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!
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.
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.
I would be surprised if there were only one misconception. But I’m interested in hearing about them.
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.
interesting article about a related issue:
http://www.sciam.com/article.cfm?articleId=7750A576-E7F2-99DF-3824E0B1C2540D47
There are also so-called “econophysicists” who work on interesting models see e.g. here
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} – > 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).
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.
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…
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.”
Regis
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.
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.
“puzzled” — I am equally puzzled. Is there no metric in economics, only an ordering?
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.
joel, give me a break:
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.
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.
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 🙂
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.
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.
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.
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.
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.)
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.
So, is economics too hard for economists, just like (according to David Hilbert), physics is too hard for physicists? 🙂
Loki:
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.