So What Have You Been Maximizing Lately?

By Sean Carroll | September 13, 2007 4:37 pm

A while back, Brad DeLong referred to Ezra Klein’s review of Tyler Cowen’s book Discover Your Inner Economist. (Which I own but haven’t yet read; if it’s as interesting as the blog, I’m sure it will be great.) The question involves rational action in the face of substantial mark-ups on the price of wine in nice restaurants:

I did once try to convince Bob Hall at a restaurant in Palo Alto not to order wine: the fact that the wine would cost four times retail would, I said, depress me and lower my utility. Even though I wasn’t paying for it, I would still feel as though I was being cheated, and as I drank the wine that would depress me more than the wine would please me.

He had two responses: (i) “You really are crazy.” (ii) “Think, instead, that it’s coming straight out of the Hoover Institution endowment, and order two bottles.”

He is crazy, of course — crazy like an economist. I left a searingly brilliant riposte in the comment section of the post, which mysteriously never appeared. He will probably claim it was a software glitch or that I hit “Preview” instead of hitting “Post,” but I know better. What are you afraid of, Brad DeLong!?

Economists have a certain way of looking at the world, in which (to simplify quite a bit) people act rationally to maximize their utility. That sort of talk pushes physicists’ buttons, because maximizing functions is something we do all the time. I’m not deeply familiar with economics in any sense; everything I know about the subject comes from reading blogs. Any social science is much harder than physics, in the sense that constructing quantitative models that usefully describe the behavior of realistic systems is made enormously difficult by the inherent nonlinearities of human interactions. (“Ignoring friction” is the basis of 98% of physics, but nearly impossible in social sciences.) But I can’t help speculating, in a completely uninformed way, how economists could improve their modeling of human behavior. Anyone who actually knows something about economics is welcome to chime in to explain why all this is crazy (very possible), or perfectly well-known to all working economists (more likely), or good stuff that they will steal for their next paper (least likely). The freedom to speculate is what blogs are all about.

Utility is a map from the space of goods (or some space of outcomes) to the real numbers:

U: {goods} -> R

The utility function encapsulates preferences by measuring how happy I would be if I had those goods. If a set of goods A brings me greater utility than a set B, and I have to choose between them, it would be rational for me to choose A. Seems reasonable. But a number of issues arise when we put this kind of philosophy into practice. So here are those that occur to me, over the course of one plane ride across a couple of time zones.

  • Utility is non-linear.

This one is so perfectly obvious that I’m sure everyone knows it; nevertheless, it’s what immediately popped into mind upon reading the wine story. We need to distinguish between two different senses of linear. One is that increasing the amount of goods leads to a proportional increase in utility: U(ax) = aU(x), where x is some collection of goods and a is a real number. Everyone really does know better than that; the notion of marginal utility captures the fact that eating five deep-fried sliders does not bring you five times the happiness that eating just one would bring you. (Likely it brings you less.)

But the other, closely related, sense of linearity is the ability to simply add together the utility associated with different kinds of goods: U(x+y) = U(x) + U(y), where x and y are different goods. In the real world, utility isn’t anything like that. It’s highly nonlinear; the presence of one good can dramatically affect the value placed on another one. I’m also pretty sure that absolutely every economist in the world must know this, and surely they use interesting non-linear utility functions when they write their microeconomics papers. But the temptation to approximate things as linear can lead, I suspect, to the kind of faulty reasoning that dissuades you from ordering wine in nice restaurants. Of course, you could have water with your meal, and then go home and have a glass of wine you bought yourself, thereby saving some money and presumably increasing your net utility. But having wine with dinner is simply a different experience than having the wine later, after you’ve returned home. There is, a physicist would say, strong coupling between the food, the wine, the atmosphere, and other aspects of the dining experience. And paying for that coupling might very well be worth it.

Physicists deal with this by working hard at isolating the correct set of variables which are (relatively) weakly-coupled, and dealing with the dynamics of those variables. It would be silly, for example, to worry about protons and neutrons if you were trying to understand chemistry — atoms and electrons are all you need. So the question is, is there an economic equivalent to the idea of an effective field theory?

  • Utility is not a function of goods.

Another in the category of “surely all the economists in the world know this, but they don’t always act that way.” A classic (if tongue-in-cheek) example is provided by this proposal to cure the economic inefficiency of Halloween by giving out money instead of candy. After all, chances are small that the candy you collect will align perfectly with the candy you would most like to have. The logical conclusion of such reasoning is that nobody should ever buy a gift for anyone else; the recipient, knowing their own preferences, could always purchase equal or greater utility if they were just given the money directly.

But there is an intrinsic utility in gift-giving; we value a certain object for having received it on a special occasion from a loved one (or from a stranger while trick-or-treating), in addition to its inherent value. Now, one can try to account for this effect by introducing “having been given as a gift” as a kind of good in its own right, but that’s clearly a stopgap. Instead, it makes sense to expand the domain set on which the utility function is defined. For example, in addition to a set of goods, we include information about the path by which those goods came to us. Path-dependent utility could easily account for the difference between being given a meaningful gift and being handed the money to buy the same item ourselves. Best of all, there are clearly a number of fascinating technical problems to be solved concerning strategies for maximizing path-dependent utility. (Could we, for example, usefully approximate the space of paths by restricting attention to the tangent bundle of the space of goods?) Full employment for mathematical economists! Other interesting variables that could be added to the domain set on which utility is defined are left as exercises for the reader.

  • People do not behave rationally.

This is the first objection everyone thinks of when they hear about rational-choice theory — rational behavior is a rare, precious subset of all human activity, not the norm that we should simply expect. And again, economists are perfectly aware of this, and incorporating “irrationality” into their models seems to be a growth business.

