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Fun With Related Goods, Broadway Edition…

June 28th, 2014 · 5 Comments
Econ 101 · Fun With Data

One of the first things we generally cover in intro microeconomics is the determinants of demand– i.e. the factors that influence how much of a good we are willing and able to purchase. The price of a good is obviously one of these determinants, but so are the prices of what economists call “related goods.” related goods are broken down into two categories:

  • Substitutes- roughly speaking, goods that are consumed instead of one another
  • Complements- roughly speaking, goods that are consumed together

More precisely, economists define substitutes and complements in terms of the relationship between the price of a related good and the demand for the good in question. By this definition, the demand for a good decreases when the price of a substitute decreases (and vice versa). Conversely, the demand for a good increases when the price of a complement decreases (and vice versa). While this definition isn’t wrong per se, I’m surprised that few (if any) textbooks address how this relationship applies when substitutes and complements enter the world in the first place. After all, it stands to reason that substitutes entering a market decreases demand for an item, and complements entering a market increases demand for an item. (Hence the existence of iTunes and the Apple app Store, for example.) In order to reconcile this with the textbook explanation, I usually have to dance around some story about how a price of an item is technically infinite if a product doesn’t exist, which then implies that a product entering the market at a finite price is a form of a price decrease (which makes the official definitions apply).

Ok, now I’m even boring myself, but I think about this more than is reasonable and therefore wanted to put it on the Internet. Now what was my actual point…oh, right- sometimes it’s not obvious whether goods are substitutes or complements, and I am often reminded of this when I make up exam questions that I think are obvious and then have students students complain when they lose points. (I actually had a student rather convincingly argue that lemons and limes are complements because lemon-lime soda is a thing.) Therefore, it’s often helpful to work backwards from the data to infer whether goods are substitutes or complements. Take Broadway musicals and movies made from them, for example- substitutes or complements? On one hand, they might be substitutes because people don’t want to watch the same story twice. On the other hand, however, they could be complements because the widespread release of the movie could make people more interested in going to New York to see the musical. Even though I didn’t know which way the relationship would go, I wasn’t expecting to see this from the data:

(You can see more on the topic here.) So I am to believe that Chicago and Chicago are complements but The Producers and The Producers are substitutes? (Yes, I realize that the chart shows revenue and not demand specifically, but revenue seems like a reasonable proxy in a way that quantity of tickets does not because revenue accounts for price changes.) The article that this chart comes from gives more detail and, at a rough level, rules out the possibility that the differences are attributable to how long the musical had been out prior to the movie or when during the year the movie came out.

I thought I would point this out not only because it could make for an interesting classroom discussion but also because we tend to make a lot of assumptions about how goods are related when we discuss intellectual property protection, and it’s important to remember that these relationships aren’t necessarily obvious or even consistent, as evidenced above. Or, put more simply, why assume when you can actually go to the data and find out for real?

Tags: Econ 101 · Fun With Data

5 responses so far ↓

  • 1 Aj // Jun 28, 2014 at 11:57 pm

    Going back the lemon and lime scenario, doesn’t the price signal of complementarity/substitutability incorporate TOO much information? For example, if you discover a rich nation that has never tasted citrus fruits, then the rise of a new market could make lemons and limes appear to be complements even when people treat them as substitutes. The appearance of a lime may signal new market growth that also allows for increased lemon demand. How do you determine substitution/complement signals when both prices move in the same direction?

  • 2 econgirl // Jun 29, 2014 at 12:42 am

    There’s an implicit “ceteris paribus” (all else being equal) assumption in the definitions as described, and yes, what we often see are scenarios with more moving parts than just the price of a related good. In the scenario you described, the demand for lemons is probably less than it would have been if everything were the same except that the price of limes hadn’t increased, which is what the substitute relationship implies.

  • 3 BC // Jun 29, 2014 at 11:12 pm

    Actually, I believe that Aj’s example is more than just an issue of ceteris paribus. certeris is not paribus because one must say whether the price change is caused by a change in demand or a change in supply. For example, demand for a good increases if the price of a substitute increases *due to a decrease in supply of the substitute* as per Jodi’s definition. However, if the price of the substitute increases *due to a increase in demand for the substitute*, then the demand for the good can either increase or decrease depending on what caused the demand change for the substitute. Similarly, demand for a good increases when the price of a complement decreases *due to an increase in supply of the complement*. However, demand for a good decreases when the price of a complement decreases *due to an decrease in demand for the complement*.

    From these examples, it looks like it may be better to define substitute and complements in terms of what happens to demand in response to *a supply change* of the substitute/complement rather than a price change. ceteris paribus in this case would mean keeping demand for the substitute/complement fixed.

    I hate to be nit-picky here because it’s not the point of your post, but we are seeing right now in all the discussion about the Great Recession, monetary policy, etc. that it is important to “never reason from a price change”. Instead, think about what happened to supply/demand to cause the price change. See, for example, here:  http://www.themoneyillusion.com/?p=5062]

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