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On The Hunt For The Elusive Upward Sloping Demand Curve…

April 5th, 2010 · 15 Comments
Behavioral Econ · Buyer Beware · Decision Making · Econ 101

It seems like such a simple concept: demand curves slope downwards. Here’s a visual for you:

When the price of the item goes up from P1 to P2, the quantity of the item that people demand decreases from Q1 to Q2. Put in real people terms, when something gets more expensive, fewer people want it. (Or the same number of people want less of it, or some combination of the two concepts.) This makes sense if for no other reason than demanding something involves being ready, willing and able to pay for it, and fewer people can afford an item when it gets more expensive.

But economists apparently like to make everything complicated, so they point out that it is mathematically possible to have a demand curve that slopes upward. Well, at least two economists have pointed out this possibility. Sir Robert Giffen pointed out that a good could be so inferior (meaning that people consume more of it when their incomes decrease and vice versa) that people actually consume more of it when its price goes up…and thus the Giffen good was born. The logic is that a price increase means that consumers are effectively poorer, since they can’t buy as much stuff as they did before. So if we’re poorer, we both substitute away from the goods that got more expensive and move toward inferior goods. Giffen goods are inferior goods where there aren’t really cheaper options to substitute to, so the latter effect dominates the former and the price increase actually leads to an increase in consumption.

Don’t worry, I find the logic a bit challenging as well. I also have never heard of an example of a Giffen good other than potatoes in Ireland. I feel like even that is a stretch, and I’m not quite sure why the example is limited to Ireland other than because of potato famine stereotypes.

On the other hand, we can theoretically have an upward-sloping demand curve for luxury goods as well. This concept was codified by Thorstein Veblen and the goods are appropriately called Veblen goods. (Sidenote: I love the pictures on that Wikipedia page.) His rationale is that conspicuous consumption and status considerations make some goods more attractive as a direct function of their prices. This increase in attractiveness can theoretically overcome the fact that the goods become less affordable, and the net result is that we see an increase in the quantity of these things demanded when the price increases (at least over some price ranges).

Okay, so I’ve got two models for why I might see an upward-sloping demand curve, but little empirical evidence for either concept. The end result of this is that I have become the nerdy economist equivalent of the people who go around searching for Bigfoot. Worse yet, since I write about this sort of thing, I’m actually more like the people who not only go around searching for Bigfoot but also set up museums and the like dedicated to this potentially nonexistent creature. (Yes, they do exist, and a guy I know does a whole comedy bit about the one located here.)

Luckily, I have people who are supportive in my quest and provide me with footage of these supposed upward-sloping demand curve sightings. For example, reader Brit pointed me towards an article in the Miami Herald that described how high tolls lure drivers to I-95′s pay lanes:

When Victoria Perkovich sees a high toll on the illuminated Interstate 95 Express signs, she steers into the toll lanes.

“I think the traffic must be pretty bad,” says Perkovich, a college student and frequent commuter. “I’d rather pay $4 than spend two hours sitting in traffic.”

Her behavior helps explain the traffic growth on the I-95 Express Lanes — and a classic misunderstanding of commuter psychology.

Traffic engineers assumed high tolls would deter drivers from using express lanes. Wrong.

Many drivers, like Perkovich, assume high tolls mean the toll-free lanes are clogged. Could be true, but the tolls rise mainly due to the number of drivers willing to pay a toll.

Fascinating. It seems like the idea here was to have some sort of congestion pricing scheme where drivers have to pay more to avoid the traffic when traffic is heavier. This makes sense, since the value proposition that an open lane presents is higher when the rest of the road is a parking lot. However, instead of using some objective method of traffic reporting to determine prices, the system sets prices as a function of how many people are going through the toll booth.