But I’d like to argue something a bit different — not simply that people don’t behave rationally, but that “rational” and “irrational” aren’t necessarily useful terms in which to think about behavior. After all, any kind of deterministic behavior — faced with equivalent circumstances, a certain person will always act the same way — can be modeled as the maximization of some function. But it might not be helpful to think of that function as utility, or as the act of maximizing it as the manifestation of rationality. If the job of science is to describe what happens in the world, then there is an empirical question about what function people go around maximizing, and figuring out that function is the beginning and end of our job. Slipping words like “rational” in there creates an impression, intentional or not, that maximizing utility is what we should be doing — a prescriptive claim rather than a descriptive one. It may, as a conceptually distinct issue, be a good thing to act in this particular way; but that’s a question of moral philosophy, not of economics.

  • People don’t even behave deterministically.

If, given a set of goods (or circumstances more generally), a certain person will always act in a certain way, we can always describe such behavior as maximizing a function. But real people don’t act that way. At least, I know I don’t — when faced with a tough choice, I might go a certain way, but I can’t guarantee that I would always do the same thing if I were faced with the identical choice another hundred times. It may be that I would be a lot more deterministic if I knew everything about my microstate — the exact configuration of every neuron and chemical transmitter in my brain, if not every atom and photon — but I certainly don’t. There is an inherent randomness in decision-making, which we can choose to ascribe to the coarse-grained description that we necessarily use in talking about realistic situations, but is there one way or the other.

The upshot of which is, a full description of behavior needs to be cast not simply in terms of the most function-maximizing choice, but in a probability distribution over different choices. The evolution of such a distribution would be essentially governed by the same function (utility or whatever) that purportedly governs deterministic behavior, in the same way that the dynamics in Boltzmann’s equation is ultimately governed by Newton’s laws. The fun part is, you’d be making better use of the whole utility function, not just those special points at which it is maximized — just like the Feynman path integral established a way to make use of the entire classical action, not just those extremal points. I have no idea whether thinking in this way would be useful for addressing any real-world problems, but at the very least it should provide full employment for mathematical economists.

Okay, I bet that’s at least three or four Sveriges Riksbank Prizes in Economic Sciences in Memory of Alfred Nobel lurking in there somewhere. Get working, people!

CATEGORIZED UNDER: Academia, Science
  • Bad

    I would say that most economists do know about, and indeed talk about these sorts of things all the time. Most people’s image of economists are the people who sit around on HeadlineNews discussing the stock market. In fact, real academic economists are really more like philosophers that use math and statistics instead of hot air.

    Take rationality for instance. Economists aren’t dogmatically wedded to the idea that every human action is rational. But the reason these models are so useful is that simply declaring some behavior “irrational” is the economic equivalent of “goddit.” In short, we’ve discovered a lot of REALLY fascinating stuff by positing that, no, there IS some rational motive in seemingly odd behavior and setting out to find it.

    I don’t think economists, at least, are confused by the concept of rationality being descriptive either. Economists don’t have any academic objection to irrational behavior. It’s just sort of outside of their field, and so inherently less interesting as a set of problems.

    Personally, I find Steven Landsburg to be by far the best and most intriguing writer on economists: he was around before Freakonomics, and does it better.

  • puzzled

    Interesting post but there is one misconception. Utility functions do not measure “happiness” or satisfaction: they are simply representations of preferences. For example: if given two bundles of goods x and y an agent prefers x over y. Then a utility function representing the agent’s preferences must satisfy U(x) > U(y). That is all. If T is a strictly increasing function then T(U(.)) represents the agent’s preferences equally well.

  • Sean

    I would be surprised if there were only one misconception. But I’m interested in hearing about them.

  • joel

    to reply to puzzled

    At the founding, economics was indellibly linked to utilitarianism (note the root of utility and Jeremy Bentham’s classic “unit of happiness” the “util”).

    So, no, utility does mean happiness in a certain sense of the word. Though I think it is fair to say that defining utility as happiness does introduce some inherently normative aspects to economics.

    Utility has since morphed into “preference” which has morphed into “money,” each the next level in the fetishization process that underlies normative economics as we know it today. This process is driven by claims of “paternalism.” In other words, because we cannot judge another person’s subjective utility evaluations, we substitute the manifestations of their utility, preference. But preference is difficult to quantify absolutely, or even relatively, (as opposed to ordinally) resulting in money being substituted for preference. The ultimate equation is money = happiness, a patently ridiculous foundation for any normative claim.

    All this is good background, now to the point.

    I think Sean is absolutely right that words like “utility” and “rational” introduce inherently moral aspects to what is claimed to be the science of economics. We should try chucking them, and see what happens. The behavioral sciences have begun invading economics, and I’m going to continue cheering them on as they come.

  • joel
  • Count Iblis

    There are also so-called “econophysicists” who work on interesting models see e.g. here

  • Michael

    It is my understanding, in closer relation to puzzled’s response than joel’s, that economists generally describe the decision making process as a preference relation rather than a utility function. This relation really is a correspondence as opposed to a function (pretty consistent with what Sean is saying). Here, given a decision to make, a consumer can have a set of preferred courses of actions as opposed to a single, well-defined, response to a choice (Preference: {situations} – &gt P({choices}), where P(S) is the power set of S). The thing that surprises me about this is that, in the most basic description of a choice, there is no value associated with the option a consumer chooses (no “utility” function) — just a preference, which might even be tied with many other choices. Of course, at some point, economists start maximizing functions, but they have pretty good understanding that at the most basic choices are best described by preference relations, which may or may not follow the Weak Axiom of Revealed Preference, and it’s certainly a substantial leap to suggest transitivity in this preference relation.

    As a physics student, I frequently find myself attempting to extract these ideas of how economics should be practiced — based on a physics student’s inherent understanding of everything — from my brother, an economics student. I’m generally impressed that economists really do think about many of their problems in the same way a physicist does, and I’m impressed today that apparently physicists think about how economics should be done in approximately the same way (I have discussed many of the same topics to my brother that Sean is suggesting in this post).

