When the price of a good changes, the demand curve for that good tells us how much consumption will change. This total change in quantity demanded, however, is a result of two distinct forces that affect consumers’ decisions: the substitution effect and the income effect. Any change in quantity demanded can be decomposed into these two effects.

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Any change in quantity demanded can be decomposed into these two effects. We introduce them in this book, but we are just scratching the surface. We’re going to be upfront with you: The distinction between income and substitution effects is one of the most subtle concepts that you will come across in this entire book. If you go on to take more advanced economics courses, income and substitution effects will come up again and again.3 Two factors make this topic difficult. First, we never separately observe these two effects in the real world, only their combined effects. Their separation is an artificial analytical tool. Put another way, as a consumer, you can (and do) figure out how much to consume without knowing or figuring out how much of the change is due to income effects and how much is due to substitution effects. Second, the income effect occurs even when the consumer’s income as measured in dollars remains constant. How rich we feel is determined both by how much income we have and how much things cost. If your income stays at $1,000 but the prices of all goods fall by half, you are effectively a lot wealthier. The income effect refers to how rich you feel, not the number of dollar bills in your pocket.

In our overview, we demonstrate income and substitution effects using graphs. The appendix to this chapter describes these effects mathematically.

Figure 5.9 shows how one consumer, Carlos, who spends his income on attending music concerts and basketball games, reacts to a fall in the price of basketball tickets. This is just like the analysis we did in Section 5.2. If basketball ticket prices fall, the budget constraint rotates outward from BC₁ to BC₂ because Carlos can now purchase more basketball tickets with his income. As a result, the optimal consumption bundle shifts from A (the point of tangency between indifference curve U₁ and budget constraint BC₁) to B (the point of tangency between indifference curve U₂ and budget constraint BC₂). Because of the fall in the price of basketball tickets, the quantity of concert tickets consumed increases from 5 to 6, and the number of basketball tickets Carlos purchases rises from 3 to 5. These overall changes in quantities consumed between bundles A and B are the total effect of the price change.

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Note that just as in Section 5.2, we figured out the optimal bundle without any reference to income or substitution effects. In the next sections, we decompose the total effect into separate substitution and income effects. That is,

Total Effect = Substitution Effect + Income Effect

Breaking down the movement from A to B into income and substitution effects helps us understand how much of the total change in Carlos’s quantity demanded occurs because Carlos switches what he purchases as a result of the reduction in the relative prices of the two goods (the substitution effect), and how much of the change is driven by the fact that the decrease in the price of basketball tickets gives Carlos more purchasing power (the income effect).

Note also that all the examples we work through involve a drop in the price of a good. When the price of a good increases, the effects work in the opposite direction.

Let’s begin by isolating the substitution effect. This part of the change in quantities demanded is due only to the change in relative prices, not to the change in Carlos’s buying power. To isolate the substitution effect, we need to figure out how many concert and basketball tickets Carlos would want to buy if, after the price change, there was no income effect, that is, if he had the same purchasing power as before the price change and felt neither richer nor poorer.

For Carlos to feel neither richer nor poorer, the bundle he consumes after the price change must provide him with the same utility he was receiving before the price change; that is, the new bundle must be on the initial indifference curve U₁.

The substitution-effect-only bundle on U₁ has to reflect the fact that the goods’ relative prices have changed. Those new relative prices are seen in the slope of the new budget line BC₂. The problem is that a point of tangency doesn’t exist between U₁ and BC₂—as we can see in Figure 5.10. However, there is a point of tangency between U₁ and a budget line with the same slope (i.e., the same relative prices) as BC₂. The budget line we’re talking about is BC′, the dashed line in panel a of Figure 5.10, and the point of tangency is point A′.

Bundle A′ is what Carlos would buy if the relative prices of concert and basketball tickets changed the same way, but Carlos experienced no change in purchasing power. This is the definition of the substitution effect. Thus, the substitution effect, in isolation, moves Carlos’s demanded bundle from A to A′. To find this effect, we have to shift the postprice-change budget line BC₂ back in parallel (to preserve the new relative prices) until it is tangent to the preprice-change indifference curve U₁ (to keep the original utility level the same). To isolate the substitution effect when a price falls, we need Carlos’s income to fall a little bit to erase how much richer he feels because the new lower price increases his effective purchasing power. It’s important to recognize that the budget line BC′ is hypothetical—Carlos never actually faces it. Instead, it is a conceptual device that lets us figure out what Carlos would do if he did face it; that is, if relative prices changed in the way they actually did, while at the same time any income gains he enjoyed as a result were taken away from him.

