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!
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.
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:
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.
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.
Simon
From John Goodman, of the National Center for Policy Analysis (NCPA):
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.)
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.
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.
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.
Ok
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.
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.
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.
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:
http://dorigo.wordpress.com/2006/06/21/martin-gardner-and-false-induction/
http://dorigo.wordpress.com/2006/06/22/wicked-wheels/
Cheers,
T.
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.
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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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. 🙂
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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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.
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.
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.
http://www.satyamag.com/jul04/laughlin.html
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