Any student of price theory will know of the theoretical possibility of an upward-sloping demand curve (when the price of the good goes up, the quantity demanded goes up). This type of good is called a “Giffen good.”

What if demand isn’t downward-sloping? Isn’t this a problem for price theory? After all, if both the supply and demand curves are upward-sloping, it is possible to get very different price responses when the supply or demand curve shifts. For example, for a Giffen good, it would be possible that sudden reduction in supply might cause a reduction in the price, depending on the slope of the demand curve relative to the supply curve. This seems counterintuitive and empirically false. Nonetheless, the fact that this is a theoretical possibility seems like it could be a pretty significant problem for price theoretic analysis.

A lot of people dismiss Giffen goods as sufficiently rare that we don’t have to think about them. Others suggest that it is a theoretical possibility, but not not empirically relevant. I would like to take a much stronger stance on the issue and argue that upward-sloping demand is entirely the result of certain assumptions of the price theoretic framework. If we take uncertainty about prices seriously or if we allow for intertemporal decision-making, then the demand for Giffen goods is actually downward-sloping like all other demand curves.

Where Does the Theoretical Possibility Come From?

Let’s start by thinking through the theoretical possibility of a good for which the quantity demanded increases in conjunction with the good’s price. Recall that in price theory, there are two ways of deriving demand curves. One way of deriving demand is by starting with a utility-maximizing framework. In that framework, the set of possible choices available to the consumer depends on their income and the prices of the goods that the consumer would like to purchase. The consumer will choose his or her basket of consumption, given those prices and given income, so that the choice maximizes the consumer’s utility.

From this framework, we can use a hypothetical set of all possible prices of a particular good and determine the precise quantity demanded for that particular good at that price (holding all of the other prices constant). The plot of those combinations of prices and quantities demanded is referred to as the Marshallian demand curve. The Marshallian quantity demanded depends on the prices of the goods and the consumer’s income. In other words, as one moves along the demand curve, utility is changing, but income is not.

Alternatively, one could derive a demand curve by starting with the idea that the consumer wants to achieve a particular level of utility. Given the prices of the goods, the consumer chooses the quantities of each good to buy that minimize the expenditure necessary to achieve that level of utility. Holding all other prices constant, one can figure out the quantity demanded by the consumer at each possible price. The plot of this combination of prices and quantities demanded are referred to as the Hicksian demand curve. The Hicksian quantity demanded depends on prices of the goods and the utility of the consumer. In other words, as one moves along the demand curve, utility isn’t changing.

The reason that all of this is important is that there is a distinct relationship between Marshallian and Hicksian demand. In particular, let e^m denote the Marshallian elasticity of demand (the percentage change in the quantity demanded from a 1 percent change in the price). It follows that

where e^M is the Hicksian elasticity of demand, s is the share of expenditure on the good, and N is the income elasticity of demand (the percentage change in the quantity demanded from a 1 percent change in income). This is known as the Slutsky equation (in elasticity form). What it shows is that the Marshallian price elasticity consists of two effects. There is a substitution effect (captured by the Hicksian elasticity) and there is an income effect.

To understand these two effects, think of an increase in the price of apples. The substitution effect says that apples are more expensive and so the consumer should buy fewer apples. The income effect says that the higher price of apples makes the consumer feel poorer, which creates an additional effect on the quantity demanded.

How the quantity demanded responds to income depends on the type of good. Most goods are “normal” goods. By that, we mean that when income goes up, people buy more of the good. However, some goods are inferior goods. For those goods, when income rises, people demand a lower quantity of those goods.

The theoretical possibility of an upward-sloping demand curve should now be apparent. Note that when goods are normal, we don’t have to worry about a Giffen good situation. e^H is negative. As long as N is positive, we know that e^M is negative. However, consider the case of an inferior good. In that case, N is negative. Now, whether the Marshallian elasticity is positive or negative is going to depend on the magnitude of the Hicksian elasticity and the income elasticity. If the income elasticity is sufficiently large (in absolute value) or if the share of expenditures spent on the inferior good is sufficiently large, then the Marshallian demand curve could be upward-sloping.

Now that we have seen the theoretical possibility, we should assess how seriously we should take this claim.

The Demand for Giffen Goods is Actually Downward-Sloping

As I stated earlier, some people are dismissive of Giffen goods as a mere theoretical possibility, but the conditions are unlikely to be met (even in theory). After all, how many people are spending a large enough share of their expenditures on an inferior good? How sensitive are inferior goods to changes in income? Others concede that Giffen goods are a theoretical possibility, but not empirically important.