  • Josh

    puzzled: Yes, the utility function is defined from statistical observations of preferences, but the preference of one good over another is usually correlated to the happiness each good provides the consumer. I don’t think it was as much a misconception as much as it was another way of expressing the same idea.

    That aside, to get any kind of deterministic analysis of economic behavior, neuroscientists need to clear some of the brush before the economists can march through. Until then though, the utility function guiding the probability distribution of human choices seems to be the best way to go.

  • Ellipsis

    Michael: it seems like that “weak axiom of revealed preference” is violated by that old Almond Joy/Mounds commercial: “sometimes you feel like a nut, sometimes you don’t”. one might wish it were so easy to violate the axiom of choice, or the second law of thermodynamics, … 😉
    Ah well, I guess it would be less dismal if human beings were less so…

  • Regis McConnell

    Astrology is irrational, is it not? The idea that an idividual human microcosom reflects & is destined ‘de stanare’, given at the moment of birth, incarnation, to unfold within the particualr paramaters of ones ‘universe’. The idea that one is experiencing as a ‘singularity’ a multiple cosmic origin riding the ‘tides of fate’ is the baby thrown out w/the modern bathwater.

    Avoiding the literal trap of ‘causation’. The subjective nature of our individual natures. Befriending our ancestoral mystery as opposed to literalizing ones familial history. Zen is a practice, a way of seeing thru our own mythological histories, to touch the ‘essence of our being’, a satori which binds the opposistes. The ying/yang, female/male, red/blue, dem/rep, bipolar reductionism that once transcended, binds two worlds as one & reveals the inner complexity ‘played out’, the illusion of our temporal nature. The eastern , maya/play, that shows four temporal forces, fire, earth, air, & water. Intuition, sensation, rational thought, & emotion, when displayed thru the lense of ‘humane’, shares in the imaginal creation.

    “We are lived by powers we pretend to understand.”


  • Michael

    Ellipsis, I’m not entirely sure why they call it an axiom. This, I think, is one of those great opportunities for us physicists to feel superior to those silly social scientists for using words differently than we would. My understanding is that there are many situations when the axiom is not used; it’s just an assumption that frequently makes problems doable.
    I don’t think things are totally violated by the claim of that commercial, though, because I don’t think Almond Joy/Mounds are suggesting that this is a case of revealed preference. Rather, it is a good example of how a preference relation represents a correspondence as opposed to a function. Given a vending machine purchase situation, a consumer has both Almond Joy and Mounds in his preference set over Skittles and pretzels (maybe the consumer’s preference relation merely prefers chocolate over non-chocolate). That consumer, however, shows no preference of Almond Joy compared to Mounds. They are merely both in the set of preferred choices.
    When exactly revealed preference kicks in is not clear to me. Here, does one say that a consumer shows revealed preference in the time averaged case when over the course of a week, the consumer bought 5 Milky Way, 5 Mounds, and 5 Almond Joy for $15. Or is revealed preference specific to a single purchase, saying that if on Monday a consumer bought and Almond Joy that immediately collapses his preference set to a single element? If revealed preference indicates the latter, I agree it seems a bit restrictive.

  • Simon DeDeo

    Sean is demonstrating something we all know: physiscs are a gabllion times smarter than economists. Seriously, though, there was a nice article about the influence of Milton Friedman, written by Paul Krugman in the NYRB.

    Bascially, Friedman (and people like him) dragged economics out of the astrology-age and it’s been an uphill battle to convince people that maybe every single thing he said was not entirely true. It’s like what I imagine physics to be right after Newton.

  • Simon DeDeo

    “puzzled” — I am equally puzzled. Is there no metric in economics, only an ordering?

  • klien4g

    Something that has always puzzled me is that how is it possible to conflate ‘happiness’ with ‘utility.’
    Since, for example, the happiness i get from immersing myself in a hot tub after a long day is of a different kind from the feeling i get from eating a delicious dish. However, it makes more sense, at a given point in time, to talk about which of the two I’d prefer over the other. In the sense, the decision process is considered a black-box and we are only interested in the outcome.
    I think this is the reason most economists i’ve come across talk about preferences.

  • Bad

    joel, give me a break:

    The ultimate equation is money = happiness, a patently ridiculous foundation for any normative claim.

    This is just pure nonsense. Economists use money to measure preferences primarily because it helps match some costs against others: i.e. it provides a useful way to compare all sorts of different good services and costs relative to each other. It has nothing to do saying that money = happiness.

    Again, what economists are most interested in is tradeoffs and how people respond to incentives. Most economists couldn’t give a crap whether you make a billion dollars or live in a ditch in the woods: they’d find both equally interesting.

  • John Baez

    Ever since I took some classes on microeconomics, I’ve been uncomfortable with a lot of assumptions that go into it. But, a lot of professional economists also question these assumptions and – the hard part – seek to develop economics based on better ones.

    I especially like Amartya Sen. His book Rationality and Freedom digs into the concept of “rationality” that underlies neoclassical economics.

    Richard Layard is also interesting. He’s written some interesting stuff on happiness, why societies don’t get happier as they get richer, and what does make people happy.

    You can see a bunch more links in my economics diary.

  • Loki

    There is a so-called Austrian school of economics, 150 years old featuring nobel laureate Fridrich Hayek among other bright people. There is a group of recent nobel laureate Daniel Kanemahn, which one could call Behaviorial Finance school. There are some other people as well.
    Their common message is (with some exaggeration) – you can throw away 95% of mainstream economics as pseudoscience.
    Mathematical models are predicting small insignificant details with some success, whereas the real economy, as well as history, politics – and even your personal life ! -is dominated by completely unpredictable deep-impact events.
    Evderybody knows about LTCM collapse, Goldman Sachs “risk-free” so-called quant funds etc.
    Guys, my background is mathematical logic and model theory and now i am an equity trader for a big investment bank.
    Markets are as life – intrinsically unpredictable.
    My deep belief = better no model than some “almost correct”, some that predicts 6-sigma events to happen 1 in a billion years (actually they happen 10-15 years).
    Be prepared to face unknown with a stupid smile :-)

  • anon on the hudson

    The much more interesting question is:how do concepts such as “maximization of the utility function” and “perfect ratonality” fit into a theroretical framework whose policy implications are very often opposed by the majority of human beings on the planet?.”Free trade” is an example of one of these policies.

