Perhaps more elusive than the (__insert favorite analogy here___), is the mythical Giffen good in economics. A Giffen good is simply one that elicits backward behavior on the part of actors. When the good gets more expensive, consumers respond by increasing their purchases of that good. These are very rare phenomenon, if they exist at all. The law of demand is a law for a reason. In any case, students seem to have a hard time recognizing the rarity of this type of good. When challenged, and it is indeed a fun thought exercise, they end up offering suggestions that confirm rather than refute the law of demand. For example, a favorite response from students is that some people purchase cars because they are more expensive than cheaper ones – and they argue that it is because the car is more expensive that they engage in the purchase.
But this is not a refutation of the law of demand and the expensive car is not itself a Giffen Good. First for a little technical wonkishness. For a good to exhibit Giffen-like properties it must first be an inferior good (we can prove this with simple math). And, it must be inferior in a very particular kind of way. What is an inferior good? It is a good for which we purchase more of when our income decreases. There are no absolute notions of inferior goods, they are relative/marginal concepts. For example, if you threw a $20 bill at me right now, my consumption of hot dogs (known as red hots in these parts) would surely increase. My guess is that for you, you might substitute away from the hot dog and into the fish fry if you had more money. So for me they are normal and for you they are inferior. And goods can be inferior at certain income levels and not others.
In any event, a good is inferior typically when (again we can prove this with math or illustrate it with images) it has many more preferred AND higher priced substitutes. This hardly characterizes a BMW or even bottled water (another favorite example used when invoking Giffen goods examples). Grains that serve as food staples in poor countries come much closer to this characterization.
But being inferior is not enough to make a good a Giffen good. It has to be really inferior. That again can be proven with a little math (for econ people out there, the magnitude of the income effect in the Slutsky equation must exceed and be of opposite sign than the magnitude of the substitution effect). This is more likely when the good in question is making up a larger portion of your expenditures than a smaller one. What do we mean by “income” and “substitution” effects? Well, when the price of a good changes, it does two things to you. First, it makes you inclined to substitute away from that good (assuming a price increase) and into the now relatively cheaper other goods. Isolating this effect in practice is a lot harder than in theory, because we have to imagine how we would make choices when prices change but that our choice does not alter our well being (imagine being compensated for the loss of wealth you feel when something is more expensive today than it used to be, and then decide if you would still consume the same amount today as yesterday). Second, when prices change, wholly aside from the fact that other goods become relatively cheaper, is that higher prices have the same effect as making us poorer. Imagine you are stuck with a 10 mile commute to and from work and can do nothing about it. And the price of driving to work increases by 50 cents per mile. Then this change is no different than if someone took a $5 bill from your wallet each and every day – the effect is in fact indistinguishable. So, because you are poorer, would you be more or less inclined to drive.
For a Giffen Good, when its price increases, the fact that it makes us poorer invokes a large income effect driving us to consume more of it (e.g. when you have income taken from you, you are likely to consume more Ramen Noodles and less filet mignon). And this effect has to be larger than the tendency to substitute away from that good. This is no way characterizes the situation where people “buy fancy cars because they are more expensive.” In the situation of the BMW, when you are buying the car, you are buying a fancy car. This is a different good than a standard sedan. The law of demand says nothing about our preferences over different priced goods, it is telling is that when the price of an existing good increases we tend to consume less of it. The fact that I prefer my $187,000 house to the $110,000 house down the street does not violate the law of demand. What would violate the law of demand would be for me to be more likely to have purchased my existing house if its price first were $197,000 or higher. That is unlikely, to put it gently. Similarly for the fancy car. Imagine you want to buy the car because it is more expensive than the cheap car (in this case you are buying a good called “status” or “car quality” so you ought not even be comparing cars to cars in the refutation of the law of demand here). Would you be even more likely to buy that same car when its price increased? Are you more likely to purchase quality or status when it becomes harder to do so?
Of course you are not. The law of demand is a very robust law. As I said, it is possible for it to be violated and we can lay out very precise conditions for when it is possible. But you should be extremely apprehensive when you see claims that it in fact has actually been violated. Almost surely the example is doing an apples-to-oranges comparison and not the apples-to-apples comparison required by the law. Of course, most of us intuitively get this, until we get involved in the policy world and start wishing for minimum wages to increase output and employment and for income taxes to increase work effort and so on. But that’s for another day.