Tuesday, July 23, 2013

The Notion of Utility

In a blog post a while back I briefly discussed the notion of utility.  The Austrian's view of utility can be summed up by a quote I provided in that post (to view the initial blog click here).  Here is the first half of the quote again for a reference.
"Finally these valuations are entirely subjective in two ways: Jones's utility or satisfaction from wearing a pair Oakley's cannot be compared quantifiably to his satisfaction from wearing a pair of Ray-Bans.  Even by his own inspection."
As I mentioned in the previous post, Austrian economists make this claim very often.  One thing I have never seen them do though is argue against von Neumann and Morgenstern who wrote in 1944 that we can make such interpersonal measurements.  Furthermore, to do so, it takes no more than a simple thought experiment which Austrians should love.

Let me point out before I summarize the von Neumann and Morgenstern argument that they acknowledge the fact that this is a controversial topic.  Also, if you want to read their full argument, and I highly suggest you do so, it is in Theory of Games and Economic Behavior in the section entitled The notion of Utility.  Hence the title of this blog post.

The first thing they point out in the section is that in the past there have been certain phenomena that were considered non-measureable up to a certain point in time.  E.G. sensations of light, heat, muscular activity etc.
"All this [utility] is strongly reminiscent of the conditions existent at the beginning of the theory of heat: that too was based on the intuitively clear concept of one body feeling warmer than another, yet there was no immediate way to express significantly by how much, or how many times, or in what sense.
This comparison with heat also shows how little one can forecast a priori  what the ultimate shape of such a theory will be.  The above crude indications do not disclose at all what, as we now know, subsequently happened.  It turned out that heat permits quantitative description not by one number but by two: the quantity of heat and temperature."
They go one further and argue that
"The historical development of the theory of heat indicates that one must be extremely careful in making any negative assertions about any concept with the claim to finality.  Even if utilities look very unnumerical today, the history of experience in the theory of heat may repeat itself, and nobody can foretell with what ramifications and variations"

As you can see, they are laying down the groundwork for numerical utilities in these arguments.  Who is to say at one point we will not have developed a certain device that measures the dopamine that is produced when we consider consuming certain goods in order to help us satisfy our wants more accurately.  Such a device would allow us to measure utility to an exact number.  If such a device were discovered, would the Austrians  reevaluate their views on this matter or would they dig in their heels while keeping their antiquated theories that have been refuted or improved?  How they would react to such findings is speculation, but I digress.

The next thing von Neumann and Morgenstern do is demonstrate how to gain information on the degree to which I might prefer one good to another by doing a thought experiment.  Let me point out that utility is just a word economists picked to discuss the topic at hand.  Clearly we do get some satisfaction out of consuming goods and utility is just the word given to such satisfaction to use in conversation.  I personally like to think of it as a "payoff" of sorts.

Consider an individual with the choice of three goods, call them A, B and C.  Without loss of generality assume this individual, Mary, prefers B to A, A to C, and B to C.  Next consider Mary having two options on how she might receive these goods.  She can either choose A automatically, or choose the option of getting either B or C with 50-50 odds between the two of them.  She will get one of them with 100% certainty.  If she chooses A over the bundle this tells her some information of how much she prefers A to C and B to A.  Now since B and C are both compared to A, she can induce a comparison between B and C.  This thought experiment gives us a way to determine "distances" between the utilities one receives from the three goods.  Since we have distances, we can enumerate them.

Morgenstern and von Neumann actually go one step further and show numerical measures can be used more directly if we consider all probabilities.  I am not going to go into that now.  I do plan on addressing it at a different time.  However, I think this thought experiment Morgenstern and von Neumann introduce is rather convincing allows us to consider how we can derive "distances" between utilities which Austrians continuously claim is not possible.

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