There are a few things to notice about the change in quantities due to the substitution effect. First, the quantity of concert tickets decreases (from 5 to 3), and the quantity of basketball tickets increases (from 3 to 4). The decrease in the quantity of concert tickets demanded occurs because the price change has caused basketball tickets to become cheaper relative to concert tickets, so Carlos wants to buy relatively more basketball tickets. Second, while points A and A′ are on the same indifference curve (and Carlos therefore gets the same utility from either bundle), it costs Carlos less to buy bundle A′ at the new prices than to buy A. We know this because point A is located above BC′ and so is infeasible if the budget constraint is BC′. (A′, however, being on BC′, is feasible with this constraint.)

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Carlos therefore responds to the decline in basketball ticket prices by substituting away from concert tickets and toward basketball tickets. By moving down along U₁, Carlos has effectively made himself better off; he is getting the same utility (he’s still on U₁) for less money (bundle A is no longer feasible even though A′ is).

The income effect is the part of the total change in quantities consumed that is due to the change in Carlos’s buying power after the price change. Why is there an income effect even though only the price of a good changed, not the actual number of dollars that Carlos had to spend? The key to understanding this outcome is to recognize that when the price of a good falls, Carlos becomes richer overall. The reduction in a good’s price means there’s a whole new set of bundles Carlos can now buy that he couldn’t afford before because he has more money left over. At the old prices, everything above and to the right of BC₁ was infeasible; at the new prices, only bundles outside BC₂ are infeasible (see panel b of Figure 5.10).

This increase in buying power allows Carlos to achieve a higher level of utility than he did before. The income effect is the change in Carlos’s choices driven by this shift in buying power while holding relative prices fixed at their new level. Finding these income-effect consumption changes is easy once we’ve isolated the substitution effect. Remember that to find bundle A′, we shifted the new budget constraint back in parallel until it was tangent to the original indifference curve. Doing that shift in reverse reflects the income effect exactly: It is the shift in consumption quantities (from bundle A′ to B in panel b of Figure 5.10) due to Carlos’s ability to reach a higher indifference curve (U₂ instead of U₁) while holding relative prices fixed (BC₂ and BC′ have the same slope).

Therefore, the income effect of the decline in the basketball ticket price is illustrated by the move from the substitution-effect bundle (point A′) to the final bundle, point B. Because the decline in basketball ticket prices has, in effect, made Carlos wealthier, he can reach a higher indifference curve U₂ and consume more of both goods. Due to the income effect, his desired quantity of concert tickets increases by 3 from 3 (at A′) to 6 (at B) and his desired quantity of basketball tickets increases by 1 from 4 (at A′) to 5 (at B).

In this particular example, the income effect led to increases in the quantities of both concert and basketball tickets. That means both goods are normal goods. In the next section, we show an example in which one of the goods is inferior.

The total effects of the decline in basketball ticket prices are shown in panel c of Figure 5.10:

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The size (and as we’ll see shortly, sometimes the direction) of the total effect of a price change depends on the relative sizes of its substitution and income effects. So it’s important to understand what factors influence how large substitution and income effects are. We discuss some of the more important factors below.

The Size of the Substitution Effect The size of the substitution effect depends on the degree of curvature of the indifference curves. You can see this in Figure 5.11. The figure’s two panels show the substitution effects of the same change in the relative prices of concert and basketball tickets for two different indifference curve shapes. (We know it’s the same relative price change because the budget constraints’ slope changes by the same amount in both panels.) When indifference curves are highly curved, as in panel a, the MRS changes quickly as one moves along them. This means any given price change won’t change consumption choices much, because one doesn’t need to move far along the indifference curve to change the MRS to match the new relative prices. Thus, the substitution effect is small. This is unsurprising, because we learned in Chapter 4 that indifference curves have more curvature when two goods are not highly substitutable. In panel a, the relative price change causes a substitution from A to A′, and the consumer moves from purchasing a bundle with 2 basketball tickets and 2 concert tickets to a bundle containing 3 basketball tickets and 1.25 concert tickets.