Could this work as an efficient congestion pricing system? Yes, if people were doing their own homework regarding traffic conditions and using that information to determine whether the toll was worth it. Given objective information about road conditions, if the toll is “too low” for the amount of traffic congestion, the system would see a high volume of traffic into the paid lanes and would raise prices. Once the traffic subsided, people would stop choosing the pay lanes and the prices would decrease. Does it work? No, since rather than checking the traffic reports, people are using the price itself as a signal of the traffic level. So what seems to be happening is something like the following: A few dudes who are really in a hurry choose the pay lane, just to be on the safe side. This raises the toll, and then other drivers see the toll increase and think “wait, what do these other guys know that I don’t?” and also choose the toll lane. This further increases the toll rate, at which point people think that traffic ahead must be REALLY bad, so even more choose the toll lane, even though there was no real traffic congestion to speak of in the first place. The behavior of people in this system is essentially crating a bubble in toll prices…and a lot of pissed off people who pay a $7 toll only to find out that their lane is more crowded than the free lanes.

This is not the only context in which people use prices as a signal of quality, but it’s one that shows the potential pitfalls from doing so particularly well. I find it especially interesting that the article specifically mentions the fact that people were educated on how the system works, so in a way they should know better. On the other hand, people have limited time and attention so perhaps either they didn’t pay attention or didn’t understand the system properly. In this setup, it seems like the only way to achieve an efficient outcome is to have a more objective pricing function- a simple fix would perhaps be to put the vehicle counters on the free lanes as opposed to the pay lanes. Gee, it sounds so simple put that way…

But back to the question at hand- is this really an example of an upward-sloping demand curve? The toll is certainly not an inferior good, so if anything it falls into Veblen good territory.

One of the important points about the demand curve is that it assumes that all factors other than price that affect demand are held constant. In most cases, this doesn’t really introduce a lot of confusion. However, in this case, the price is actually changing people’s tastes for the item because of the information that the price supposedly conveys. so are we really seeing this?

I argue that we aren’t, and that we are instead seeing something more like this:

This setup is consistent with the evidence that we see in the article- when the price goes up from P1 to P2, the quantity demanded goes up from Q1 to Q2. But this is because the price increase served to increase people’s taste for the toll lanes, which shifted demand to the right. To a certain degree, this is a question of semantics that exists with the explanation of Veblen goods in general- how direct is the price effect on quantity? In this sense, the latter model seems more appropriate in one important way- let’s say that you could communicate the information that the price increase supposedly conveys here without actually changing the price. What would happen to demand in this case? Logically speaking, it should be higher than with that same information conveyed through a price increase. In the diagram above, this point is labeled as Q3, and is in fact higher than point Q2. In the upward-sloping demand curve model, we would be stuck at quantity Q1 in the absence of a price increase.

To summarize: My economic Bigfoot, despite being a great example of one of the biases present in consumer decision-making, was really a dude in a gorilla suit that had been dragged through some mud and leaves. And my quest continues…

Tags: Behavioral Econ · Buyer Beware · Decision Making · Econ 101

15 responses so far ↓

  • 1 Tony // Apr 5, 2010 at 7:16 pm

    I also <3 the quest for Giffen goods. Apparently, so does Robert Jensen. In a series of guest posts at Freakonomics, he described his quest:

    http://freakonomics.blogs.nytimes.com/tag/robert-jensen/

    I love the moniker *The Indiana Jones of Economics.* Too bad it is taken.

  • 2 Warren Jensen // Apr 5, 2010 at 8:13 pm

    Well, here’s another “Jensen” confirming the presence of the upward-sloping demand curve. As a consultant, we actually find that we win more contracts when we bid higher than our actual cost to produce the services. Yes, we have data showing this. No, I’m not sharing. :) Our educated guesses tell us that the higher we bid, the higher the perceived marginal value of our services. Thus, our clients choose us more often when we bid higher.

    And that’s a good thing to know…

  • 3 Adam Alonso // Apr 5, 2010 at 10:47 pm

    Warren,

    It would seem that this would not be an upward-sloping demand curve, unless of course you first bid the lower price. An upward-sloping demand curve would suggest that they chose you at the higher price after declining your original price, which I sincerely doubt.

