## Sunday, February 8, 2015

### A Socratic dialog on the simple model of information equilibrium

Here is the dialog I mentioned in the footnotes of this post ...

...

Oikomenia: Wait, wait ... what about diminishing marginal utility? What about the stuff they show in those MR university videos?? Supply and demand can't be as simple as taking the equation (total cost) = (gallons sold) x (price per gallon) and holding either total cost or gallons sold constant and letting the other vary! That's dumb!

Informatio: What specifically is wrong with it?

Oikomenia: Well, for one, the total sale isn't the quantity demanded. And you need to account for the observed fact the number of gallons of gas demanded goes down as the price goes up, all else being equal, not the total price of the gas supplied.

Informatio: We measure aggregate demand as the value of goods sold -- NGDP. And the quantity sold (equal to the amount demanded) does go down as the price goes up.

Oikomenia: Touche on NGDP. But in your model demand falls as the price goes up because you've fixed the relationship (total sale) = (gallons sold) x (price per gallon), not because of people decide to spend their money on other stuff than gasoline or can't afford the increase.

Informatio: Actually, all I said was the two numbers (gallons) and (total sale) were in information equilibrium. And now the price of gasoline in your story depends on the prices of all other goods -- and those change depending on location. The demand curve and hence the price of gas in Seattle depends more on the price of salmon than the price of gas in Houston?

Oikomenia: Yes! But the influence is so miniscule relative to the total basket of goods we consume that it's hard to measure directly.

Informatio: Then how do you know it's there?

Oikomenia: Because that's how incentives work.

Informatio: So what you are saying is that you assume a human behavioral relationship between price and demand that implies something you can't measure? And then you take the observed relationship between demand and price as the model of that human behavior?

Oikomenia: Well, it sounds a bit circular if you put it like that.

Informatio: The demand curve slopes down because of human behavior. And we know what that human behavior is because the demand curve slopes down? What would you have done if it sloped up?

Oikomenia: That's a Veblen good! In that case, higher price makes it more desirable.

Informatio: So you have a human behavior explanation for a positive or negative slope of a demand curve?

Oikomenia: Another possibility is a Giffen good ... anyway, your model implies the price elasticities of supply are all one. The relative change in the quantity supplied is exactly equal to the relative change in price.

Informatio: That's because I chose the simplest case of information equilibrium where the units of information are the same for both numbers. I could change the units and get any price elasticity of supply you threw at me.

Oikomenia: Won't that change the total sale = gallons sold x price per gallon equation? That equation implies an elasticity of one.

Informatio: The equation does change.

Oikomenia: Then that means your reasoning for supply and demand has to change!

Informatio: Not really. The equation gets more complicated, but the essence of it is captured in the simple case. In order for two numbers to be in information equilibrium where variations in one show up in a deterministic way in the other, they basically have to be proportional in logarithm.

Oikomenia: So supply and demand for gasoline are just the result of keeping the numbers for the total sale and gallons sold in information equilibrium? There's no human behavior in it? I find that hard to believe.

Informatio: Do markets always behave like textbook cases of supply and demand?

Oikomenia: No, there are all kinds of market failures and behavioral effects.

Informatio: That's your answer. When markets work like economics 101, it's because human behavior isn't having an impact. It averages out. All you are left with is some basic mathematics of how two numbers can register the same amount of information.

Oikomenia: Whoa. You are assuming supply and demand represent more of a Platonic ideal than we economists do!

Informatio: Hahaha! I guess you're right! As markets become more ideal, they lose more and more of their dependence on the specifics of human behavior. That's how economics can be so mathematical, but be entirely about the behavior of human beings.

Oikomenia: But that also means that when we see there is human behavior affecting the outcome in empirical research and experiments, then your model is wrong. If you do surveys and find that people decide not to buy something because the price went up, then your reason -- it's just information equilibrium -- is wrong.

