Tuesday, January 26, 2010

Ecocomics Explains: Preferences and Indifference

Ecocomics Explains is a new feature of this blog. Each episode, we will discuss a different economics concept--ranging from more basic ones to more advanced and mathematically involved ones--and highlight some examples from comic books that reflect the ideas.

In our last lesson, we discussed the concepts of opportunity cost and budget constraints. Namely, we analyzed a situation where our friendly, neighborhood Spider-Man was had choice between spending an hour of free time fighting criminals on the street or attending Aunt May's rehearsal dinner and earning some brownie points with the family. We learned in order to be efficient, Spider-Man should have chosen a combination of fighting criminals and earning brownie points that would have allowed him to spend all 60 minutes of the hour doing one of the two activities.

Unfortunately, this doesn't exactly tell us what combination Spider-Man should or would have picked. It merely gave us the range of possibilities that Spider-Man could pick from. The bundle he actually chooses depends on his preferences and utility. We'll focus on utility in another post, but for now let's talk about Spider-Man's preferences.

Note: when Spidey refers to taking photographs, he is talking about the photos he takes of Spider-Man fighting crime The Amazing Spider Man #600 by Dan Slott and John Romita Jr. (2009)

Recall that the situation we are analyzing, depicted in The Amazing Spider-Man #600, is just one of many examples of the sort of choices Spider-Man has to face as a masked vigilante. Either Spider-Man surrenders to his obligation to fight crime and sacrifice personal time with his family, or works on his family/personal life and runs the risk of keeping some criminals on the street for the time being. Unfortunately, Spider-Man never explicitly states that he has an hour and never discusses just how happy his family will be to see him, so those are numbers we made up for simplicity.

Basically what we're going to do from here on out is build a consumer choice problem for Spider-Man from the ground-up. The first thing we need to realize is that Spider-Man's preference fit certain axioms, or rules.

First, Spider-Man's preferences are complete. Basically this means that Spider-Man can rank his preferences over any goods or combination of goods. Given putting criminals in jail and brownie points, for instance, Spider-Man can say that he'd rather bag one criminal than earn one brownie point, vice versa, or even be indifferent between the two. There is no way that they are noncomprable, however. When given a choice, he cannot just shrug and say "I just don't know!"

Second, his preferences are transitive. Say a third good enters the mix: watching TV. Now say that Spidey would rather spend time with family than fight criminals, but would rather fight criminals than watch TV . Well, then Spidey obviously also prefers spending time with family to watching TV. So if:

brownie > criminal and
criminal > TV
==> brownie>TV.

Finally, there's non-satiation. This means that there is never a maximum amount of a particular good that will fully satisfy Spider-Man. That is, there is never a point where Spider-Man would cease to derive enjoyment from putting criminals in jail. The more criminals he bags, the more enjoyment he sees.

There are a few more axioms and some more mathematically rigorous ways that we can define these three (which we'll go over eventually), but for now this is all we need to know. Consider the following graph:

Suppose Spider-Man is at point A of the graph. That means that he chooses to spend his 48 minutes hunting down 2 criminals and spending enough time with Aunt May to earn 4 brownie points. We know from last time that this combination is in Spidey's feasible set (even though it's not efficient).

Now let's say that Mephisto shows up and decides to offer Spider-Man a deal. He says that in exchange for handing back one of the two criminals he just captured, Mephisto will use his magic to alter the Spider-Man timeline (again) and have it seem as though Peter had been spending time with his family instead. Obviously Spider-Man would not make the deal if he would rather be hunting criminals. So Mephisto says that he'll give Spider-Man just enough brownie ponits to make up for the lost criminal, but no more. Spider-Man tells Mephisto that he'd need 3 brownie points to make him equally satisfied. Deal done (but for some reason no one seems to remember Spider-Man's identity anymore).

Post-deal, Spider-Man is at point B of the graph. He has taken out only one criminal, but earned an incredible 7 brownie points with his family! And he is equally happy. This means that Spider-Man is indifferent between points A and B. He derives the same enjoyment out of both combinations of actions.

Looking at the graph, we can now map out Spider-Man's indifference curve (labeled L2). This curve marks all the points, or combinations of brownie points and criminals, that Spider-Man is indifferent between. As you can see, Spider-Man would get the same satisfaction whether he takes out one criminal and earns 7 brownie points (point A) or whether he takes out 3 criminals and only earns 2 brownie point (point C).

You might be wondering why the curve is not a line, similar to the budget constraint. Well, this is due to a phenomenon known as diminishing marginal rate of substitution. In microeconomics, dMRS is another axiom that defines the convex shape of the indifference curves.

The marginal rate of substitution is basically the slope of the curve at various points. It's tell you what individuals are willing to give up of one good to get another. Note that this is different from an opportunity cost, which tells you how much an individual would HAVE to give up of one good to obtain another. At point B for instance, Spider-Man is willing to give up around 3 brownie points to get 1 more criminal (to get from B to A). That's a slope of 3 so his MRS at point B is about 3. At point C, Spider-Man is willing to give up about 1 brownie point to get one more criminal. That's a slope of 1, so his MRS at point C is 1.

The intuition behind assuming a diminishing marginal rate of substitution is not very difficult to grasp. When Spider-Man is at point A, he has lots and lots of brownie points but very few criminals. Catching another criminal is looking very attractive to him at this point, so he'd be willing to give up a little more to get one. At point C, however, Spider-Man has used up more of his hour to catch more of criminals, but in doing so has sacrificed much needed time with his family and is dangerously close to alienating himself with only 2 brownie points. He would be willing to sacrifice less brownie points at point C for another criminal.

We'll continue with this next time on Ecocomics Explains!

Questions and comments are welcome. Also, if anyone has any suggestions of economics topics they would like covered, please feel free to drop us a comment.


kmitcham said...

Thank you for the informative content.
I think you have a typo on the graph- point C seems to be mislabeled.

ShadowBanker said...

Woops, the typo is actually in the text. Should be fixed now.

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