  • 4 Brishen // Apr 6, 2010 at 7:24 am

    I would like to know if there are any other “Giffen Goods”, as they seem to point out an interesting exception which proves the rule. It should be taught in economics classes, as it really is an interesting case.

  • 5 Mike Brown // Apr 6, 2010 at 9:25 am

    I agree with Adam that this is probably more the case of Chivas Regal effect than upward sloping demand.

    Brishen: A couple examples I have heard are rice in China and gasoline. When a family consumes a basket of mostly rice and a bit of meat, and the price of rice goes up, the family will stop buying meat and buy more rice to continue to consume the same number of calories.
    Gasoline is a bit shakier, but roughly, when gas prices go up, people spend less on car maintenance, which makes their engine run less efficiently, requiring them to buy more gasoline.

  • 6 Mike D // Apr 6, 2010 at 5:10 pm

    Nitpick

    Above your graph of the upward sloping demand curve, you state “However, in this case, the price is actually changing people’s tastes for the item because of the information that the price supposedly conveys.”

    It seems odd to view this as changing people’s tastes (utility fcns)… more like their expectations.

    When I’m teaching, I often confront get “but a price increase makes people think there’s going to be a shortage, which could trigger further buying, so the D curve could slope up, right?”

    My response: “The expected future price increase is one of those ‘other than price’ variables. Example: when would you be more likely to buy a house?
    Scenario A: It’s more expensive to buy than rent and house prices have gone up by 10% for the last few years.
    Scenario B: It’s less expensive to buy than rent and house prices have gone up by 10% for the last few years.”

    Just as you’ve illustrated here, I do the expectations as two separate D curves, w/ Scenario A farther to the left.

  • 7 steve // Mar 28, 2013 at 9:10 am

    an urban legend i grew up with was when Timex first came out with durable but cheap watches, no one bought them thinking perhaps the low cost meant low quality (i’m wondering if this relates to the early use of synthetic jewels for bearings). so, the legend is Timex doubled the price of watches to where people then assumed they must now have better quality and started buying them.

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  • 10 Jeff // Jul 3, 2013 at 12:55 am

    “But this is because the price increase served to increase people’s taste for the toll lanes, which shifted demand to the right. To a certain degree, this is a question of semantics that exists with the explanation of Veblen goods in general- how direct is the price effect on quantity?”

    I would not consider Veblen and Giffen to be orthogonal choices. In general, you cannot say that A and C lack correlation because B causes C. Rather the opposite, if B can be shown to reliably cause C and B and A were correlated, then that would only strengthen the case for A varying in a correlated manner with B.

  • 11 JTapp // Aug 16, 2013 at 7:15 pm

    When you properly understand that the height of the demand curve measures marginal benefit of the nth unit, then the only explanation that makes sense is for the curve to shift– people’s marginal benefit of taking the toll lanes increases.

  • 12 Jeff // Aug 16, 2013 at 9:44 pm

    “When you properly understand that the height of the demand curve measures marginal benefit of the nth unit, then the only explanation that makes sense is for the curve to shift–”

    This may make sense to an economist, but it makes no sense to someone of a mathematical persuasion. Despite seeing somewhere on the order of 6 million references to the difference between moving along the curve in response to changing conditions vs shifting the curve in response to shifting conditions, I have never seen someone define this distinction rigorously.

    If I were to try to define this, then there are several approaches I would consider taking. One would be to assume that the curve is measuring impacts of price on quantity desired in the short term, but any changes to the market that would affect these dynamics that take more than a certain amount of time will be considered a long term structural change that creates a new curve. Another approach would be to look at the relationship between price and quantity as a mathematical relationship and all other variables would be held constant. In this envisioning, the relationship between price and quantity is a mathematical manifold, which is a surface of dimension M in a space of dimension M + 1. Then each price/quantity curve is a projection in which all other variables are either held constant or held to some precise relationship with price and quantity.

