‘Debunking Economics’, Part I: Demand Curves Can Have Any Shape

The first substantive chapterof Steve Keen’s book Debunking Economics explores the idea that the demand curve for a market does not necessarily slope downwards, as is the norm in economics textbooks. Instead, once you move past the individual level, then according to neoclassical principles a demand curve can have any shape at all, as long as it doesn’t double back or intersect itself.

This idea was first expounded by the (neoclassical) economist William Gorman in 1953. Gorman, on discovering this, went to great lengths to introduce assumptions that nullified the result, but these assumptions effectively amounted to assuming there was only one consumer, what Keen calls a ‘proof by contradiction:’ starting from an analysis of market demand curves, but eventually having to assume the demand curve is not for a market but for an individual. Keen does an impressive job of communicating this argument, which is obscurely and abstractly stated in Gorman’s paper.

Keen starts with the observation that price changes can have many different impacts, due to the interlinked nature of markets. Demand curves depend on the condition that income remains constant, so that we can study changes in price independent of other effects.  However, if we consider somebody buying a ‘basket’ of goods, an increase in the price of one good might make another good unaffordable. The resultant boost in income (from not buying the second good) may well increase demand for the good whose price went up. The various interactions between goods depending on whether they are necessities, luxuries and so forth can create some interesting looking demand curves.

Economists are well aware of this problem, and have of course managed to assume it away! This is known as the Hicksian compensated demand function. I won’t go into too much detail here, but this involves adjusting income until utility is the same level as before, then allowing for adjustments in income. This allows us to separate out the ‘income effect’ (the one listed above) and ‘substitution effect’ (the ‘pure’ effect of price on demand).

The problem is that once you introduce more than one party to the economy, it is impossible to separate out changes in income from changes in demand, as one person’s spending is another’s income. This interplay between spending and income brings back all the problems glossed over by the Hicksian demand function. This is well documented, and known as the Sonnenschein–Mantel–Debreu theorem.

Naturally, economists have managed to assume this away, too. But here their assumptions jump the shark. Here is Gorman in his 1953 paper:

The necessary and sufficient condition quoted above is intuitively reasonable. It says, in effect, that an extra unit of purchasing power should be spent in the same way no matter to whom it is given.

Even when stated in this form, this is obviously not a reasonable proposition. If you give Peter money, he’s not going to spend it in the same way as Paul. It’s really that simple. However, Gorman is slightly disingenuous with this statement, as the real conditions are laid bare later on in the paper:

The older work of Allen and Bowley was based on the assumption that the classical Engel curves for difference individuals at the same prices were parallel straight lines, but this has been rejected in the more recent work of Houthakker in favour of a doubly logarithmic form. However, the earlier assumption fits the data remarkably well.

Keen points out that since all utility functions pass through (0,0) (zero consumption yields zero utility), and all parallel straight lines that pass through the same point are the same line, this amounts to an assumption that consumers are all exactly the same – effectively, that there is only one consumer.

In other words: the only way we can make a market demand curve the same as an individual demand curve, is if we assume that it is an individual demand curve. There is an obvious logical problem with this approach.

The funny thing about this chapter is that Keen concludes that, generally speaking, “there are reasonable grounds to expect that…demand will rise as price falls.” So why go to all the trouble?

The first reason is to show that ‘more is different’ – theories should not necessarily be built up from individual behaviour. Keen notes that the assumptions that all consumers are the same is only defensible if one analyses from the classical perspective of different classes, something the neoclassicists were trying to avoid.

The second reason is to show that, despite economist’s assertions to the contrary, it cannot be proved that a market economy will necessarily maximise social welfare, as, even on their own terms, it is logically possible to have multiple equilibria, some of which are more socially desirable.

The third reason is that the SMD conditions also establish that it is impossible to measure these things independent of the distribution of income, highlighting more general problems with neoclassical ceteris paribus analysis.

I myself experienced some cognitive dissonance when Keen came to that conclusion (I don’t know what it is about studying economics that creates this), but the fact is that this kind of logical inconsistency must be exposed, and, contra Friedman, this does not depend on whether the conclusions are completely sound or not. As I noted in my opening, these problems are all well documented by neoclassical economists themselves. So how can they excuse ignoring them?

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  1. #1 by john77 on June 25, 2012 - 10:33 am

    This is not a new idea – my ‘O’ level economics textbook included the concept of negative price elasticity, with bread as the standard example (when the price of bread went up people ate less cake and more bread).