    No doubt, these bedrock theoretical constructs reflect a conception of human nature that are compatible with the interests of the greedy cheating owner/ investor class.

    It would be interesting to see the logical links from “maximization of utility function” and “perfect rationality” to these economic policy recommendations.

    I’ll tell ya, that Brad Delong looks so professorial and very important behind that podium with pen in hand. Obey professor Delong’s grand pronouncements. That rotten stinking Cuban Goverment. They wouldn’t obey the Brad’s former boss-the Clinton war criminal family(Bill and Hill. Hey HillBill, you know like Brangelina) divine edict to impose Neo-Liberal economic policy on the Cuban people.

  • Doug

    Mathematical Game Theory is a powerful tool.
    Mathematicians have been awarded Nobel Prizes in economics.
    Guess What?
    Engineers [applied physicists] also use mathematical game theory.

    Paul AM Dirac had no physics degree, but did have a BS electrical engineering and PhD mathematics.
    John von Neumann developed an algebra used in physics and the minimax theorem used in game theory.
    Terence Tao demonstrated that these two facets of von Neumann are related by degree mapping.

    Energy economics may be part of the future.

    Tamar Basar and Geert Jan Olsder demonstrated the value of pursuit evasion games used extensively in robotics.

    Maybe the curricula of physicists should think about embracing mathematical game theory.

  • anon on the hudson

    A few more thoughts on Brad Delong’s-he is a very importatant person…seriously!!!- maximized utility fuction.

    Here is another example of one of those lovely policy implications of “utility maximation” and “perfect rationality” theoretical constructs. In this case, it appears that the policy implications are quite direct and clear. Interestingly, this comes from the devious mind of Brad Delong’s Harvard PHD advisor Lawrence Summers.

    In an internal memo leaked from the World Bank, former World Bank president Lawrence Summers wrote”the Bank should encourage migration of dirty industries to less developed countries because, amongst other reasons health-imparing and death-causing pollution would be lower and inasmuch as these costs are based on the lost earnings of the affected workers in a country of very low wages, the computed costs would be much lower. I think the economic logic behind dumping a load of toxic waste in the lowest-wage country is impeccable and we should face up ti it”

    Shortly after this memo was leaked in 1993, the Clinton administration-Sean’s favorite trendy liberal power couple-appointed Larence Summers-the very very important Brad Delong’s (who is currerntly shaping the minds of the children of H-1 B vissa theives from you all know where at Berkely) PHD advisor at Harvard-to Undersecretary of the Treasury for International Affairs and then Secretary of the Treasury.

    Bravo Lawrence Sumers, you did an excellent job of maximizing your utility function. You may be a cockroach. But you have a marvelous sense of humor.

  • Ian B Gibson

    Any social science is much harder than physics, in the sense that constructing quantitative models that usefully describe the behavior of realistic systems is made enormously difficult by the inherent nonlinearities of human interactions.

    On the other hand, it’s much easier than physics, in the sense that you can get away with spouting barmy old cack much more easily, without getting ostracised by your peers for it.

  • TomC

    Sean is demonstrating something we all know: physiscs are a gabllion times smarter than economists.

    And Simon is demonstrating yet another thing we all know: truly smart people can’t be bothered with spelling details.

    (Extra points for misspelling “gabillion,” which isn’t even a word.)

  • Simon DeDeo

    I’m actually not that smart — the spelling mistakes are deilberate.

    A friend of mine in grad school had a notion of “Type I” and “Type II” genius characteristics. Type I genius characteristics were things like “revolutionizing the field” and “incredible intuition and insight”. Type II were things like “forgetting your socks” and “walking into things while thinking.” Unfortunately, Type II characteristics are far more widespread than Type I.

  • Count Iblis

    So, is economics too hard for economists, just like (according to David Hilbert), physics is too hard for physicists? :)

  • Bad


    Mathematical models are predicting small insignificant details with some success, whereas the real economy, as well as history, politics – and even your personal life ! -is dominated by completely unpredictable deep-impact events.

    This is something of a misconception too: economists rarely claim that they can predict EVENTS. Economists is not some sort of universal history predictor. What they seek to characterize is how people will respond to particular events: what sorts of responses they will make to changing incentives. And at this they have proven very effective.

    Again, very few economists actually spend their time trying to predict the stock market.

    anon on the hudson:

    The old boring anti-Lawrence Summers smear. Snore. I guess people like you don’t like to think about reality, but can you leave the rest of us to do so?

    The fact is, what Summers was saying was not only true, but already a reality. Developing countries do not care as much about the environment as developed ones. Environmental concerns are largely a LUXURY of relatively rich people. As such, they are more than willing to trade waste for jobs and money, and acknowledging this fact, and thinking about what it means and what its policy applications are, is not something anyone who cares about intelligent debate should seek to cast as some sort of pariah activity.

  • Run Up The Score

    eating five deep-fried sliders does not bring you five times the happiness that eating just one would bring you.

    Sadly, this is correct. It only brings your cardiologist multiple DVD players in his Lexus SUV’s headrests.

  • spyder

    Economists (sic) is not some sort of universal history predictor. What they seek to characterize is how people will respond to particular events: what sorts of responses they will make to changing incentives. And at this they have proven very effective.
    OR NOT:

    Former Federal Reserve Chairman Alan Greenspan acknowledges he failed to see early on that an explosion of mortgages to people with questionable credit histories could pose a danger to the US economy.