Informatio: How do you do an experiment where you cause a market price to go up? If you directly influence the price, then it isn't a market price anymore. If you increase demand, the this supposed fall in demand is from an artificially created higher demand. And if you reduce supply, there is actually less to go around, so somehow some people have to buy less of it, regardless of their feelings!

Oikomenia: But what about Vernon Smith's experiments?

Informatio: He gave his participants defined utilities in terms of numbers. If you assume a utility function behaves like a number you've forced the system to exhibit supply and demand. The use of numbers enforces consistent preferences ... because numbers have a total order. You can't have A < B, B < C and C < A with numbers.

Oikomenia: Yes, yes. Afriat's theorem. Revealed preference or transitivity alone don't result in diminshing marginal utility.

Informatio: They do if the numbers you chose for utility are dollar amounts that are the unit account!

Oikomenia: What about natural experiments? Like when one state raises its minimum wage and another doesn't? You can survey the owners of businesses and ask if they had to layoff workers, or not hire workers as planned.

Informatio: Ask business owners if raising the minimum wage made them hire fewer workers than they planned to? While you're at it, you should ask car company executives if higher CAFE standards will hurt their business.

Oikomenia: You can get data on their hiring, revenues and expenses.

Informatio: Even in mainstream economics you can't draw any conclusions from that natural experiment -- you have no way of knowing whether or not your system jumped from one Arrow-Debreu equilibrium to another.

Oikomenia: But if we observe that employment or hours worked go down and prices go up, then that is evidence that the supply and demand model is correct.

Informatio: Yes, that is true ... regardless of whether that supply and demand model is derived from human behavior, information theory ... or even if it was just made up by Alfred Marshall.

Oikomenia: Gah!! Isn't obvious? If bacon gets more expensive at the store, you won't buy as much of it because you don't think it is worth it at that price!

Informatio: Yes, if bacon went to 50 bucks a pound, I'd probably use it less often. But if it goes from 6 to 7 bucks? If I'm making bacon miso soup, then I'm buying bacon. The price of bacon goes up because there is more demand or less supply and in either case bacon becomes more scarce per person, so fewer people are going to buy it, whatever their reasoning. Sometimes they're sold out of the bacon that I like. I didn't buy less of it because it was too expensive or because I'd rather spend money on something else. It wasn't there. Sometimes bacon isn't there and so I forget that I need it, and don't end up stopping by another store on the way home. So, yes, at 50 bucks there is probably a human behavior component, but for smaller changes near equilibrium there are so many things that could be going on. The economics 101 approach to the supply and demand curves would have to take into account the fact that if the supply goes down, some stores won't get stocked with enough bacon. And that someone seeing two packages left, takes only one because someone else might want some. And then there are the people that would take both. And then there are the people who go back and forth between those behaviors depending on the song playing in the store. And then there are grocery stores that randomly raise the price of bacon because they know people don't check that often and will buy it out of habit. A market is so complicated from a human behavior perspective, that it's best to be agnostic.

Oikomenia: Bacon miso soup? Gross.

Informatio: Were you listening to me?

Oikomenia: Not really. You seemed to be on a roll there, though.

Informatio: [Sigh] The thing is that all of that complex human behavior, the basic concept of supply and demand ... Adam Smith's invisible hand ... seems to work in the real world as a good first order approximation. That's pretty amazing to me.

Oikomenia: I agree, it's pretty cool.

Informatio: I don't think you believe it is as cool as I think it is.

Oikomenia: What is this, grade school?

Informatio: No, really. You keep wanting to describe supply and demand with some simplistic model of human behavior that's all about utility maximization. It's like using a tic-tac-toe playing computer program instead of HAL 9000 or Lt. Cmdr. Data. And you're saying it's pretty cool that supply and demand works in a market made of tic-tac-toe programs. But I'm saying it's pretty cool it works with humans!

Oikomenia: Yes! Incentives matter, and humans do work like utility maximizers a lot of the time. The theory works well for certain problems and you want to throw it away.