When indifference curves are less curved, as in panel b, the MRS doesn’t change much along the curve, so the same relative price change causes a much greater substitution effect. The substitution from A to A′ in panel b involves much larger changes in basketball and concert ticket consumption than that caused by the same relative price change in panel a.4 In panel b, the quantity of basketball game tickets purchased grows to 4 (rather than 3) and the quantity of music concert tickets purchased falls to 0.75 (rather than 1.25). Again, we can relate this to what we learned about the curvature of indifference curves in Chapter 4. Indifference curves with little curvature indicate that the two goods are close substitutes. Thus, it makes sense that a price change will lead to a much greater adjustment in the quantities in the consumer’s preferred bundle.

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The Size of the Income Effect The size of the income effect is related to the quantity of each good the consumer purchases before the price change. The more the consumer was spending on the good before the price change, the greater the fraction of the consumer’s budget affected by the price change. A price drop of a good that the consumer is initially buying a lot of will leave him with more income left over than a price drop of a good with a small budget share (and a price increase will sap a greater share of the consumer’s income). For example, think of how a change in the prices of electricity and pest control affect a typical homeowner. A typical consumer spends much more of his budget on electricity. Therefore, a change in the price of electricity will affect his income and alter his purchases by more than a similar change in the price of pest control. (At the extreme, if the consumer currently purchases no pest control, a change in the price of pest control will have no income effect at all.)

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Figure 5.12 provides another example of breaking out quantity changes into income and substitution effects. Here, however, one of the goods is inferior.

The graph shows Judi’s utility-maximizing bundles of steak and ramen noodles for two sets of prices. The optimal bundle at the original prices is shown at point A. The price of ramen noodles then drops, rotating the budget constraint outward. With the new budget constraint BC₂, Judi can reach a higher level of utility U₂ and chooses bundle B to maximize her utility.

To split the shift from bundle A to bundle B into its substitution and income effects, we follow the steps we described in the previous section.

The fact that a price drop leads to a reduction in the quantity consumed due to the income effect does not mean that the demand curve for ramen noodles slopes up because the substitution effect increases the quantity demanded by more than the income effect decreases it. Thus, the quantity of ramen noodles demanded still rises when their price falls even though ramen noodles are an inferior good. We see this outcome in panel c of Figure 5.13 because the total effect on the quantity of ramen noodles is still positive: The optimal bundle after ramen noodles become cheaper (bundle B) has a higher quantity of ramen than the optimal bundle before their price fell (bundle A). As a result, the demand curve for ramen slopes down. This is generally the case for inferior goods in the economy—while the income effect will make people want to consume less of them as their price falls, the substitution effect has a larger impact in the opposite direction, leading to a net increase in their consumption.

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If the income effect is large enough, however, it is possible that a reduction in the price of an inferior good could actually lead to a net decrease in its consumption. A good that exhibits this trait is called a Giffen good.

Giffen goods are goods for which a fall in price leads the consumer to want less of the good. (They are named after British economist and statistician Sir Robert Giffen.) That is, an inverse relationship does not exist between price and quantity demanded and the demand curves of Giffen goods slope up! The more expensive a Giffen good is, the higher the quantity demanded. This happens because, for Giffen goods, the substitution effect of a price drop, which acts to increase the quantity a consumer demands of the good, is smaller than the reduction in the desired quantity caused by the income effect. Note that this means Giffen goods must be inferior goods.

Figure 5.14 gives a graphical example. The two goods are potatoes and meat, and potatoes are the Giffen good. The utility-maximizing bundle at the original prices is shown at point A. When potatoes become cheaper, the budget constraint rotates out from BC₁ to BC₂ and the optimal bundle shifts from A to B. Notice that in this case, the quantity of potatoes consumed at point B is smaller than the quantity consumed at A even though potatoes are now cheaper.

Giffen goods are extremely rare because they need to have limited substitutability with other goods (small substitution effects with highly curved indifference curves) while also having a large income effect. Large income effects generally occur when a good accounts for a large fraction of a consumer’s budget. If the price of the good falls because the consumer is already spending most of her income on it, she’s likely to feel a larger bump in effective buying power than if the good were only a small share of her budget. Finding goods that are a huge share of the budget but do not have many substitutes is really unusual.

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