    In an upcoming interview, Greenspan said he was aware of “subprime” lending practices where homebuyers got very low initial rates only to see them later jacked up, causing severe payment shock. But he said he didn’t initially realize the harm they could do.

    “While I was aware a lot of these practices were going on, I had no notion of how significant they had become until very late,” he said in a CBS “60 Minutes” interview to be broadcast Sunday. “I really didn’t get it until very late in 2005 and 2006,” Greenspan said.

    An excerpt of the interview was released Thursday.

  • Lord

    On DeLong’s site you must confirm every post, so that post button is actually a preview button.

    Rationality only exists within a context of a set of facts, propositions, and theories, and is an attempt to determine which of these is relevant. Beyond the pale lies psychology, sociology, values, judgments, and customs, but the presumption is an economic/evolutionary basis exists behind them. Other than saying one is indifferent to a selection, or indifferent to a proportion, indeterminacy is ignored, choices are usually limited to two, and money as the measure of all things economic, are vast simplifications, but known ones.

  • Simon

    Hey Sean,

    I think ‘rationality’ in economics is a technical term with a rather precise meaning. Economist friends tell me that they use the term in the following sense: a person is rational if they have a complete and transitive set of preferences. I.e. for any two outcomes A and B the person will tell you which they prefer (or they might like them equally), and if they prefer A to B and B to C, then they also prefer A to C (transitivity). So I’m not sure that the word rational is “slipped in … to create an impression” – it’s just the word chosen to represent the above property.


  • Chris W.

    From John Goodman, of the National Center for Policy Analysis (NCPA):

    Jost offers a lot of interesting institutional background on the consumer directed health care movement and the people involved before getting down to two main points. He says CDHC advocates, including yours truly, rely on the neoclassical economic model to understand the health care system (which is true), and he implies that there is some alternative model that could be used instead (which is not true).

    Jost devotes quite a few pages to explaining why the market for medical care is not like the market for breakfast cereal. If you were otherwise inclined to think of those two markets as pretty much the same, his book is a good read. That’s as a prelude to his finding fault with virtually all of economic theory.

    Simple economic models, he says, ignore transactions costs, imperfect information, externalities, and anticompetitive behavior. Economists have learned to deal with these factors in more sophisticated versions of the model, he admits, but he doesn’t say how. The case for the prosecution is so lengthy and varied, there is literally no time for the defense.

    Jost doesn’t even remind the reader that the model he is attacking is the very same model that is used to calculate the value of stock options and regulate the money supply; or that it is used by government agencies to forecast the effects of every bill before Congress, including all health legislation; or that it is used ubiquitously by the private sector to predict the effects of external shocks on markets, including all health markets.

    I don’t know any economist who thinks all markets are the same or that neoclassical theory is beyond reproach. The more important point here is one that even a lot of very bright people do not understand: There is only one social science model that allows us to think in a consistent, non-contradictory way about complex social phenomena. That model is economics. There are not two or three or four models from which one can pick and choose. There is only one.

    Jost quotes from an email message I sent him, but without attribution. So I want to publicly own up to having said the following: “In all of social science – whether economics, politics, sociology, history, etc. – there is only one model that (a) is internally consistent and (b) can explain and predict. That is the model developed by economists. All the rest is gobbledygook. And more often than not, it is highly opinionated, value-laden gobbledygook.” [from Health Wars: The Empire Strikes Back]

    I’m tempted to say that John Goodman isn’t really an economist, but he plays one on TV. (He does have a Ph.D in economics from Columbia.)

  • Chris W.

    Sean, you should read some of Steve Hsu’s many posts touching upon economics and reflections on its foundations. My sense is that among physicists he is exceptionally well-informed on the subject. In particular see this recent one about a paper by Tyler Cowen.

  • Jonathan Yedidia

    I agree with you that the term “rational” is dangerously over-used by economists. I think you might be interested in this blog entry “On Rationality”, where I discussed some of the same issues that you raise, and show examples of games where game-theoretical “rational” behavior is clearly ill-advised. There was also some interesting comments to that post from David MacKay and Yoav Freund, with their own alternatives to game-theoretic rationality.

  • notsneaky

    Chapter 3 of the standard grad level textbook “Microeconomic Theory” by Mas Collel et. al has a very nice discussion of how the theory goes from preferences to utility to demand and also some of the philosophical issues involved. It is also one of the less mathematical chapters in that book. Unfortunately it’s pricey.

    Also the WARP – the weak axiom of revealed preference – actually is “weak” enough so that you can sort of call it an axiom. It does not involve transitivity as it only concerns choices between two options and of course for transitivity to be relevant you need at least three.

    The standard assumptions about utility functions (which are just representations of preferences – so yes, there’s no metric just a ordering) which are alluded to above are also derived from assumptions about preferences. For example the fact that utility is generally non-linear (quasi-concave in fact) is derived from the fact that preferences are convex, that is roughly speaking, people prefer diverse bundles of “goods” to bundles with just one thing in’em.

    And pretty much all economic research uses strictly non linear functions (which is why so much emphasis is placed on nonlinear optimization in your first grad school course) because a lot of action is precisely in how demand for different goods depends on substitution and complementarity effects – some people only get utility from coffee if they have cream and sugar in it.


  • Quasar9

    The economics of a £6 billion LHC
    is that it created a number of contracts in industry
    and created 5000 well paid jobs for scientists …

    and the money gets spent on housing, cars, clothing, utilities, IT, food, leisure, entertainment, travel, holidays, health, pensions – does money make the world go round? – no, but it does make people do things for money. And money (or ability to pay) allows some of the people to do or ‘choose’ some of the things you have to pay for.

