the tax collector takes 28 percent of your real income away and gives it to me, or vice versa. Such madness would be beyond all bearing.”

    This statement confuses me. Isn’t that what any progressive taxation system does? Given our present degree of wealth and income inequality, isn’t that a defensible policy?

  3. January 21, 2014 at 11:26 am

    Excuse what is probably a stupid question from a non-economist. I don’t get this unless there is some special meaning for the term “market clearing”

    You have said

    “In the total model the price must increase in order to clear the market.”

    Why? To me the words “clear the market” means “sell all the goods on offer”. So there is no need for the price to rise, because presumably the consumers will still buy all the product; the output has not changed. What is clear is that there will be money left over, and that violates your stipulation that we spend all the income. But why should we do that? Why not save up? Perhaps it is because there is nothing else to spend money on in this model where there is no second firm nor any alternative goods to spend the money on. Already such modelling is absurd, and not only for the reasons you cite. At least that is how it seems to a lay person. To me it looks as if you have imported a consequence of the profit motive, predicated on a shortage of the goods under discussion: yet the model denies such a factor in order to achieve simplicity. Without such a motive there is no reason at all to increase the price though there is reason to use the surplus to make more of the goods for sale if we assume that the consumers might want more of them.

  4. January 22, 2014 at 12:23 pm

    there is no real reason to ‘clear the market’—though its easy to ‘complete the market’ by simply putting in the savings account. (just as the original arrow-hahn GET theory could add money—which was not in the model—-as another factor of production or consumer good). (could always add in transaction costs–coase).
    these are abstract mathematical excercizes, but then so was the internetat the beginning.
    ‘non-economist laypersons’ often are way ahead of the ‘experts’; but they don’t formalize it.
    only thing i would question is the idea that ‘consumers want more goods’—consumers, and their preferences or wants, are conventions (including addictions, etc). they may want more goods, or retirement accounts, based on their ‘discount rate’, but ‘why’ they do is a slightly different issue—-basic needs, status striving, higher education, alienation, manufactured consent, etc.?

  5. January 23, 2014 at 10:15 pm

    Thanks for your response.

    I agree that we need not assume that consumers want more goods, but I think that is a separate issue. I really just wanted to understand why this article makes sense. I suppose I assumed that “clearing the market” must have some specialised meaning to economists: like lots of other terms do. It only serves to obfuscate what is being said when they use a term like “demand” which bears no relation to its ordinary meaning. I wondered if this was yet another example, for the reasons I gave.

    Abstract exercises are intellectual masturbation unless they have some insight into how things work to offer. But to do that they have to include everything that is relevant, and I do not get the impression that economists have the slightest idea what is relevant. They “simplify” in line with their pre-determined position so far as I can see: it ought to be the other way around, I think

  6. January 30, 2014 at 12:25 pm

    To Fiona

    You are of course right to point out that people can save. All we have to do in our example is to lift the condition of budget balancing. I have done this at length elsewhere (see link below). To restrict the analysis to market clearing and budget balancing focuses the argument but does not make the special case under consideration absurd.

    Market clearing means that the quantity produced is equal to the quantity sold, hence there is no need to deal with inventory changes on this occasion. Markets never clear in the period under consideration but this, too, is a topic for another occasion.

    To ishi

    You are right to point out that I have not dealt with the question of how the distribution of nominal incomes comes about in the first place, but have taken the example from Cassidy.

    My argument is that the price system translates any distribution of nominal incomes anonymously into real shares of output and that this function matters more than the information function. What is ultimately of importance for everybody’s living standard is the real share which is jointly determined by nominal incomes and the price structure of final output.

    To Bob Hall

    Sorry for my misplaced irony. What I wanted to express is that there is some kind of double standard with regard to redistribution. Analytically, redistribution via the tax system or the price system is on equal footing with regard to the ultimate result in real terms for the economy as a whole. For an objective observer there is no point in condemning the first alternative or praising the second as Pareto-efficient. Clearly, for the individual agent it makes a huge psychological difference but this myopic view is not relevant for the assessment of the final result.

  7. January 30, 2014 at 12:28 pm
  8. JW Mason
    January 31, 2014 at 5:37 pm

    The example here is about odd since these questions are normally discussed in terms of real goods, not money incomes. Few if any economists would describe a situation in which your money income was constant but all prices rose as one where your income was unchanged.

    However, the general point here is correct. Changes in prices that result from market transactions are never taken into account as externalities, even though it seems obvious that they affect the well being of third parties. In trade contexts, this problem is “solved” (or at least pushed out of view) by the compensation principle. But I’m not sure how mainstream economists justify ignoring the welfare implications of price changes generally.

    Do you have any sense of what is the usual way of resolving this problem?

  9. February 2, 2014 at 1:37 pm

    To JW Mason

    The crucial point is this. General equilibrium models are “real” in the sense that money and nominal magnitudes play no role. In a more critical vein it can be said that these models cannot deal with a monetary economy at all. Yet, as we all know, that is the economy we live in. Hence the “real” core of standard economics has, as a matter of principle, nothing to say about the real reality.

    You correctly point out that the example I have taken from Cassidy is odd because the criterion of Pareto-efficiency applies in the strict sense exclusively to a “real” model.

    This, however, is forgotten when it comes to the discussion about efficient markets and optimal allocation. For a monetary economy the efficiency results have never been proven. It is only by analogy that people think that, admittedly under idealized conditions, the price system works also in a monetary economy towards Pareto-efficiency. Cassidy’s example is a case in point. But Cassidy is only echoing Hayek.

    The really odd thing is that you have readily identified the weak spot but that Cassidy himself and the referees, proofreaders, consultants and whoever was involved in producing his qualitatively outstanding book overlooked it. It seems that Cassidy never got a critical comment from a neoclassical economist about the misrepresentation of the Pareto criterion.

    My idea of resolving the problem is simply not to apply the Pareto criterion to the monetary economy. It was not designed for this environment and it is positively misleading in any discussion about the working of the price system. If you accept Pareto-efficiency as a benchmark then most real-world markets “fail”. Is a thunderstorm a “failure” of an otherwise optimal weather system? Definitively not. The Pareto criterion establishes an unacceptable frame of reference.

    In sum: The marvel of the price system consists not so much in informational and allocative efficiency, which is not defined for the monetary economy with flexible nominal prices, but in smooth real redistribution.

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