Friday, January 30, 2015

Is the demand curve shaped by human behavior? How can we tell?

I'm in the process of writing (yet another) simple introduction to the information equilibrium view of supply and demand, but stumbled onto an issue that -- while I may be wrong about it -- really seems to fly in the face of basic economics. I asked myself the question: how would we go about determining the shape of the demand curve -- especially in a way that let's us see human behavior at work?

You might think experiments would help here. However e.g. Vernon Smith's approach assumes utility. If you give your agents utility functions that obey the conditions of the Arrow-Debreu theorem, then an equilibrium must result from just the pure mathematics of it, along with the mechanics of supply and demand -- regardless of human behavior. This is basically just a restatement of the idea that assuming homo economicus (by giving people well-defined utility functions) effectively implies ideal markets.

I started to look at some classroom experiments ... and saw that they don't actually demonstrate what they set out to demonstrate.

Take this experiment [1] for example (it is not unusual). The idea is that students write down a reservation price and the instructor collects the cards and tallies up the number that would buy at a given price (or they all stand up and sit down as the price called out gets too high in this version [2]). As the price goes up, the number of students willing to pay goes down. Makes sense.

But is this measuring a demand curve (i.e. things like diminishing marginal utility)? No. And it is especially clear in [1] if you look at their graph. It's not a demand curve, it's an inverse survival curve for a normal distribution:



That is to say it's a cumulative distribution function of a normal distribution turned on it's side (see the second graph here). What this is measuring is the (normal) distribution of price guesses from the students:


It is especially telling that in experiment [2] above, they leave off the last few students -- i.e. the last piece of the CDF where it stops being linear.

This doesn't have anything to do with human behavior. Why is that? Because I can get the exact same "demand curve" using brainless atoms. The contribution to the pressure from one atom is based on the force it exerts against the container -- the change in momentum as it reflects off the wall. That change in momentum is proportional to its velocity, and in an ideal gas, the atoms follow a Maxwell distribution:


If we asked atoms to sit down as different velocities were called out if the velocity was higher than theirs, we'd get the following "demand curve":


I used this example since both price vs demand and pressure (velocity) vs volume come from the same derivation in the information transfer model and neither require human behavior to explain.

Now you might say that students' knowledge of the average price of M&M's (in the example) shows how human behavior enters the equation; they see the value of other goods and make utility judgments. But! Atoms also seem to 'know' the average velocity of the ideal gas in the analogous experiment -- set by the thermodynamic temperature. The students know the value of a packet of M&M's because it is set by the value of money (perhaps set by an economic temperature) -- something controlled by the central bank in most economic models.

So how do we see a demand curve in a way that incorporates human behavior?

In the MR University video, after using 'Black Friday' as an example (which is actually the experiment discussed above), they move on to describing it in terms of substitution. That is definitely human behavior, right? We decide to buy other things with our money!

Well, actually ... how is that different from the experiment above? When you have an estimate of the price of M&M's and the price goes above that reservation price you are effectively making the statement "I'd rather spend my money on something else" (or "I don't have that much money" in some cases). Something being "too expensive" and opting to save the money for something else are logically equivalent statements.

Now you might say that in the case of atoms when things get "too expensive" (too high a velocity) it's because they "can't afford it" (their velocity is all they have), not because they've decided to keep their "money" (velocity) for something else.

And that would be true ... for a single container with an ideal gas. But multiple markets is like multiple containers (with the same number of atoms**, i.e. students) at different temperatures (i.e. prices). So while 20% of atoms have a velocity of at least 1 in one market, 20% will have a velocity of more or less in another, corresponding to 'money' they'd 'spend' on something else.

So, again, how do we see a demand curve in a way that incorporates human behavior?

I'm probably missing something. There could be other experiments*** that show human behavior shining through. Just because I don't know what they are doesn't mean they don't exist.

There is an ulterior motive here, and it's not just that I think starting with humans as optimizing agents is likely not only intractable, but unnecessary. It's that in writing that simple introduction I mentioned at the top of this post I realized that the information transfer model, in an ideal market, has literally nothing to do with the behavior of the agents. Supply and demand are a property of two quantities that are in information equilibrium ... and the mechanics follow**** from D = κ P S. Hold D constant and as S goes up, P must fall (a demand curve). Hold S constant and as D goes up, P must go up (supply curve).

That's all there is ... and if that's all there is ...



Footnotes:

** We are glossing over the the fact that we have the capability to distinguish different people and e.g. assign a particular price estimate in each market to a particular person -- something we can't really do for identical atoms. However, there is the question of whether the market can see people as distinguishable ... using money makes transactions anonymous.

*** You might think of an experiment where you reduce the supply and watch how the price goes up and take a survey and ask why people decided not to buy something. However 1) the mechanism you are using assumes supply and demand, and 2) since you are reducing the supply, some people will have to buy less regardless of how they feel about it. (Humans are subject to post-hoc rationalizations, so the survey would be suspect, anyway.)

**** You can get different shaped demand curves from this equation -- it's actually just an instantaneous equation and P is a derivative (dD/dS).

15 comments:

  1. This comment has been removed by the author.

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  2. Nice post Jason!... I'll have to wait till I'm home to see your 1st two graphs for some reason (I don't know why, but I have trouble with a lot of them from my machine at work).

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    1. Thanks Tom. And I'm not sure why that is either. The first two graphs look almost exactly like the second two graphs (in reverse order and in blue instead of red).