    You know we could build more homes than we need, we could build luxury eco-homes for everybody. But its more fun to increase existing house prices, have people mortgage themselves into a shoe box – and call it economics.

    You know we could build affordable electric cars in Korea or China, and price petrol cars out of the market – but it could & would damage Oil economics.

    You know we could pay people to ‘heal’ and cure people, but it’s more fun to bleed people dry with the promise of miracle cures. The economics of Medicine?

    PS – I’m being si-si-cynical. Does not require ‘serious’ debate.

  • Mike Schuler

    A common misconception among consumers is that the price of a good or service should always be a small percentage higher than the cost of materials paid by the provider of the good or service. This thinking makes it seem like paying four times the retail cost for a glass of wine is a bad transaction.

    The cost you pay for the glass of wine also has to pay for the insurance premium (which is probably the highest overhead), the labor to serve the wine, the facility to serve it in, the utilities, the taxes, the advertising, and many other incidental costs of doing business that are over and above the cost of the wine itself.

    It has been my experience that if you base your spending decisions soley on price, you get very poor quality.

  • Ike Solem

    Another possibility is that the human behavior function is discontinuous, meaning efforts to maximize are futile. A lot of psychology seems to indicate that this is true. Does advertising rely on rational arguments? Generally not. Most advertising relies on trying to associate things like attractiveness and sex with things like cars and airplane tickets… and advertising is effective!

    It actually seems to be that economic theory has regressed since the days of Adam Smith and David Ricardo. Their notions of free markets, trade and competitive advantage do seem to make a lot of sense. Most people would likely be surprised by Smith’s take on corporations, for example:

    “It is to prevent this reduction of price, and consequently of wages and profit, by restraining that free competition which would most certainly occasion it, that all corporations, and the greater part of corporation law, has been established.”

    Similarly, David Ricardo’s theory of competetive advantage is widely quoted by modern ‘free trade’ enthusiasts, but they always leave out the necessary conditions Ricardo laid out in 1817: “Three conditions, among others, are fundamental to this outcome: capital must not be allowed to cross national borders from a high-wage to a low-wage country, trade between the participating countries must be balanced, and each country must have full employment.”

    Modern economics, whether of the Karl Marx or Milton Friedman variety, is just long winded nonsense, and the Nobel Prize in Economics is the laughingstock of the scientific community – really.

    Essentially, how can one trust forecasts about the future made by people who never learned the First and Second Laws of Thermodynamics, yet who attempt to use mathematical models as predictive tools? What were those ‘economic models of the effects of NAFTA’ predicting? Increased wages in Mexico and the US, as I recall – or is that old history?

    However, there is this very interesting subject known as ‘physical economics’ promoted by people like Chernavskii. That might save economics – but they’re going to have to switch departments. Great post, by the way.

  • tommaso dorigo

    Nice post, Sean (see, I’m not angry at you and your crew picturing me as a sexist!).

    I would like to add a bit to this discussion: a simple example made by Martin Gardner on how one person confronted with different utility functions, might make counter-intuitive, counter-inductive choices. See these two posts:


  • Alex F

    Well, as a current PhD student studying economic theory, and a former (undergrad) student of Sean’s, lemme take a shot at this. Sorry for replicating some of the comments above, and also for giving imprecise and overly simplified explanations.

    1) “Utility is nonlinear.”

    Economists capture this idea with the concept of “complement” and “substitute” goods. To make some simplifications, if we measure “How much I want something” by “How much I’m willing to pay to get it”, these are goods for which (the amount I’m willing to pay for X) is a function of (quantity of Y consumed). There are a bunch of formal mathematical ways to model this given different types of goods and different available measurements. Almost any utility function used by economists will take these into account, with one sort-of exception. It’s convenient in many contexts to say that all goods affect valuations of other goods… except for money. (The term for this is quasilinear utility — you’d model this by U(goods, money)=V(goods)+money). When you make this sort of assumption, it lets you measure things like “total consumer surplus” in dollars, but it also implies that people should be risk-neutral over money and, in many contexts, it suggests that a dollar given to a rich person is just as good as a dollar given to a poor person. Economists are well aware of these complaints, but sometimes you just need to make simplifying assumptions if you want to get an answer. It happens.

    But yeah, in econo-speak, wine is a complement to good food and good company.

    2) “Utility is not a function of goods.”

    No, it’s not. We can make models for whatever it is that we want to study, but goods — or, more generally, outcomes — are what we can measure, so that’s what tends to be useful to put in our models. A lot of recent work by behavioral economists these days studies more psychological issues like the gift-giving example you mention, though.

    Very rarely do the behavioralists use any sort of high-level math suggested by your path-dependence and tangent spaces, though. (Neoclassical economists really do sometimes). It’s easy to make a specific simple model to cover gift-giving, but aside from gifts and inheritances, does the path an object takes really matter much? (The simple model would be something along the lines of my utility function over goods includes a good-specific sentimentality component, or that my utility function over everything includes a function for how much I think people care about me…) The issue with behavioral economics is that individual “quirks” are easy to model by themselves in specific contexts, but it’s hard to put them together in a way that rivals the generality of the standard model of utility as a map from outcomes to numbers. If we’re not specifically studying gift-giving, it’s probably not worth including paths in our utility functions.

    3. “People do not behave rationally”.

    When economists talk about rationality, we mean very specific things. In the make-a-single-choice-from-a-set context, it means behaving *as if* you have a preference ordering over possible objects. In the making a choice under uncertainty situation, it essentially means treating multiple-stage lotteries over outcomes the same way as equivalent single-stage lotteries. There are theorems formalizing how to go from preferences to utility functions; it’s very rarely a problem. Your complaints here aren’t really about economics so much as semantics.

    4. “People don’t behave deterministically”.