I think that both of those arguments concede too much. Instead, we should recognize that the demand for Giffen goods is downward-sloping like all other goods. However, to make that point, we need to discuss what is missing from our analysis.

The exercise that I just described for generating both Marshallian and Hicksian demand curves generates demand curves by considering the quantity demanded associated with a set of hypothetical prices. If the price equals Y, then the consumer will choose a quantity X. If the price equals Z, then the consumer will choose a quantity W.

It is important to note that this is not always the same as saying that when the price changes from Z to Y, the quantity demanded will change from W to X. That might be true, but it is not guaranteed. Whether or not these two things are the same depends on the expectations of the consumer. Only in the case in which a change in the price is completely unexpected would these things be the same. If, on the other hand, the consumer knows that there might be a change in the price, we should expect that to factor into the consumer’s decision-making process and that the consumer makes contingency plans.

It might help to illustrate this with an example.

Consider a Giffen good. Suppose that the prices of all other goods are constant, but that the price of the Giffen good could be high, with some positive probability. Otherwise, the Giffen good’s price is low.

Given the uncertainty over prices, the consumer might want to purchase insurance against the fluctuations in price. The reason is as follows. In the state of the world in which the Giffen good’s price is high, this will make the consumer feel poorer (and thus the marginal utility income will be high). In the state of the world in which the Giffen good’s price is low, this will make the consumer feel richer (and thus the marginal utility of income will be low). However, an optimizing consumer would like to equalize the marginal utility of income across these states. This requires transferring income from the low price state to the high price state. It is better to have an extra dollar to spend in the high price state than the low price state. How does one do that? Buy insurance.

Now, let’s think about the implications of the insurance.

If the consumer insures against these price changes, then income will be high when the price is high and income will be low when the price is low. Recall also that Giffen goods must also be inferior goods. One consumes less of the inferior good when income goes up and more of the inferior good when income goes down. Thus, with insurance, since income is high when the price is high and since the good is inferior, the consumer will consume less of the Giffen good when the price is high and more of the Giffen good when the price is low. In other words, the demand for the Giffen good is downward-sloping.

Critics might argue that this logic only applies when there is insurance to buy. There are two responses to this. First, this moves the goalpost. An upper-sloping demand curve would now require not only the typical Giffen good characteristics, but also would require incomplete markets.

Second, and more importantly, insurance isn’t even necessary here. Suppose that we allow for intertemporal decision-making rather than one-period decision-making. Now consider a world in which the Giffen good is storable. If you can store the Giffen good, then storage actually replicates the insurance policy. Why? Buffer stocks are a form of insurance. In periods when the price of the Giffen good is high, the person storing Giffen good now has more “income.” In periods when the price of the Giffen good is low, the person storing the Giffen good will now have less “income.” Since the good is inferior, we get the standard result that quantity demanded is lower when the price is high than when the price is low.

This can be extended further to intertemporal substitution more generally, although it requires more technical details. As Yoram Barzel and Wing Suen show in their paper on the topic, if a consumer is maximizing over both different goods and time, one of the maximizing conditions is that the marginal utility of income is constant across all periods. Thus, what we need to think about is how the price of the Giffen good affects the marginal utility of income. Barzel and Suen show that the marginal utility of income is high when the price of the Giffen good is high because this is true of inferior goods more generally. Thus, just like the case of insurance, the quantity demanded of the Giffen good is lower when its price is high than when its price is low.

It is important to note, however, that this intertemporal result is not deriving a structural demand curve. It is a time series of price-quantity pairs that shows a negative relationship between price and quantity demanded for the Giffen good.

There is one final caveat here is that the change in the price must be anticipated. People cannot plan for things they don’t expect to occur.

Concluding Thoughts

The theoretical possibility of a Giffen good is something that many students are taught, even in introductory courses. Economists are often quick to dismiss this theoretical possibility as unlikely to hold or empirically irrelevant. Yet, there is a broader lesson to be learned. People optimize on many margins. If prices fluctuate over time, people might take actions to mitigate the costs of such price fluctuations. The very actions that people take to mitigate those costs actually result in negative relationships between the price and quantity demanded of a Giffen good. All of this follows from straightforward applications of price theoretic logic and concepts that any student who has learned about Giffen goods would understand. The problem with the analysis of Giffen goods seems to be that it doesn’t take the price theoretic logic far enough.

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