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  3. I had the opportunity to watch a mouse residence a while back. I knew it was a mouse residence because mice mostly eat grass and here was a hole with grass eaten entirely away close around the hole.

    As I watched, a mouse poked his head up from the hole and looked around. Then he darted out, grabbed a mouth full of grass, and ducked back into his hole. The whole outside venture took less than two seconds.

    Like the mouse, humans are driven by survival behavior. I think this explains why one person will eat hamburger, live in low cost housing, and drive old cars. Another person will eat caviar, live in a mansion and drive a new, big car. Each person is making choices that make survival as pleasant as possible within a limited number of possibilities.

    It is akin to having a human choice of living in a low temperature or living in high temperature environment. Sometimes it is our choice, and sometimes choice is made for us.

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    1. Sorry for the delay in getting back to your comment -- I had to think about it (especially in connection with what I was basically uncertain about above). The information transfer framework seems to lead to zero influence of choice by man or mouse; that idea makes me uncomfortable. But I think what saves the idea is that it is only in the case of ideal markets.

      Ideal markets are abstract mathematical construct (like ADM equilibrium), but if a system simplifies in any meaningful way, it must simplify to some abstract mathematical construct.

      What is interesting (to me at least) is that the idea of well-defined utility functions and the idea of commerce as a random gas lead to the same abstract mathematical construct.

      Does that make the assumption of humans having well-defined utility functions (with consistent preferences) equivalent to the assumption that behavior is random? A world of Lt Cmdr Data's and a world of Johnny Rotten's lead to the same market economics? Well, intuitively, if you think economics is well defined ... it kind of has to!

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  4. how are atoms in the multiple containers linked?

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    1. Hi LAL,

      You could imagine the containers being in thermal contact with each other -- if one became warmer, another would have to become cooler, by energy conservation.

      http://en.wikipedia.org/wiki/Thermal_contact_conductance

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    2. I might have an experiment that would be helpful ... inside each gas chamber is a mix of gasses. But all the chambers potentially contain some of each gas. Would the theory of demand should have each gas able to communicate to its own gas type in another container more efficiently than it is with other gasses?...the analogy is that one individual may participate in multiple markets including markets for substitutes compliments etc...so his demands can adjust instantaneously...this I think picks one among many possible ways for the gasses to transfer energy

      further some chamber could be empty of one gas or another but when pressures change substantially, the velocity of the gas in said chamber goes from 0 to >0. (this is a wealth effect moving a corner solution to an interior solution)

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    3. Using thermal transfer between different boxes effectively makes the distributions of the different molecules invisible -- using heat to transfer energy makes the source of the heat "anonymous". It probably carries the analogy too far although I would not discount the possibility of designing a physical model of an economy ... like this one:

      http://en.wikipedia.org/wiki/MONIAC_Computer

      I would actually expect looking at particular individuals would allow you to see where the information equilibrium theory breaks down, much like how looking at molecules lets you see where e.g. an ideal gas will liquify under increasing pressure and the ideal gas law breaks down ...

      http://informationtransfereconomics.blogspot.com/2014/09/insights-from-non-ideal-information.html

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  5. Well, as a non-economist, I am not at all surprised to see something that looks like a normal distribution in the classroom experiment. And I would think that, by definition, the cumulative distribution is a demand curve. Maybe just not what the economists say that a demand curve should look like.

    As for normal distributions describing human behavior, why not? Here we have independent judgements of a large enough group of people, so I would expect a normal distribution. If you conducted an actual auction, so that the judgments were not independent, you might see a different distribution.

    Human behavior is going to exhibit a number of familiar distributions, normal and Poisson distributions included. So what? What is interesting is when it doesn't.

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    1. Hi Bill,

      The interesting thing about the post above isn't that it's a normal distribution vs Cauchy vs whatever -- it's that a demand curve isn't supposed to be the integral of a normal distribution. The demand curve isn't -- as far as the economics goes -- the survival curve derived from a normal distribution. It's supposed to be the result of utility maximizing agents making trade-offs.

      That is to say the purported demand curve in the classroom experiment isn't actually a demand curve. It's like if economists tried to show an experiment that demonstrated the Earth wasn't the center of the solar system and decided to use a Foucault pendulum -- which only demonstrates the Earth is rotating, not its position in the solar system.

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    2. Unlearned as I am in economics, I am not sure about what shape the demand curve is supposed to take. However, one thing I am pretty sure of is that it is unlikely to look like an individual utility curve. In fact, if the individual judgements are independent and their number is large, I would be surprised if the distribution of reservation prices was not normal. I don't care how they arrive at their judgments, as long as the judgements are independent. AFAIK, if they arrive at their judgements by making tradeoffs in order to maximize their utility, that should not matter.

      There was a famous psychology experiment in which rats ran a T maze and were always rewarded for turning the same way each time. When it was published it had a graph showing how many rats turned the right way at each number trial, until all of the rats learned the maze. That gradual curve was supposed to represent the learning curve for each rat. But in fact, a close look at the data revealed that each rat made a decision to turn the correct way all the time. The individual learning curves were not gradual at all. It was just that some rats caught on more quickly than others.

      P. S. Foucault pendulums are cool, aren't they?

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    3. I mean each rat was rewarded for turning either right or left each time, regardless of how it had turned before. Sorry for the ambiguity.

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    4. OIC, maybe.

      It is not a demand curve because the students were not asked how many they would buy at each price.

      But if that is the right question, why wasn't it asked?

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