    • #2 by Unlearningecon on June 25, 2012 - 11:18 am

      As noted repeatedly, it is not at all new. However, the core theory remains taught as ‘market demand curves slope downwards’ and is forever preserved, despite these well known criticisms.

      • #3 by isomorphismes on June 27, 2012 - 8:56 pm

        Gifford goods are seen as a rare case not typical of the economy.

        I think your larger point here is: one-dimensional analysis (ceteris paribus) along ANY one dimension misses a lot of what’s relevant in the real world.

        And in order to talk about ceteris-paribus claims, one has to do weird adjustments like “income-constant” elasticity of (eg labour supply). http://blog.supplysideliberal.com/post/23959666073/what-is-a-supply-side-liberal

        @mathpunk pointed out an interesting possible resolution by Eric Weinstein: use gauge theory rather than assuming something that’s constant, is not constant. In physics the problem of “paralel transport” deals with constant motions on curved or bumpy surfaces. They use a “gauge connection” to connect different indices (or different locally flat patches) — which gets around the type of problem raised by a compensated demand function.

        http://tmblr.co/ZdCxIyNmQrRP

      • #4 by john77 on June 27, 2012 - 10:26 pm

        Or, as Unlearningecon accepts life is more complicated because we are all different.
        Economic theory is like a recipe – it tells us what would happen if the world was twisted to fit its assumptions; I just remember the bits I have to do differently to get something edible.

  2. #5 by Freedom to... on June 25, 2012 - 12:27 pm

    The interlinked nature of markets reminds me of the problem physicists faced when trying to predict the future positions of more than two objects in space, the so called ‘three body problem.’ In his research, Poincaré was unable to solve the problem but became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. Is this an equal opportunity for economics?

    • #6 by Unlearningecon on June 25, 2012 - 3:47 pm

      This parallel has been drawn before and is very apt. Economists are afraid of not using their assumptions because they say it will make things ‘too complicated.’ This may have been valid in the 19th Century but is no longer so, as the first neoclassical economists predicted.

      • #7 by isomorphismes on June 27, 2012 - 6:21 pm

        The parallel was drawn a few days ago by me as well!

        UL, I’d like your comment on the following. Let’s assert that “Economists didn’t see the crisis of 2008 coming” or in other words “Economic theory failed to predict/prevent the crisis”. Then there are at least two possible reasons for the failure.

        1) The theory itself needs to improve. (I.e., some quirks of psychology that are left out of the equations, would have been sufficient to foresee the problem.)

        2) The current equations would have worked if there had been more detail. But since most of what’s to model in the global financial markets is [a] private info, [b] gobs of data, [c] changes at least a bit every day, there were too many missing pieces in the Finite Element Model for the mesh to approximate what was going on. But with all or almost-all of the mesh being covered, the “rigid rods” of economic theory actually would have been sufficient to predict/prevent the problems. (Does people’s personality and unique quirks really matter that much when you’re trying to predict if they’ll walk away from an underwater mortgage? Or is that specific behaviour actually easy to predict.)

        I’m drawing a parallel to Finite-Element Models, which are actually used in finance so it’s not a totally daft analogy. These are essentially piecewise-linear models of curved surfaces.

        If you read The Big Short, you might remember the MBS consultant Cornwall Capital hired for $50k/month. He commanded such a high price because he was the only person who actually had detailed models of the securities in ququestion (i.e., his cheapy Excel-model without any fancy algorithms actually had data down to the neighbourhood level and linkages between securities and intrasecurity). Combine that with most reports from regulators that I’ve read said “We don’t even know the size of the market” let alone the players … it seems like lack of information going into the models could be the problem ratehr than the character of the models.

      • #8 by Unlearningecon on June 30, 2012 - 1:39 pm

        1. Yes, but not ‘psychological quirks’ – it’s far deeper than that. It’s the entire methodology – preference driven individuals and equilibrium – that needs to be abandoned.

        2. I don’t think the lack of knowledge is a practical problem – it’s a symptom of economist’s failure to deal with knowledge on any substantive level. What if the transaction costs for acquiring knowledge are higher than the gains from the use of the knowledge? What if something is unknowable?

  3. #9 by Blue Aurora on June 25, 2012 - 1:53 pm

    Something I’ve noticed about Steve Keen…

    I’ve noticed that people have described him as a “mathematician” by training or as a “dynamical systems engineer” by training.

