Giffen Goods

One of the most fascinating occurrences in microeconomic theory is the concept of the “Giffen good,” first illustrated by Giffen’s Paradox in the 19th century. To arrive at a satisfying explanation of the Giffen good, however, we have to start with the fundamentals of consumer theory. Consumer theory is the explanation for how we as economic actors think about spending money on various goods. This may seem intuitive, but the actual mathematical underpinnings are quite interesting. The first core idea is the idea of utility. We assume that the consumption of various goods confer utility to people in accordance to some function. For a simple example, imagine you get two units of utility for every one consumed unit of a good, say an apple (we’ll call it good x), and no other good provides you any utility. So your utility function would be U(x) = 2x. Given that we are utility-maximizing actors, you would notice that a linear function has no absolute maximum, and you would therefore buy and consume as many apples as possible (i.e. spending all your money). However, in the real world, there are many goods that provide utility, and diminishing returns on nearly every good in terms of the utility it confers (i.e. eating the 1000th apple doesn’t provide as much marginal utility to someone as eating the 2nd apple). So a fair way to encapsulate this in a utility function would be to say that x represents the good of concern (apples above) and z represents all other goods. Put plainly, this would mean that any money not spend on good x could be spent on all other goods z. But if you want to simplify further, you could really says that what is left after purchasing x is an amount of currency y that can provide utility by purchasing a basket of goods z. So really, we can think of utility as a function of x and y. And to account for the diminishing returns piece, we should use a function like a natural log. So a classic utility function would be something like U(x,y) = 0.5ln(x)+0.5ln(y).

Let’s now think about this looks graphically. Below is a graph of the utility for an individual if you vary the amount of good x for a fixed level of good y (1, 2, 3, 4, and 5).

Notice how the slope of the line is diminishing as we increase the number of goods (this fits with our diminishing returns piece). Also, this same exercise could be repeated varying y and fixing x, and the graph would look the same.

We can then take these discrete lines and plot them in the 3-D space. This is done below.

Now imagine this is done for good y as well. We can then put the two 2-D plots together to make the 3-D plot, done below.

This graph is the plot of the U(x,y) = 0.5ln(x)+0.5ln(y) and it allows you to map any given bundle of x and y to a level of utility on the graph. So a utility-maximizing person would then take stock of their income and figure out what the optimal combination of x and y would be to maximize their utility). But how do we show this easily? We use indifference curves.

To do this, we take the 3-D graph and take the contours of it. Each of the contours is essentially a slice of the 3-D shape at a fixed utility level. Therefore, at any point on a given contour, you have the same overall utility.

Now that we have these contours, we can plot them on a normal 2-D graph with quantity of good x and quantity of good y as the axes.

Each of these red lines matches up to a given level of utility that any point on that line (a combination of good x and y) confers to the consumer. Notice the shape of the lines — the bend is the diminishing marginal returns piece. For the sixth line radiating out from the origin, you can see that 3 of each good is the same as 5 of one and 2 of the other… so 6 goods can be just as good as 7 as long as they’re split evenly in this case.

With these indifference curves, we can then start visualizing how a utility-maximizing person would make choices. To do so, we start with a budget constraint. This is just the line that shows all possible combinations of goods x and y that we can buy given our income. So lets say y represents $ and x represents some good priced at $2/unit, and we have $100 of income. The budget constraint would be a line from (0,100) to (50,0). Now the other thing to realize about indifference curves is that there are infinite numbers of them — imagine taking the slices of the 3-D shape at infinitesimally small increments above one another. So what you would do is plot your budget constraint and then see which utility indifference curve you could intersect or run tangent to that has the most utility ascribed to it. Graphically, that looks like this.

The numbers are obviously different here, but the concept remains. The budget constraint is drawn (here bananas cost 2x as much as apples), and the farthest out indifference curve we can intersect is IC1, which is therefore utility maximizing.

The next thing to realize is that the shape of the field of indifference curves is dependent on the nature of the good. There are generally three types of goods — inferior goods, normal goods, and superior/luxury goods. Inferior goods are the goods that people consume more of when their incomes decrease and less of when their incomes increase. Think of packets of Ramen, shitty fast food, or bus transportation — you buy more when you lose money, and if you’re given a raise or something, you would probably then reduce your consumption of that, given that you can afford the better version of those goods (except if you’re Adil). Normal goods are goods where your consumption of the good increases as income goes up, and decreases as it goes down. You can think of coffee, basic food, and movie tickets as basic examples. Superior/luxury goods are those that your consumption would not only increase when your income increases, but by a greater percentage than your income increased. Classic examples are sports tickets, jewelry, private jets, things like that.

Now as I mentioned, the nature of the field of indifference curves matches the type of good. For a normal good, the indifference curves will radiate from the origin roughly along the y=x line. The apples and bananas example above is what indifference curves look like for a normal good. As your budget constraint radiates outward, you would essentially just consume more of each of the two goods, with roughly the percentage increase in each as your income has changed.

For inferior goods, the curves are biased away from the axis of the inferior good. For superior/luxury goods, it’s the opposite. In a two-good model (including the x and y version we’ve been using), one complication is that a good can only be inferior or superior relative to the other. So in the example below, the steaks are by default superior/luxury because the burgers are inferior. You can also see how the income increase leads to a decrease in burger consumption and, by default, a disproportionate increase in steak consumption relative to the income increase.