    A couple responses to this. First of all, in the theoretical literature, it tends to be convenient to suppose that people do behave deterministically. It makes solving models a lot easier. It lets us make predictions. In your terminology, this is an example of “ignoring friction”. 98% of economics involves ignoring friction, too — it’s just less accurate than when physicists do it. Physicists ignore friction and get an answer that’s right to 5 decimal places; economists ignore friction and hope that the sign of a derivative is right.

    When we go to data to test the models, the empiricists understand that these are just simplifications. Empirical models always deal with randomness. If our model says that rich people buy more caviar, we don’t consider it falsified if we find a single poor person who buys more caviar than one particular rich person. Empiricists work hard to extend the simple models of theorists in ways to incorporate the randomness of human behavior.

    Theorists also do think about randomness, though. The literature tends to look at things like “How robust are our deterministic models to a little bit of randomness?” Or “What are reasonable ways to model learning in which people start by groping around randomly? Under what conditions will this eventually approximate rational equilibrium behavior?”

    Separately, of course, there are also “mixed strategies” in which people rationally act randomly, most obviously in a game like Rock-Paper-Scissors. That’s a different issue than the one you’re raising, I think.


    Basically, the take-away here is that economists really do try to think like physicists. Our field takes inspiration from yours. We’re not as good at math — in part because high level math isn’t as useful with objects of study that don’t follow as precise and predictable trajectories. But the issues you’ve been idly considering really have been thought about and picked apart by economists. As some of the commenters above note, a lot of the development of economics has come from people outside the field who see some economic application to their mathematical ideas.

  • krishna

    1. “Utility” is not really measurable in any meaningful sense.

    2. Utility functions are not unique. Reason: The idea of preferences is that there is
    a partial ordering over the set of choices. Since the ordering is partial, there are
    an infinite number of utility functions. E.g let’s say ones preferences between A
    & B are that A > B always. Any function that gives a number to A and a lesser
    number to B would be a valid utility function.

    3. Fundamental problem with partial ordering is that one’s preferences could vary even if the choice is presented differently (eg. Kahneman & Tversky).

    4. Probability distributions over utility functions would be meaningful if i) there is some nice limit like the law of large numbers, or if said distributions did not arbitrarily fluctuate. If one considers small groups of people, these functions themselves would vary randomly in time.

    5. A lot of economic decisions are made based on some assumptions or expectations about the future. This makes the problem of modeling a lot more difficult (no real causality), and which is why there are issues of time consistency and the like (I could be wrong about the time consistency). After all herd behavior, of the sort that has given rise to the current housing crisis is due to such expectations.

    There is a very nice discussion of 1-3 in Kreps, Microeconomic Theory. Finally, I dont want to be rude, but I agree with Ian Gibson in 21.

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  • Bad

    Does advertising rely on rational arguments? Generally not. Most advertising relies on trying to associate things like attractiveness and sex with things like cars and airplane tickets… and advertising is effective!

    It’s worth noting that there are good reasons to think that there is more to it than that. Products can also be valuable as status symbols, and companies brand products to appeal to that: there’s nothing necessarily irrational about that. Plus, there are also a lot of hidden signals contained in things like unqualified celebrity endorsements. A company with money and reputation to blow on hiring Paris Hilton to advertise is far less likely to be one that puts out crappy products and then folds up shop, screwing consumers. Companies are trying to signal that they are longtime cultural and legal players in the market rather than fly-by-night operations. And so on. And again, while things like this can sound like idle speculation, economists have done lots of interesting work testing these ideas.

    I highly recommend that people check out Steven Landsburg’s “The Armchair Economist” if they can find it: it’s a fabulous layperson introduction to how and why economists think the way they think.

    And he explains why popcorn isn’t so expensive in the movie theater for the reason you probably think it is. :)

  • Johan Richter

    I think you seem to have a reasonable idea of what economics is, Sean.

    I think the term economists use instead of your linear is (additively) separable. And yes, it’s an assumption sometimes used for convience. But in general utility functions are defined on the whole bundle of goods you consume so you are also correct that economists are well aware of the point you make.

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  • Loki

    1. The problem with getting away with “friction” in economics, is that, unlike physics, those 2% you choose to ignore for simplicity of calculations, can change the result not by 2%, or 20%, not even 200%!
    Imagine you want to know the average weight of a US citizen. Take 1000 people, calculate the average. How much can change with one person added? Well, if that is extremely obese guy – he will up the average by 0.5%. This is physics, and you can use math to predict, describe etc.
    Now imagine you want to measure average income. If the 1001-st person is Bill Gates – the average will multiply by 1000 times. This is economics.
    2. The problem with individual preferences is that people change their mind very quickly and often for no “reasonable” reason. in 1972 D.Kanemahn discovered what he called “anchoring” effect which works as follows:
    Test-group had been told that there will be several independent tests.
    i) they were first asked to choose one card out of 2, with the number on the other side. One number was, say 20, the other – 80.
    ii) than they were asked a question like “how many lovers had russian empress Katherine the Great?”.
    Well, it’s hard to beleive it, but those who got 80 on i) -gave higher figures on ii) !
    3) Also, it’s obviously wrong to average people’s preferences, taking individual violations as “noise”. Vice versa – people tend to flock to some newfangled thing in herds.

  • reason

    A couple of points on utility not explicitly clarified yet.
    1. Utility functions are never actually evaluated or specified by economists, it is just a theoretical construct from which other results can be derived.
    2. Utility can be considered the “value” to an individual of a particular basket of goods. It does not necessarily relate directly to overall happiness (which is impacted by many things not related to economics).
    3. Utility functions are strictly personal.

    There is a concept of cardinal utility (i.e. some number that measures absolute utility) but economists want to ignore it (explicitly since Friedman). Considering cardinal utility would have nasty implications for Libertarian economists because given that utility is non-linear (diminishing returns to scale) it means that inequality necessarily reduces total utility. So they keep quiet about it and say you can’t add up different peoples utility and should concentrate only on allowing individuals to optimise their own utility.