Informatio: You're right, humans as utility maximizers does work in many cases. And maybe utility maximization is a good theory to use in particular markets or situations. But its assumptions are wrong in general. And the fact that supply and demand works even with complicated humans makes me think that there is a much more general principle at work than utility maximization ... something like information equilibrium.

Oikomenia: I'm not sure I follow you. Both utility maximization and information equilibrium lead to supply and demand -- how can information equilibrium be "better"? As you said earlier, the mechanics of the supply and demand diagram are the same.

Informatio: It's better in that it doesn't make any assumptions about human behavior. No rational expectations, no utility maximization. Instead of taking utility maximization as your fundamental principle and looking for violations and then adding new behavioral theories for those violations, you can start with information equilibrium as your fundamental principle. The particular violation is specified by  the model -- non-ideal information transfer results in a price that is lower than the ideal price. That's when human behavior matters. Maybe figuring out why the price is lower than the ideal involves utility maximization over multiple markets. Maybe it is some behavioral theory such as prospect theory.

Oikomenia: That just seems like a methodological change. There isn't a change in the content of the theory.

Informatio: But there are some changes. Expectations set by a central bank can't hold onto an inflation target forever in the information transfer model. If you start from some rational expectations theory, then undershooting inflation is due to a lack of credibility of your central bank, that the undershoot is the real target of a credible central bank or some other kind of de-anchoring. Starting from a perspective of human behavior makes you not only see a puzzle but assume its conclusion ... and neither the puzzle nor its solution are true.

Oikomenia: I don't agree with your example ... look at Canada ...

Informatio:  You said before that there are experiments and empirical research where human behavior appears to affect the outcome?

Oikomenia: Feels like hours ago.

Informatio: Well, maybe your assumptions of the baseline human behavior were wrong? Then your assumptions might lead you to see a human behavioral effect where there isn't one!

Oikomenia:  I think I see what you are saying. If you start with particular human behavior assumptions, then you have to see the violation as a puzzle and come up with a solution that references your original assumption. That is a good point. So does that mean you see utility maximization as a particular expansion around information equilibrium, rather than around, say, and Arrow-Debreu equilibrium?

Informatio: That's kind of it. It's more like an information equilibrium is more a general kind of equilibrium, and an Arrow-Debreu equilibrium is a particular case where utility maximization is a good theory to use to look at the fluctuations. An economic equilibrium might be an information equilibrium and an Arrow-Debreu equilbrium. It might just be an information equilibrium. I don't think it is possible for an economic equilibrium to be an Arrow-Debreu equilibrium and not an information equilibrium, but I haven't proven that yet. But that's why I don't think you need human behavior to come up with the basics of economics like supply and demand, or the quantity theory of money.

Oikomenia: The quantity theory? Not this again ...

Informatio: It's not really the quantity theory, I just say that as a shorthand for economists like you to get a basic picture in your head. In most cases, printing a lot of money should lead to inflation, right?

Oikomenia: Not in a liquidity trap.

Informatio: I'm thinking more like Zimbabwe. There's a liquidity trap in the information transfer model, too.

Oikomenia: A liquidity trap without human behavior!!?

Informatio: [Sigh] Yes, it's an emergent property ... it's an entropic force holding prices down.

Oikomenia: I just got a text message! Oh, dear. I have to go ... I'll talk to you later!

Informatio: [Sigh]

1. This mostly encompassed by Gary Becker's analysis in terms of opportunity sets -- he says that even irrational people will behave rationally in aggregate (i.e. follow the laws of supply and demand):

http://informationtransfereconomics.blogspot.com/2015/10/gary-beckers-emergent-rational-agents.html

2. This mostly encompassed by Gary Becker's analysis in terms of opportunity sets -- he says that even irrational people will behave rationally in aggregate (i.e. follow the laws of supply and demand):

http://informationtransfereconomics.blogspot.com/2015/10/gary-beckers-emergent-rational-agents.html