Notes on Income and Substitution Effects

At various times in this course (and in microeconomics more generally), you will hear

the expression ‘decompose a price change into income and substitution effects.’ What

is this all about?

The basic idea is as follows: when the price of some good that you consume changes,

you (usually) change how much of the good you buy. Economists think that when

prices change there are two major psychological effects that occur. One the one hand, a

price change affects your real income, so when the price of some good goes up, you feel

poorer because your purchasing power has gone down. On the other hand, price changes

affect relative prices. So if the price of one good goes up, that good becomes relatively

more expensive. We know you change your behavior, but the question is how much of

the change is because of relative price changes, and how much is because of perceived

changes in your wealth. This is what we mean by ‘decomposing’ the price change.

To make things concrete, suppose that you consume two general goods: clothing

(x1) and restaurant meals (x2). Furthermore, suppose the price of clothing falls. What

happens next?

•You feel richer because it doesn’t cost as much to the same amount of

clothing you are already buying. If clothing is a normal good, you will buy

more clothes because you feel richer. (If meals are also a normal good, you will

buy more meals too). If clothing is an inferior good, you will buy fewer clothes

when you feel richer. In any case, the change in clothing you buy due to a change

in your wealth is called the INCOME EFFECT. Depending on what kind of good

we are talking about — normal or inferior — demand can rise or fall due to the

income effect.

•Clothing becomes relatively cheaper too. That is, you give up fewer restau-

rant meals when you buy more clothes. Because indifference curves slope down

(or at least never slope up for two goods), the tradeoff towards clothing is more in

your favor. So you should never consume less clothing when the price of clothing

falls (consume the same amount or more). This is called the SUBSTITUTION

EFFECT.

The overall change in clothing (or meals) that you buy is a combination of these two

effects.

How do we do this ‘decomposition?’ To find how much change in demand is due

to the income effect, we need to keep prices constant and identify how much your real

income changes because of the change in price. To find the substitution effect we need

to keep real income constant but change relative prices. Then we can ‘boil out’ how the

change in overall consumption is created by the two effects.

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At various times in this course (and in microeconomics more generally), you will hear the expression ‘decompose a price change into income and substitution effects.’ What is this all about?

The basic idea is as follows: when the price of some good that you consume changes, you (usually) change how much of the good you buy. Economists think that when prices change there are two major psychological effects that occur. One the one hand, a price change affects your real income, so when the price of some good goes up, you feel poorer because your purchasing power has gone down. On the other hand, price changes affect relative prices. So if the price of one good goes up, that good becomes relatively more expensive. We know you change your behavior, but the question is how much of the change is because of relative price changes, and how much is because of perceived changes in your wealth. This is what we mean by ‘decomposing’ the price change.

To make things concrete, suppose that you consume two general goods: clothing (x 1 ) and restaurant meals (x 2 ). Furthermore, suppose the price of clothing falls. What happens next?

You feel richer because it doesn’t cost as much to the same amount of clothing you are already buying. If clothing is a normal good, you will buy more clothes because you feel richer. (If meals are also a normal good, you will buy more meals too). If clothing is an inferior good, you will buy fewer clothes when you feel richer. In any case, the change in clothing you buy due to a change in your wealth is called the INCOME EFFECT. Depending on what kind of good we are talking about — normal or inferior — demand can rise or fall due to the income effect.
Clothing becomes relatively cheaper too. That is, you give up fewer restau- rant meals when you buy more clothes. Because indifference curves slope down (or at least never slope up for two goods), the tradeoff towards clothing is more in your favor. So you should never consume less clothing when the price of clothing falls (consume the same amount or more). This is called the SUBSTITUTION EFFECT.

The overall change in clothing (or meals) that you buy is a combination of these two effects.

How do we do this ‘decomposition?’ To find how much change in demand is due to the income effect, we need to keep prices constant and identify how much your real income changes because of the change in price. To find the substitution effect we need to keep real income constant but change relative prices. Then we can ‘boil out’ how the change in overall consumption is created by the two effects.

The key idea is that price changes cause you to make a new choice on a new in- difference curve. Call your original consumption bundle ‘a.’ Note that when a price falls, you will be on a higher indifference curve (unless we have a corner solution that doesn’t change — let’s assume this is not the case). Call your new consumption bundle ‘b.’ We now do a little ‘trick’ that is completely hypothetical. Suppose we go ahead with reducing the price of clothing. Next, we take away just enough of your income so that you could reach your original utility level at the new (lower) price of clothing. This exercise would produce a new hypothetical demand point: one where you have lower income, but also face lower prices. Call this new hypothetical point ‘c.’ Note that your actual choices are a and b — this is what an outside observer would see as your behavior changes. But in your mind, c matters alot!

The SUBSTITUTION EFFECT is found by keeping real income constant, but changing prices. This is the movement from a to c.
The INCOME EFFECT is found by changing real income, but keeping prices constant. This is the movement from c to b.
The OVERALL EFFECT is a to b.

This is how we always decompose price changes: 1. Identify the overall change in demand 2. Hypothetically ‘compensate’ the consumer by taking away income (if a price falls) or giving more income (if a price rises), just enough so that they can reach their original utility at the new prices 3. Find the point c on this new ‘compensated budget line’ 4. Decompose the overall effect.

Now let’s turn to a few graphical examples. In each case the original utility is called uo, the new utility is called u^1 , and only p 1 (the price of clothing) is changing. The compensated budget line is the ‘dashed’ line and c is the hypothetical bundle.

Figure 1: The price of clothing falls, and it is a NORMAL GOOD. The substitution effect is xa to xc (price down, demand up), and the income effect is xc to xb (price down, real income up, demand up). Both effects work in the same direction, encouraging the consumer to buy more clothing when its price goes down.
Figure 2: The price of clothing falls, and it is an INFERIOR GOOD. The substi- tution effect is xa to xc (price down, demand up), and the income effect is xc to xb (price down, real income up, demand DOWN). Now the income effect works in the opposite direction from before — overall demand for clothing still rises when price falls, but only because the substitution effect is bigger than the income effect.
Figure 3: The price of clothing falls, and it is an GIFFEN GOOD. The overall effect is for demand for clothing to to FALL when its price FALLS. The substitution effect is xa to xc (price down, demand up), and the income effect is xc to xb (price down, real income up, demand DOWN). Clothing is inferior since the income

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Notes on Income and Substitution Effects