    There are other options, but I think the field is complicated enough with just these two for the moment. Notice that the behavior of the two approaches is quite different. In the first case, you are not really graphing anything that is “true” in any large scale sense and rather are making an approximation in which you count on distance being small enough for the relationship to be well defined. Just as any continuous curve will look like a line for any small enough neighborhood around a solution point, we can also assume that things like spoilage expectations, product fashion cycles, and markets for competing goods will be relatively constant for a short time. In any case, if you define the Price/Demand graph as a graph of the Demand vs Price values for a good over a short time period, then regardless of how well your justification works out, that’s your definition. Any price and demand change for any reason whatsoever has to be included in the curve. If someone with massive cultural power like a religious leader is watching the prices and says “Thou shalt consume rice!” when the price hits a certain threshold, then if that happens in a short enough period of time, that is an upwardly sloping demand curve by our definition.

    Looking at the other possibility, notice that it’s meaning is quite different. There is no guarantee and not even a very strong expectation that as you measure prices and quantities the relationship between these prices and quantities will bear any resemblance whatsoever to the instantaneous curve that relates price to demanded quantity as any one of the individual measurements is taken. At least not without a model covering the other known inputs to dynamic prices and quantities. If by adding some other factors you are able to create a model that predicts the measurements pretty well, then that can give you encouragement, but that will not be demonstrable as a one-dimensional curve in a two-dimensional plot. In particular, you can expect that the projection down to just price and demand quantity will likely have many different possible demand quantities for a given price depending on the state of other variables in your model. but ignoring this complexity, based on our original definition, if you are looking at the price of good x vs the quantity of good x, then price and quantity of good y would be included in the set of variables we are holding constant so we can isolate just the x’s and understand those. According to this model, the inferior goods model would not dictate an upwardly sloping curve, but rather a family of curves with each curve identified with a state of other variables including price and demand of good y.

    You can also define the difference between changes to the environment that are modeled into a demand curve vs changes to the environment that “reset the test” and cause you to be measuring a different curve based on different assumptions “along an axis that matters for that purpose”, but that definition needs to be provided, and depending on which definition is chosen, an awfully large number of textbooks will need to be re-written.

    In any case, when you say “the height of the demand curve measures marginal benefit of the nth unit” (Now that we know about trans-fats will we start having to measure buttery benefits again?), I would suggest that the very act of assuming that marginal benefit is a well-defined concept is bending your model in a particular manner. By defining the demand curve that way, you have implicitly stated that anything which marginal benefit depends on is by implication held constant for this model (for example, I would argue that while talking about good x, marginal benefit of good x depends on supply and demand of good y, so assuming that marginal benefit of quantity q of x given price p is a single distinct value means that we are excluding any impacts of fluctuations of supply and demand of good y on marginal benefit of x (else there would be multiple heights for a given price) .

  • 13 Jeff // Aug 16, 2013 at 10:32 pm

    In any case, all of the semantic discussion above should not distract from the fact that the degree to which traditional cause and effect relations holds varies considerably with the economic strata you are operating in. When you are buying goods for immediate consumption (what 99% of us do with a very large portion of our income), then the rules of supply and demand pretty reliably work in the “correct direction” for even the simplest models. At the very low end, you could imagine that when you eat out at a place like McDonalds or Taco Bell, you are almost literally able to apply the math of commodities to your purchase. Go up a level and you are making irrational choices from a nutrition per dollar perspective, but you are pursuing individual choices and supporting a much more varied economic ecosystem. Go up another level and you see conspicuous consumption and status purchases. Above that you have collectibles and investments.

    This is oversimplified, but there are two important generalizations here.
    1) At every level positive feedback loops where supply and demand push the price in the same direction for a while is more common than it is in the level below.
    2) At every level except for the lowest couple, the potential for these feedback loops is far greater in America today than it was in 1980. From 1933-1980, we could pretty much ignore ideas like Hyman Minsky’s instability hypothesis, but these have grown more and more relevant to the every day person as the ratio of liquidity in the hands of the financial industry to the liquidity available to the physical economy has grown.

    The fact that these big picture issues that affect all of us come down to predictable failures of assumptions in a model taught in the first few weeks of any economic education should not be underestimated.

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