    Yet from what I’ve been able to dig up, it seems that he wasn’t either by training – at least for his undergraduate days. When I read his doctoral dissertation, he seems to suggest that he received his training in maths after his undergraduate days.

    While mathematicians do use “proof by contradiction”, I’m not sure about the extent of Steve Keen’s mathematical capabilities. Steve Keen seems to embellish his mathematical skills up a bit, but that could be just my impression.

  4. #10 by Mathieu Dufresne on June 25, 2012 - 4:55 pm

    If you compare him to physicists or professional mathematicians, his mathematical skills are not so hot and he’s quite happy to concede it. But if you compare him to economists, he’s among the very best. His dynamic modelling provides the best framework to model the economy and is gonna eventually replace conventionnal macro tools for sure. He’s just aeons ahead of any other economists on that front and he’s now working with professional mathematicians to extend it further. Here’s a presentation of it’s modelling at the Fields intitute of Toronto.

    http://www.debtdeflation.com/blogs/2012/06/24/fields-institute-presentation-series-video-2/

    • #11 by Blue Aurora on June 26, 2012 - 2:55 am

      I’ve read an interview of Steve Keen before and I know he has acknowledged there are scholars in economics with better mathematical skills than he does. He named Peter Flaschel and Carl Chiarella (sp?) as two examples of that.

      As for whether his Minsky simulation program will eventually replace conventional macro tools in economics, time will tell. Agent-based modelling programs have existed prior to the global financial crisis, so they may be the ones to do it instead.

  5. #12 by Isaac Izzy Marmolejo on June 26, 2012 - 7:47 pm

    “The first reason is to show that ‘more is different’ – theories cannot and should not be built up from individual behaviour. Keen notes that the assumptions that all consumers are the same is only defensible if one analyses from the classical perspective of different classes, something the neoclassicists were trying to avoid.”

    I have the book, but only read parts of it..so take what I have to say with a grain of salt. But how does the above passage follow itself? To say 1) theories shouldn’t be built upon by individual behavior and 2) then the next sentence says that assuming all consumers are the same is not reliable. Isn’t the problem the second, but how does the second problem lead us to conclude that we shouldn’t build upon individual behavior?

    Also what of expectations? You must appeal to individual behavior for that, and if it wasn’t for that, there would be no liquidity preference theory or entrepreneurship theory

    • #13 by Unlearningecon on June 26, 2012 - 8:15 pm

      I just realised how poorly that sentence is put – theories should not necessarily be built up from individual behaviour. The problem with aggregating demand curves from an individual perspective, despite the fact that an inverse relationship between price and demand is not unreasonable, demonstrates the folly of the approach.

      • #14 by john77 on June 26, 2012 - 10:53 pm

        Good answer.
        Minor niggle – zero consumption implies zero utility but zero utility does not necessarily imply zero consumption.
        Curves *cannot* be (parallel or not) straight lines – has something been lost in translation?

      • #15 by Unlearningecon on June 27, 2012 - 8:32 am

        ‘Engel Curve’ is just a name so I wouldn’t read too much into it. What you say about (0, 0) is true but bear in mind utility is the dependent variable and consumption the independent one, for the purposes of this theory.

      • #16 by isomorphismes on June 27, 2012 - 6:22 pm

        If the theory works, then it doesn’t really matter how it was invented.

      • #17 by isomorphismes on June 27, 2012 - 6:27 pm

        john77, “curves” in the mathematical sense does include straight lines. Hence the terms “rectilinear curve” and “curvilinear curve”. It is one of those vocabulary things like how “subset” includes the set itself.

    • #18 by john77 on June 27, 2012 - 7:23 pm

      You are using mathematical jargon that is *not* used by mathematicians talking to non-mathematicians to justify the misuse of English in a non-mathematical subject, A straight line is a special case of a curve in geometry but not in English. Unlearningecon’s explanation was fully sufficient.
      “subset” does *not* include the set itself except in the special case of “the set of the whole set”. What you *should* have said is that a “subset” is itself a set. When teaching your grandmother to suck eggs, include a correct example.

  6. #19 by Isaac "Izzy" Marmolejo on June 26, 2012 - 8:27 pm

    Gotcha… That sounds a little more reasonable.

  7. #20 by moiracathleen (@moiracathleen) on June 27, 2012 - 4:30 am

    Great post! Grateful you are recording your thoughts on Professor Keen’s Debunking Economics. Looking forward to reading the upcoming posts. Appreciate that outline in the first paragraph. Excellent.