  • Arun

    On the principle that one should call bullshit when one sees it – Bullshit!

    Environmental concerns are largely a LUXURY of relatively rich people. As such, they are more than willing to trade waste for jobs and money, and acknowledging this fact, and thinking about what it means and what its policy applications are, is not something anyone who cares about intelligent debate should seek to cast as some sort of pariah activity.

    Most chronically poor people have managed to come to a equilibrium with the environment, and their sustainance at whatever level is sustainable (e.g., forest dwelling tribals in India, or fishermen on the coast). Then along comes globalization, capitalism, etc. and disrupts their life support systems, and offers them nothing useful in return (e.g., B&0 port development that disrupts fish spawning grounds or Enron power plant that pollutes the tribal areas). In both cases, the benefits are to distant city dwellers and to investors in foreign countries.

    Environmental concerns are matters of life and death for poor people, and merely matters of aesthetics for the rich.

    The problem is that usually the poor do not have the political power to change things. But they have been willing to give up their lives.

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  • Tracy W

    Hmm, some thoughts

    a) Economists are perfectly agreed that utility is non-linear. Indeed, the concept of marginal utility is of incredible importance in determining prices. Economists talk about the value of the marginal unit all the time, which doesn’t make sense if the marginal unit’s value is the same as the average value.

    b) I think your statement (b) is too strong. Utility is a function of goods. It’s also a function of other things, but goods definitely come into it. Imagine, for example, that you have hiked with your loved ones into the wilderness, two days away from the nearest road or shop or cafe. You have a wonderful camp spot, a beautiful view of a sunset over a local gate, and any other immaterial good you care to add in (I don’t know if that means you’ve just finished two hours of yoga or whatever). I’m willing to bet that, all other things being equal, your utility will be higher if you also have some material objects, like some food.
    There’s nothing in economics to stop one adding non-material utility in to a person’s utility function. For example, once my husband asked me what I meant when I said that I loved him, and I blinked in surprise and replied “That’s simple, I mean your utility is part of my utility function.” I would have gone on to add that my utility function increased with respect to his utility but he was laughing too hard for me to get a word in edgewise. I don’t know why.

    Economists do use linear equations in modelling budget constraints. For example, a person cannot spend more money than they have (taking into account their ability to borrow). So we can write that someone is maximising their utility with respect to goods available on the market subject to a budget constraint, where the sum of all the goods they buy multiplied by the price must be less than or equal to a set amount of money. Perhaps you have been confused by these budget constraints?

    c)I agree that the world “rational” can be confusing. But I also agree with Bad that the impulse to assume that people are rational unless proven otherwise has lead to some really fascinating discoveries.

    d) I’m not sure how much value would be added by including non-deterministic models of utility. Economists don’t try to model every single behaviour someone does, we don’t know anyone’s actual utility functions so even with a deterministic model we don’t know what any one person would actually choose. What we use utility models for is things like explaining how prices are calculated (price = marginal utility), or saying that we don’t know if labour supply increases or decreases in response to an increase in the hourly wage. (This is something taught in Econ 101. Basically, imagine a self-employed worker called Carol who can increase or decrease her hours at will. And for a moment just think of Carol as only being interested in money and leisure. Her hourly rate goes up. Now Carol can earn more each hour she works, which creates an incentive to increase her hours, the substitution effect. But, since she’s richer, she can also increase her leisure while maintaining the same money income by decreasing hours – the income effect. The conclusion is that we don’t know if the subsitutition effect or the income effect will dominate in Carol’s case so we don’t know if she will work more or less hours in response to an increase in her hourly rate). Now, if we can’t tell what Carol, or you, would do, with a deterministic model, what’s the value of going to a non-deterministic model?

  • reason

    wrt d)
    What you are saying is that if the utility function of any individual is unknown to us, it doesn’t make it any less unknown to allow it be indeterminate. True enough. But if for instance we were to build an object oriented model of the world to similate individual behaviour in response to a particular environment it might indeed matter that an individual’s behaviour is not consistant over time (i.e. that observed behaviour in the past is not a foolproof guide to observed behaviour in the future). For a marketing firm for instance, that might be important (implying for instance they cannot be as narrowly focused on a particular subset of customers as they might think from past experience).

  • Scott Wood

    Within the context of hte current conversation, astrology is not irrational. Astrology may be mistaken, but astrology is not irrational.

    The concept of “rationality” in economics deals with decisions made given your beliefs about the world. It doesn’t, at this level, say what those beliefs should be.

    Making costly (in the literal sense of cost > 0, not the figurative sense of cost = a lot) decisions on the basis of astrological advice when you don’t believe in astrology would be irrational. Not doing so when you do believe in astrology would also be irrational.

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  • Peter D

    As a transport economist I know that the models that we use do not assume that people behave deterministically. In fact there is a whole field of behavioural modelling based on Random Utility, where utility is treated as a random variable with a specified probability distribution.

    It works best in analysing simpler systems – such as making a selection from a fixed set of discrete choices (such as “Will I drive, or catch a bus?”). Of course the analysis gets pretty ugly pretty quickly unless you make some pretty heroic assumptions. Any non-simulation based solution requires very simple models, with identically distributed terms, no covariance, and simple normal-like distributions.

    At least in my experience, there are still not too many models using the tools that I understand that computational physicists are using, such as Markov Chain Monte-Carlo models etc. But they are coming…

  • Hag

    You could make things path dependent in a flat space with a multiply connected topology. Then homotopic paths (assuming we are parallely propagating the goods from a source to a recipient throughout some path) would have path independent values amongst themselves but different values from a curve which is not of the same homotopy type. Cheers

  • Count Iblis
  • zadren

    well….guys…..what do you think are some errors that occurs when solving or evaluating the #’s of utility..using the cardinal method?


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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