Now, so far, we’ve only discussed changes in income and how they relate to changes in consumption. This is called the “income effect.” Basically, when you have a change in income, you would re-maximize your utility along the field of indifference curves based on your new constraint. There is another effect to consider, however. Remember that we are using a “two-good” model, but good y is just money left over for other consumption. So what happens when the price of good x changes? Because this is part of your spending, your effective income has changed. Imagine we think of good x as Uber rides. If the price of an Uber goes down 10%, your ability to pay for Ubers has increased. And, more importantly, if you consume the same number of Ubers that you did in previous months, your leftover income (good y) has increased. So in this scenario, there are two effects. There is a new “substitution effect” because the slope of the budget constraint has changed, as well as an “income effect” because your effective income has increased. So let’s examine these two effects in detail. The best way to do it is to break the change into two discrete parts in a method called Hicks’ decomposition. In the image below, let’s think of x2 as equivalent to what we’ve previously called y (sorry for the confusion, I’m pulling images from various sources). So x2 is leftover money, and x1 is Uber rides. To start, we have some nominal price for Ubers (p1), and a budget constraint (labeled R_A). You maximize your utility and end up at point A, which says how many Uber rides you take and the corresponding money you have left. Now, let’s imagine p1 changes (goes down) and Ubers are cheaper. The new budget constraint is R_B. But instead of going straight there in one step, let’s decompose to two steps. In the first step, we take R_A and change it to the red line (unlabeled). This red line is an artificial budget constraint — it is a hypothetical where the price of the Ubers has changed, but but someone actually takes money away from you until your income is such that if you were to utility-maximize, you would end up just as well off as you were before. You can see this by noticing that the red line intersects the same indifference curve at point C (recall that you are just as happy at one point on U_A as you are at any other point on the curve). Basically, this red line is meant to isolate the impact of the price change on your consumption behavior. For this step, we are simply acting according to the law of demand — as price decreases, demand increases, and vice versa. This is totally independent of the type of good it is (that will be accounted for in the next step). It is important to note that economists consider this “law of demand” to be nearly unassailable.

So we’ve done the first step of the decomposition, moving from A to C, and isolated the substitution effect that says as price decreases, demand increases. Now, moving from the red line to R_B is a pure parallel shift of the budget constraint, or an income effect. Notice that that movement looks exactly like the examples above, like the steak/burger one. It is in this second movement that we can account for the type of good that we are dealing with. We again utility-maximize with R_B as our constraint, and end up consuming according to point B. It is important to note that we will be considering the impact of the income effect on consumption comparing point B to point C, not point A. If good x1 is a normal good, then with this “extra” income, we would consume more compared to point C. This is displayed above. If it was an inferior good, then the curve U_B would be up on the top left of the graph, and we’d consume less of the good at B than we did at C.

The above example all dealt with a price decrease. But what happens if there’s a price increase? We have a substitution effect away from the good (more pricey, less demand based on the law of demand). We also have a negative income effect, because our effective income has decreased. This is shown in the same graphical way below. We move from our original point A to point C with the dotted pink artificial budget line (substitution effect, less consumption of x because the price of x increased) and then move from C to B because of the income effect. In this example, good x is a normal good, where less income means less consumption. If it was an inferior good, point B would be to the right of C, but only slightly.

Now here is the key question — can B ever be so far to the right of C that it’s actually to the right of A? Put another way, can good x be so inferior that it outweighs the substitution effect? Or, even more simply, can there ever be a good that someone would demand more when the price increases, seemingly contrary to the law of demand? Glad you asked.

The notion of a good that could do this, that could be so inferior, is called a Giffen good. It’s important to first dispel a common misconception. There is another type of good called a Veblen or snob good where demand would increase when the price increases, but only because the perceived value of the good has now changed too. Imagine a fancy piece of jewelry or a Louis Vuitton bag. If they increased the price, people may think it’s even more prestigious and flock to buy it. This is not a Giffen good because the actual nature of the good has changed, not just the price.

A Giffen good would hypothetically look like this graph below. We move from Point A to Point B due to the substitution effect, and then from Point B to C due to the income effect. In this case, bananas are such an inferior good that we end up consuming more of it than we originally did at point A.

This only happens in extremely unique circumstances. It was originally stated in Giffen’s Paradox in 19th century Ireland where Sir Giffen described the economic behavior of Irish peasants. He noticed that their diet consisted primarily of potatoes, and a little bit of meat, and nothing else. When the price of potatoes increased, one would think they’d simply reduce their potato consumption, right? (Think of Point A to Point B in the graph two above with the pink dotted line). The Irish peasants were so dependent on potatoes for the majority of their diet that they could only reduce consumption by so much. When they reached this limit of reduction of potato consumption, the price increase meant that they had very little money left. So little, in fact, that they wouldn’t have enough left to purchase even one unit of the much more pricey meat. So, instead, they pivoted to a potato-only diet, and ended up consuming even more potatoes than they ever did before. This is one of only a few noted historical examples, and most have to do with a price increase on a staple foodstuff like potatoes or rice.

Another example I once used while TA’ing was that of an individual who uses a personal chef, but buys the ingredients for this chef. If the price of the ingredients increases by too much, the person may not be able to afford the chef’s fees and the ingredients. So instead, he’ll have to go back to cooking for himself. Because of this, he ends up spending his entire budget on ingredients, rather than some split between the chef and ingredients. It’s plausible that he could then actually purchase more ingredients than he did previously, which would definitionally make the ingredients a Giffen good.

Hope you guys enjoyed this foray into consumer theory. If you followed all of it, you just learned the first half of Econ 201 at Duke.

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