  8. #21 by isomorphismes on June 27, 2012 - 5:50 pm

    Such an important point. All you have to do is try to actually sell something to see how lumpy “the market” is (not to mention some information & search constraints that dominate price considerations).

    Consideration of which has to undercut the meaningfulness of talking about “the” value of something. Example: http://tmblr.co/ZdCxIy5VplM6

  9. #22 by isomorphismes on June 27, 2012 - 9:05 pm

    The fact that straight lines fit data well probably just indicates that the “more is better” assumption is true.

    http://isomorphismes.tumblr.com/post/22921219690/krauss

    Lawrence Krauss: “The reason we know Hubble was a great scientist was that he knew to draw a straight line through this data.” (later) “That was before the scientific discovery that log-log plots make everything look more like a straight line.”

    Straight line out of the origin + ε in SOME space is so frequently a reasonable assumption, that linear algebra is actually taught in school, to future engineers.

    Looking for a quote from mathbabe’s blog (one of her ML posts) or maybe it was NuclearPhynance, “Simple models are to be preferred to complex ones, but complex models always fit the data better.” At the most Ockham-ish end of simplicity versus accuracy, there you have your linear term plus error.

    • #23 by isomorphismes on June 27, 2012 - 9:06 pm

      …although, I’m a sceptical what “the data” actually were. How was it collected, who was asked, etc. Insert complaint about how economists have no business experience.

  10. #24 by isomorphismes on June 27, 2012 - 9:15 pm

    You probably take this perspective as well–but why is it necessary to show the existence of multiple equilibria in the model t oprove that X is not welfare-maximising? The natural question to ask about a welfare maximum is “Maximum in what sense?” Is it maximum output per day given the raw materials in the Earth? Usually some model amounts to saying, “Assume argmax by agents, result argmax in sum!” Which it’s unclear what that has proved about the actual world.

    PS Much nicer to have you read Keen’s book to me than have to read it myself! =)

    • #25 by john77 on June 27, 2012 - 10:02 pm

      Welfare is subjective, as is value.
      I tried going vegetarian when I was young and found that it didn’t fit my metabolism. My wife tells me to cut down on drink (I asked the quack for a check-up and my liver was fine).
      So welfare maximum has to be that observed by individuals.

    • #26 by Unlearningecon on June 30, 2012 - 1:42 pm

      I think ‘efficiency’ is a more appropriate term, which in economics means highest q lowest p. If there are multiple equilibria then obviously one will be more desirable than others on these terms.

  11. #27 by Roman P. on June 30, 2012 - 10:41 am

    What Keen says on the point of demand is absolutely right. But…

    Having dug at various sourses, I think that Marshall, the father of neoclassical economics, pretty much recognized the impossibility of clean aggregation in the general equilibrium. That’s why he preferred short casual chains (partial equilibrium) to the GE analysis. And, when you take a single market where buyers are not sellers, you probably could draw D and S curves. As a rule of thumb, it is safe to say in that situation that demand curve has a ‘nice’ shape. I feel that Menger’s model of buying horses (or modern Varian’s version of renting flats) is insightful and useful, if very elementary, way to look at economic behavior.

    • #28 by Unlearningecon on July 4, 2012 - 10:19 am

      Downwards sloping demand is indeed entirely plausible, and likely. Do you have a link to Menger’s model? I’m not familiar with it.

  12. #29 by Roger Chittum on July 4, 2012 - 12:03 am

    Can a demand curve double back? I don’t know, but a supply curve can. I think it’s pretty clear that at very high prices sovereign oil producers will sell more oil as the price declines because they are not profit maximizers but budget balancers, long-term customer nurturers, and patrimony managers. I wrote about that, and included a link to an early Krugman paper postulating a serpentine supply curve for crude oil, here: http://www.realitybase.org/journal/2009/4/5/update-on-why-crude-oil-prices-spiked-last-year.html

    • #30 by Unlearningecon on July 4, 2012 - 2:36 pm

      That is interesting. It was also well known that supply curves for labour bend backwards, as past a certain point higher wages will mean people have to work less.

      I reject the idea of a useful or coherent labour supply ‘curve’ at all, but obviously there’s some truth in that argument.

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  3. ‘Debunking Economics’, Part II: Perfect Competition, Profit Maximisation and Non-Existent Supply Curves « Unlearning Economics
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